%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN486-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:18 AM UTC 2025
% Result : Unsatisfiable 0.87s 1.06s
% Output : Proof 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN486-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:37:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.87/1.06 % SZS status Unsatisfiable
% 0.87/1.06 % SZS output start Proof
% 0.87/1.06 tff(c2_1_type, type, (
% 0.87/1.06 c2_1: $i > $o)).
% 0.87/1.06 tff(a2186_type, type, (
% 0.87/1.06 a2186: $i)).
% 0.87/1.06 tff(c0_1_type, type, (
% 0.87/1.06 c0_1: $i > $o)).
% 0.87/1.06 tff(a2195_type, type, (
% 0.87/1.06 a2195: $i)).
% 0.87/1.06 tff(c1_1_type, type, (
% 0.87/1.06 c1_1: $i > $o)).
% 0.87/1.06 tff(c3_1_type, type, (
% 0.87/1.06 c3_1: $i > $o)).
% 0.87/1.06 tff(ndr1_0_type, type, (
% 0.87/1.06 ndr1_0: $o)).
% 0.87/1.06 tff(hskp0_type, type, (
% 0.87/1.06 hskp0: $o)).
% 0.87/1.06 tff(hskp16_type, type, (
% 0.87/1.06 hskp16: $o)).
% 0.87/1.06 tff(a2179_type, type, (
% 0.87/1.06 a2179: $i)).
% 0.87/1.06 tff(a2197_type, type, (
% 0.87/1.06 a2197: $i)).
% 0.87/1.06 tff(hskp21_type, type, (
% 0.87/1.06 hskp21: $o)).
% 0.87/1.06 tff(a2216_type, type, (
% 0.87/1.06 a2216: $i)).
% 0.87/1.06 tff(hskp18_type, type, (
% 0.87/1.06 hskp18: $o)).
% 0.87/1.06 tff(a2198_type, type, (
% 0.87/1.06 a2198: $i)).
% 0.87/1.06 tff(hskp17_type, type, (
% 0.87/1.06 hskp17: $o)).
% 0.87/1.06 tff(hskp26_type, type, (
% 0.87/1.06 hskp26: $o)).
% 0.87/1.06 tff(hskp24_type, type, (
% 0.87/1.06 hskp24: $o)).
% 0.87/1.06 tff(a2174_type, type, (
% 0.87/1.06 a2174: $i)).
% 0.87/1.06 tff(a2188_type, type, (
% 0.87/1.06 a2188: $i)).
% 0.87/1.06 tff(a2177_type, type, (
% 0.87/1.06 a2177: $i)).
% 0.87/1.06 tff(hskp3_type, type, (
% 0.87/1.06 hskp3: $o)).
% 0.87/1.06 tff(hskp13_type, type, (
% 0.87/1.06 hskp13: $o)).
% 0.87/1.06 tff(a2194_type, type, (
% 0.87/1.06 a2194: $i)).
% 0.87/1.06 tff(hskp10_type, type, (
% 0.87/1.06 hskp10: $o)).
% 0.87/1.06 tff(a2187_type, type, (
% 0.87/1.06 a2187: $i)).
% 0.87/1.06 tff(hskp11_type, type, (
% 0.87/1.06 hskp11: $o)).
% 0.87/1.06 tff(a2191_type, type, (
% 0.87/1.06 a2191: $i)).
% 0.87/1.06 tff(a2176_type, type, (
% 0.87/1.06 a2176: $i)).
% 0.87/1.06 tff(hskp7_type, type, (
% 0.87/1.06 hskp7: $o)).
% 0.87/1.06 tff(hskp28_type, type, (
% 0.87/1.06 hskp28: $o)).
% 0.87/1.06 tff(a2178_type, type, (
% 0.87/1.06 a2178: $i)).
% 0.87/1.06 tff(hskp27_type, type, (
% 0.87/1.06 hskp27: $o)).
% 0.87/1.06 tff(hskp22_type, type, (
% 0.87/1.06 hskp22: $o)).
% 0.87/1.06 tff(a2219_type, type, (
% 0.87/1.06 a2219: $i)).
% 0.87/1.06 tff(hskp15_type, type, (
% 0.87/1.06 hskp15: $o)).
% 0.87/1.06 tff(a2175_type, type, (
% 0.87/1.06 a2175: $i)).
% 0.87/1.06 tff(hskp1_type, type, (
% 0.87/1.06 hskp1: $o)).
% 0.87/1.06 tff(hskp30_type, type, (
% 0.87/1.06 hskp30: $o)).
% 0.87/1.06 tff(a2208_type, type, (
% 0.87/1.06 a2208: $i)).
% 0.87/1.06 tff(a2182_type, type, (
% 0.87/1.06 a2182: $i)).
% 0.87/1.06 tff(a2265_type, type, (
% 0.87/1.06 a2265: $i)).
% 0.87/1.06 tff(hskp25_type, type, (
% 0.87/1.06 hskp25: $o)).
% 0.87/1.06 tff(a2193_type, type, (
% 0.87/1.06 a2193: $i)).
% 0.87/1.06 tff(a2211_type, type, (
% 0.87/1.06 a2211: $i)).
% 0.87/1.06 tff(hskp19_type, type, (
% 0.87/1.06 hskp19: $o)).
% 0.87/1.06 tff(hskp14_type, type, (
% 0.87/1.06 hskp14: $o)).
% 0.87/1.06 tff(hskp9_type, type, (
% 0.87/1.06 hskp9: $o)).
% 0.87/1.06 tff(a2185_type, type, (
% 0.87/1.06 a2185: $i)).
% 0.87/1.06 tff(hskp2_type, type, (
% 0.87/1.06 hskp2: $o)).
% 0.87/1.06 tff(a2262_type, type, (
% 0.87/1.06 a2262: $i)).
% 0.87/1.06 tff(a2268_type, type, (
% 0.87/1.06 a2268: $i)).
% 0.87/1.06 tff(a2196_type, type, (
% 0.87/1.06 a2196: $i)).
% 0.87/1.06 tff(hskp29_type, type, (
% 0.87/1.06 hskp29: $o)).
% 0.87/1.06 tff(hskp4_type, type, (
% 0.87/1.06 hskp4: $o)).
% 0.87/1.06 tff(1,plain,
% 0.87/1.06 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(2,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[1])).
% 0.87/1.06 tff(3,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(4,plain,
% 0.87/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(5,plain,
% 0.87/1.06 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[4])).
% 0.87/1.06 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.87/1.06 tff(7,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.87/1.06 tff(8,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.87/1.06 tff(9,plain,(
% 0.87/1.06 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.87/1.06 inference(skolemize,[status(sab)],[8])).
% 0.87/1.06 tff(10,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.87/1.06 tff(11,assumption,(~hskp16), introduced(assumption)).
% 0.87/1.06 tff(12,plain,
% 0.87/1.06 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(13,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[12])).
% 0.87/1.06 tff(14,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(15,plain,
% 0.87/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(16,plain,
% 0.87/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[15])).
% 0.87/1.06 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.87/1.06 tff(18,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.87/1.06 tff(19,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.87/1.06 tff(20,plain,(
% 0.87/1.06 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(skolemize,[status(sab)],[19])).
% 0.87/1.06 tff(21,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.87/1.06 tff(22,assumption,(hskp21), introduced(assumption)).
% 0.87/1.06 tff(23,plain,
% 0.87/1.06 (((~hskp21) | (~c3_1(a2216))) <=> ((~hskp21) | (~c3_1(a2216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(24,plain,
% 0.87/1.06 (((~c3_1(a2216)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a2216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(25,axiom,((~c3_1(a2216)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.87/1.06 tff(26,plain,
% 0.87/1.06 ((~hskp21) | (~c3_1(a2216))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.87/1.06 tff(27,plain,
% 0.87/1.06 ((~hskp21) | (~c3_1(a2216))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.87/1.06 tff(28,plain,
% 0.87/1.06 (~c3_1(a2216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[27, 22])).
% 0.87/1.06 tff(29,plain,
% 0.87/1.06 (((~hskp21) | (~c2_1(a2216))) <=> ((~hskp21) | (~c2_1(a2216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(30,plain,
% 0.87/1.06 (((~c2_1(a2216)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a2216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(31,axiom,((~c2_1(a2216)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.87/1.06 tff(32,plain,
% 0.87/1.06 ((~hskp21) | (~c2_1(a2216))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.87/1.06 tff(33,plain,
% 0.87/1.06 ((~hskp21) | (~c2_1(a2216))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.87/1.06 tff(34,plain,
% 0.87/1.06 (~c2_1(a2216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.87/1.06 tff(35,plain,
% 0.87/1.06 (((~hskp21) | c0_1(a2216)) <=> ((~hskp21) | c0_1(a2216))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(36,axiom,((~hskp21) | c0_1(a2216)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.87/1.06 tff(37,plain,
% 0.87/1.06 ((~hskp21) | c0_1(a2216)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.87/1.06 tff(38,plain,
% 0.87/1.06 ((~hskp21) | c0_1(a2216)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.87/1.06 tff(39,plain,
% 0.87/1.06 ((~hskp21) | c0_1(a2216)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.87/1.06 tff(40,plain,
% 0.87/1.06 ((~hskp21) | c0_1(a2216)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.87/1.06 tff(41,plain,
% 0.87/1.06 ((~hskp21) | c0_1(a2216)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.87/1.06 tff(42,plain,
% 0.87/1.06 (c0_1(a2216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[41, 22])).
% 0.87/1.06 tff(43,plain,
% 0.87/1.06 (^[U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(44,plain,
% 0.87/1.06 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[43])).
% 0.87/1.06 tff(45,plain,
% 0.87/1.06 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(46,plain,
% 0.87/1.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(47,plain,
% 0.87/1.06 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[46])).
% 0.87/1.06 tff(48,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.87/1.06 tff(49,plain,
% 0.87/1.06 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.87/1.06 tff(50,plain,
% 0.87/1.06 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.87/1.06 tff(51,plain,(
% 0.87/1.06 ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.87/1.06 inference(skolemize,[status(sab)],[50])).
% 0.87/1.06 tff(52,plain,
% 0.87/1.06 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.87/1.06 tff(53,assumption,(hskp18), introduced(assumption)).
% 0.87/1.06 tff(54,plain,
% 0.87/1.06 (((~hskp18) | (~c2_1(a2198))) <=> ((~hskp18) | (~c2_1(a2198)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(55,plain,
% 0.87/1.06 (((~c2_1(a2198)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2198)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(56,axiom,((~c2_1(a2198)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.87/1.06 tff(57,plain,
% 0.87/1.06 ((~hskp18) | (~c2_1(a2198))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.87/1.06 tff(58,plain,
% 0.87/1.06 ((~hskp18) | (~c2_1(a2198))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.87/1.06 tff(59,plain,
% 0.87/1.06 (~c2_1(a2198)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[58, 53])).
% 0.87/1.06 tff(60,plain,
% 0.87/1.06 (((~hskp18) | (~c1_1(a2198))) <=> ((~hskp18) | (~c1_1(a2198)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(61,plain,
% 0.87/1.06 (((~c1_1(a2198)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a2198)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(62,axiom,((~c1_1(a2198)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.87/1.06 tff(63,plain,
% 0.87/1.06 ((~hskp18) | (~c1_1(a2198))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.87/1.06 tff(64,plain,
% 0.87/1.06 ((~hskp18) | (~c1_1(a2198))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.87/1.06 tff(65,plain,
% 0.87/1.06 (~c1_1(a2198)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[64, 53])).
% 0.87/1.06 tff(66,plain,
% 0.87/1.06 (((~hskp18) | c0_1(a2198)) <=> ((~hskp18) | c0_1(a2198))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(67,axiom,((~hskp18) | c0_1(a2198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.87/1.06 tff(68,plain,
% 0.87/1.06 ((~hskp18) | c0_1(a2198)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.87/1.06 tff(69,plain,
% 0.87/1.06 ((~hskp18) | c0_1(a2198)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[68, 66])).
% 0.87/1.06 tff(70,plain,
% 0.87/1.06 ((~hskp18) | c0_1(a2198)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.87/1.06 tff(71,plain,
% 0.87/1.06 ((~hskp18) | c0_1(a2198)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.87/1.06 tff(72,plain,
% 0.87/1.06 ((~hskp18) | c0_1(a2198)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.87/1.06 tff(73,plain,
% 0.87/1.06 (c0_1(a2198)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[72, 53])).
% 0.87/1.06 tff(74,assumption,(~ndr1_0), introduced(assumption)).
% 0.87/1.06 tff(75,plain,
% 0.87/1.06 ((ndr1_0 | (~hskp17)) <=> (ndr1_0 | (~hskp17))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(76,plain,
% 0.87/1.06 (((~hskp17) | ndr1_0) <=> (ndr1_0 | (~hskp17))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(77,axiom,((~hskp17) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 0.87/1.06 tff(78,plain,
% 0.87/1.06 (ndr1_0 | (~hskp17)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.87/1.06 tff(79,plain,
% 0.87/1.06 (ndr1_0 | (~hskp17)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.87/1.06 tff(80,plain,
% 0.87/1.06 (~hskp17),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[79, 74])).
% 0.87/1.06 tff(81,plain,
% 0.87/1.06 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(82,plain,
% 0.87/1.06 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(83,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.87/1.06 tff(84,plain,
% 0.87/1.06 (ndr1_0 | (~hskp26)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.87/1.06 tff(85,plain,
% 0.87/1.06 (ndr1_0 | (~hskp26)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[84, 81])).
% 0.87/1.06 tff(86,plain,
% 0.87/1.06 (~hskp26),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[85, 74])).
% 0.87/1.06 tff(87,plain,
% 0.87/1.06 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(88,plain,
% 0.87/1.06 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(89,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.87/1.06 tff(90,plain,
% 0.87/1.06 (ndr1_0 | (~hskp24)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.87/1.06 tff(91,plain,
% 0.87/1.06 (ndr1_0 | (~hskp24)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.87/1.06 tff(92,plain,
% 0.87/1.06 (~hskp24),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[91, 74])).
% 0.87/1.06 tff(93,plain,
% 0.87/1.06 ((hskp26 | hskp24 | hskp17) <=> (hskp26 | hskp24 | hskp17)),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(94,plain,
% 0.87/1.06 (((hskp24 | hskp26) | hskp17) <=> (hskp26 | hskp24 | hskp17)),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(95,axiom,((hskp24 | hskp26) | hskp17), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.87/1.06 tff(96,plain,
% 0.87/1.06 (hskp26 | hskp24 | hskp17),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.87/1.06 tff(97,plain,
% 0.87/1.06 (hskp26 | hskp24 | hskp17),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[96, 93])).
% 0.87/1.06 tff(98,plain,
% 0.87/1.06 (hskp26 | hskp24 | hskp17),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.87/1.06 tff(99,plain,
% 0.87/1.06 (hskp26 | hskp24 | hskp17),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[98, 93])).
% 0.87/1.06 tff(100,plain,
% 0.87/1.06 (hskp26 | hskp24 | hskp17),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[99, 93])).
% 0.87/1.06 tff(101,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[100, 92, 86, 80])).
% 0.87/1.06 tff(102,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(103,plain,
% 0.87/1.06 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(104,plain,
% 0.87/1.06 ((hskp16 | (~ndr1_0) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198))) <=> (hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(105,plain,
% 0.87/1.06 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[104])).
% 0.87/1.06 tff(106,plain,
% 0.87/1.06 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[105, 103])).
% 0.87/1.06 tff(107,plain,
% 0.87/1.06 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(108,plain,
% 0.87/1.06 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2198))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.87/1.06 tff(109,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[108, 102, 11, 73, 65, 59, 52])).
% 0.87/1.06 tff(110,plain,((~hskp18) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(111,plain,
% 0.87/1.06 (~hskp18),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[110, 11])).
% 0.87/1.06 tff(112,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(113,plain,
% 0.87/1.06 ((hskp18 | (~ndr1_0) | (~c0_1(a2216)) | c3_1(a2216) | (~c1_1(a2216)) | c2_1(a2216) | (~c1_1(a2216)) | (~c0_1(a2216))) <=> (hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(114,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2216)) | c3_1(a2216) | (~c1_1(a2216)) | c2_1(a2216) | (~c1_1(a2216)) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[113])).
% 0.87/1.06 tff(115,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2216)) | c3_1(a2216) | (~c1_1(a2216)) | c2_1(a2216) | (~c1_1(a2216)) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[114, 112])).
% 0.87/1.06 tff(116,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2216)) | c3_1(a2216) | (~c1_1(a2216)) | c2_1(a2216) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(117,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp18 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.87/1.06 tff(118,plain,
% 0.87/1.06 (~c1_1(a2216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[117, 102, 111, 42, 34, 28, 21])).
% 0.87/1.06 tff(119,plain,
% 0.87/1.06 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(120,plain,
% 0.87/1.06 ((hskp16 | (~ndr1_0) | c2_1(a2216) | c1_1(a2216) | (~c0_1(a2216))) <=> (hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(121,plain,
% 0.87/1.06 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2216) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[120])).
% 0.87/1.06 tff(122,plain,
% 0.87/1.06 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2216) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[121, 119])).
% 0.87/1.06 tff(123,plain,
% 0.87/1.06 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2216) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(124,plain,
% 0.87/1.06 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.87/1.06 tff(125,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[124, 102, 11, 42, 34, 52, 118])).
% 0.87/1.06 tff(126,plain,((~hskp21) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(127,plain,
% 0.87/1.06 (~hskp21),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[126, 11])).
% 0.87/1.06 tff(128,plain,
% 0.87/1.06 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(129,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[128])).
% 0.87/1.06 tff(130,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(131,plain,
% 0.87/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(132,plain,
% 0.87/1.06 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[131])).
% 0.87/1.06 tff(133,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.87/1.06 tff(134,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.87/1.06 tff(135,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.87/1.06 tff(136,plain,(
% 0.87/1.06 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(skolemize,[status(sab)],[135])).
% 0.87/1.06 tff(137,plain,
% 0.87/1.06 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.87/1.06 tff(138,assumption,(~c0_1(a2174)), introduced(assumption)).
% 0.87/1.06 tff(139,plain,
% 0.87/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 0.87/1.06 inference(bind,[status(th)],[])).
% 0.87/1.06 tff(140,plain,
% 0.87/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.06 inference(quant_intro,[status(thm)],[139])).
% 0.87/1.06 tff(141,plain,
% 0.87/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(142,plain,
% 0.87/1.06 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(143,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[142])).
% 0.87/1.07 tff(144,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(U)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.87/1.07 tff(145,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.87/1.07 tff(146,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.87/1.07 tff(147,plain,(
% 0.87/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(skolemize,[status(sab)],[146])).
% 0.87/1.07 tff(148,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.87/1.07 tff(149,assumption,(hskp17), introduced(assumption)).
% 0.87/1.07 tff(150,plain,
% 0.87/1.07 (((~hskp17) | (~c1_1(a2197))) <=> ((~hskp17) | (~c1_1(a2197)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(151,plain,
% 0.87/1.07 (((~c1_1(a2197)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2197)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(152,axiom,((~c1_1(a2197)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.87/1.07 tff(153,plain,
% 0.87/1.07 ((~hskp17) | (~c1_1(a2197))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.87/1.07 tff(154,plain,
% 0.87/1.07 ((~hskp17) | (~c1_1(a2197))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[153, 150])).
% 0.87/1.07 tff(155,plain,
% 0.87/1.07 (~c1_1(a2197)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[154, 149])).
% 0.87/1.07 tff(156,plain,
% 0.87/1.07 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(157,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[156])).
% 0.87/1.07 tff(158,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(159,plain,
% 0.87/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(160,plain,
% 0.87/1.07 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[159])).
% 0.87/1.07 tff(161,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.87/1.07 tff(162,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.87/1.07 tff(163,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.87/1.07 tff(164,plain,(
% 0.87/1.07 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.87/1.07 inference(skolemize,[status(sab)],[163])).
% 0.87/1.07 tff(165,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.87/1.07 tff(166,plain,
% 0.87/1.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(167,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[166])).
% 0.87/1.07 tff(168,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(169,plain,
% 0.87/1.07 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(170,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[169])).
% 0.87/1.07 tff(171,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.87/1.07 tff(172,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.87/1.07 tff(173,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.87/1.07 tff(174,plain,(
% 0.87/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(skolemize,[status(sab)],[173])).
% 0.87/1.07 tff(175,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.87/1.07 tff(176,assumption,(~hskp10), introduced(assumption)).
% 0.87/1.07 tff(177,assumption,(~c3_1(a2191)), introduced(assumption)).
% 0.87/1.07 tff(178,assumption,(~c1_1(a2191)), introduced(assumption)).
% 0.87/1.07 tff(179,plain,
% 0.87/1.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(180,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[179])).
% 0.87/1.07 tff(181,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(182,plain,
% 0.87/1.07 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(183,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[182])).
% 0.87/1.07 tff(184,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.87/1.07 tff(185,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.87/1.07 tff(186,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.87/1.07 tff(187,plain,(
% 0.87/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.87/1.07 inference(skolemize,[status(sab)],[186])).
% 0.87/1.07 tff(188,plain,
% 0.87/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.87/1.07 tff(189,assumption,(~c0_1(a2191)), introduced(assumption)).
% 0.87/1.07 tff(190,assumption,(~hskp28), introduced(assumption)).
% 0.87/1.07 tff(191,plain,
% 0.87/1.07 (^[U: $i] : refl((hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(192,plain,
% 0.87/1.07 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[191])).
% 0.87/1.07 tff(193,plain,
% 0.87/1.07 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(194,plain,
% 0.87/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp22) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp22))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp22) <=> (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(195,plain,
% 0.87/1.07 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp22) <=> ![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[194])).
% 0.87/1.07 tff(196,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.87/1.07 tff(197,plain,
% 0.87/1.07 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.87/1.07 tff(198,plain,
% 0.87/1.07 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.87/1.07 tff(199,plain,(
% 0.87/1.07 ![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.87/1.07 inference(skolemize,[status(sab)],[198])).
% 0.87/1.07 tff(200,plain,
% 0.87/1.07 (![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[199, 192])).
% 0.87/1.07 tff(201,assumption,(~c1_1(a2219)), introduced(assumption)).
% 0.87/1.07 tff(202,assumption,(~c2_1(a2219)), introduced(assumption)).
% 0.87/1.07 tff(203,assumption,(~c3_1(a2219)), introduced(assumption)).
% 0.87/1.07 tff(204,assumption,(hskp11), introduced(assumption)).
% 0.87/1.07 tff(205,plain,
% 0.87/1.07 (((~hskp11) | (~c1_1(a2187))) <=> ((~hskp11) | (~c1_1(a2187)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(206,plain,
% 0.87/1.07 (((~c1_1(a2187)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a2187)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(207,axiom,((~c1_1(a2187)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.87/1.07 tff(208,plain,
% 0.87/1.07 ((~hskp11) | (~c1_1(a2187))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.87/1.07 tff(209,plain,
% 0.87/1.07 ((~hskp11) | (~c1_1(a2187))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[208, 205])).
% 0.87/1.07 tff(210,plain,
% 0.87/1.07 (~c1_1(a2187)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[209, 204])).
% 0.87/1.07 tff(211,plain,
% 0.87/1.07 (((~hskp11) | c2_1(a2187)) <=> ((~hskp11) | c2_1(a2187))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(212,axiom,((~hskp11) | c2_1(a2187)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.87/1.07 tff(213,plain,
% 0.87/1.07 ((~hskp11) | c2_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.87/1.07 tff(214,plain,
% 0.87/1.07 ((~hskp11) | c2_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[213, 211])).
% 0.87/1.07 tff(215,plain,
% 0.87/1.07 ((~hskp11) | c2_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[214, 211])).
% 0.87/1.07 tff(216,plain,
% 0.87/1.07 ((~hskp11) | c2_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.87/1.07 tff(217,plain,
% 0.87/1.07 ((~hskp11) | c2_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[216, 211])).
% 0.87/1.07 tff(218,plain,
% 0.87/1.07 (c2_1(a2187)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[217, 204])).
% 0.87/1.07 tff(219,plain,
% 0.87/1.07 (((~hskp11) | c0_1(a2187)) <=> ((~hskp11) | c0_1(a2187))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(220,axiom,((~hskp11) | c0_1(a2187)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.87/1.07 tff(221,plain,
% 0.87/1.07 ((~hskp11) | c0_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.87/1.07 tff(222,plain,
% 0.87/1.07 ((~hskp11) | c0_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[221, 219])).
% 0.87/1.07 tff(223,plain,
% 0.87/1.07 ((~hskp11) | c0_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[222, 219])).
% 0.87/1.07 tff(224,plain,
% 0.87/1.07 ((~hskp11) | c0_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.87/1.07 tff(225,plain,
% 0.87/1.07 ((~hskp11) | c0_1(a2187)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[224, 219])).
% 0.87/1.07 tff(226,plain,
% 0.87/1.07 (c0_1(a2187)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[225, 204])).
% 0.87/1.07 tff(227,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(228,plain,
% 0.87/1.07 (((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191)) <=> (c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(229,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[228])).
% 0.87/1.07 tff(230,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[229, 227])).
% 0.87/1.07 tff(231,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(232,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.87/1.07 tff(233,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[232, 102, 202, 189, 226, 218, 201, 203, 178, 177, 210, 188])).
% 0.87/1.07 tff(234,plain,((~hskp11) | c2_1(a2219) | c0_1(a2191) | c1_1(a2219) | c3_1(a2219) | c1_1(a2191) | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(235,plain,
% 0.87/1.07 (~hskp11),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[234, 203, 189, 201, 202, 178, 177])).
% 0.87/1.07 tff(236,plain,
% 0.87/1.07 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(237,plain,
% 0.87/1.07 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[236])).
% 0.87/1.07 tff(238,plain,
% 0.87/1.07 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(239,plain,
% 0.87/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) | hskp11))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) | hskp10) <=> ((hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) | hskp10))), rewrite(((hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U)) | hskp10) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) | hskp10) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(240,plain,
% 0.87/1.07 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) | hskp10) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[239])).
% 0.87/1.07 tff(241,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp11) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.87/1.07 tff(242,plain,
% 0.87/1.07 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.87/1.07 tff(243,plain,
% 0.87/1.07 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.87/1.07 tff(244,plain,(
% 0.87/1.07 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 0.87/1.07 inference(skolemize,[status(sab)],[243])).
% 0.87/1.07 tff(245,plain,
% 0.87/1.07 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.87/1.07 tff(246,assumption,(hskp28), introduced(assumption)).
% 0.87/1.07 tff(247,plain,
% 0.87/1.07 (((~hskp28) | c2_1(a2188)) <=> ((~hskp28) | c2_1(a2188))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(248,axiom,((~hskp28) | c2_1(a2188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.87/1.07 tff(249,plain,
% 0.87/1.07 ((~hskp28) | c2_1(a2188)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.87/1.07 tff(250,plain,
% 0.87/1.07 ((~hskp28) | c2_1(a2188)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[249, 247])).
% 0.87/1.07 tff(251,plain,
% 0.87/1.07 ((~hskp28) | c2_1(a2188)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[250, 247])).
% 0.87/1.07 tff(252,plain,
% 0.87/1.07 ((~hskp28) | c2_1(a2188)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.87/1.07 tff(253,plain,
% 0.87/1.07 ((~hskp28) | c2_1(a2188)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[252, 247])).
% 0.87/1.07 tff(254,plain,
% 0.87/1.07 (c2_1(a2188)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[253, 246])).
% 0.87/1.07 tff(255,plain,
% 0.87/1.07 (((~hskp28) | c0_1(a2188)) <=> ((~hskp28) | c0_1(a2188))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(256,axiom,((~hskp28) | c0_1(a2188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.87/1.07 tff(257,plain,
% 0.87/1.07 ((~hskp28) | c0_1(a2188)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.87/1.07 tff(258,plain,
% 0.87/1.07 ((~hskp28) | c0_1(a2188)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[257, 255])).
% 0.87/1.07 tff(259,plain,
% 0.87/1.07 ((~hskp28) | c0_1(a2188)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[258, 255])).
% 0.87/1.08 tff(260,plain,
% 0.87/1.08 ((~hskp28) | c0_1(a2188)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.87/1.08 tff(261,plain,
% 0.87/1.08 ((~hskp28) | c0_1(a2188)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[260, 255])).
% 0.87/1.08 tff(262,plain,
% 0.87/1.08 (c0_1(a2188)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[261, 246])).
% 0.87/1.08 tff(263,assumption,(~hskp11), introduced(assumption)).
% 0.87/1.08 tff(264,plain,
% 0.87/1.08 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(265,plain,
% 0.87/1.08 ((hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188)) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(266,plain,
% 0.87/1.08 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188)))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[265])).
% 0.87/1.08 tff(267,plain,
% 0.87/1.08 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188))),
% 0.87/1.08 inference(transitivity,[status(thm)],[266, 264])).
% 0.87/1.08 tff(268,plain,
% 0.87/1.08 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(269,plain,
% 0.87/1.08 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.87/1.08 tff(270,plain,
% 0.87/1.08 (c3_1(a2188)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[269, 102, 263, 176, 262, 254, 245])).
% 0.87/1.08 tff(271,plain,
% 0.87/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(272,plain,
% 0.87/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[271])).
% 0.87/1.08 tff(273,plain,
% 0.87/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(274,plain,
% 0.87/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(275,plain,
% 0.87/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[274])).
% 0.87/1.08 tff(276,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 0.87/1.08 tff(277,plain,
% 0.87/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.87/1.08 tff(278,plain,
% 0.87/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.87/1.08 tff(279,plain,(
% 0.87/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.87/1.08 inference(skolemize,[status(sab)],[278])).
% 0.87/1.08 tff(280,plain,
% 0.87/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.87/1.08 tff(281,plain,
% 0.87/1.08 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(282,plain,
% 0.87/1.08 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[281])).
% 0.87/1.08 tff(283,plain,
% 0.87/1.08 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(284,plain,
% 0.87/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(285,plain,
% 0.87/1.08 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[284])).
% 0.87/1.08 tff(286,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.87/1.08 tff(287,plain,
% 0.87/1.08 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.87/1.08 tff(288,plain,
% 0.87/1.08 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.87/1.08 tff(289,plain,(
% 0.87/1.08 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.08 inference(skolemize,[status(sab)],[288])).
% 0.87/1.08 tff(290,plain,
% 0.87/1.08 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[289, 282])).
% 0.87/1.08 tff(291,assumption,(~hskp0), introduced(assumption)).
% 0.87/1.08 tff(292,plain,
% 0.87/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(293,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[292])).
% 0.92/1.08 tff(294,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(295,plain,
% 0.92/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(296,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[295])).
% 0.92/1.08 tff(297,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.92/1.08 tff(298,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.92/1.08 tff(299,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.92/1.08 tff(300,plain,(
% 0.92/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(skolemize,[status(sab)],[299])).
% 0.92/1.08 tff(301,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.92/1.08 tff(302,assumption,(~c1_1(a2194)), introduced(assumption)).
% 0.92/1.08 tff(303,plain,
% 0.92/1.08 (^[U: $i] : refl((hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) <=> (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(304,plain,
% 0.92/1.08 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[303])).
% 0.92/1.08 tff(305,plain,
% 0.92/1.08 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(306,plain,
% 0.92/1.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | hskp0))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | hskp0) <=> (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(307,plain,
% 0.92/1.08 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[306])).
% 0.92/1.08 tff(308,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp15) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.92/1.08 tff(309,plain,
% 0.92/1.08 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.92/1.08 tff(310,plain,
% 0.92/1.08 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[309, 305])).
% 0.92/1.08 tff(311,plain,(
% 0.92/1.08 ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 0.92/1.08 inference(skolemize,[status(sab)],[310])).
% 0.92/1.08 tff(312,plain,
% 0.92/1.08 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[311, 304])).
% 0.92/1.08 tff(313,plain,
% 0.92/1.08 ((hskp13 | hskp10 | hskp0) <=> (hskp13 | hskp10 | hskp0)),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(314,plain,
% 0.92/1.08 (((hskp13 | hskp0) | hskp10) <=> (hskp13 | hskp10 | hskp0)),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(315,plain,
% 0.92/1.08 ((hskp13 | hskp0) <=> (hskp13 | hskp0)),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(316,plain,
% 0.92/1.08 (((hskp13 | hskp0) | hskp10) <=> ((hskp13 | hskp0) | hskp10)),
% 0.92/1.08 inference(monotonicity,[status(thm)],[315])).
% 0.92/1.08 tff(317,plain,
% 0.92/1.08 (((hskp13 | hskp0) | hskp10) <=> (hskp13 | hskp10 | hskp0)),
% 0.92/1.08 inference(transitivity,[status(thm)],[316, 314])).
% 0.92/1.08 tff(318,axiom,((hskp13 | hskp0) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.92/1.08 tff(319,plain,
% 0.92/1.08 (hskp13 | hskp10 | hskp0),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.92/1.08 tff(320,plain,
% 0.92/1.08 (hskp13 | hskp10 | hskp0),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[319, 313])).
% 0.92/1.08 tff(321,plain,
% 0.92/1.08 (hskp13 | hskp10 | hskp0),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[320, 313])).
% 0.92/1.08 tff(322,plain,
% 0.92/1.08 (hskp13 | hskp10 | hskp0),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[321, 313])).
% 0.92/1.08 tff(323,plain,
% 0.92/1.08 (hskp13 | hskp10 | hskp0),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[322, 313])).
% 0.92/1.08 tff(324,plain,
% 0.92/1.08 (hskp13),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[323, 291, 176])).
% 0.92/1.08 tff(325,plain,
% 0.92/1.08 (((~hskp13) | (~c3_1(a2191))) <=> ((~hskp13) | (~c3_1(a2191)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(326,plain,
% 0.92/1.08 (((~c3_1(a2191)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a2191)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(327,axiom,((~c3_1(a2191)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.92/1.08 tff(328,plain,
% 0.92/1.08 ((~hskp13) | (~c3_1(a2191))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.92/1.08 tff(329,plain,
% 0.92/1.08 ((~hskp13) | (~c3_1(a2191))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[328, 325])).
% 0.92/1.08 tff(330,plain,
% 0.92/1.08 (~c3_1(a2191)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[329, 324])).
% 0.92/1.08 tff(331,plain,
% 0.92/1.08 (((~hskp13) | (~c1_1(a2191))) <=> ((~hskp13) | (~c1_1(a2191)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(332,plain,
% 0.92/1.08 (((~c1_1(a2191)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a2191)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(333,axiom,((~c1_1(a2191)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.92/1.08 tff(334,plain,
% 0.92/1.08 ((~hskp13) | (~c1_1(a2191))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.92/1.08 tff(335,plain,
% 0.92/1.08 ((~hskp13) | (~c1_1(a2191))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[334, 331])).
% 0.92/1.08 tff(336,plain,
% 0.92/1.08 (~c1_1(a2191)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[335, 324])).
% 0.92/1.08 tff(337,plain,
% 0.92/1.08 (((~hskp13) | c0_1(a2191)) <=> ((~hskp13) | c0_1(a2191))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(338,axiom,((~hskp13) | c0_1(a2191)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.92/1.08 tff(339,plain,
% 0.92/1.08 ((~hskp13) | c0_1(a2191)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.92/1.08 tff(340,plain,
% 0.92/1.08 ((~hskp13) | c0_1(a2191)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[339, 337])).
% 0.92/1.08 tff(341,plain,
% 0.92/1.08 ((~hskp13) | c0_1(a2191)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[340, 337])).
% 0.92/1.08 tff(342,plain,
% 0.92/1.08 ((~hskp13) | c0_1(a2191)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[341, 337])).
% 0.92/1.08 tff(343,plain,
% 0.92/1.08 ((~hskp13) | c0_1(a2191)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[342, 337])).
% 0.92/1.08 tff(344,plain,
% 0.92/1.08 (c0_1(a2191)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[343, 324])).
% 0.92/1.08 tff(345,plain,
% 0.92/1.08 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(346,plain,
% 0.92/1.08 ((hskp15 | hskp0 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191)) <=> (hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(347,plain,
% 0.92/1.08 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[346])).
% 0.92/1.08 tff(348,plain,
% 0.92/1.08 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 0.92/1.08 inference(transitivity,[status(thm)],[347, 345])).
% 0.92/1.08 tff(349,plain,
% 0.92/1.08 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | (hskp15 | hskp0 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(350,plain,
% 0.92/1.08 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))) | hskp15 | hskp0 | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.92/1.08 tff(351,plain,
% 0.92/1.08 (hskp15),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[350, 102, 291, 344, 336, 330, 312])).
% 0.92/1.08 tff(352,plain,
% 0.92/1.08 (((~hskp15) | (~c2_1(a2194))) <=> ((~hskp15) | (~c2_1(a2194)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(353,plain,
% 0.92/1.08 (((~c2_1(a2194)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a2194)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(354,axiom,((~c2_1(a2194)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.92/1.08 tff(355,plain,
% 0.92/1.08 ((~hskp15) | (~c2_1(a2194))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.92/1.08 tff(356,plain,
% 0.92/1.08 ((~hskp15) | (~c2_1(a2194))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[355, 352])).
% 0.92/1.08 tff(357,plain,
% 0.92/1.08 (~c2_1(a2194)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[356, 351])).
% 0.92/1.08 tff(358,plain,
% 0.92/1.08 (((~hskp15) | c0_1(a2194)) <=> ((~hskp15) | c0_1(a2194))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(359,axiom,((~hskp15) | c0_1(a2194)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.92/1.08 tff(360,plain,
% 0.92/1.08 ((~hskp15) | c0_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.92/1.08 tff(361,plain,
% 0.92/1.08 ((~hskp15) | c0_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[360, 358])).
% 0.92/1.08 tff(362,plain,
% 0.92/1.08 ((~hskp15) | c0_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[361, 358])).
% 0.92/1.08 tff(363,plain,
% 0.92/1.08 ((~hskp15) | c0_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[362, 358])).
% 0.92/1.08 tff(364,plain,
% 0.92/1.08 ((~hskp15) | c0_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[363, 358])).
% 0.92/1.08 tff(365,plain,
% 0.92/1.08 (c0_1(a2194)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[364, 351])).
% 0.92/1.08 tff(366,plain,
% 0.92/1.08 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(367,plain,
% 0.92/1.08 ((hskp16 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194))) <=> (hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(368,plain,
% 0.92/1.08 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194)))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[367])).
% 0.92/1.08 tff(369,plain,
% 0.92/1.08 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 0.92/1.08 inference(transitivity,[status(thm)],[368, 366])).
% 0.92/1.08 tff(370,plain,
% 0.92/1.08 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(371,plain,
% 0.92/1.08 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.92/1.08 tff(372,plain,
% 0.92/1.08 (hskp16 | c1_1(a2194)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[371, 102, 365, 357, 52])).
% 0.92/1.08 tff(373,plain,
% 0.92/1.08 (hskp16),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[372, 302])).
% 0.92/1.08 tff(374,plain,
% 0.92/1.08 (((~hskp16) | (~c3_1(a2195))) <=> ((~hskp16) | (~c3_1(a2195)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(375,plain,
% 0.92/1.08 (((~c3_1(a2195)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a2195)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(376,axiom,((~c3_1(a2195)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.92/1.08 tff(377,plain,
% 0.92/1.08 ((~hskp16) | (~c3_1(a2195))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.92/1.08 tff(378,plain,
% 0.92/1.08 ((~hskp16) | (~c3_1(a2195))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[377, 374])).
% 0.92/1.08 tff(379,plain,
% 0.92/1.08 (~c3_1(a2195)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[378, 373])).
% 0.92/1.08 tff(380,plain,
% 0.92/1.08 (((~hskp16) | (~c2_1(a2195))) <=> ((~hskp16) | (~c2_1(a2195)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(381,plain,
% 0.92/1.08 (((~c2_1(a2195)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a2195)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(382,axiom,((~c2_1(a2195)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.92/1.08 tff(383,plain,
% 0.92/1.08 ((~hskp16) | (~c2_1(a2195))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.92/1.08 tff(384,plain,
% 0.92/1.08 ((~hskp16) | (~c2_1(a2195))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[383, 380])).
% 0.92/1.08 tff(385,plain,
% 0.92/1.08 (~c2_1(a2195)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[384, 373])).
% 0.92/1.08 tff(386,plain,
% 0.92/1.08 (((~hskp16) | (~c1_1(a2195))) <=> ((~hskp16) | (~c1_1(a2195)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(387,plain,
% 0.92/1.08 (((~c1_1(a2195)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a2195)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(388,axiom,((~c1_1(a2195)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.92/1.08 tff(389,plain,
% 0.92/1.08 ((~hskp16) | (~c1_1(a2195))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.92/1.08 tff(390,plain,
% 0.92/1.08 ((~hskp16) | (~c1_1(a2195))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[389, 386])).
% 0.92/1.08 tff(391,plain,
% 0.92/1.08 (~c1_1(a2195)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[390, 373])).
% 0.92/1.08 tff(392,plain,
% 0.92/1.08 (((~hskp15) | c3_1(a2194)) <=> ((~hskp15) | c3_1(a2194))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(393,axiom,((~hskp15) | c3_1(a2194)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.92/1.08 tff(394,plain,
% 0.92/1.08 ((~hskp15) | c3_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.92/1.08 tff(395,plain,
% 0.92/1.08 ((~hskp15) | c3_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[394, 392])).
% 0.92/1.08 tff(396,plain,
% 0.92/1.08 ((~hskp15) | c3_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[395, 392])).
% 0.92/1.08 tff(397,plain,
% 0.92/1.08 ((~hskp15) | c3_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[396, 392])).
% 0.92/1.08 tff(398,plain,
% 0.92/1.08 ((~hskp15) | c3_1(a2194)),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[397, 392])).
% 0.92/1.08 tff(399,plain,
% 0.92/1.08 (c3_1(a2194)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[398, 351])).
% 0.92/1.08 tff(400,plain,
% 0.92/1.08 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(401,plain,
% 0.92/1.08 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[400])).
% 0.92/1.08 tff(402,plain,
% 0.92/1.08 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(403,plain,
% 0.92/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(404,plain,
% 0.92/1.09 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[403])).
% 0.92/1.09 tff(405,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.92/1.09 tff(406,plain,
% 0.92/1.09 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.92/1.09 tff(407,plain,
% 0.92/1.09 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[406, 402])).
% 0.92/1.09 tff(408,plain,(
% 0.92/1.09 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.92/1.09 inference(skolemize,[status(sab)],[407])).
% 0.92/1.09 tff(409,plain,
% 0.92/1.09 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[408, 401])).
% 0.92/1.09 tff(410,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(411,plain,
% 0.92/1.09 ((hskp28 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195)) <=> (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(412,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[411])).
% 0.92/1.09 tff(413,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[412, 410])).
% 0.92/1.09 tff(414,plain,
% 0.92/1.09 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(415,plain,
% 0.92/1.09 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2191))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.92/1.09 tff(416,plain,
% 0.92/1.09 (hskp28),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[415, 102, 344, 391, 385, 379, 336, 330, 409])).
% 0.92/1.09 tff(417,plain,
% 0.92/1.09 (c2_1(a2188)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[253, 416])).
% 0.92/1.09 tff(418,plain,
% 0.92/1.09 (c0_1(a2188)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[261, 416])).
% 0.92/1.09 tff(419,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(420,plain,
% 0.92/1.09 (((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(421,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194)))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[420])).
% 0.92/1.09 tff(422,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194))),
% 0.92/1.09 inference(transitivity,[status(thm)],[421, 419])).
% 0.92/1.09 tff(423,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(424,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2194)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.92/1.09 tff(425,plain,
% 0.92/1.09 (~c3_1(a2188)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[424, 102, 418, 417, 365, 399, 391, 385, 379, 175, 302])).
% 0.92/1.09 tff(426,plain,
% 0.92/1.09 (hskp11),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[269, 102, 176, 418, 417, 245, 425])).
% 0.92/1.09 tff(427,plain,
% 0.92/1.09 (~c1_1(a2187)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[209, 426])).
% 0.92/1.09 tff(428,plain,
% 0.92/1.09 (^[U: $i] : refl((hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(429,plain,
% 0.92/1.09 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[428])).
% 0.92/1.09 tff(430,plain,
% 0.92/1.09 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(431,plain,
% 0.92/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp22) <=> ((hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) | hskp22))), rewrite(((hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U))) | hskp22) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp22) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(432,plain,
% 0.92/1.09 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp22) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[431])).
% 0.92/1.09 tff(433,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.92/1.09 tff(434,plain,
% 0.92/1.09 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.92/1.09 tff(435,plain,
% 0.92/1.09 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[434, 430])).
% 0.92/1.09 tff(436,plain,(
% 0.92/1.09 ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[435])).
% 0.92/1.09 tff(437,plain,
% 0.92/1.09 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[436, 429])).
% 0.92/1.09 tff(438,plain,
% 0.92/1.09 (((~hskp28) | c1_1(a2188)) <=> ((~hskp28) | c1_1(a2188))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(439,axiom,((~hskp28) | c1_1(a2188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.92/1.09 tff(440,plain,
% 0.92/1.09 ((~hskp28) | c1_1(a2188)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.92/1.09 tff(441,plain,
% 0.92/1.09 ((~hskp28) | c1_1(a2188)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[440, 438])).
% 0.92/1.09 tff(442,plain,
% 0.92/1.09 ((~hskp28) | c1_1(a2188)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[441, 438])).
% 0.92/1.09 tff(443,plain,
% 0.92/1.09 ((~hskp28) | c1_1(a2188)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[442, 438])).
% 0.92/1.09 tff(444,plain,
% 0.92/1.09 ((~hskp28) | c1_1(a2188)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[443, 438])).
% 0.92/1.09 tff(445,plain,
% 0.92/1.09 (c1_1(a2188)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[444, 416])).
% 0.92/1.09 tff(446,plain,
% 0.92/1.09 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))) | hskp22 | hskp0 | (~ndr1_0) | (~c2_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(447,plain,
% 0.92/1.09 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(448,plain,
% 0.92/1.09 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)))) | hskp22 | hskp0 | (~ndr1_0) | (~c2_1(a2188)) | c3_1(a2188) | (~c1_1(a2188))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.92/1.09 tff(449,plain,
% 0.92/1.09 (hskp22),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[448, 102, 291, 445, 417, 437, 425])).
% 0.92/1.09 tff(450,plain,
% 0.92/1.09 (((~hskp22) | (~c3_1(a2219))) <=> ((~hskp22) | (~c3_1(a2219)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(451,plain,
% 0.92/1.09 (((~c3_1(a2219)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a2219)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(452,axiom,((~c3_1(a2219)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.92/1.09 tff(453,plain,
% 0.92/1.09 ((~hskp22) | (~c3_1(a2219))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.92/1.09 tff(454,plain,
% 0.92/1.09 ((~hskp22) | (~c3_1(a2219))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[453, 450])).
% 0.92/1.09 tff(455,plain,
% 0.92/1.09 (~c3_1(a2219)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[454, 449])).
% 0.92/1.09 tff(456,plain,
% 0.92/1.09 (c2_1(a2187)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[217, 426])).
% 0.92/1.09 tff(457,plain,
% 0.92/1.09 (c0_1(a2187)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[225, 426])).
% 0.92/1.09 tff(458,plain,
% 0.92/1.09 (((~hskp22) | c2_1(a2219)) <=> ((~hskp22) | c2_1(a2219))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(459,axiom,((~hskp22) | c2_1(a2219)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.92/1.09 tff(460,plain,
% 0.92/1.09 ((~hskp22) | c2_1(a2219)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.92/1.09 tff(461,plain,
% 0.92/1.09 ((~hskp22) | c2_1(a2219)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[460, 458])).
% 0.92/1.09 tff(462,plain,
% 0.92/1.09 ((~hskp22) | c2_1(a2219)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[461, 458])).
% 0.92/1.09 tff(463,plain,
% 0.92/1.09 ((~hskp22) | c2_1(a2219)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[462, 458])).
% 0.92/1.09 tff(464,plain,
% 0.92/1.09 ((~hskp22) | c2_1(a2219)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[463, 458])).
% 0.92/1.09 tff(465,plain,
% 0.92/1.09 (c2_1(a2219)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[464, 449])).
% 0.92/1.09 tff(466,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(467,plain,
% 0.92/1.09 (((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2219) | c0_1(a2219) | (~c2_1(a2219))) <=> (c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(468,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[467])).
% 0.92/1.09 tff(469,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[468, 466])).
% 0.92/1.09 tff(470,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(471,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2219) | c2_1(a2194) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2194)) | (~c3_1(a2194)) | c0_1(a2219) | (~c2_1(a2219))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.92/1.09 tff(472,plain,
% 0.92/1.09 (c0_1(a2219)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[471, 102, 465, 365, 399, 457, 456, 455, 357, 427, 301])).
% 0.92/1.09 tff(473,plain,
% 0.92/1.09 (((~hskp22) | (~c1_1(a2219))) <=> ((~hskp22) | (~c1_1(a2219)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(474,plain,
% 0.92/1.09 (((~c1_1(a2219)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a2219)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(475,axiom,((~c1_1(a2219)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.92/1.09 tff(476,plain,
% 0.92/1.09 ((~hskp22) | (~c1_1(a2219))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.92/1.09 tff(477,plain,
% 0.92/1.09 ((~hskp22) | (~c1_1(a2219))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[476, 473])).
% 0.92/1.09 tff(478,plain,
% 0.92/1.09 (~c1_1(a2219)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[477, 449])).
% 0.92/1.09 tff(479,assumption,(~c3_1(a2188)), introduced(assumption)).
% 0.92/1.09 tff(480,plain,
% 0.92/1.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(481,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[480])).
% 0.92/1.09 tff(482,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(483,plain,
% 0.92/1.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(484,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[483])).
% 0.92/1.09 tff(485,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 0.92/1.09 tff(486,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.92/1.09 tff(487,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[486, 482])).
% 0.92/1.09 tff(488,plain,(
% 0.92/1.09 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[487])).
% 0.92/1.09 tff(489,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[488, 481])).
% 0.92/1.09 tff(490,assumption,(c2_1(a2219)), introduced(assumption)).
% 0.92/1.09 tff(491,assumption,(c1_1(a2188)), introduced(assumption)).
% 0.92/1.09 tff(492,assumption,(c0_1(a2188)), introduced(assumption)).
% 0.92/1.09 tff(493,assumption,(hskp30), introduced(assumption)).
% 0.92/1.09 tff(494,plain,
% 0.92/1.09 (((~hskp30) | c3_1(a2208)) <=> ((~hskp30) | c3_1(a2208))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(495,axiom,((~hskp30) | c3_1(a2208)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.92/1.09 tff(496,plain,
% 0.92/1.09 ((~hskp30) | c3_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.92/1.09 tff(497,plain,
% 0.92/1.09 ((~hskp30) | c3_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[496, 494])).
% 0.92/1.09 tff(498,plain,
% 0.92/1.09 ((~hskp30) | c3_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[497, 494])).
% 0.92/1.09 tff(499,plain,
% 0.92/1.09 ((~hskp30) | c3_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[498, 494])).
% 0.92/1.09 tff(500,plain,
% 0.92/1.09 ((~hskp30) | c3_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[499, 494])).
% 0.92/1.09 tff(501,plain,
% 0.92/1.09 (c3_1(a2208)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[500, 493])).
% 0.92/1.09 tff(502,plain,
% 0.92/1.09 (((~hskp30) | c1_1(a2208)) <=> ((~hskp30) | c1_1(a2208))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(503,axiom,((~hskp30) | c1_1(a2208)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.92/1.09 tff(504,plain,
% 0.92/1.09 ((~hskp30) | c1_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.92/1.09 tff(505,plain,
% 0.92/1.09 ((~hskp30) | c1_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[504, 502])).
% 0.92/1.09 tff(506,plain,
% 0.92/1.09 ((~hskp30) | c1_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[505, 502])).
% 0.92/1.09 tff(507,plain,
% 0.92/1.09 ((~hskp30) | c1_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[506, 502])).
% 0.92/1.09 tff(508,plain,
% 0.92/1.09 ((~hskp30) | c1_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[507, 502])).
% 0.92/1.09 tff(509,plain,
% 0.92/1.09 (c1_1(a2208)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[508, 493])).
% 0.92/1.09 tff(510,plain,
% 0.92/1.09 (((~hskp30) | c0_1(a2208)) <=> ((~hskp30) | c0_1(a2208))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(511,axiom,((~hskp30) | c0_1(a2208)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.92/1.09 tff(512,plain,
% 0.92/1.09 ((~hskp30) | c0_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.92/1.09 tff(513,plain,
% 0.92/1.09 ((~hskp30) | c0_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[512, 510])).
% 0.92/1.09 tff(514,plain,
% 0.92/1.09 ((~hskp30) | c0_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[513, 510])).
% 0.92/1.09 tff(515,plain,
% 0.92/1.09 ((~hskp30) | c0_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[514, 510])).
% 0.92/1.09 tff(516,plain,
% 0.92/1.09 ((~hskp30) | c0_1(a2208)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[515, 510])).
% 0.92/1.09 tff(517,plain,
% 0.92/1.09 (c0_1(a2208)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[516, 493])).
% 0.92/1.09 tff(518,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(519,plain,
% 0.92/1.09 (((~ndr1_0) | (~c0_1(a2208)) | (~c3_1(a2208)) | (~c1_1(a2208)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2219) | c1_1(a2219) | (~c2_1(a2219))) <=> (c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(520,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2208)) | (~c3_1(a2208)) | (~c1_1(a2208)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2219) | c1_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[519])).
% 0.92/1.09 tff(521,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2208)) | (~c3_1(a2208)) | (~c1_1(a2208)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2219) | c1_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[520, 518])).
% 0.92/1.09 tff(522,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2208)) | (~c3_1(a2208)) | (~c1_1(a2208)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2219) | c1_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(523,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2208)) | (~c0_1(a2208)) | (~c1_1(a2208)) | (~c2_1(a2219))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.92/1.09 tff(524,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[523, 102, 517, 509, 501, 492, 491, 490, 201, 203, 489, 479])).
% 0.92/1.09 tff(525,plain,((~hskp30) | (~c0_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2219)) | c1_1(a2219) | c3_1(a2219) | c3_1(a2188)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(526,plain,
% 0.92/1.09 (~hskp30),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[525, 418, 445, 465, 478, 455, 425])).
% 0.92/1.09 tff(527,plain,
% 0.92/1.09 (^[U: $i] : refl((hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(528,plain,
% 0.92/1.09 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[527])).
% 0.92/1.09 tff(529,plain,
% 0.92/1.09 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(530,plain,
% 0.92/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(531,plain,
% 0.92/1.10 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp1) <=> ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[530])).
% 0.92/1.10 tff(532,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.92/1.10 tff(533,plain,
% 0.92/1.10 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.92/1.10 tff(534,plain,
% 0.92/1.10 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[533, 529])).
% 0.92/1.10 tff(535,plain,(
% 0.92/1.10 ![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[534])).
% 0.92/1.10 tff(536,plain,
% 0.92/1.10 (![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[535, 528])).
% 0.92/1.10 tff(537,plain,
% 0.92/1.10 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(538,plain,
% 0.92/1.10 ((hskp30 | hskp1 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194))) <=> (hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(539,plain,
% 0.92/1.10 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[538])).
% 0.92/1.10 tff(540,plain,
% 0.92/1.10 (((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))) <=> ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194))),
% 0.92/1.10 inference(transitivity,[status(thm)],[539, 537])).
% 0.92/1.10 tff(541,plain,
% 0.92/1.10 ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp1 | (~ndr1_0) | c2_1(a2194) | c1_1(a2194) | (~c0_1(a2194)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(542,plain,
% 0.92/1.10 ((~![U: $i] : (hskp30 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp1 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | c1_1(a2194)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.92/1.10 tff(543,plain,
% 0.92/1.10 (hskp30 | hskp1 | c1_1(a2194)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[542, 102, 365, 357, 536])).
% 0.92/1.10 tff(544,plain,
% 0.92/1.10 (hskp1),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[543, 526, 302])).
% 0.92/1.10 tff(545,plain,
% 0.92/1.10 (((~hskp1) | (~c3_1(a2175))) <=> ((~hskp1) | (~c3_1(a2175)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(546,plain,
% 0.92/1.10 (((~c3_1(a2175)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2175)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(547,axiom,((~c3_1(a2175)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.92/1.10 tff(548,plain,
% 0.92/1.10 ((~hskp1) | (~c3_1(a2175))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.92/1.10 tff(549,plain,
% 0.92/1.10 ((~hskp1) | (~c3_1(a2175))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[548, 545])).
% 0.92/1.10 tff(550,plain,
% 0.92/1.10 (~c3_1(a2175)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[549, 544])).
% 0.92/1.10 tff(551,plain,
% 0.92/1.10 (((~hskp1) | (~c0_1(a2175))) <=> ((~hskp1) | (~c0_1(a2175)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(552,plain,
% 0.92/1.10 (((~c0_1(a2175)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a2175)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(553,axiom,((~c0_1(a2175)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.92/1.10 tff(554,plain,
% 0.92/1.10 ((~hskp1) | (~c0_1(a2175))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.92/1.10 tff(555,plain,
% 0.92/1.10 ((~hskp1) | (~c0_1(a2175))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[554, 551])).
% 0.92/1.10 tff(556,plain,
% 0.92/1.10 (~c0_1(a2175)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[555, 544])).
% 0.92/1.10 tff(557,plain,
% 0.92/1.10 (((~hskp1) | c2_1(a2175)) <=> ((~hskp1) | c2_1(a2175))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(558,axiom,((~hskp1) | c2_1(a2175)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.92/1.10 tff(559,plain,
% 0.92/1.10 ((~hskp1) | c2_1(a2175)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.92/1.10 tff(560,plain,
% 0.92/1.10 ((~hskp1) | c2_1(a2175)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[559, 557])).
% 0.92/1.10 tff(561,plain,
% 0.92/1.10 ((~hskp1) | c2_1(a2175)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[560, 557])).
% 0.92/1.10 tff(562,plain,
% 0.92/1.10 ((~hskp1) | c2_1(a2175)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[561, 557])).
% 0.92/1.10 tff(563,plain,
% 0.92/1.10 ((~hskp1) | c2_1(a2175)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[562, 557])).
% 0.92/1.10 tff(564,plain,
% 0.92/1.10 (c2_1(a2175)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[563, 544])).
% 0.92/1.10 tff(565,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(566,plain,
% 0.92/1.10 (((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175))) <=> (c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(567,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[566])).
% 0.92/1.10 tff(568,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[567, 565])).
% 0.92/1.10 tff(569,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c3_1(a2194)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(570,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c2_1(a2194) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c0_1(a2194)) | (~c3_1(a2194)) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.92/1.10 tff(571,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[570, 102, 465, 365, 399, 564, 478, 357, 556, 550, 301, 472])).
% 0.92/1.10 tff(572,plain,(c1_1(a2194) | hskp0 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(573,plain,
% 0.92/1.10 (c1_1(a2194)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[572, 291, 176])).
% 0.92/1.10 tff(574,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(575,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[574])).
% 0.92/1.10 tff(576,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(577,plain,
% 0.92/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp10) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp10))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp10) <=> (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(578,plain,
% 0.92/1.10 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp10) <=> ![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[577])).
% 0.92/1.10 tff(579,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.92/1.10 tff(580,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.92/1.10 tff(581,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[580, 576])).
% 0.92/1.10 tff(582,plain,(
% 0.92/1.10 ![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[581])).
% 0.92/1.10 tff(583,plain,
% 0.92/1.10 (![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[582, 575])).
% 0.92/1.10 tff(584,plain,
% 0.92/1.10 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(585,plain,
% 0.92/1.10 ((hskp17 | hskp10 | (~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c1_1(a2194))) <=> (hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(586,plain,
% 0.92/1.10 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c1_1(a2194)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[585])).
% 0.92/1.10 tff(587,plain,
% 0.92/1.10 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c1_1(a2194)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[586, 584])).
% 0.92/1.10 tff(588,plain,
% 0.92/1.10 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2194) | (~c0_1(a2194)) | (~c1_1(a2194)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(589,plain,
% 0.92/1.10 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2194) | (~ndr1_0) | (~c0_1(a2194)) | (~c1_1(a2194))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.92/1.10 tff(590,plain,
% 0.92/1.10 (hskp17 | (~c1_1(a2194))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[589, 102, 176, 365, 357, 583])).
% 0.92/1.10 tff(591,plain,
% 0.92/1.10 (hskp17),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[590, 573])).
% 0.92/1.10 tff(592,plain,
% 0.92/1.10 (~c1_1(a2197)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[154, 591])).
% 0.92/1.10 tff(593,plain,
% 0.92/1.10 (((~hskp17) | c3_1(a2197)) <=> ((~hskp17) | c3_1(a2197))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(594,axiom,((~hskp17) | c3_1(a2197)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.92/1.10 tff(595,plain,
% 0.92/1.10 ((~hskp17) | c3_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.92/1.10 tff(596,plain,
% 0.92/1.10 ((~hskp17) | c3_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[595, 593])).
% 0.92/1.10 tff(597,plain,
% 0.92/1.10 ((~hskp17) | c3_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[596, 593])).
% 0.92/1.10 tff(598,plain,
% 0.92/1.10 ((~hskp17) | c3_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[597, 593])).
% 0.92/1.10 tff(599,plain,
% 0.92/1.10 ((~hskp17) | c3_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[598, 593])).
% 0.92/1.10 tff(600,plain,
% 0.92/1.10 (c3_1(a2197)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[599, 591])).
% 0.92/1.10 tff(601,plain,
% 0.92/1.10 (((~hskp17) | c2_1(a2197)) <=> ((~hskp17) | c2_1(a2197))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(602,axiom,((~hskp17) | c2_1(a2197)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.92/1.10 tff(603,plain,
% 0.92/1.10 ((~hskp17) | c2_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.92/1.10 tff(604,plain,
% 0.92/1.10 ((~hskp17) | c2_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[603, 601])).
% 0.92/1.10 tff(605,plain,
% 0.92/1.10 ((~hskp17) | c2_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[604, 601])).
% 0.92/1.10 tff(606,plain,
% 0.92/1.10 ((~hskp17) | c2_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[605, 601])).
% 0.92/1.10 tff(607,plain,
% 0.92/1.10 ((~hskp17) | c2_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[606, 601])).
% 0.92/1.10 tff(608,plain,
% 0.92/1.10 (c2_1(a2197)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[607, 591])).
% 0.92/1.10 tff(609,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(610,plain,
% 0.92/1.10 ((hskp10 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197))) <=> (hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(611,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[610])).
% 0.92/1.10 tff(612,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[611, 609])).
% 0.92/1.10 tff(613,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(614,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.92/1.10 tff(615,plain,
% 0.92/1.10 (~c0_1(a2197)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[614, 102, 176, 608, 600, 592, 290])).
% 0.92/1.10 tff(616,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(617,plain,
% 0.92/1.10 ((hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197))) <=> (hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(618,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[617])).
% 0.92/1.10 tff(619,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.10 inference(transitivity,[status(thm)],[618, 616])).
% 0.92/1.10 tff(620,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(621,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | c2_1(a2194) | (~ndr1_0) | (~c3_1(a2194)) | (~c1_1(a2194)) | (~c3_1(a2197)) | c0_1(a2197)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.92/1.10 tff(622,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[621, 102, 291, 600, 399, 592, 357, 165, 573, 615])).
% 0.92/1.10 tff(623,plain,(hskp0 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(624,plain,
% 0.92/1.10 (hskp0),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[623, 176])).
% 0.92/1.10 tff(625,plain,
% 0.92/1.10 (((~hskp0) | (~c0_1(a2174))) <=> ((~hskp0) | (~c0_1(a2174)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(626,plain,
% 0.92/1.10 (((~c0_1(a2174)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2174)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(627,axiom,((~c0_1(a2174)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.92/1.10 tff(628,plain,
% 0.92/1.10 ((~hskp0) | (~c0_1(a2174))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.92/1.10 tff(629,plain,
% 0.92/1.10 ((~hskp0) | (~c0_1(a2174))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[628, 625])).
% 0.92/1.10 tff(630,plain,
% 0.92/1.10 (~c0_1(a2174)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[629, 624])).
% 0.92/1.10 tff(631,plain,
% 0.92/1.10 (((~hskp0) | c2_1(a2174)) <=> ((~hskp0) | c2_1(a2174))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(632,axiom,((~hskp0) | c2_1(a2174)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.92/1.10 tff(633,plain,
% 0.92/1.10 ((~hskp0) | c2_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.92/1.10 tff(634,plain,
% 0.92/1.10 ((~hskp0) | c2_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[633, 631])).
% 0.92/1.10 tff(635,plain,
% 0.92/1.10 ((~hskp0) | c2_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[634, 631])).
% 0.92/1.10 tff(636,plain,
% 0.92/1.10 ((~hskp0) | c2_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[635, 631])).
% 0.92/1.10 tff(637,plain,
% 0.92/1.10 ((~hskp0) | c2_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[636, 631])).
% 0.92/1.10 tff(638,plain,
% 0.92/1.10 (c2_1(a2174)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[637, 624])).
% 0.92/1.10 tff(639,plain,
% 0.92/1.10 (((~hskp0) | c1_1(a2174)) <=> ((~hskp0) | c1_1(a2174))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(640,axiom,((~hskp0) | c1_1(a2174)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.92/1.10 tff(641,plain,
% 0.92/1.10 ((~hskp0) | c1_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.92/1.10 tff(642,plain,
% 0.92/1.10 ((~hskp0) | c1_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[641, 639])).
% 0.92/1.10 tff(643,plain,
% 0.92/1.10 ((~hskp0) | c1_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[642, 639])).
% 0.92/1.10 tff(644,plain,
% 0.92/1.10 ((~hskp0) | c1_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[643, 639])).
% 0.92/1.10 tff(645,plain,
% 0.92/1.10 ((~hskp0) | c1_1(a2174)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[644, 639])).
% 0.92/1.10 tff(646,plain,
% 0.92/1.10 (c1_1(a2174)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[645, 624])).
% 0.92/1.10 tff(647,plain,
% 0.92/1.10 (c1_1(a2188)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[444, 246])).
% 0.92/1.10 tff(648,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(649,plain,
% 0.92/1.10 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(650,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[649])).
% 0.92/1.10 tff(651,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[650, 648])).
% 0.92/1.10 tff(652,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(653,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2191))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.92/1.10 tff(654,plain,
% 0.92/1.10 ((~c3_1(a2188)) | (~c2_1(a2191))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[653, 102, 262, 647, 189, 646, 638, 178, 630, 280])).
% 0.92/1.10 tff(655,plain,
% 0.92/1.10 (~c2_1(a2191)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[654, 270])).
% 0.92/1.10 tff(656,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(657,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[656])).
% 0.92/1.10 tff(658,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(659,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(660,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[659])).
% 0.92/1.10 tff(661,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.92/1.10 tff(662,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.92/1.10 tff(663,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[662, 658])).
% 0.92/1.10 tff(664,plain,(
% 0.92/1.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.92/1.10 inference(skolemize,[status(sab)],[663])).
% 0.92/1.10 tff(665,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[664, 657])).
% 0.92/1.10 tff(666,plain,
% 0.92/1.10 (^[U: $i] : refl((hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(667,plain,
% 0.92/1.10 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[666])).
% 0.92/1.10 tff(668,plain,
% 0.92/1.10 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(669,plain,
% 0.92/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp11))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp1) <=> ((hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp1))), rewrite(((hskp11 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp1) <=> (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp1) <=> (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(670,plain,
% 0.92/1.10 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp1) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[669])).
% 0.92/1.10 tff(671,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.92/1.10 tff(672,plain,
% 0.92/1.10 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[671, 670])).
% 0.92/1.11 tff(673,plain,
% 0.92/1.11 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[672, 668])).
% 0.92/1.11 tff(674,plain,(
% 0.92/1.11 ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[673])).
% 0.92/1.11 tff(675,plain,
% 0.92/1.11 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[674, 667])).
% 0.92/1.11 tff(676,plain,
% 0.92/1.11 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(677,plain,
% 0.92/1.11 ((hskp11 | hskp1 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188))) <=> (hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(678,plain,
% 0.92/1.11 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[677])).
% 0.92/1.11 tff(679,plain,
% 0.92/1.11 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[678, 676])).
% 0.92/1.11 tff(680,plain,
% 0.92/1.11 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(681,plain,
% 0.92/1.11 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp11 | hskp1 | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.92/1.11 tff(682,plain,
% 0.92/1.11 (hskp1 | (~c3_1(a2188))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[681, 102, 263, 262, 254, 675])).
% 0.92/1.11 tff(683,plain,
% 0.92/1.11 (hskp1),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[682, 270])).
% 0.92/1.11 tff(684,plain,
% 0.92/1.11 (~c3_1(a2175)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[549, 683])).
% 0.92/1.11 tff(685,plain,
% 0.92/1.11 (~c0_1(a2175)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[555, 683])).
% 0.92/1.11 tff(686,plain,
% 0.92/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(687,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[686])).
% 0.92/1.11 tff(688,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(689,plain,
% 0.92/1.11 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(690,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[689])).
% 0.92/1.11 tff(691,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.92/1.11 tff(692,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.92/1.11 tff(693,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[692, 688])).
% 0.92/1.11 tff(694,plain,(
% 0.92/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.11 inference(skolemize,[status(sab)],[693])).
% 0.92/1.11 tff(695,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[694, 687])).
% 0.92/1.11 tff(696,plain,
% 0.92/1.11 (c2_1(a2175)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[563, 683])).
% 0.92/1.11 tff(697,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(698,plain,
% 0.92/1.11 (((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191)) <=> (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(699,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[698])).
% 0.92/1.11 tff(700,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[699, 697])).
% 0.92/1.11 tff(701,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(702,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.92/1.11 tff(703,plain,
% 0.92/1.11 (~c3_1(a2174)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[702, 102, 189, 696, 646, 178, 177, 685, 684, 630, 695])).
% 0.92/1.11 tff(704,plain,
% 0.92/1.11 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(705,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[704])).
% 0.92/1.11 tff(706,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(707,plain,
% 0.92/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(708,plain,
% 0.92/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[707])).
% 0.92/1.11 tff(709,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.92/1.11 tff(710,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.92/1.11 tff(711,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[710, 706])).
% 0.92/1.11 tff(712,plain,(
% 0.92/1.11 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[711])).
% 0.92/1.11 tff(713,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[712, 705])).
% 0.92/1.11 tff(714,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(715,plain,
% 0.92/1.11 ((hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(716,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[715])).
% 0.92/1.11 tff(717,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[716, 714])).
% 0.92/1.11 tff(718,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(719,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.92/1.11 tff(720,plain,
% 0.92/1.11 (hskp7),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[719, 102, 262, 254, 646, 638, 713, 270, 703])).
% 0.92/1.11 tff(721,plain,
% 0.92/1.11 (((~hskp7) | (~c0_1(a2182))) <=> ((~hskp7) | (~c0_1(a2182)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(722,plain,
% 0.92/1.11 (((~c0_1(a2182)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a2182)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(723,axiom,((~c0_1(a2182)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.92/1.11 tff(724,plain,
% 0.92/1.11 ((~hskp7) | (~c0_1(a2182))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[723, 722])).
% 0.92/1.11 tff(725,plain,
% 0.92/1.11 ((~hskp7) | (~c0_1(a2182))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[724, 721])).
% 0.92/1.11 tff(726,plain,
% 0.92/1.11 (~c0_1(a2182)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[725, 720])).
% 0.92/1.11 tff(727,plain,
% 0.92/1.11 (((~hskp7) | c3_1(a2182)) <=> ((~hskp7) | c3_1(a2182))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(728,axiom,((~hskp7) | c3_1(a2182)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.92/1.11 tff(729,plain,
% 0.92/1.11 ((~hskp7) | c3_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[728, 727])).
% 0.92/1.11 tff(730,plain,
% 0.92/1.11 ((~hskp7) | c3_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[729, 727])).
% 0.92/1.11 tff(731,plain,
% 0.92/1.11 ((~hskp7) | c3_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[730, 727])).
% 0.92/1.11 tff(732,plain,
% 0.92/1.11 ((~hskp7) | c3_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[731, 727])).
% 0.92/1.11 tff(733,plain,
% 0.92/1.11 ((~hskp7) | c3_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[732, 727])).
% 0.92/1.11 tff(734,plain,
% 0.92/1.11 (c3_1(a2182)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[733, 720])).
% 0.92/1.11 tff(735,plain,
% 0.92/1.11 (((~hskp7) | c2_1(a2182)) <=> ((~hskp7) | c2_1(a2182))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(736,axiom,((~hskp7) | c2_1(a2182)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.92/1.11 tff(737,plain,
% 0.92/1.11 ((~hskp7) | c2_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.92/1.11 tff(738,plain,
% 0.92/1.11 ((~hskp7) | c2_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[737, 735])).
% 0.92/1.11 tff(739,plain,
% 0.92/1.11 ((~hskp7) | c2_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[738, 735])).
% 0.92/1.11 tff(740,plain,
% 0.92/1.11 ((~hskp7) | c2_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[739, 735])).
% 0.92/1.11 tff(741,plain,
% 0.92/1.11 ((~hskp7) | c2_1(a2182)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[740, 735])).
% 0.92/1.11 tff(742,plain,
% 0.92/1.11 (c2_1(a2182)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[741, 720])).
% 0.92/1.11 tff(743,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(744,plain,
% 0.92/1.11 (((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2191) | c0_1(a2191) | c2_1(a2191)) <=> (c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(745,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2191) | c0_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191)))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[744])).
% 0.92/1.11 tff(746,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2191) | c0_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191))),
% 0.92/1.11 inference(transitivity,[status(thm)],[745, 743])).
% 0.92/1.11 tff(747,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2191) | c0_1(a2191) | c2_1(a2191))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(748,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c2_1(a2191)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.92/1.11 tff(749,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[748, 102, 189, 742, 734, 696, 178, 726, 685, 684, 665, 655])).
% 0.92/1.11 tff(750,plain,((~hskp28) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | hskp11 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(751,plain,
% 0.92/1.11 (~hskp28),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[750, 235, 178, 177, 189, 176])).
% 0.92/1.11 tff(752,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(753,plain,
% 0.92/1.11 ((hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219)) <=> (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(754,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[753])).
% 0.92/1.11 tff(755,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[754, 752])).
% 0.92/1.11 tff(756,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(757,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2219))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.92/1.11 tff(758,plain,
% 0.92/1.11 (hskp28 | (~c0_1(a2219))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[757, 102, 202, 201, 203, 409])).
% 0.92/1.11 tff(759,plain,
% 0.92/1.11 (~c0_1(a2219)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[758, 190])).
% 0.92/1.11 tff(760,plain,
% 0.92/1.11 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(761,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[760])).
% 0.92/1.11 tff(762,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(763,plain,
% 0.92/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp28))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(764,plain,
% 0.92/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[763])).
% 0.92/1.11 tff(765,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.92/1.11 tff(766,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.92/1.11 tff(767,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[766, 762])).
% 0.92/1.11 tff(768,plain,(
% 0.92/1.11 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.92/1.11 inference(skolemize,[status(sab)],[767])).
% 0.92/1.11 tff(769,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[768, 761])).
% 0.92/1.11 tff(770,plain,
% 0.92/1.11 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(771,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[770])).
% 0.92/1.11 tff(772,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(773,plain,
% 0.92/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(774,plain,
% 0.92/1.11 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[773])).
% 0.92/1.12 tff(775,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.92/1.12 tff(776,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.92/1.12 tff(777,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[776, 772])).
% 0.92/1.12 tff(778,plain,(
% 0.92/1.12 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(skolemize,[status(sab)],[777])).
% 0.92/1.12 tff(779,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[778, 771])).
% 0.92/1.12 tff(780,plain,
% 0.92/1.12 (~hskp22),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[464, 202])).
% 0.92/1.12 tff(781,assumption,(~hskp17), introduced(assumption)).
% 0.92/1.12 tff(782,plain,
% 0.92/1.12 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(783,plain,
% 0.92/1.12 ((hskp17 | hskp10 | (~ndr1_0) | c2_1(a2216) | (~c0_1(a2216)) | (~c1_1(a2216))) <=> (hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(784,plain,
% 0.92/1.12 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2216) | (~c0_1(a2216)) | (~c1_1(a2216)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[783])).
% 0.92/1.12 tff(785,plain,
% 0.92/1.12 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2216) | (~c0_1(a2216)) | (~c1_1(a2216)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[784, 782])).
% 0.92/1.12 tff(786,plain,
% 0.92/1.12 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2216) | (~c0_1(a2216)) | (~c1_1(a2216)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(787,plain,
% 0.92/1.12 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2216) | (~ndr1_0) | (~c1_1(a2216)) | (~c0_1(a2216))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.92/1.12 tff(788,plain,
% 0.92/1.12 (~c1_1(a2216)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[787, 102, 781, 176, 42, 34, 583])).
% 0.92/1.12 tff(789,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(790,plain,
% 0.92/1.12 ((hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219)) <=> (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(791,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[790])).
% 0.92/1.12 tff(792,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[791, 789])).
% 0.92/1.12 tff(793,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(794,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[793, 792])).
% 0.92/1.12 tff(795,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[794, 102, 190, 202, 42, 201, 203, 28, 409, 788])).
% 0.92/1.12 tff(796,plain,((~hskp21) | hskp28 | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | hskp17 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(797,plain,
% 0.92/1.12 (~hskp21),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[796, 190, 202, 201, 203, 781, 176])).
% 0.92/1.12 tff(798,plain,
% 0.92/1.12 ((hskp25 | hskp22 | hskp21) <=> (hskp25 | hskp22 | hskp21)),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(799,plain,
% 0.92/1.12 (((hskp21 | hskp25) | hskp22) <=> (hskp25 | hskp22 | hskp21)),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(800,axiom,((hskp21 | hskp25) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.92/1.12 tff(801,plain,
% 0.92/1.12 (hskp25 | hskp22 | hskp21),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.92/1.12 tff(802,plain,
% 0.92/1.12 (hskp25 | hskp22 | hskp21),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[801, 798])).
% 0.92/1.12 tff(803,plain,
% 0.92/1.12 (hskp25 | hskp22 | hskp21),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[802, 798])).
% 0.92/1.12 tff(804,plain,
% 0.92/1.12 (hskp25 | hskp22 | hskp21),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[803, 798])).
% 0.92/1.12 tff(805,plain,
% 0.92/1.12 (hskp25 | hskp22 | hskp21),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[804, 798])).
% 0.92/1.12 tff(806,plain,
% 0.92/1.12 (hskp25),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[805, 797, 780])).
% 0.92/1.12 tff(807,plain,
% 0.92/1.12 (((~hskp25) | (~c2_1(a2265))) <=> ((~hskp25) | (~c2_1(a2265)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(808,plain,
% 0.92/1.12 (((~c2_1(a2265)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a2265)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(809,axiom,((~c2_1(a2265)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.92/1.12 tff(810,plain,
% 0.92/1.12 ((~hskp25) | (~c2_1(a2265))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.92/1.12 tff(811,plain,
% 0.92/1.12 ((~hskp25) | (~c2_1(a2265))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[810, 807])).
% 0.92/1.12 tff(812,plain,
% 0.92/1.12 (~c2_1(a2265)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[811, 806])).
% 0.92/1.12 tff(813,plain,
% 0.92/1.12 (((~hskp25) | c3_1(a2265)) <=> ((~hskp25) | c3_1(a2265))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(814,axiom,((~hskp25) | c3_1(a2265)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.92/1.12 tff(815,plain,
% 0.92/1.12 ((~hskp25) | c3_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[814, 813])).
% 0.92/1.12 tff(816,plain,
% 0.92/1.12 ((~hskp25) | c3_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[815, 813])).
% 0.92/1.12 tff(817,plain,
% 0.92/1.12 ((~hskp25) | c3_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[816, 813])).
% 0.92/1.12 tff(818,plain,
% 0.92/1.12 ((~hskp25) | c3_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[817, 813])).
% 0.92/1.12 tff(819,plain,
% 0.92/1.12 ((~hskp25) | c3_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[818, 813])).
% 0.92/1.12 tff(820,plain,
% 0.92/1.12 (c3_1(a2265)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[819, 806])).
% 0.92/1.12 tff(821,plain,
% 0.92/1.12 (((~hskp25) | c1_1(a2265)) <=> ((~hskp25) | c1_1(a2265))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(822,axiom,((~hskp25) | c1_1(a2265)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.92/1.12 tff(823,plain,
% 0.92/1.12 ((~hskp25) | c1_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.92/1.12 tff(824,plain,
% 0.92/1.12 ((~hskp25) | c1_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[823, 821])).
% 0.92/1.12 tff(825,plain,
% 0.92/1.12 ((~hskp25) | c1_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[824, 821])).
% 0.92/1.12 tff(826,plain,
% 0.92/1.12 ((~hskp25) | c1_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[825, 821])).
% 0.92/1.12 tff(827,plain,
% 0.92/1.12 ((~hskp25) | c1_1(a2265)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[826, 821])).
% 0.92/1.12 tff(828,plain,
% 0.92/1.12 (c1_1(a2265)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[827, 806])).
% 0.92/1.12 tff(829,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(830,plain,
% 0.92/1.12 ((hskp27 | (~ndr1_0) | c2_1(a2265) | (~c3_1(a2265)) | (~c1_1(a2265)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(831,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2265) | (~c3_1(a2265)) | (~c1_1(a2265)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[830])).
% 0.92/1.12 tff(832,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2265) | (~c3_1(a2265)) | (~c1_1(a2265)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[831, 829])).
% 0.92/1.12 tff(833,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2265) | (~c3_1(a2265)) | (~c1_1(a2265)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(834,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2265) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2265)) | (~c1_1(a2265))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[833, 832])).
% 0.92/1.12 tff(835,plain,
% 0.92/1.12 (hskp27),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[834, 102, 828, 820, 646, 638, 812, 630, 779])).
% 0.92/1.12 tff(836,plain,
% 0.92/1.12 (((~hskp27) | c3_1(a2178)) <=> ((~hskp27) | c3_1(a2178))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(837,axiom,((~hskp27) | c3_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.92/1.12 tff(838,plain,
% 0.92/1.12 ((~hskp27) | c3_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[837, 836])).
% 0.92/1.12 tff(839,plain,
% 0.92/1.12 ((~hskp27) | c3_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[838, 836])).
% 0.92/1.12 tff(840,plain,
% 0.92/1.12 ((~hskp27) | c3_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[839, 836])).
% 0.92/1.12 tff(841,plain,
% 0.92/1.12 ((~hskp27) | c3_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[840, 836])).
% 0.92/1.12 tff(842,plain,
% 0.92/1.12 ((~hskp27) | c3_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[841, 836])).
% 0.92/1.12 tff(843,plain,
% 0.92/1.12 (c3_1(a2178)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[842, 835])).
% 0.92/1.12 tff(844,plain,
% 0.92/1.12 (((~hskp27) | c2_1(a2178)) <=> ((~hskp27) | c2_1(a2178))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(845,axiom,((~hskp27) | c2_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.92/1.12 tff(846,plain,
% 0.92/1.12 ((~hskp27) | c2_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.92/1.12 tff(847,plain,
% 0.92/1.12 ((~hskp27) | c2_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[846, 844])).
% 0.92/1.12 tff(848,plain,
% 0.92/1.12 ((~hskp27) | c2_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[847, 844])).
% 0.92/1.12 tff(849,plain,
% 0.92/1.12 ((~hskp27) | c2_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[848, 844])).
% 0.92/1.12 tff(850,plain,
% 0.92/1.12 ((~hskp27) | c2_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[849, 844])).
% 0.92/1.12 tff(851,plain,
% 0.92/1.12 (c2_1(a2178)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[850, 835])).
% 0.92/1.12 tff(852,plain,
% 0.92/1.12 (((~hskp27) | c0_1(a2178)) <=> ((~hskp27) | c0_1(a2178))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(853,axiom,((~hskp27) | c0_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.92/1.12 tff(854,plain,
% 0.92/1.12 ((~hskp27) | c0_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[853, 852])).
% 0.92/1.12 tff(855,plain,
% 0.92/1.12 ((~hskp27) | c0_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[854, 852])).
% 0.92/1.12 tff(856,plain,
% 0.92/1.12 ((~hskp27) | c0_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[855, 852])).
% 0.92/1.12 tff(857,plain,
% 0.92/1.12 ((~hskp27) | c0_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[856, 852])).
% 0.92/1.12 tff(858,plain,
% 0.92/1.12 ((~hskp27) | c0_1(a2178)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[857, 852])).
% 0.92/1.12 tff(859,plain,
% 0.92/1.12 (c0_1(a2178)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[858, 835])).
% 0.92/1.12 tff(860,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(861,plain,
% 0.92/1.12 ((hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2219) | c2_1(a2219) | c0_1(a2219)) <=> (hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(862,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2219) | c2_1(a2219) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[861])).
% 0.92/1.12 tff(863,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2219) | c2_1(a2219) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219))),
% 0.92/1.12 inference(transitivity,[status(thm)],[862, 860])).
% 0.92/1.12 tff(864,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2219) | c2_1(a2219) | c0_1(a2219))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(865,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2219) | c3_1(a2219) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2219)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.92/1.12 tff(866,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[865, 102, 190, 859, 851, 843, 202, 203, 769, 759])).
% 0.92/1.12 tff(867,plain,(hskp28 | c2_1(a2219) | c3_1(a2219) | c1_1(a2219) | hskp17 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(868,plain,
% 0.92/1.12 (hskp17),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[867, 751, 203, 201, 202, 176])).
% 0.92/1.12 tff(869,plain,
% 0.92/1.12 (~c1_1(a2197)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[154, 868])).
% 0.92/1.12 tff(870,plain,
% 0.92/1.12 (c2_1(a2197)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[607, 868])).
% 0.92/1.12 tff(871,plain,
% 0.92/1.12 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(872,plain,
% 0.92/1.12 ((hskp28 | hskp22 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197))) <=> (hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(873,plain,
% 0.92/1.12 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[872])).
% 0.92/1.12 tff(874,plain,
% 0.92/1.12 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[873, 871])).
% 0.92/1.12 tff(875,plain,
% 0.92/1.12 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(876,plain,
% 0.92/1.12 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[875, 874])).
% 0.92/1.12 tff(877,plain,
% 0.92/1.12 (~c0_1(a2197)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[876, 102, 751, 780, 870, 869, 200])).
% 0.92/1.12 tff(878,plain,
% 0.92/1.12 (c3_1(a2197)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[599, 868])).
% 0.92/1.12 tff(879,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(880,plain,
% 0.92/1.12 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2219) | c1_1(a2219) | c2_1(a2219)) <=> (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(881,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2219) | c1_1(a2219) | c2_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[880])).
% 0.92/1.12 tff(882,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2219) | c1_1(a2219) | c2_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.12 inference(transitivity,[status(thm)],[881, 879])).
% 0.92/1.12 tff(883,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2219) | c1_1(a2219) | c2_1(a2219))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(884,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.92/1.12 tff(885,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[884, 102, 202, 878, 646, 638, 201, 203, 869, 630, 148, 877])).
% 0.92/1.12 tff(886,plain,(c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | hskp10 | c1_1(a2191) | c3_1(a2191) | c0_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(887,plain,
% 0.92/1.12 (c3_1(a2219)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[886, 202, 201, 176, 178, 177, 189])).
% 0.92/1.12 tff(888,assumption,(c3_1(a2219)), introduced(assumption)).
% 0.92/1.12 tff(889,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(890,plain,
% 0.92/1.12 ((hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2216) | c2_1(a2216) | c1_1(a2216)) <=> (hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(891,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2216) | c2_1(a2216) | c1_1(a2216))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[890])).
% 0.92/1.12 tff(892,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2216) | c2_1(a2216) | c1_1(a2216))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[891, 889])).
% 0.92/1.12 tff(893,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216)) | c3_1(a2216) | c3_1(a2216) | c2_1(a2216) | c1_1(a2216))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(894,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c2_1(a2216) | c3_1(a2216) | (~ndr1_0) | c1_1(a2216) | (~c0_1(a2216))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[893, 892])).
% 0.92/1.12 tff(895,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[894, 102, 190, 42, 34, 28, 409, 788])).
% 0.92/1.12 tff(896,plain,((~hskp21) | hskp28 | hskp17 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(897,plain,
% 0.92/1.12 (~hskp21),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[896, 781, 190, 176])).
% 0.92/1.12 tff(898,plain,
% 0.92/1.12 (hskp25),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[805, 897, 780])).
% 0.92/1.12 tff(899,plain,
% 0.92/1.12 (~c2_1(a2265)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[811, 898])).
% 0.92/1.12 tff(900,plain,
% 0.92/1.12 (c1_1(a2265)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[827, 898])).
% 0.92/1.12 tff(901,plain,
% 0.92/1.12 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(902,plain,
% 0.92/1.12 ((hskp17 | hskp10 | (~ndr1_0) | c2_1(a2265) | (~c0_1(a2265)) | (~c1_1(a2265))) <=> (hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(903,plain,
% 0.92/1.12 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2265) | (~c0_1(a2265)) | (~c1_1(a2265)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[902])).
% 0.92/1.12 tff(904,plain,
% 0.92/1.12 (((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2265) | (~c0_1(a2265)) | (~c1_1(a2265)))) <=> ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[903, 901])).
% 0.92/1.12 tff(905,plain,
% 0.92/1.12 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp17 | hskp10 | (~ndr1_0) | c2_1(a2265) | (~c0_1(a2265)) | (~c1_1(a2265)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(906,plain,
% 0.92/1.12 ((~![U: $i] : (hskp17 | hskp10 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp17 | hskp10 | c2_1(a2265) | (~ndr1_0) | (~c0_1(a2265)) | (~c1_1(a2265))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[905, 904])).
% 0.92/1.12 tff(907,plain,
% 0.92/1.12 (~c0_1(a2265)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[906, 102, 781, 176, 900, 899, 583])).
% 0.92/1.12 tff(908,plain,
% 0.92/1.12 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(909,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[908])).
% 0.92/1.12 tff(910,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(911,plain,
% 0.92/1.12 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(912,plain,
% 0.92/1.12 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[911])).
% 0.92/1.12 tff(913,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.92/1.12 tff(914,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.92/1.12 tff(915,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[914, 910])).
% 0.92/1.12 tff(916,plain,(
% 0.92/1.12 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(skolemize,[status(sab)],[915])).
% 0.92/1.12 tff(917,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[916, 909])).
% 0.92/1.12 tff(918,plain,
% 0.92/1.12 (c3_1(a2265)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[819, 898])).
% 0.92/1.12 tff(919,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(920,plain,
% 0.92/1.13 ((hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2265) | c0_1(a2265) | (~c3_1(a2265))) <=> (hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(921,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2265) | c0_1(a2265) | (~c3_1(a2265)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[920])).
% 0.92/1.13 tff(922,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2265) | c0_1(a2265) | (~c3_1(a2265)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[921, 919])).
% 0.92/1.13 tff(923,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2265) | c0_1(a2265) | (~c3_1(a2265)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(924,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2265) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2265) | (~c3_1(a2265))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.92/1.13 tff(925,plain,
% 0.92/1.13 (~c2_1(a2191)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[924, 102, 176, 918, 899, 178, 177, 917, 907])).
% 0.92/1.13 tff(926,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(927,plain,
% 0.92/1.13 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191)) <=> (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(928,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[927])).
% 0.92/1.13 tff(929,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219))),
% 0.92/1.13 inference(transitivity,[status(thm)],[928, 926])).
% 0.92/1.13 tff(930,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(931,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | c0_1(a2219)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[930, 929])).
% 0.92/1.13 tff(932,plain,
% 0.92/1.13 ((~c3_1(a2219)) | c2_1(a2191) | c0_1(a2219)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[931, 102, 646, 638, 201, 178, 177, 630, 148])).
% 0.92/1.13 tff(933,plain,
% 0.92/1.13 (c0_1(a2219)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[932, 925, 888])).
% 0.92/1.13 tff(934,plain,
% 0.92/1.13 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(935,plain,
% 0.92/1.13 ((hskp16 | (~ndr1_0) | c2_1(a2219) | c1_1(a2219) | (~c0_1(a2219))) <=> (hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(936,plain,
% 0.92/1.13 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2219) | c1_1(a2219) | (~c0_1(a2219)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[935])).
% 0.92/1.13 tff(937,plain,
% 0.92/1.13 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2219) | c1_1(a2219) | (~c0_1(a2219)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[936, 934])).
% 0.92/1.13 tff(938,plain,
% 0.92/1.13 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2219) | c1_1(a2219) | (~c0_1(a2219)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(939,plain,
% 0.92/1.13 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c2_1(a2219) | c1_1(a2219) | (~ndr1_0) | (~c0_1(a2219))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.92/1.13 tff(940,plain,
% 0.92/1.13 (hskp16 | c2_1(a2219) | (~c0_1(a2219))),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[939, 102, 201, 52])).
% 0.92/1.13 tff(941,plain,
% 0.92/1.13 (hskp16),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[940, 933, 202])).
% 0.92/1.13 tff(942,plain,
% 0.92/1.13 (~c3_1(a2195)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[378, 941])).
% 0.92/1.13 tff(943,plain,
% 0.92/1.13 (~c2_1(a2195)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[384, 941])).
% 0.92/1.13 tff(944,plain,
% 0.92/1.13 (~c1_1(a2195)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[390, 941])).
% 0.92/1.13 tff(945,plain,
% 0.92/1.13 (hskp27),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[834, 102, 900, 918, 646, 638, 899, 630, 779])).
% 0.92/1.13 tff(946,plain,
% 0.92/1.13 (c3_1(a2178)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[842, 945])).
% 0.92/1.13 tff(947,plain,
% 0.92/1.13 (c2_1(a2178)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[850, 945])).
% 0.92/1.13 tff(948,plain,
% 0.92/1.13 (c0_1(a2178)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[858, 945])).
% 0.92/1.13 tff(949,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(950,plain,
% 0.92/1.13 (((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2219) | (~c3_1(a2219)) | (~c0_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(951,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2219) | (~c3_1(a2219)) | (~c0_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[950])).
% 0.92/1.13 tff(952,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2219) | (~c3_1(a2219)) | (~c0_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[951, 949])).
% 0.92/1.13 tff(953,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2219) | (~c3_1(a2219)) | (~c0_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(954,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c0_1(a2219))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.92/1.13 tff(955,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[954, 102, 948, 947, 946, 201, 888, 944, 943, 942, 175, 933])).
% 0.92/1.13 tff(956,plain,(hskp17 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2219) | c1_1(a2191) | c3_1(a2191) | hskp10 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(957,plain,
% 0.92/1.13 (hskp17),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[956, 190, 887, 202, 178, 177, 176, 201])).
% 0.92/1.13 tff(958,plain,
% 0.92/1.13 (~c1_1(a2197)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[154, 957])).
% 0.92/1.13 tff(959,plain,
% 0.92/1.13 (c2_1(a2197)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[607, 957])).
% 0.92/1.13 tff(960,plain,
% 0.92/1.13 (~c0_1(a2197)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[876, 102, 190, 780, 959, 958, 200])).
% 0.92/1.13 tff(961,plain,
% 0.92/1.13 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(962,plain,
% 0.92/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[961])).
% 0.92/1.13 tff(963,plain,
% 0.92/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(964,plain,
% 0.92/1.13 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(965,plain,
% 0.92/1.13 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[964])).
% 0.92/1.13 tff(966,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.92/1.13 tff(967,plain,
% 0.92/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.92/1.13 tff(968,plain,
% 0.92/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[967, 963])).
% 0.92/1.13 tff(969,plain,(
% 0.92/1.13 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.92/1.13 inference(skolemize,[status(sab)],[968])).
% 0.92/1.13 tff(970,plain,
% 0.92/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[969, 962])).
% 0.92/1.13 tff(971,plain,
% 0.92/1.13 (c3_1(a2197)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[599, 957])).
% 0.92/1.13 tff(972,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(973,plain,
% 0.92/1.13 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191)) <=> (c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(974,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[973])).
% 0.92/1.13 tff(975,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.13 inference(transitivity,[status(thm)],[974, 972])).
% 0.92/1.13 tff(976,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2191) | c1_1(a2191) | c2_1(a2191))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(977,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2191) | (~c3_1(a2197)) | c0_1(a2197)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.92/1.13 tff(978,plain,
% 0.92/1.13 (c2_1(a2191)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[977, 102, 971, 646, 638, 958, 178, 177, 630, 148, 960])).
% 0.92/1.13 tff(979,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(980,plain,
% 0.92/1.13 ((hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219))) <=> (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(981,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[980])).
% 0.92/1.13 tff(982,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219))),
% 0.92/1.13 inference(transitivity,[status(thm)],[981, 979])).
% 0.92/1.13 tff(983,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2191) | (~c2_1(a2191)) | c3_1(a2191) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(984,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2219)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.92/1.13 tff(985,plain,
% 0.92/1.13 ((~c3_1(a2219)) | (~c2_1(a2191)) | c0_1(a2219)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[984, 102, 176, 202, 178, 177, 917])).
% 0.92/1.13 tff(986,plain,
% 0.92/1.13 (c0_1(a2219)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[985, 978, 887])).
% 0.92/1.13 tff(987,plain,
% 0.92/1.13 (hskp16),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[940, 986, 202])).
% 0.92/1.13 tff(988,plain,
% 0.92/1.13 (~c3_1(a2195)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[378, 987])).
% 0.92/1.13 tff(989,plain,
% 0.92/1.13 (~c2_1(a2195)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[384, 987])).
% 0.92/1.13 tff(990,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(991,plain,
% 0.92/1.14 (((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2197)) | (~c2_1(a2197))) <=> (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(992,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2197)) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[991])).
% 0.92/1.14 tff(993,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2197)) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.14 inference(transitivity,[status(thm)],[992, 990])).
% 0.92/1.14 tff(994,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2197)) | (~c2_1(a2197)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(995,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.92/1.14 tff(996,plain,
% 0.92/1.14 (~c0_1(a2195)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[995, 102, 959, 971, 958, 989, 988, 970, 960])).
% 0.92/1.14 tff(997,plain,
% 0.92/1.14 (~c1_1(a2195)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[390, 987])).
% 0.92/1.14 tff(998,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(999,plain,
% 0.92/1.14 (((~ndr1_0) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)) | c1_1(a2195) | c0_1(a2195) | c2_1(a2195)) <=> (c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1000,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)) | c1_1(a2195) | c0_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[999])).
% 0.92/1.14 tff(1001,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)) | c1_1(a2195) | c0_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1000, 998])).
% 0.92/1.14 tff(1002,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)) | c1_1(a2195) | c0_1(a2195) | c2_1(a2195))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1003,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2191) | c1_1(a2195) | c2_1(a2195) | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 0.92/1.14 tff(1004,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1003, 102, 959, 971, 189, 997, 989, 177, 665, 978, 960, 996])).
% 0.92/1.14 tff(1005,plain,(hskp28 | c0_1(a2191) | c3_1(a2191) | c2_1(a2219) | c1_1(a2219) | hskp10 | c1_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(1006,plain,
% 0.92/1.14 (hskp28),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1005, 202, 177, 189, 201, 176, 178])).
% 0.92/1.14 tff(1007,plain,
% 0.92/1.14 (hskp11),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[750, 1006, 178, 177, 189, 176])).
% 0.92/1.14 tff(1008,plain,
% 0.92/1.14 (~c1_1(a2187)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[209, 1007])).
% 0.92/1.14 tff(1009,plain,
% 0.92/1.14 (c2_1(a2187)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[217, 1007])).
% 0.92/1.14 tff(1010,plain,
% 0.92/1.14 (c0_1(a2187)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[225, 1007])).
% 0.92/1.14 tff(1011,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1012,plain,
% 0.92/1.14 (((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191)) <=> (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1013,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191)))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1012])).
% 0.92/1.14 tff(1014,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1013, 1011])).
% 0.92/1.14 tff(1015,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1016,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c2_1(a2191)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 0.92/1.14 tff(1017,plain,
% 0.92/1.14 (c2_1(a2191)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1016, 102, 189, 1010, 1009, 178, 177, 1008, 188])).
% 0.92/1.14 tff(1018,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1019,plain,
% 0.92/1.14 ((hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187))) <=> (hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1020,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1019])).
% 0.92/1.14 tff(1021,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1020, 1018])).
% 0.92/1.14 tff(1022,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1023,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.92/1.14 tff(1024,plain,
% 0.92/1.14 (~c3_1(a2187)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1023, 102, 176, 1010, 1009, 1008, 290])).
% 0.92/1.14 tff(1025,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1026,plain,
% 0.92/1.14 ((hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219))) <=> (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1027,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219)))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1026])).
% 0.92/1.14 tff(1028,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1027, 1025])).
% 0.92/1.14 tff(1029,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2187) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2219) | c0_1(a2219) | (~c3_1(a2219)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1030,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a2219) | (~c3_1(a2219)) | c1_1(a2187) | (~ndr1_0) | c3_1(a2187) | (~c2_1(a2187)) | c0_1(a2219)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.92/1.14 tff(1031,plain,
% 0.92/1.14 (c0_1(a2219)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1030, 102, 176, 202, 1009, 887, 1008, 917, 1024])).
% 0.92/1.14 tff(1032,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1033,plain,
% 0.92/1.14 (((~ndr1_0) | c2_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1034,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1033])).
% 0.92/1.14 tff(1035,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1034, 1032])).
% 0.92/1.14 tff(1036,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1037,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2219) | c0_1(a2191) | (~c3_1(a2219)) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2219))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 0.92/1.14 tff(1038,plain,
% 0.92/1.14 ((~c2_1(a2191)) | (~c0_1(a2219))),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1037, 102, 202, 189, 1010, 1009, 887, 177, 1008, 301])).
% 0.92/1.14 tff(1039,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1038, 1031, 1017])).
% 0.92/1.14 tff(1040,plain,(c2_1(a2219) | c0_1(a2191) | c3_1(a2191) | hskp10 | c1_1(a2191) | c1_1(a2219)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(1041,plain,
% 0.92/1.14 (c2_1(a2219)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1040, 201, 177, 176, 178, 189])).
% 0.92/1.14 tff(1042,plain,
% 0.92/1.14 (~hskp13),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[343, 189])).
% 0.92/1.14 tff(1043,assumption,(~c0_1(a2219)), introduced(assumption)).
% 0.92/1.14 tff(1044,assumption,(c2_1(a2174)), introduced(assumption)).
% 0.92/1.14 tff(1045,assumption,(c1_1(a2174)), introduced(assumption)).
% 0.92/1.14 tff(1046,plain,
% 0.92/1.14 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1047,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1046])).
% 0.92/1.14 tff(1048,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1049,plain,
% 0.92/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(1050,plain,
% 0.92/1.14 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[1049])).
% 0.92/1.14 tff(1051,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.92/1.14 tff(1052,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 0.92/1.14 tff(1053,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1052, 1048])).
% 0.92/1.14 tff(1054,plain,(
% 0.92/1.14 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.14 inference(skolemize,[status(sab)],[1053])).
% 0.92/1.14 tff(1055,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1054, 1047])).
% 0.92/1.14 tff(1056,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1057,plain,
% 0.92/1.14 ((hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219))) <=> (hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1058,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[1057])).
% 0.92/1.14 tff(1059,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[1058, 1056])).
% 0.92/1.14 tff(1060,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(1061,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219) | (~c2_1(a2219))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 0.92/1.14 tff(1062,plain,
% 0.92/1.14 (hskp27 | c0_1(a2219) | (~c2_1(a2219))),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1061, 102, 1045, 1044, 201, 138, 1055])).
% 0.92/1.14 tff(1063,plain,
% 0.92/1.14 (hskp27),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1062, 1043, 490])).
% 0.92/1.14 tff(1064,plain,
% 0.92/1.14 (c3_1(a2178)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[842, 1063])).
% 0.92/1.14 tff(1065,plain,
% 0.92/1.14 (c0_1(a2178)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[858, 1063])).
% 0.92/1.14 tff(1066,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1067,plain,
% 0.92/1.14 (((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219))) <=> (c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(1068,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1067])).
% 0.92/1.15 tff(1069,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1068, 1066])).
% 0.92/1.15 tff(1070,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c2_1(a2219)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1071,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2219) | (~c2_1(a2219))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 0.92/1.15 tff(1072,plain,
% 0.92/1.15 (~c1_1(a2178)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1071, 102, 1065, 1064, 490, 1045, 1044, 201, 138, 280, 1043])).
% 0.92/1.15 tff(1073,plain,
% 0.92/1.15 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(1074,plain,
% 0.92/1.15 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[1073])).
% 0.92/1.15 tff(1075,plain,
% 0.92/1.15 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1076,plain,
% 0.92/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp16) <=> ((hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp16))), rewrite(((hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(1077,plain,
% 0.92/1.15 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp16) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[1076])).
% 0.92/1.15 tff(1078,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.92/1.15 tff(1079,plain,
% 0.92/1.15 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 0.92/1.15 tff(1080,plain,
% 0.92/1.15 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1079, 1075])).
% 0.92/1.15 tff(1081,plain,(
% 0.92/1.15 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.15 inference(skolemize,[status(sab)],[1080])).
% 0.92/1.15 tff(1082,plain,
% 0.92/1.15 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1081, 1074])).
% 0.92/1.15 tff(1083,assumption,(~hskp13), introduced(assumption)).
% 0.92/1.15 tff(1084,plain,
% 0.92/1.15 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1085,plain,
% 0.92/1.15 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c3_1(a2178))) <=> (hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1086,plain,
% 0.92/1.15 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c3_1(a2178)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178)))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1085])).
% 0.92/1.15 tff(1087,plain,
% 0.92/1.15 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c3_1(a2178)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1086, 1084])).
% 0.92/1.15 tff(1088,plain,
% 0.92/1.15 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c3_1(a2178)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1089,plain,
% 0.92/1.15 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | (~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.92/1.15 tff(1090,plain,
% 0.92/1.15 (hskp16),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1089, 102, 1083, 1065, 1064, 1082, 1072])).
% 0.92/1.15 tff(1091,plain,
% 0.92/1.15 (~c3_1(a2195)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[378, 1090])).
% 0.92/1.15 tff(1092,plain,
% 0.92/1.15 (~c2_1(a2195)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[384, 1090])).
% 0.92/1.15 tff(1093,plain,
% 0.92/1.15 (~c1_1(a2195)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[390, 1090])).
% 0.92/1.15 tff(1094,plain,
% 0.92/1.15 (c2_1(a2178)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[850, 1063])).
% 0.92/1.15 tff(1095,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1096,plain,
% 0.92/1.15 (((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1097,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178)))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1096])).
% 0.92/1.15 tff(1098,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1097, 1095])).
% 0.92/1.15 tff(1099,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1100,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178)),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.92/1.15 tff(1101,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1100, 102, 1065, 1094, 1064, 1093, 1092, 1091, 175, 1072])).
% 0.92/1.15 tff(1102,plain,(c0_1(a2219) | hskp13 | (~c2_1(a2219)) | (~c1_1(a2174)) | (~c2_1(a2174)) | c1_1(a2219) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.15 tff(1103,plain,
% 0.92/1.15 (c0_1(a2219)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1102, 1041, 1042, 646, 638, 201, 630])).
% 0.92/1.15 tff(1104,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1105,plain,
% 0.92/1.15 (((~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c2_1(a2219)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191)) <=> (c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1106,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c2_1(a2219)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1105])).
% 0.92/1.15 tff(1107,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c2_1(a2219)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1106, 1104])).
% 0.92/1.15 tff(1108,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c2_1(a2219)) | c3_1(a2191) | c2_1(a2191) | c1_1(a2191) | c3_1(a2191) | c1_1(a2191) | c0_1(a2191))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(1109,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2191) | c1_1(a2219) | c1_1(a2191) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.92/1.15 tff(1110,plain,
% 0.92/1.15 (c2_1(a2191) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1109, 102, 189, 201, 178, 177, 188])).
% 0.92/1.15 tff(1111,plain,
% 0.92/1.15 (c2_1(a2191)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1110, 1103, 1041])).
% 0.92/1.15 tff(1112,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1113,plain,
% 0.92/1.15 ((hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(1114,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[1113])).
% 0.92/1.15 tff(1115,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[1114, 1112])).
% 0.92/1.15 tff(1116,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 1.00/1.15 inference(quant_inst,[status(thm)],[])).
% 1.00/1.15 tff(1117,plain,
% 1.00/1.15 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2191))),
% 1.00/1.15 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 1.00/1.15 tff(1118,plain,
% 1.00/1.15 (hskp27 | c0_1(a2191) | (~c2_1(a2191))),
% 1.00/1.15 inference(unit_resolution,[status(thm)],[1117, 102, 646, 638, 178, 630, 1055])).
% 1.00/1.15 tff(1119,plain,
% 1.00/1.15 (hskp27),
% 1.00/1.15 inference(unit_resolution,[status(thm)],[1118, 1111, 189])).
% 1.00/1.15 tff(1120,plain,
% 1.00/1.15 (c3_1(a2178)),
% 1.00/1.15 inference(unit_resolution,[status(thm)],[842, 1119])).
% 1.00/1.15 tff(1121,plain,
% 1.00/1.15 (c0_1(a2178)),
% 1.00/1.15 inference(unit_resolution,[status(thm)],[858, 1119])).
% 1.00/1.15 tff(1122,plain,
% 1.00/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191)))),
% 1.00/1.15 inference(rewrite,[status(thm)],[])).
% 1.00/1.15 tff(1123,plain,
% 1.00/1.15 (((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191)))),
% 1.00/1.15 inference(rewrite,[status(thm)],[])).
% 1.00/1.15 tff(1124,plain,
% 1.00/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191))))),
% 1.00/1.15 inference(monotonicity,[status(thm)],[1123])).
% 1.00/1.15 tff(1125,plain,
% 1.00/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191)))),
% 1.00/1.15 inference(transitivity,[status(thm)],[1124, 1122])).
% 1.00/1.15 tff(1126,plain,
% 1.00/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 1.00/1.15 inference(quant_inst,[status(thm)],[])).
% 1.00/1.15 tff(1127,plain,
% 1.00/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c1_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2191))),
% 1.00/1.15 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.00/1.15 tff(1128,plain,
% 1.00/1.15 (~c1_1(a2178)),
% 1.00/1.15 inference(unit_resolution,[status(thm)],[1127, 102, 1121, 1120, 189, 646, 638, 178, 630, 280, 1111])).
% 1.00/1.15 tff(1129,plain,
% 1.00/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.00/1.15 inference(rewrite,[status(thm)],[])).
% 1.00/1.15 tff(1130,plain,
% 1.00/1.15 ((hskp10 | (~ndr1_0) | c1_1(a2219) | (~c2_1(a2219)) | (~c3_1(a2219)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219))) <=> (hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.00/1.15 inference(rewrite,[status(thm)],[])).
% 1.00/1.15 tff(1131,plain,
% 1.00/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2219) | (~c2_1(a2219)) | (~c3_1(a2219)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219))))),
% 1.00/1.15 inference(monotonicity,[status(thm)],[1130])).
% 1.00/1.15 tff(1132,plain,
% 1.00/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2219) | (~c2_1(a2219)) | (~c3_1(a2219)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.00/1.15 inference(transitivity,[status(thm)],[1131, 1129])).
% 1.00/1.15 tff(1133,plain,
% 1.00/1.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2219) | (~c2_1(a2219)) | (~c3_1(a2219)) | c1_1(a2219) | (~c2_1(a2219)) | (~c0_1(a2219)))),
% 1.00/1.15 inference(quant_inst,[status(thm)],[])).
% 1.00/1.15 tff(1134,plain,
% 1.00/1.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | c1_1(a2219) | (~c3_1(a2219)) | (~ndr1_0) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 1.00/1.15 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.00/1.15 tff(1135,plain,
% 1.00/1.15 ((~c3_1(a2219)) | (~c2_1(a2219)) | (~c0_1(a2219))),
% 1.00/1.15 inference(unit_resolution,[status(thm)],[1134, 102, 176, 201, 290])).
% 1.00/1.15 tff(1136,plain,
% 1.00/1.15 (~c3_1(a2219)),
% 1.00/1.15 inference(unit_resolution,[status(thm)],[1135, 1103, 1041])).
% 1.00/1.15 tff(1137,plain,
% 1.00/1.15 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.00/1.15 inference(bind,[status(th)],[])).
% 1.00/1.15 tff(1138,plain,
% 1.00/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.00/1.15 inference(quant_intro,[status(thm)],[1137])).
% 1.00/1.15 tff(1139,plain,
% 1.00/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.00/1.15 inference(rewrite,[status(thm)],[])).
% 1.00/1.15 tff(1140,plain,
% 1.00/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.00/1.15 inference(bind,[status(th)],[])).
% 1.00/1.15 tff(1141,plain,
% 1.00/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.00/1.15 inference(quant_intro,[status(thm)],[1140])).
% 1.00/1.15 tff(1142,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.00/1.15 tff(1143,plain,
% 1.00/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.00/1.15 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 1.00/1.15 tff(1144,plain,
% 1.00/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.00/1.15 inference(modus_ponens,[status(thm)],[1143, 1139])).
% 1.00/1.15 tff(1145,plain,(
% 1.00/1.15 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.00/1.15 inference(skolemize,[status(sab)],[1144])).
% 1.00/1.15 tff(1146,plain,
% 1.00/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.00/1.15 inference(modus_ponens,[status(thm)],[1145, 1138])).
% 1.00/1.15 tff(1147,plain,
% 1.00/1.15 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219)))),
% 1.00/1.15 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1148,plain,
% 1.00/1.16 ((hskp18 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1149,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[1148])).
% 1.00/1.16 tff(1150,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[1149, 1147])).
% 1.00/1.16 tff(1151,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(1152,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2219) | c3_1(a2219) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2219))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.00/1.16 tff(1153,plain,
% 1.00/1.16 (hskp18 | c3_1(a2219) | (~c0_1(a2219))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1152, 102, 646, 638, 201, 630, 1146])).
% 1.00/1.16 tff(1154,plain,
% 1.00/1.16 (hskp18),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1153, 1103, 1136])).
% 1.00/1.16 tff(1155,plain,
% 1.00/1.16 (~c2_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[58, 1154])).
% 1.00/1.16 tff(1156,plain,
% 1.00/1.16 (~c1_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[64, 1154])).
% 1.00/1.16 tff(1157,plain,
% 1.00/1.16 (c0_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[72, 1154])).
% 1.00/1.16 tff(1158,plain,
% 1.00/1.16 (hskp16),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[108, 102, 1157, 1156, 1155, 52])).
% 1.00/1.16 tff(1159,plain,
% 1.00/1.16 (~c3_1(a2195)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[378, 1158])).
% 1.00/1.16 tff(1160,plain,
% 1.00/1.16 (~c2_1(a2195)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[384, 1158])).
% 1.00/1.16 tff(1161,plain,
% 1.00/1.16 (~c1_1(a2195)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[390, 1158])).
% 1.00/1.16 tff(1162,plain,
% 1.00/1.16 (c2_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[850, 1119])).
% 1.00/1.16 tff(1163,plain,
% 1.00/1.16 ($false),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1100, 102, 1121, 1162, 1120, 1161, 1160, 1159, 175, 1128])).
% 1.00/1.16 tff(1164,plain,(c1_1(a2219) | c0_1(a2191) | c1_1(a2191) | hskp10 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.16 tff(1165,plain,
% 1.00/1.16 (c1_1(a2219)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1164, 189, 178, 176, 177])).
% 1.00/1.16 tff(1166,plain,
% 1.00/1.16 (~hskp22),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[477, 1165])).
% 1.00/1.16 tff(1167,assumption,(~hskp27), introduced(assumption)).
% 1.00/1.16 tff(1168,assumption,(hskp25), introduced(assumption)).
% 1.00/1.16 tff(1169,plain,
% 1.00/1.16 (~c2_1(a2265)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[811, 1168])).
% 1.00/1.16 tff(1170,plain,
% 1.00/1.16 (c3_1(a2265)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[819, 1168])).
% 1.00/1.16 tff(1171,plain,
% 1.00/1.16 (c1_1(a2265)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[827, 1168])).
% 1.00/1.16 tff(1172,plain,
% 1.00/1.16 ($false),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[834, 102, 1167, 1171, 1170, 1045, 1044, 1169, 138, 779])).
% 1.00/1.16 tff(1173,plain,((~hskp25) | hskp27 | (~c1_1(a2174)) | (~c2_1(a2174)) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.16 tff(1174,plain,
% 1.00/1.16 (~hskp25),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1173, 1167, 646, 638, 630])).
% 1.00/1.16 tff(1175,plain,
% 1.00/1.16 (hskp21),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[805, 1174, 1166])).
% 1.00/1.16 tff(1176,plain,
% 1.00/1.16 (hskp17),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[896, 1175, 190, 176])).
% 1.00/1.16 tff(1177,plain,
% 1.00/1.16 (~c1_1(a2197)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[154, 1176])).
% 1.00/1.16 tff(1178,plain,
% 1.00/1.16 (c2_1(a2197)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[607, 1176])).
% 1.00/1.16 tff(1179,plain,
% 1.00/1.16 (~c0_1(a2197)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[876, 102, 190, 1166, 1178, 1177, 200])).
% 1.00/1.16 tff(1180,plain,
% 1.00/1.16 (~c2_1(a2191)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1118, 1167, 189])).
% 1.00/1.16 tff(1181,plain,
% 1.00/1.16 (c3_1(a2197)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[599, 1176])).
% 1.00/1.16 tff(1182,plain,
% 1.00/1.16 ($false),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[977, 102, 1181, 646, 638, 1177, 178, 177, 630, 148, 1180, 1179])).
% 1.00/1.16 tff(1183,plain,(hskp27 | c1_1(a2191) | c3_1(a2191) | hskp28 | hskp10 | c0_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.16 tff(1184,plain,
% 1.00/1.16 (hskp27),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1183, 190, 177, 178, 176, 189])).
% 1.00/1.16 tff(1185,plain,
% 1.00/1.16 (c2_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[850, 1184])).
% 1.00/1.16 tff(1186,plain,
% 1.00/1.16 (c0_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[858, 1184])).
% 1.00/1.16 tff(1187,plain,
% 1.00/1.16 (c3_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[842, 1184])).
% 1.00/1.16 tff(1188,assumption,(c3_1(a2178)), introduced(assumption)).
% 1.00/1.16 tff(1189,assumption,(c2_1(a2178)), introduced(assumption)).
% 1.00/1.16 tff(1190,assumption,(c0_1(a2178)), introduced(assumption)).
% 1.00/1.16 tff(1191,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1192,plain,
% 1.00/1.16 ((hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2191) | c2_1(a2191) | c0_1(a2191)) <=> (hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1193,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2191) | c2_1(a2191) | c0_1(a2191))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191)))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[1192])).
% 1.00/1.16 tff(1194,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2191) | c2_1(a2191) | c0_1(a2191))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191))),
% 1.00/1.16 inference(transitivity,[status(thm)],[1193, 1191])).
% 1.00/1.16 tff(1195,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2191) | c2_1(a2191) | c0_1(a2191))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(1196,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2191) | c3_1(a2191) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c2_1(a2191)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.00/1.16 tff(1197,plain,
% 1.00/1.16 (hskp28 | c2_1(a2191)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1196, 102, 1190, 1189, 1188, 189, 177, 769])).
% 1.00/1.16 tff(1198,plain,
% 1.00/1.16 (c2_1(a2191)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1197, 190])).
% 1.00/1.16 tff(1199,assumption,(~hskp22), introduced(assumption)).
% 1.00/1.16 tff(1200,plain,
% 1.00/1.16 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1201,plain,
% 1.00/1.16 ((hskp28 | hskp22 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178))) <=> (hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1202,plain,
% 1.00/1.16 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178)))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[1201])).
% 1.00/1.16 tff(1203,plain,
% 1.00/1.16 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178))),
% 1.00/1.16 inference(transitivity,[status(thm)],[1202, 1200])).
% 1.00/1.16 tff(1204,plain,
% 1.00/1.16 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(1205,plain,
% 1.00/1.16 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | c1_1(a2178)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 1.00/1.16 tff(1206,plain,
% 1.00/1.16 (hskp28 | c1_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1205, 102, 1199, 1190, 1189, 200])).
% 1.00/1.16 tff(1207,plain,
% 1.00/1.16 (c1_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1206, 190])).
% 1.00/1.16 tff(1208,plain,
% 1.00/1.16 ((~c1_1(a2178)) | (~c2_1(a2191))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1127, 102, 1190, 1188, 189, 1045, 1044, 178, 138, 280])).
% 1.00/1.16 tff(1209,plain,
% 1.00/1.16 ($false),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1208, 1207, 1198])).
% 1.00/1.16 tff(1210,plain,(hskp28 | (~c0_1(a2178)) | (~c3_1(a2178)) | c0_1(a2191) | (~c1_1(a2174)) | (~c2_1(a2174)) | c1_1(a2191) | c0_1(a2174) | hskp22 | (~c2_1(a2178)) | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.16 tff(1211,plain,
% 1.00/1.16 ($false),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1210, 1187, 1186, 190, 189, 646, 638, 178, 630, 1166, 1185, 177])).
% 1.00/1.16 tff(1212,plain,(hskp28 | c0_1(a2191) | c1_1(a2191) | c3_1(a2191) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.00/1.16 tff(1213,plain,
% 1.00/1.16 (hskp28),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1212, 189, 178, 177, 176])).
% 1.00/1.16 tff(1214,plain,
% 1.00/1.16 (hskp11),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[750, 1213, 178, 177, 189, 176])).
% 1.00/1.16 tff(1215,plain,
% 1.00/1.16 (~c1_1(a2187)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[209, 1214])).
% 1.00/1.16 tff(1216,plain,
% 1.00/1.16 (c2_1(a2187)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[217, 1214])).
% 1.00/1.16 tff(1217,plain,
% 1.00/1.16 (c0_1(a2187)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[225, 1214])).
% 1.00/1.16 tff(1218,plain,
% 1.00/1.16 (c2_1(a2191)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1016, 102, 189, 1217, 1216, 178, 177, 1215, 188])).
% 1.00/1.16 tff(1219,plain,
% 1.00/1.16 (~c3_1(a2187)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1023, 102, 176, 1217, 1216, 1215, 290])).
% 1.00/1.16 tff(1220,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1221,plain,
% 1.00/1.16 ((hskp18 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | c3_1(a2187) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1222,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | c3_1(a2187) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187)))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[1221])).
% 1.00/1.16 tff(1223,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | c3_1(a2187) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187))),
% 1.00/1.16 inference(transitivity,[status(thm)],[1222, 1220])).
% 1.00/1.16 tff(1224,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | c3_1(a2187) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(1225,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.00/1.16 tff(1226,plain,
% 1.00/1.16 (hskp18),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1225, 102, 1217, 646, 638, 1215, 630, 1146, 1219])).
% 1.00/1.16 tff(1227,plain,
% 1.00/1.16 (~c2_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[58, 1226])).
% 1.00/1.16 tff(1228,plain,
% 1.00/1.16 (c0_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[72, 1226])).
% 1.00/1.16 tff(1229,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1230,plain,
% 1.00/1.16 (((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191))) <=> (c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1231,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[1230])).
% 1.00/1.16 tff(1232,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[1231, 1229])).
% 1.00/1.16 tff(1233,plain,
% 1.00/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2191) | c0_1(a2191) | (~c2_1(a2191)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(1234,plain,
% 1.00/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2191) | c2_1(a2198) | c3_1(a2191) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c2_1(a2191)) | (~c0_1(a2198)) | (~c3_1(a2198))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 1.00/1.16 tff(1235,plain,
% 1.00/1.16 (~c3_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1234, 102, 1228, 189, 1217, 1216, 1227, 177, 1215, 301, 1218])).
% 1.00/1.16 tff(1236,plain,
% 1.00/1.16 (c1_1(a2188)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[444, 1213])).
% 1.00/1.16 tff(1237,plain,
% 1.00/1.16 (c0_1(a2188)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[261, 1213])).
% 1.00/1.16 tff(1238,plain,
% 1.00/1.16 ((~c3_1(a2188)) | (~c2_1(a2191))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[653, 102, 1237, 1236, 189, 646, 638, 178, 630, 280])).
% 1.00/1.16 tff(1239,plain,
% 1.00/1.16 (~c3_1(a2188)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1238, 1218])).
% 1.00/1.16 tff(1240,plain,
% 1.00/1.16 (hskp27),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1118, 1218, 189])).
% 1.00/1.16 tff(1241,plain,
% 1.00/1.16 (c3_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[842, 1240])).
% 1.00/1.16 tff(1242,plain,
% 1.00/1.16 (c0_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[858, 1240])).
% 1.00/1.16 tff(1243,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1244,plain,
% 1.00/1.16 (((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2187) | c1_1(a2187) | (~c2_1(a2187))) <=> (c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1245,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2187) | c1_1(a2187) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[1244])).
% 1.00/1.16 tff(1246,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2187) | c1_1(a2187) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[1245, 1243])).
% 1.00/1.16 tff(1247,plain,
% 1.00/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2188)) | c3_1(a2187) | c1_1(a2187) | (~c2_1(a2187)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(1248,plain,
% 1.00/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c3_1(a2187) | (~c2_1(a2187))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 1.00/1.16 tff(1249,plain,
% 1.00/1.16 (~c1_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1248, 102, 1237, 1236, 1242, 1241, 1216, 1215, 489, 1239, 1219])).
% 1.00/1.16 tff(1250,plain,
% 1.00/1.16 (~c1_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[64, 1226])).
% 1.00/1.16 tff(1251,plain,
% 1.00/1.16 (c2_1(a2178)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[850, 1240])).
% 1.00/1.16 tff(1252,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1253,plain,
% 1.00/1.16 (((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2198) | c1_1(a2198) | c2_1(a2198)) <=> (c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1254,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2198) | c1_1(a2198) | c2_1(a2198))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198)))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[1253])).
% 1.00/1.16 tff(1255,plain,
% 1.00/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2198) | c1_1(a2198) | c2_1(a2198))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198))),
% 1.00/1.16 inference(transitivity,[status(thm)],[1254, 1252])).
% 1.00/1.16 tff(1256,plain,
% 1.00/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | (~c3_1(a2178)) | (~c0_1(a2178)) | c3_1(a2198) | c1_1(a2198) | c2_1(a2198))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(1257,plain,
% 1.00/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2198) | c2_1(a2198) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c1_1(a2178) | c3_1(a2198)),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 1.00/1.16 tff(1258,plain,
% 1.00/1.16 ($false),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1257, 102, 1242, 1251, 1241, 1250, 1227, 175, 1249, 1235])).
% 1.00/1.16 tff(1259,plain,(c0_1(a2191) | c3_1(a2191) | c1_1(a2191) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.00/1.16 tff(1260,plain,
% 1.00/1.16 (c0_1(a2191)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1259, 178, 177, 176])).
% 1.00/1.16 tff(1261,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1262,plain,
% 1.00/1.16 ((hskp18 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1263,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191))))),
% 1.00/1.16 inference(monotonicity,[status(thm)],[1262])).
% 1.00/1.16 tff(1264,plain,
% 1.00/1.16 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191)))),
% 1.00/1.16 inference(transitivity,[status(thm)],[1263, 1261])).
% 1.00/1.16 tff(1265,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2191) | (~c0_1(a2191)) | c3_1(a2191) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.00/1.16 inference(quant_inst,[status(thm)],[])).
% 1.00/1.16 tff(1266,plain,
% 1.00/1.16 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2191) | c3_1(a2191) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2191))),
% 1.00/1.16 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 1.00/1.16 tff(1267,plain,
% 1.00/1.16 (hskp18 | (~c0_1(a2191))),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1266, 102, 646, 638, 178, 177, 630, 1146])).
% 1.00/1.16 tff(1268,plain,
% 1.00/1.16 (hskp18),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[1267, 1260])).
% 1.00/1.16 tff(1269,plain,
% 1.00/1.16 (~c2_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[58, 1268])).
% 1.00/1.16 tff(1270,plain,
% 1.00/1.16 (~c1_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[64, 1268])).
% 1.00/1.16 tff(1271,plain,
% 1.00/1.16 (c0_1(a2198)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[72, 1268])).
% 1.00/1.16 tff(1272,plain,
% 1.00/1.16 (hskp16),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[108, 102, 1271, 1270, 1269, 52])).
% 1.00/1.16 tff(1273,plain,
% 1.00/1.16 (~c3_1(a2195)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[378, 1272])).
% 1.00/1.16 tff(1274,plain,
% 1.00/1.16 (~c2_1(a2195)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[384, 1272])).
% 1.00/1.16 tff(1275,plain,
% 1.00/1.16 (~c1_1(a2195)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[390, 1272])).
% 1.00/1.16 tff(1276,plain,
% 1.00/1.16 (hskp28),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[415, 102, 1260, 1275, 1274, 1273, 178, 177, 409])).
% 1.00/1.16 tff(1277,plain,
% 1.00/1.16 (c2_1(a2188)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[253, 1276])).
% 1.00/1.16 tff(1278,plain,
% 1.00/1.16 (c0_1(a2188)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[261, 1276])).
% 1.00/1.16 tff(1279,plain,
% 1.00/1.16 (c1_1(a2188)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[444, 1276])).
% 1.00/1.16 tff(1280,assumption,(hskp7), introduced(assumption)).
% 1.00/1.16 tff(1281,plain,
% 1.00/1.16 (c2_1(a2182)),
% 1.00/1.16 inference(unit_resolution,[status(thm)],[741, 1280])).
% 1.00/1.16 tff(1282,assumption,(c2_1(a2188)), introduced(assumption)).
% 1.00/1.16 tff(1283,assumption,(c0_1(a2198)), introduced(assumption)).
% 1.00/1.16 tff(1284,assumption,(~c2_1(a2198)), introduced(assumption)).
% 1.00/1.16 tff(1285,assumption,(~c1_1(a2198)), introduced(assumption)).
% 1.00/1.16 tff(1286,plain,
% 1.00/1.16 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.00/1.16 inference(bind,[status(th)],[])).
% 1.00/1.16 tff(1287,plain,
% 1.00/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.16 inference(quant_intro,[status(thm)],[1286])).
% 1.00/1.16 tff(1288,plain,
% 1.00/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.16 inference(rewrite,[status(thm)],[])).
% 1.00/1.16 tff(1289,plain,
% 1.00/1.16 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(1290,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[1289])).
% 1.00/1.17 tff(1291,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.00/1.17 tff(1292,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 1.00/1.17 tff(1293,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1292, 1288])).
% 1.00/1.17 tff(1294,plain,(
% 1.00/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(skolemize,[status(sab)],[1293])).
% 1.00/1.17 tff(1295,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1294, 1287])).
% 1.00/1.17 tff(1296,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1297,plain,
% 1.00/1.17 (((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174))) <=> (c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1298,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[1297])).
% 1.00/1.17 tff(1299,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[1298, 1296])).
% 1.00/1.17 tff(1300,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | c3_1(a2188) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(1301,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2188)) | (~c0_1(a2188)) | c3_1(a2188) | (~c0_1(a2198))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 1.00/1.17 tff(1302,plain,
% 1.00/1.17 ((~c3_1(a2174)) | c3_1(a2188)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1301, 102, 492, 1282, 1283, 638, 1285, 1284, 630, 1295])).
% 1.00/1.17 tff(1303,plain,
% 1.00/1.17 (~c3_1(a2174)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1302, 479])).
% 1.00/1.17 tff(1304,plain,
% 1.00/1.17 (hskp11 | c3_1(a2188)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[269, 102, 176, 492, 1282, 245])).
% 1.00/1.17 tff(1305,plain,
% 1.00/1.17 (hskp11),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1304, 479])).
% 1.00/1.17 tff(1306,plain,
% 1.00/1.17 (~c1_1(a2187)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[209, 1305])).
% 1.00/1.17 tff(1307,plain,
% 1.00/1.17 (c2_1(a2187)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[217, 1305])).
% 1.00/1.17 tff(1308,plain,
% 1.00/1.17 (c0_1(a2187)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[225, 1305])).
% 1.00/1.17 tff(1309,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1310,plain,
% 1.00/1.17 (((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174))) <=> (c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1311,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[1310])).
% 1.00/1.17 tff(1312,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[1311, 1309])).
% 1.00/1.17 tff(1313,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2198) | (~c0_1(a2198)) | (~c3_1(a2198)) | c1_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2187)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(1314,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a2198) | c1_1(a2187) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2198)) | (~c3_1(a2198))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 1.00/1.17 tff(1315,plain,
% 1.00/1.17 (~c3_1(a2198)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1314, 102, 1283, 1308, 1307, 638, 1284, 1306, 630, 301, 1303])).
% 1.00/1.17 tff(1316,plain,
% 1.00/1.17 (hskp16),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[108, 102, 1283, 1285, 1284, 52])).
% 1.00/1.17 tff(1317,plain,
% 1.00/1.17 (~c3_1(a2195)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[378, 1316])).
% 1.00/1.17 tff(1318,plain,
% 1.00/1.17 (~c2_1(a2195)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[384, 1316])).
% 1.00/1.17 tff(1319,plain,
% 1.00/1.17 (~c1_1(a2195)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[390, 1316])).
% 1.00/1.17 tff(1320,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1321,plain,
% 1.00/1.17 (((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | c3_1(a2195) | c1_1(a2195) | c0_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1322,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | c3_1(a2195) | c1_1(a2195) | c0_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195)))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[1321])).
% 1.00/1.17 tff(1323,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | c3_1(a2195) | c1_1(a2195) | c0_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195))),
% 1.00/1.17 inference(transitivity,[status(thm)],[1322, 1320])).
% 1.00/1.17 tff(1324,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | c3_1(a2195) | c1_1(a2195) | c0_1(a2195))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(1325,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c0_1(a2195)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.00/1.17 tff(1326,plain,
% 1.00/1.17 (c0_1(a2195)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1325, 102, 1308, 1307, 1319, 1318, 1317, 1306, 188])).
% 1.00/1.17 tff(1327,plain,
% 1.00/1.17 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(1328,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[1327])).
% 1.00/1.17 tff(1329,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1330,plain,
% 1.00/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(1331,plain,
% 1.00/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[1330])).
% 1.00/1.17 tff(1332,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.00/1.17 tff(1333,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.00/1.17 tff(1334,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1333, 1329])).
% 1.00/1.17 tff(1335,plain,(
% 1.00/1.17 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.00/1.17 inference(skolemize,[status(sab)],[1334])).
% 1.00/1.17 tff(1336,plain,
% 1.00/1.17 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1335, 1328])).
% 1.00/1.17 tff(1337,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1338,plain,
% 1.00/1.17 ((hskp19 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c1_1(a2195) | (~c0_1(a2195))) <=> (hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1339,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195))))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[1338])).
% 1.00/1.17 tff(1340,plain,
% 1.00/1.17 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.00/1.17 inference(transitivity,[status(thm)],[1339, 1337])).
% 1.00/1.17 tff(1341,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(1342,plain,
% 1.00/1.17 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c0_1(a2195))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 1.00/1.17 tff(1343,plain,
% 1.00/1.17 (hskp19),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1342, 102, 1308, 1307, 1319, 1317, 1306, 1336, 1326])).
% 1.00/1.17 tff(1344,plain,
% 1.00/1.17 (((~hskp19) | (~c3_1(a2211))) <=> ((~hskp19) | (~c3_1(a2211)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1345,plain,
% 1.00/1.17 (((~c3_1(a2211)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a2211)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1346,axiom,((~c3_1(a2211)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.00/1.17 tff(1347,plain,
% 1.00/1.17 ((~hskp19) | (~c3_1(a2211))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 1.00/1.17 tff(1348,plain,
% 1.00/1.17 ((~hskp19) | (~c3_1(a2211))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1347, 1344])).
% 1.00/1.17 tff(1349,plain,
% 1.00/1.17 (~c3_1(a2211)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1348, 1343])).
% 1.00/1.17 tff(1350,plain,
% 1.00/1.17 (((~hskp19) | (~c0_1(a2211))) <=> ((~hskp19) | (~c0_1(a2211)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1351,plain,
% 1.00/1.17 (((~c0_1(a2211)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a2211)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1352,axiom,((~c0_1(a2211)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.00/1.17 tff(1353,plain,
% 1.00/1.17 ((~hskp19) | (~c0_1(a2211))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.00/1.17 tff(1354,plain,
% 1.00/1.17 ((~hskp19) | (~c0_1(a2211))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1353, 1350])).
% 1.00/1.17 tff(1355,plain,
% 1.00/1.17 (~c0_1(a2211)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1354, 1343])).
% 1.00/1.17 tff(1356,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1357,plain,
% 1.00/1.17 (((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c2_1(a2198) | c1_1(a2198) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211)) <=> (c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1358,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c2_1(a2198) | c1_1(a2198) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211)))),
% 1.00/1.17 inference(monotonicity,[status(thm)],[1357])).
% 1.00/1.17 tff(1359,plain,
% 1.00/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c2_1(a2198) | c1_1(a2198) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211))),
% 1.00/1.17 inference(transitivity,[status(thm)],[1358, 1356])).
% 1.00/1.17 tff(1360,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c2_1(a2198) | c1_1(a2198) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))),
% 1.00/1.17 inference(quant_inst,[status(thm)],[])).
% 1.00/1.17 tff(1361,plain,
% 1.00/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2198) | c2_1(a2198) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2198) | c1_1(a2211)),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.00/1.17 tff(1362,plain,
% 1.00/1.17 (c1_1(a2211)),
% 1.00/1.17 inference(unit_resolution,[status(thm)],[1361, 102, 1308, 1307, 1355, 1349, 1285, 1284, 1306, 188, 1315])).
% 1.00/1.17 tff(1363,plain,
% 1.00/1.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(1364,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[1363])).
% 1.00/1.17 tff(1365,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.00/1.17 inference(rewrite,[status(thm)],[])).
% 1.00/1.17 tff(1366,plain,
% 1.00/1.17 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.00/1.17 inference(bind,[status(th)],[])).
% 1.00/1.17 tff(1367,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.00/1.17 inference(quant_intro,[status(thm)],[1366])).
% 1.00/1.17 tff(1368,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.00/1.17 tff(1369,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.00/1.17 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 1.00/1.17 tff(1370,plain,
% 1.00/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1369, 1365])).
% 1.00/1.18 tff(1371,plain,(
% 1.00/1.18 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.00/1.18 inference(skolemize,[status(sab)],[1370])).
% 1.00/1.18 tff(1372,plain,
% 1.00/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1371, 1364])).
% 1.00/1.18 tff(1373,plain,
% 1.00/1.18 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(1374,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[1373])).
% 1.00/1.18 tff(1375,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1376,plain,
% 1.00/1.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(1377,plain,
% 1.00/1.18 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[1376])).
% 1.00/1.18 tff(1378,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.00/1.18 tff(1379,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 1.00/1.18 tff(1380,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1379, 1375])).
% 1.00/1.18 tff(1381,plain,(
% 1.00/1.18 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.18 inference(skolemize,[status(sab)],[1380])).
% 1.00/1.18 tff(1382,plain,
% 1.00/1.18 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1381, 1374])).
% 1.00/1.18 tff(1383,plain,
% 1.00/1.18 (((~hskp19) | (~c2_1(a2211))) <=> ((~hskp19) | (~c2_1(a2211)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1384,plain,
% 1.00/1.18 (((~c2_1(a2211)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a2211)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1385,axiom,((~c2_1(a2211)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.00/1.18 tff(1386,plain,
% 1.00/1.18 ((~hskp19) | (~c2_1(a2211))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 1.00/1.18 tff(1387,plain,
% 1.00/1.18 ((~hskp19) | (~c2_1(a2211))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1386, 1383])).
% 1.00/1.18 tff(1388,plain,
% 1.00/1.18 (~c2_1(a2211)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1387, 1343])).
% 1.00/1.18 tff(1389,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1390,plain,
% 1.00/1.18 ((hskp14 | (~ndr1_0) | c2_1(a2211) | c3_1(a2211) | (~c1_1(a2211)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211))) <=> (hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1391,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2211) | c3_1(a2211) | (~c1_1(a2211)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[1390])).
% 1.00/1.18 tff(1392,plain,
% 1.00/1.18 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2211) | c3_1(a2211) | (~c1_1(a2211)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[1391, 1389])).
% 1.00/1.18 tff(1393,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2211) | c3_1(a2211) | (~c1_1(a2211)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(1394,plain,
% 1.00/1.18 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c1_1(a2211))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 1.00/1.18 tff(1395,plain,
% 1.00/1.18 (hskp14),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1394, 102, 1355, 1388, 1349, 1382, 1362])).
% 1.00/1.18 tff(1396,plain,
% 1.00/1.18 (((~hskp14) | (~c1_1(a2193))) <=> ((~hskp14) | (~c1_1(a2193)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1397,plain,
% 1.00/1.18 (((~c1_1(a2193)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a2193)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1398,axiom,((~c1_1(a2193)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.00/1.18 tff(1399,plain,
% 1.00/1.18 ((~hskp14) | (~c1_1(a2193))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 1.00/1.18 tff(1400,plain,
% 1.00/1.18 ((~hskp14) | (~c1_1(a2193))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1399, 1396])).
% 1.00/1.18 tff(1401,plain,
% 1.00/1.18 (~c1_1(a2193)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1400, 1395])).
% 1.00/1.18 tff(1402,plain,
% 1.00/1.18 (((~hskp14) | c3_1(a2193)) <=> ((~hskp14) | c3_1(a2193))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1403,axiom,((~hskp14) | c3_1(a2193)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.00/1.18 tff(1404,plain,
% 1.00/1.18 ((~hskp14) | c3_1(a2193)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.00/1.18 tff(1405,plain,
% 1.00/1.18 ((~hskp14) | c3_1(a2193)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1404, 1402])).
% 1.00/1.18 tff(1406,plain,
% 1.00/1.18 ((~hskp14) | c3_1(a2193)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1405, 1402])).
% 1.00/1.18 tff(1407,plain,
% 1.00/1.18 ((~hskp14) | c3_1(a2193)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1406, 1402])).
% 1.00/1.18 tff(1408,plain,
% 1.00/1.18 ((~hskp14) | c3_1(a2193)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1407, 1402])).
% 1.00/1.18 tff(1409,plain,
% 1.00/1.18 (c3_1(a2193)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1408, 1395])).
% 1.00/1.18 tff(1410,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1411,plain,
% 1.00/1.18 (((~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211))) <=> (c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1412,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[1411])).
% 1.00/1.18 tff(1413,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[1412, 1410])).
% 1.00/1.18 tff(1414,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c3_1(a2211) | c0_1(a2211) | (~c1_1(a2211)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(1415,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2211) | c3_1(a2211) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2193)) | (~c3_1(a2193)) | (~c1_1(a2211))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.00/1.18 tff(1416,plain,
% 1.00/1.18 (~c0_1(a2193)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1415, 102, 1409, 646, 638, 1355, 1349, 1401, 630, 1372, 1362])).
% 1.00/1.18 tff(1417,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1418,plain,
% 1.00/1.18 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1419,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[1418])).
% 1.00/1.18 tff(1420,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[1419, 1417])).
% 1.00/1.18 tff(1421,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(1422,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2193) | (~c3_1(a2193))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.00/1.18 tff(1423,plain,
% 1.00/1.18 ($false),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1422, 102, 1409, 646, 638, 1319, 1318, 1317, 1401, 630, 148, 1416])).
% 1.00/1.18 tff(1424,plain,(c3_1(a2188) | c1_1(a2198) | c2_1(a2198) | (~c0_1(a2198)) | hskp10 | (~c0_1(a2188)) | (~c2_1(a2188))), inference(lemma,lemma(discharge,[]))).
% 1.00/1.18 tff(1425,plain,
% 1.00/1.18 (c3_1(a2188)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1424, 1285, 1284, 1283, 176, 492, 1282])).
% 1.00/1.18 tff(1426,plain,
% 1.00/1.18 (~c0_1(a2182)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[725, 1280])).
% 1.00/1.18 tff(1427,plain,
% 1.00/1.18 (c3_1(a2182)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[733, 1280])).
% 1.00/1.18 tff(1428,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1429,plain,
% 1.00/1.18 (((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1430,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[1429])).
% 1.00/1.18 tff(1431,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[1430, 1428])).
% 1.00/1.18 tff(1432,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | (~c3_1(a2187)) | c1_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(1433,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)) | (~c2_1(a2187))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 1.00/1.18 tff(1434,plain,
% 1.00/1.18 (~c3_1(a2187)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1433, 102, 226, 218, 1319, 1318, 1317, 210, 175])).
% 1.00/1.18 tff(1435,assumption,(~c0_1(a2182)), introduced(assumption)).
% 1.00/1.18 tff(1436,assumption,(c3_1(a2182)), introduced(assumption)).
% 1.00/1.18 tff(1437,assumption,(c2_1(a2182)), introduced(assumption)).
% 1.00/1.18 tff(1438,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1439,plain,
% 1.00/1.18 (((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182))) <=> (c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198)))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1440,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198))))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[1439])).
% 1.00/1.18 tff(1441,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198)))),
% 1.00/1.18 inference(transitivity,[status(thm)],[1440, 1438])).
% 1.00/1.18 tff(1442,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2198) | c1_1(a2198) | (~c0_1(a2198)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(1443,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2198) | c2_1(a2198) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2198))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 1.00/1.18 tff(1444,plain,
% 1.00/1.18 ($false),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1443, 102, 1283, 226, 218, 1437, 1436, 1285, 1284, 1435, 1295, 1434])).
% 1.00/1.18 tff(1445,plain,((~hskp11) | (~c0_1(a2198)) | (~c2_1(a2182)) | (~c3_1(a2182)) | c1_1(a2198) | c2_1(a2198) | c0_1(a2182)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.18 tff(1446,plain,
% 1.00/1.18 (~hskp11),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1445, 1281, 1283, 1427, 1285, 1284, 1426])).
% 1.00/1.18 tff(1447,plain,
% 1.00/1.18 (hskp11 | hskp1 | (~c3_1(a2188))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[681, 102, 492, 1282, 675])).
% 1.00/1.18 tff(1448,plain,
% 1.00/1.18 (hskp1),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1447, 1446, 1425])).
% 1.00/1.18 tff(1449,plain,
% 1.00/1.18 (~c3_1(a2175)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[549, 1448])).
% 1.00/1.18 tff(1450,plain,
% 1.00/1.18 (~c0_1(a2175)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[555, 1448])).
% 1.00/1.18 tff(1451,assumption,(c3_1(a2188)), introduced(assumption)).
% 1.00/1.18 tff(1452,plain,
% 1.00/1.18 (c2_1(a2197)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[607, 149])).
% 1.00/1.18 tff(1453,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1454,plain,
% 1.00/1.18 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197))) <=> (c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(1455,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197)))),
% 1.00/1.18 inference(monotonicity,[status(thm)],[1454])).
% 1.00/1.18 tff(1456,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.00/1.18 inference(transitivity,[status(thm)],[1455, 1453])).
% 1.00/1.18 tff(1457,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(1458,plain,
% 1.00/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2197)) | c0_1(a2197)),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[1457, 1456])).
% 1.00/1.18 tff(1459,plain,
% 1.00/1.18 (c0_1(a2197)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[1458, 102, 492, 491, 1452, 1045, 1044, 155, 138, 280, 1451])).
% 1.00/1.18 tff(1460,assumption,(~c3_1(a2195)), introduced(assumption)).
% 1.00/1.18 tff(1461,assumption,(~c2_1(a2195)), introduced(assumption)).
% 1.00/1.18 tff(1462,assumption,(~c1_1(a2195)), introduced(assumption)).
% 1.00/1.18 tff(1463,plain,
% 1.00/1.18 (c3_1(a2197)),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[599, 149])).
% 1.00/1.18 tff(1464,plain,
% 1.00/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(1465,plain,
% 1.00/1.19 (((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2197) | (~c3_1(a2197)) | (~c0_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(1466,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2197) | (~c3_1(a2197)) | (~c0_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[1465])).
% 1.00/1.19 tff(1467,plain,
% 1.00/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2197) | (~c3_1(a2197)) | (~c0_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.00/1.19 inference(transitivity,[status(thm)],[1466, 1464])).
% 1.00/1.19 tff(1468,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2197) | (~c3_1(a2197)) | (~c0_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(1469,plain,
% 1.00/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c3_1(a2197)) | (~c0_1(a2197))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 1.00/1.19 tff(1470,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1469, 102, 492, 1282, 1463, 155, 1462, 1461, 1460, 175, 1451, 1459])).
% 1.00/1.19 tff(1471,plain,((~hskp17) | (~c0_1(a2188)) | (~c2_1(a2188)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c1_1(a2174)) | (~c2_1(a2174)) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(1472,plain,
% 1.00/1.19 (~hskp17),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1471, 492, 1282, 1319, 1318, 1317, 1425, 491, 646, 638, 630])).
% 1.00/1.19 tff(1473,assumption,(hskp15), introduced(assumption)).
% 1.00/1.19 tff(1474,plain,
% 1.00/1.19 (~c2_1(a2194)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[356, 1473])).
% 1.00/1.19 tff(1475,plain,
% 1.00/1.19 (c0_1(a2194)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[364, 1473])).
% 1.00/1.19 tff(1476,plain,
% 1.00/1.19 (~c1_1(a2194)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[589, 102, 781, 176, 1475, 1474, 583])).
% 1.00/1.19 tff(1477,plain,
% 1.00/1.19 (c3_1(a2194)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[398, 1473])).
% 1.00/1.19 tff(1478,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[424, 102, 492, 1282, 1475, 1477, 1462, 1461, 1460, 175, 1451, 1476])).
% 1.00/1.19 tff(1479,plain,((~hskp15) | (~c0_1(a2188)) | (~c2_1(a2188)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~c3_1(a2188)) | hskp17 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(1480,plain,
% 1.00/1.19 (~hskp15),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[1479, 492, 1282, 1319, 1318, 1317, 1425, 1472, 176])).
% 1.00/1.19 tff(1481,plain,
% 1.00/1.19 (^[U: $i] : refl((hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.03/1.19 inference(bind,[status(th)],[])).
% 1.03/1.19 tff(1482,plain,
% 1.03/1.19 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/1.19 inference(quant_intro,[status(thm)],[1481])).
% 1.03/1.19 tff(1483,plain,
% 1.03/1.19 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1484,plain,
% 1.03/1.19 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp3) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp3) <=> (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.03/1.19 inference(bind,[status(th)],[])).
% 1.03/1.19 tff(1485,plain,
% 1.03/1.19 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp3) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/1.19 inference(quant_intro,[status(thm)],[1484])).
% 1.03/1.19 tff(1486,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.03/1.19 tff(1487,plain,
% 1.03/1.19 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 1.03/1.19 tff(1488,plain,
% 1.03/1.19 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1487, 1483])).
% 1.03/1.19 tff(1489,plain,(
% 1.03/1.19 ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/1.19 inference(skolemize,[status(sab)],[1488])).
% 1.03/1.19 tff(1490,plain,
% 1.03/1.19 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1489, 1482])).
% 1.03/1.19 tff(1491,plain,
% 1.03/1.19 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1492,plain,
% 1.03/1.19 ((hskp15 | hskp3 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1493,plain,
% 1.03/1.19 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[1492])).
% 1.03/1.19 tff(1494,plain,
% 1.03/1.19 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[1493, 1491])).
% 1.03/1.19 tff(1495,plain,
% 1.03/1.19 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(1496,plain,
% 1.03/1.19 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp3 | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.03/1.19 tff(1497,plain,
% 1.03/1.19 (hskp15 | hskp3),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1496, 102, 646, 638, 630, 1490])).
% 1.03/1.19 tff(1498,plain,
% 1.03/1.19 (hskp3),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1497, 1480])).
% 1.03/1.19 tff(1499,plain,
% 1.03/1.19 (c2_1(a2175)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[563, 1448])).
% 1.03/1.19 tff(1500,assumption,(c1_1(a2182)), introduced(assumption)).
% 1.03/1.19 tff(1501,assumption,(hskp3), introduced(assumption)).
% 1.03/1.19 tff(1502,plain,
% 1.03/1.19 (((~hskp3) | (~c1_1(a2177))) <=> ((~hskp3) | (~c1_1(a2177)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1503,plain,
% 1.03/1.19 (((~c1_1(a2177)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a2177)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1504,axiom,((~c1_1(a2177)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.03/1.19 tff(1505,plain,
% 1.03/1.19 ((~hskp3) | (~c1_1(a2177))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 1.03/1.19 tff(1506,plain,
% 1.03/1.19 ((~hskp3) | (~c1_1(a2177))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1505, 1502])).
% 1.03/1.19 tff(1507,plain,
% 1.03/1.19 (~c1_1(a2177)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1506, 1501])).
% 1.03/1.19 tff(1508,plain,
% 1.03/1.19 (((~hskp3) | (~c0_1(a2177))) <=> ((~hskp3) | (~c0_1(a2177)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1509,plain,
% 1.03/1.19 (((~c0_1(a2177)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a2177)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1510,axiom,((~c0_1(a2177)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.03/1.19 tff(1511,plain,
% 1.03/1.19 ((~hskp3) | (~c0_1(a2177))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.03/1.19 tff(1512,plain,
% 1.03/1.19 ((~hskp3) | (~c0_1(a2177))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1511, 1508])).
% 1.03/1.19 tff(1513,plain,
% 1.03/1.19 (~c0_1(a2177)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1512, 1501])).
% 1.03/1.19 tff(1514,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1515,plain,
% 1.03/1.19 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2182) | (~c2_1(a2182)) | (~c1_1(a2182)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177))) <=> (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1516,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2182) | (~c2_1(a2182)) | (~c1_1(a2182)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[1515])).
% 1.03/1.19 tff(1517,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2182) | (~c2_1(a2182)) | (~c1_1(a2182)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[1516, 1514])).
% 1.03/1.19 tff(1518,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2182) | (~c2_1(a2182)) | (~c1_1(a2182)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(1519,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | (~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)) | (~c2_1(a2182)) | (~c1_1(a2182))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 1.03/1.19 tff(1520,plain,
% 1.03/1.19 (~c2_1(a2177)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1519, 102, 492, 491, 1437, 1435, 1513, 1507, 280, 1451, 1500])).
% 1.03/1.19 tff(1521,assumption,(~c3_1(a2175)), introduced(assumption)).
% 1.03/1.19 tff(1522,assumption,(~c0_1(a2175)), introduced(assumption)).
% 1.03/1.19 tff(1523,assumption,(c2_1(a2175)), introduced(assumption)).
% 1.03/1.19 tff(1524,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1525,plain,
% 1.03/1.19 (((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2177) | c0_1(a2177) | c2_1(a2177)) <=> (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1526,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2177) | c0_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[1525])).
% 1.03/1.19 tff(1527,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2177) | c0_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[1526, 1524])).
% 1.03/1.19 tff(1528,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2182) | (~c2_1(a2182)) | (~c3_1(a2182)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c1_1(a2177) | c0_1(a2177) | c2_1(a2177))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(1529,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a2182) | c0_1(a2177) | c1_1(a2177) | c0_1(a2175) | c3_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | c2_1(a2177) | (~c2_1(a2182)) | (~c3_1(a2182))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 1.03/1.19 tff(1530,plain,
% 1.03/1.19 ($false),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1529, 102, 1437, 1436, 1523, 1435, 1513, 1507, 1522, 1521, 665, 1520])).
% 1.03/1.19 tff(1531,plain,((~hskp3) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c2_1(a2175)) | c0_1(a2182) | c0_1(a2175) | c3_1(a2175) | (~c0_1(a2188)) | (~c1_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2182))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.19 tff(1532,plain,
% 1.03/1.19 (~c1_1(a2182)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1531, 1499, 1498, 1427, 1426, 1450, 1449, 492, 491, 1425, 1281])).
% 1.03/1.19 tff(1533,plain,
% 1.03/1.19 (^[U: $i] : refl((hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.03/1.19 inference(bind,[status(th)],[])).
% 1.03/1.19 tff(1534,plain,
% 1.03/1.19 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.03/1.19 inference(quant_intro,[status(thm)],[1533])).
% 1.03/1.19 tff(1535,plain,
% 1.03/1.19 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1536,plain,
% 1.03/1.19 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp10) <=> ((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp10))), rewrite(((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp10) <=> (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp10) <=> (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.03/1.19 inference(bind,[status(th)],[])).
% 1.03/1.19 tff(1537,plain,
% 1.03/1.19 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp10) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.03/1.19 inference(quant_intro,[status(thm)],[1536])).
% 1.03/1.19 tff(1538,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.03/1.19 tff(1539,plain,
% 1.03/1.19 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 1.03/1.19 tff(1540,plain,
% 1.03/1.19 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1539, 1535])).
% 1.03/1.19 tff(1541,plain,(
% 1.03/1.19 ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.03/1.19 inference(skolemize,[status(sab)],[1540])).
% 1.03/1.19 tff(1542,plain,
% 1.03/1.19 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1541, 1534])).
% 1.03/1.19 tff(1543,assumption,(~c1_1(a2175)), introduced(assumption)).
% 1.03/1.19 tff(1544,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1545,plain,
% 1.03/1.19 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2175) | c0_1(a2175) | (~c2_1(a2175))) <=> (c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1546,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[1545])).
% 1.03/1.19 tff(1547,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[1546, 1544])).
% 1.03/1.19 tff(1548,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2175) | c0_1(a2175) | (~c2_1(a2175)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(1549,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c2_1(a2175)) | c1_1(a2175) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 1.03/1.19 tff(1550,plain,
% 1.03/1.19 ($false),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1549, 102, 492, 491, 1523, 1045, 1044, 1522, 138, 280, 1451, 1543])).
% 1.03/1.19 tff(1551,plain,(c1_1(a2175) | (~c0_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2175)) | (~c1_1(a2174)) | (~c2_1(a2174)) | c0_1(a2175) | c0_1(a2174) | (~c3_1(a2188))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.19 tff(1552,plain,
% 1.03/1.19 (c1_1(a2175)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1551, 1499, 491, 1450, 646, 638, 492, 630, 1425])).
% 1.03/1.19 tff(1553,assumption,(c1_1(a2175)), introduced(assumption)).
% 1.03/1.19 tff(1554,assumption,(hskp9), introduced(assumption)).
% 1.03/1.19 tff(1555,plain,
% 1.03/1.19 (((~hskp9) | (~c1_1(a2185))) <=> ((~hskp9) | (~c1_1(a2185)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1556,plain,
% 1.03/1.19 (((~c1_1(a2185)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a2185)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1557,axiom,((~c1_1(a2185)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.03/1.19 tff(1558,plain,
% 1.03/1.19 ((~hskp9) | (~c1_1(a2185))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 1.03/1.19 tff(1559,plain,
% 1.03/1.19 ((~hskp9) | (~c1_1(a2185))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1558, 1555])).
% 1.03/1.19 tff(1560,plain,
% 1.03/1.19 (~c1_1(a2185)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1559, 1554])).
% 1.03/1.19 tff(1561,plain,
% 1.03/1.19 (((~hskp9) | (~c0_1(a2185))) <=> ((~hskp9) | (~c0_1(a2185)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1562,plain,
% 1.03/1.19 (((~c0_1(a2185)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a2185)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1563,axiom,((~c0_1(a2185)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.03/1.19 tff(1564,plain,
% 1.03/1.19 ((~hskp9) | (~c0_1(a2185))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 1.03/1.19 tff(1565,plain,
% 1.03/1.19 ((~hskp9) | (~c0_1(a2185))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1564, 1561])).
% 1.03/1.19 tff(1566,plain,
% 1.03/1.19 (~c0_1(a2185)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1565, 1554])).
% 1.03/1.19 tff(1567,plain,
% 1.03/1.19 (((~hskp9) | c2_1(a2185)) <=> ((~hskp9) | c2_1(a2185))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1568,axiom,((~hskp9) | c2_1(a2185)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.03/1.19 tff(1569,plain,
% 1.03/1.19 ((~hskp9) | c2_1(a2185)),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 1.03/1.19 tff(1570,plain,
% 1.03/1.19 ((~hskp9) | c2_1(a2185)),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1569, 1567])).
% 1.03/1.19 tff(1571,plain,
% 1.03/1.19 ((~hskp9) | c2_1(a2185)),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1570, 1567])).
% 1.03/1.19 tff(1572,plain,
% 1.03/1.19 ((~hskp9) | c2_1(a2185)),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1571, 1567])).
% 1.03/1.19 tff(1573,plain,
% 1.03/1.19 ((~hskp9) | c2_1(a2185)),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1572, 1567])).
% 1.03/1.19 tff(1574,plain,
% 1.03/1.19 (c2_1(a2185)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1573, 1554])).
% 1.03/1.19 tff(1575,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1576,plain,
% 1.03/1.19 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2175) | (~c2_1(a2175)) | (~c1_1(a2175)) | c1_1(a2185) | c0_1(a2185) | (~c2_1(a2185))) <=> (c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1577,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2175) | (~c2_1(a2175)) | (~c1_1(a2175)) | c1_1(a2185) | c0_1(a2185) | (~c2_1(a2185)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[1576])).
% 1.03/1.19 tff(1578,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2175) | (~c2_1(a2175)) | (~c1_1(a2175)) | c1_1(a2185) | c0_1(a2185) | (~c2_1(a2185)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[1577, 1575])).
% 1.03/1.19 tff(1579,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2175) | (~c2_1(a2175)) | (~c1_1(a2175)) | c1_1(a2185) | c0_1(a2185) | (~c2_1(a2185)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(1580,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2185) | c1_1(a2185) | c0_1(a2175) | (~ndr1_0) | (~c2_1(a2175)) | (~c1_1(a2175)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2185))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 1.03/1.19 tff(1581,plain,
% 1.03/1.19 ($false),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1580, 102, 492, 491, 1574, 1523, 1566, 1560, 1522, 280, 1451, 1553])).
% 1.03/1.19 tff(1582,plain,((~hskp9) | (~c0_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2175)) | c0_1(a2175) | (~c3_1(a2188)) | (~c1_1(a2175))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.19 tff(1583,plain,
% 1.03/1.19 (~hskp9),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1582, 1552, 491, 1499, 1450, 1425, 492])).
% 1.03/1.19 tff(1584,plain,
% 1.03/1.19 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1585,plain,
% 1.03/1.19 ((hskp10 | hskp9 | (~ndr1_0) | c1_1(a2182) | c0_1(a2182) | (~c3_1(a2182))) <=> (hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(1586,plain,
% 1.03/1.19 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2182) | c0_1(a2182) | (~c3_1(a2182)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[1585])).
% 1.03/1.19 tff(1587,plain,
% 1.03/1.19 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2182) | c0_1(a2182) | (~c3_1(a2182)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[1586, 1584])).
% 1.03/1.19 tff(1588,plain,
% 1.03/1.19 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2182) | c0_1(a2182) | (~c3_1(a2182)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(1589,plain,
% 1.03/1.19 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c0_1(a2182) | (~ndr1_0) | c1_1(a2182) | (~c3_1(a2182))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.03/1.19 tff(1590,plain,
% 1.03/1.19 ($false),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1589, 102, 176, 1583, 1427, 1426, 1542, 1532])).
% 1.03/1.19 tff(1591,plain,((~hskp7) | hskp10 | (~c1_1(a2188)) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c0_1(a2198)) | c1_1(a2198) | c2_1(a2198)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(1592,plain,
% 1.03/1.20 (~hskp7),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1591, 1279, 176, 1278, 1277, 1271, 1270, 1269])).
% 1.03/1.20 tff(1593,plain,
% 1.03/1.20 (c3_1(a2188)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1424, 1270, 1269, 1271, 176, 1278, 1277])).
% 1.03/1.20 tff(1594,plain,
% 1.03/1.20 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(1595,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[1594])).
% 1.03/1.20 tff(1596,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1597,plain,
% 1.03/1.20 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(1598,plain,
% 1.03/1.20 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[1597])).
% 1.03/1.20 tff(1599,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.03/1.20 tff(1600,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 1.03/1.20 tff(1601,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1600, 1596])).
% 1.03/1.20 tff(1602,plain,(
% 1.03/1.20 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/1.20 inference(skolemize,[status(sab)],[1601])).
% 1.03/1.20 tff(1603,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1602, 1595])).
% 1.03/1.20 tff(1604,plain,
% 1.03/1.20 (~hskp17),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1471, 1278, 1277, 1275, 1274, 1273, 1593, 1279, 646, 638, 630])).
% 1.03/1.20 tff(1605,plain,
% 1.03/1.20 (~hskp15),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1479, 1278, 1277, 1275, 1274, 1273, 1593, 1604, 176])).
% 1.03/1.20 tff(1606,plain,
% 1.03/1.20 (hskp3),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1497, 1605])).
% 1.03/1.20 tff(1607,plain,
% 1.03/1.20 (((~hskp3) | (~c3_1(a2177))) <=> ((~hskp3) | (~c3_1(a2177)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1608,plain,
% 1.03/1.20 (((~c3_1(a2177)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a2177)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1609,axiom,((~c3_1(a2177)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.03/1.20 tff(1610,plain,
% 1.03/1.20 ((~hskp3) | (~c3_1(a2177))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.03/1.20 tff(1611,plain,
% 1.03/1.20 ((~hskp3) | (~c3_1(a2177))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1610, 1607])).
% 1.03/1.20 tff(1612,plain,
% 1.03/1.20 (~c3_1(a2177)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1611, 1606])).
% 1.03/1.20 tff(1613,plain,
% 1.03/1.20 (~c1_1(a2177)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1506, 1606])).
% 1.03/1.20 tff(1614,plain,
% 1.03/1.20 (~c0_1(a2177)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1512, 1606])).
% 1.03/1.20 tff(1615,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1616,plain,
% 1.03/1.20 ((hskp2 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177)) <=> (hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1617,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[1616])).
% 1.03/1.20 tff(1618,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[1617, 1615])).
% 1.03/1.20 tff(1619,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(1620,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1619, 1618])).
% 1.03/1.20 tff(1621,plain,
% 1.03/1.20 (hskp2),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1620, 102, 1278, 1277, 1614, 1613, 1612, 1603, 1593])).
% 1.03/1.20 tff(1622,plain,
% 1.03/1.20 (((~hskp2) | (~c3_1(a2176))) <=> ((~hskp2) | (~c3_1(a2176)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1623,plain,
% 1.03/1.20 (((~c3_1(a2176)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2176)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1624,axiom,((~c3_1(a2176)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.03/1.20 tff(1625,plain,
% 1.03/1.20 ((~hskp2) | (~c3_1(a2176))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 1.03/1.20 tff(1626,plain,
% 1.03/1.20 ((~hskp2) | (~c3_1(a2176))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1625, 1622])).
% 1.03/1.20 tff(1627,plain,
% 1.03/1.20 (~c3_1(a2176)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1626, 1621])).
% 1.03/1.20 tff(1628,plain,
% 1.03/1.20 (((~hskp2) | c1_1(a2176)) <=> ((~hskp2) | c1_1(a2176))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1629,axiom,((~hskp2) | c1_1(a2176)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.03/1.20 tff(1630,plain,
% 1.03/1.20 ((~hskp2) | c1_1(a2176)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 1.03/1.20 tff(1631,plain,
% 1.03/1.20 ((~hskp2) | c1_1(a2176)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1630, 1628])).
% 1.03/1.20 tff(1632,plain,
% 1.03/1.20 ((~hskp2) | c1_1(a2176)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1631, 1628])).
% 1.03/1.20 tff(1633,plain,
% 1.03/1.20 ((~hskp2) | c1_1(a2176)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1632, 1628])).
% 1.03/1.20 tff(1634,plain,
% 1.03/1.20 ((~hskp2) | c1_1(a2176)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1633, 1628])).
% 1.03/1.20 tff(1635,plain,
% 1.03/1.20 (c1_1(a2176)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1634, 1621])).
% 1.03/1.20 tff(1636,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1637,plain,
% 1.03/1.20 ((hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2176) | (~c2_1(a2176)) | (~c1_1(a2176))) <=> (hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1638,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2176) | (~c2_1(a2176)) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[1637])).
% 1.03/1.20 tff(1639,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2176) | (~c2_1(a2176)) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[1638, 1636])).
% 1.03/1.20 tff(1640,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c3_1(a2176) | (~c2_1(a2176)) | (~c1_1(a2176)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(1641,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c3_1(a2176) | (~ndr1_0) | (~c2_1(a2176)) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2176))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1640, 1639])).
% 1.03/1.20 tff(1642,plain,
% 1.03/1.20 (hskp7 | (~c2_1(a2176))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1641, 102, 1278, 1277, 1635, 1627, 713, 1593])).
% 1.03/1.20 tff(1643,plain,
% 1.03/1.20 (~c2_1(a2176)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1642, 1592])).
% 1.03/1.20 tff(1644,plain,
% 1.03/1.20 (((~hskp2) | (~c0_1(a2176))) <=> ((~hskp2) | (~c0_1(a2176)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1645,plain,
% 1.03/1.20 (((~c0_1(a2176)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a2176)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1646,axiom,((~c0_1(a2176)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.03/1.20 tff(1647,plain,
% 1.03/1.20 ((~hskp2) | (~c0_1(a2176))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 1.03/1.20 tff(1648,plain,
% 1.03/1.20 ((~hskp2) | (~c0_1(a2176))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1647, 1644])).
% 1.03/1.20 tff(1649,plain,
% 1.03/1.20 (~c0_1(a2176)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1648, 1621])).
% 1.03/1.20 tff(1650,assumption,(hskp14), introduced(assumption)).
% 1.03/1.20 tff(1651,plain,
% 1.03/1.20 (~c1_1(a2193)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1400, 1650])).
% 1.03/1.20 tff(1652,plain,
% 1.03/1.20 (c3_1(a2193)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1408, 1650])).
% 1.03/1.20 tff(1653,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1654,plain,
% 1.03/1.20 (((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2193) | (~c3_1(a2193)) | (~c0_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1655,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2193) | (~c3_1(a2193)) | (~c0_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[1654])).
% 1.03/1.20 tff(1656,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2193) | (~c3_1(a2193)) | (~c0_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[1655, 1653])).
% 1.03/1.20 tff(1657,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188)) | c1_1(a2193) | (~c3_1(a2193)) | (~c0_1(a2193)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(1658,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c1_1(a2193) | (~ndr1_0) | (~c2_1(a2188)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c0_1(a2193)) | (~c3_1(a2193))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 1.03/1.20 tff(1659,plain,
% 1.03/1.20 (~c0_1(a2193)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1658, 102, 492, 1282, 1652, 1462, 1461, 1460, 1651, 175, 1451])).
% 1.03/1.20 tff(1660,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1422, 102, 1652, 1045, 1044, 1462, 1461, 1460, 1651, 138, 148, 1659])).
% 1.03/1.20 tff(1661,plain,((~hskp14) | (~c1_1(a2174)) | (~c2_1(a2174)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~c0_1(a2188)) | (~c2_1(a2188)) | (~c3_1(a2188))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(1662,plain,
% 1.03/1.20 (~hskp14),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1661, 1275, 638, 646, 1274, 1273, 630, 1278, 1277, 1593])).
% 1.03/1.20 tff(1663,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1664,plain,
% 1.03/1.20 ((hskp14 | (~ndr1_0) | c2_1(a2176) | c3_1(a2176) | (~c1_1(a2176)) | c3_1(a2176) | c0_1(a2176) | (~c1_1(a2176))) <=> (hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1665,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2176) | c3_1(a2176) | (~c1_1(a2176)) | c3_1(a2176) | c0_1(a2176) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[1664])).
% 1.03/1.20 tff(1666,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2176) | c3_1(a2176) | (~c1_1(a2176)) | c3_1(a2176) | c0_1(a2176) | (~c1_1(a2176)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[1665, 1663])).
% 1.03/1.20 tff(1667,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2176) | c3_1(a2176) | (~c1_1(a2176)) | c3_1(a2176) | c0_1(a2176) | (~c1_1(a2176)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(1668,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp14 | c0_1(a2176) | c3_1(a2176) | (~ndr1_0) | c2_1(a2176) | (~c1_1(a2176))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 1.03/1.20 tff(1669,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1668, 102, 1662, 1635, 1649, 1627, 1382, 1643])).
% 1.03/1.20 tff(1670,plain,(c1_1(a2191) | hskp10 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(1671,plain,
% 1.03/1.20 (c1_1(a2191)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1670, 177, 176])).
% 1.03/1.20 tff(1672,plain,
% 1.03/1.20 (~hskp13),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[335, 1671])).
% 1.03/1.20 tff(1673,assumption,(hskp27), introduced(assumption)).
% 1.03/1.20 tff(1674,plain,
% 1.03/1.20 (c3_1(a2178)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[842, 1673])).
% 1.03/1.20 tff(1675,plain,
% 1.03/1.20 (c0_1(a2178)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[858, 1673])).
% 1.03/1.20 tff(1676,plain,
% 1.03/1.20 (c1_1(a2178)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1089, 102, 11, 1083, 1675, 1674, 1082])).
% 1.03/1.20 tff(1677,plain,
% 1.03/1.20 (^[U: $i] : refl((hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(1678,plain,
% 1.03/1.20 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[1677])).
% 1.03/1.20 tff(1679,plain,
% 1.03/1.20 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1680,plain,
% 1.03/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp19) <=> ((hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp19))), rewrite(((hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp19) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(1681,plain,
% 1.03/1.20 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp19) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[1680])).
% 1.03/1.20 tff(1682,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.03/1.20 tff(1683,plain,
% 1.03/1.20 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.03/1.20 tff(1684,plain,
% 1.03/1.20 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1683, 1679])).
% 1.03/1.20 tff(1685,plain,(
% 1.03/1.20 ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(skolemize,[status(sab)],[1684])).
% 1.03/1.20 tff(1686,plain,
% 1.03/1.20 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1685, 1678])).
% 1.03/1.20 tff(1687,plain,
% 1.03/1.20 (c2_1(a2178)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[850, 1673])).
% 1.03/1.20 tff(1688,plain,
% 1.03/1.20 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1689,plain,
% 1.03/1.20 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(1690,plain,
% 1.03/1.20 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 1.03/1.20 tff(1691,plain,
% 1.03/1.20 (hskp19),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1690, 102, 1083, 1687, 1674, 1686, 1676])).
% 1.03/1.20 tff(1692,plain,
% 1.03/1.20 (~c3_1(a2211)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1348, 1691])).
% 1.03/1.20 tff(1693,plain,
% 1.03/1.20 (~c2_1(a2211)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1387, 1691])).
% 1.03/1.20 tff(1694,plain,
% 1.03/1.20 (~c0_1(a2211)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1354, 1691])).
% 1.03/1.20 tff(1695,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1696,plain,
% 1.03/1.20 ((hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2211) | c2_1(a2211) | c0_1(a2211)) <=> (hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1697,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2211) | c2_1(a2211) | c0_1(a2211))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[1696])).
% 1.03/1.20 tff(1698,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2211) | c2_1(a2211) | c0_1(a2211))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[1697, 1695])).
% 1.03/1.20 tff(1699,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2211) | c2_1(a2211) | c0_1(a2211))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(1700,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c0_1(a2211) | c2_1(a2211) | c3_1(a2211) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 1.03/1.20 tff(1701,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1700, 102, 190, 1675, 1687, 1674, 1694, 1693, 1692, 769])).
% 1.03/1.20 tff(1702,plain,((~hskp27) | hskp28 | hskp13 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(1703,plain,
% 1.03/1.20 (~hskp27),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1702, 11, 1083, 190])).
% 1.03/1.20 tff(1704,plain,
% 1.03/1.20 (^[U: $i] : refl((hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(1705,plain,
% 1.03/1.20 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[1704])).
% 1.03/1.20 tff(1706,plain,
% 1.03/1.20 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(1707,plain,
% 1.03/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp16) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp16))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp16) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(1708,plain,
% 1.03/1.21 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp16) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[1707])).
% 1.03/1.21 tff(1709,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.03/1.21 tff(1710,plain,
% 1.03/1.21 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 1.03/1.21 tff(1711,plain,
% 1.03/1.21 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1710, 1706])).
% 1.03/1.21 tff(1712,plain,(
% 1.03/1.21 ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.21 inference(skolemize,[status(sab)],[1711])).
% 1.03/1.21 tff(1713,plain,
% 1.03/1.21 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1712, 1705])).
% 1.03/1.21 tff(1714,plain,
% 1.03/1.21 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1715,plain,
% 1.03/1.21 ((hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174))) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1716,plain,
% 1.03/1.21 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1715])).
% 1.03/1.21 tff(1717,plain,
% 1.03/1.21 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[1716, 1714])).
% 1.03/1.21 tff(1718,plain,
% 1.03/1.21 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(1719,plain,
% 1.03/1.21 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 1.03/1.21 tff(1720,plain,
% 1.03/1.21 (hskp27 | hskp16 | (~c3_1(a2174))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1719, 102, 1045, 1044, 1713])).
% 1.03/1.21 tff(1721,plain,
% 1.03/1.21 (~c3_1(a2174)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1720, 1703, 11])).
% 1.03/1.21 tff(1722,plain,
% 1.03/1.21 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(1723,plain,
% 1.03/1.21 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[1722])).
% 1.03/1.21 tff(1724,plain,
% 1.03/1.21 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1725,plain,
% 1.03/1.21 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(1726,plain,
% 1.03/1.21 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[1725])).
% 1.03/1.21 tff(1727,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.03/1.21 tff(1728,plain,
% 1.03/1.21 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 1.03/1.21 tff(1729,plain,
% 1.03/1.21 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1728, 1724])).
% 1.03/1.21 tff(1730,plain,(
% 1.03/1.21 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.21 inference(skolemize,[status(sab)],[1729])).
% 1.03/1.21 tff(1731,plain,
% 1.03/1.21 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1730, 1723])).
% 1.03/1.21 tff(1732,plain,
% 1.03/1.21 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1733,plain,
% 1.03/1.21 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174))) <=> (hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1734,plain,
% 1.03/1.21 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1733])).
% 1.03/1.21 tff(1735,plain,
% 1.03/1.21 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.03/1.21 inference(transitivity,[status(thm)],[1734, 1732])).
% 1.03/1.21 tff(1736,plain,
% 1.03/1.21 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(1737,plain,
% 1.03/1.21 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 1.03/1.21 tff(1738,plain,
% 1.03/1.21 (hskp16 | hskp15 | c3_1(a2174)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1737, 102, 1045, 138, 1731])).
% 1.03/1.21 tff(1739,plain,
% 1.03/1.21 (hskp15),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1738, 1721, 11])).
% 1.03/1.21 tff(1740,plain,
% 1.03/1.21 (~c2_1(a2194)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[356, 1739])).
% 1.03/1.21 tff(1741,plain,
% 1.03/1.21 (c3_1(a2194)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[398, 1739])).
% 1.03/1.21 tff(1742,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1743,plain,
% 1.03/1.21 ((hskp27 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1744,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1743])).
% 1.03/1.21 tff(1745,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[1744, 1742])).
% 1.03/1.21 tff(1746,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(1747,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp27 | c2_1(a2194) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2194)) | (~c1_1(a2194))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 1.03/1.21 tff(1748,plain,
% 1.03/1.21 (~c1_1(a2194)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1747, 102, 1703, 1741, 1045, 1044, 1740, 138, 779])).
% 1.03/1.21 tff(1749,plain,
% 1.03/1.21 (c0_1(a2194)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[364, 1739])).
% 1.03/1.21 tff(1750,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[371, 102, 11, 1749, 1740, 52, 1748])).
% 1.03/1.21 tff(1751,plain,(hskp16 | (~c1_1(a2174)) | (~c2_1(a2174)) | c0_1(a2174) | hskp13 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(1752,plain,
% 1.03/1.21 (hskp16),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1751, 190, 638, 630, 1083, 646])).
% 1.03/1.21 tff(1753,plain,
% 1.03/1.21 (~c3_1(a2195)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[378, 1752])).
% 1.03/1.21 tff(1754,plain,
% 1.03/1.21 (~c1_1(a2195)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[390, 1752])).
% 1.03/1.21 tff(1755,plain,
% 1.03/1.21 (~c2_1(a2195)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[384, 1752])).
% 1.03/1.21 tff(1756,plain,
% 1.03/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1757,plain,
% 1.03/1.21 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1758,plain,
% 1.03/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1757])).
% 1.03/1.21 tff(1759,plain,
% 1.03/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219))),
% 1.03/1.21 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.03/1.21 tff(1760,plain,
% 1.03/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2219) | c0_1(a2219) | (~c3_1(a2219)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(1761,plain,
% 1.03/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2219) | (~c3_1(a2219)) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c0_1(a2219)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.03/1.21 tff(1762,plain,
% 1.03/1.21 ((~c3_1(a2219)) | c0_1(a2219)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1761, 102, 1045, 1044, 201, 1462, 1461, 1460, 138, 148])).
% 1.03/1.21 tff(1763,plain,
% 1.03/1.21 (c0_1(a2219)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1762, 888])).
% 1.03/1.21 tff(1764,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1765,plain,
% 1.03/1.21 ((hskp28 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195)) <=> (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1766,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1765])).
% 1.03/1.21 tff(1767,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[1766, 1764])).
% 1.03/1.21 tff(1768,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(1769,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2195))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 1.03/1.21 tff(1770,plain,
% 1.03/1.21 (~c0_1(a2195)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1769, 102, 190, 1462, 1461, 1460, 409])).
% 1.03/1.21 tff(1771,plain,
% 1.03/1.21 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(1772,plain,
% 1.03/1.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[1771])).
% 1.03/1.21 tff(1773,plain,
% 1.03/1.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1774,plain,
% 1.03/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(1775,plain,
% 1.03/1.21 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[1774])).
% 1.03/1.21 tff(1776,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.03/1.21 tff(1777,plain,
% 1.03/1.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1776, 1775])).
% 1.03/1.21 tff(1778,plain,
% 1.03/1.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1777, 1773])).
% 1.03/1.21 tff(1779,plain,(
% 1.03/1.21 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.03/1.21 inference(skolemize,[status(sab)],[1778])).
% 1.03/1.21 tff(1780,plain,
% 1.03/1.21 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1779, 1772])).
% 1.03/1.21 tff(1781,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1782,plain,
% 1.03/1.21 ((hskp11 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195)) <=> (hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1783,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1782])).
% 1.03/1.21 tff(1784,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[1783, 1781])).
% 1.03/1.21 tff(1785,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp11 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | (~c3_1(a2219)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(1786,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp11 | c1_1(a2219) | (~c3_1(a2219)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c0_1(a2219))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 1.03/1.21 tff(1787,plain,
% 1.03/1.21 (hskp11 | (~c3_1(a2219)) | (~c0_1(a2219))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1786, 102, 201, 1461, 1460, 1780, 1770])).
% 1.03/1.21 tff(1788,plain,
% 1.03/1.21 (hskp11),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1787, 888, 1763])).
% 1.03/1.21 tff(1789,plain,
% 1.03/1.21 (~c1_1(a2187)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[209, 1788])).
% 1.03/1.21 tff(1790,plain,
% 1.03/1.21 (c2_1(a2187)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[217, 1788])).
% 1.03/1.21 tff(1791,plain,
% 1.03/1.21 (c0_1(a2187)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[225, 1788])).
% 1.03/1.21 tff(1792,plain,
% 1.03/1.21 (~hskp22),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[454, 888])).
% 1.03/1.21 tff(1793,plain,
% 1.03/1.21 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1794,plain,
% 1.03/1.21 ((hskp28 | hskp22 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187))) <=> (hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(1795,plain,
% 1.03/1.21 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[1794])).
% 1.03/1.21 tff(1796,plain,
% 1.03/1.21 (((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)))) <=> ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[1795, 1793])).
% 1.03/1.22 tff(1797,plain,
% 1.03/1.22 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp28 | hskp22 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c2_1(a2187)))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(1798,plain,
% 1.03/1.22 ((~![U: $i] : (hskp28 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp28 | hskp22 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 1.03/1.22 tff(1799,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1798, 102, 190, 1792, 1791, 1790, 1789, 200])).
% 1.03/1.22 tff(1800,plain,((~c3_1(a2219)) | hskp28 | c1_1(a2219) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2174)) | (~c2_1(a2174)) | c1_1(a2195) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(1801,plain,
% 1.03/1.22 (~c3_1(a2219)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1800, 201, 190, 1461, 1460, 646, 638, 1462, 630])).
% 1.03/1.22 tff(1802,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1803,plain,
% 1.03/1.22 ((hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195)) <=> (hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1804,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1803])).
% 1.03/1.22 tff(1805,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219)))),
% 1.03/1.22 inference(transitivity,[status(thm)],[1804, 1802])).
% 1.03/1.22 tff(1806,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp28 | (~ndr1_0) | c1_1(a2219) | (~c0_1(a2219)) | c3_1(a2219) | c3_1(a2195) | c2_1(a2195) | c1_1(a2195))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(1807,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp28 | c1_1(a2219) | c3_1(a2219) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2219))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 1.03/1.22 tff(1808,plain,
% 1.03/1.22 (c3_1(a2219) | (~c0_1(a2219))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1807, 102, 190, 201, 1462, 1461, 1460, 409])).
% 1.03/1.22 tff(1809,plain,
% 1.03/1.22 (~c0_1(a2219)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1808, 203])).
% 1.03/1.22 tff(1810,plain,
% 1.03/1.22 (c2_1(a2219)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[867, 203, 190, 201, 781, 176])).
% 1.03/1.22 tff(1811,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1102, 1810, 1809, 201, 646, 638, 1083, 630])).
% 1.03/1.22 tff(1812,plain,(c3_1(a2219) | c1_1(a2219) | hskp13 | hskp28 | hskp17 | hskp10 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(1813,plain,
% 1.03/1.22 (hskp17),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1812, 1801, 1083, 190, 201, 176, 1462, 1461, 1460])).
% 1.03/1.22 tff(1814,plain,
% 1.03/1.22 (~c1_1(a2197)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[154, 1813])).
% 1.03/1.22 tff(1815,plain,
% 1.03/1.22 (c3_1(a2197)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[599, 1813])).
% 1.03/1.22 tff(1816,plain,
% 1.03/1.22 (~c0_1(a2219)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1808, 1801])).
% 1.03/1.22 tff(1817,plain,
% 1.03/1.22 (~c2_1(a2219)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1102, 1816, 201, 646, 638, 1083, 630])).
% 1.03/1.22 tff(1818,plain,
% 1.03/1.22 (c0_1(a2197)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[884, 102, 1817, 1815, 646, 638, 201, 1801, 1814, 630, 148])).
% 1.03/1.22 tff(1819,plain,
% 1.03/1.22 (c2_1(a2197)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[607, 1813])).
% 1.03/1.22 tff(1820,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1821,plain,
% 1.03/1.22 (((~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2219) | c0_1(a2219)) <=> (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1822,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2219) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1821])).
% 1.03/1.22 tff(1823,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2219) | c0_1(a2219))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219))),
% 1.03/1.22 inference(transitivity,[status(thm)],[1822, 1820])).
% 1.03/1.22 tff(1824,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c2_1(a2197)) | c3_1(a2219) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2219) | c0_1(a2219))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(1825,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2219) | c1_1(a2219) | c3_1(a2219) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2197)) | c0_1(a2219)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.03/1.22 tff(1826,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1825, 102, 1817, 1819, 201, 1801, 1814, 188, 1816, 1818])).
% 1.03/1.22 tff(1827,plain,(c1_1(a2219) | hskp13 | hskp28 | hskp10 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(1828,plain,
% 1.03/1.22 (c1_1(a2219)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1827, 1462, 190, 176, 1083, 1461, 1460])).
% 1.03/1.22 tff(1829,plain,
% 1.03/1.22 (~hskp22),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[477, 1828])).
% 1.03/1.22 tff(1830,assumption,(~c0_1(a2195)), introduced(assumption)).
% 1.03/1.22 tff(1831,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1832,plain,
% 1.03/1.22 ((hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195)) <=> (hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1833,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1832])).
% 1.03/1.22 tff(1834,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195))),
% 1.03/1.22 inference(transitivity,[status(thm)],[1833, 1831])).
% 1.03/1.22 tff(1835,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c3_1(a2195) | c2_1(a2195) | c0_1(a2195))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(1836,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp28 | c2_1(a2195) | c3_1(a2195) | (~ndr1_0) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c3_1(a2178)) | c0_1(a2195)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 1.03/1.22 tff(1837,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1836, 102, 190, 1675, 1687, 1674, 1461, 1460, 769, 1830])).
% 1.03/1.22 tff(1838,plain,((~hskp27) | hskp28 | c2_1(a2195) | c3_1(a2195) | c0_1(a2195)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(1839,plain,
% 1.03/1.22 (~hskp27),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1838, 1770, 1461, 1460, 190])).
% 1.03/1.22 tff(1840,plain,
% 1.03/1.22 (~hskp25),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1173, 1839, 646, 638, 630])).
% 1.03/1.22 tff(1841,plain,
% 1.03/1.22 (hskp21),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[805, 1840, 1829])).
% 1.03/1.22 tff(1842,plain,
% 1.03/1.22 (hskp17),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[896, 1841, 190, 176])).
% 1.03/1.22 tff(1843,plain,
% 1.03/1.22 (~c1_1(a2197)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[154, 1842])).
% 1.03/1.22 tff(1844,plain,
% 1.03/1.22 (c2_1(a2197)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[607, 1842])).
% 1.03/1.22 tff(1845,plain,
% 1.03/1.22 (~c0_1(a2197)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[876, 102, 190, 1829, 1844, 1843, 200])).
% 1.03/1.22 tff(1846,plain,
% 1.03/1.22 (c3_1(a2197)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[599, 1842])).
% 1.03/1.22 tff(1847,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1848,plain,
% 1.03/1.22 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1849,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1848])).
% 1.03/1.22 tff(1850,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.03/1.22 inference(transitivity,[status(thm)],[1849, 1847])).
% 1.03/1.22 tff(1851,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(1852,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 1.03/1.22 tff(1853,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1852, 102, 1846, 646, 638, 1843, 1462, 1461, 1460, 630, 148, 1845])).
% 1.03/1.22 tff(1854,plain,(c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | hskp28 | hskp10 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(1855,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1854, 1755, 1754, 1753, 190, 176, 1083])).
% 1.03/1.22 tff(1856,plain,(hskp28 | hskp10 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(1857,plain,
% 1.03/1.22 (hskp28),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1856, 1083, 176])).
% 1.03/1.22 tff(1858,plain,
% 1.03/1.22 (c2_1(a2188)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[253, 1857])).
% 1.03/1.22 tff(1859,plain,
% 1.03/1.22 (c1_1(a2188)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[444, 1857])).
% 1.03/1.22 tff(1860,plain,
% 1.03/1.22 (c0_1(a2188)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[261, 1857])).
% 1.03/1.22 tff(1861,plain,
% 1.03/1.22 (hskp11 | c3_1(a2188)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[269, 102, 176, 1860, 1858, 245])).
% 1.03/1.22 tff(1862,plain,
% 1.03/1.22 (c3_1(a2188)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1861, 263])).
% 1.03/1.22 tff(1863,plain,
% 1.03/1.22 (hskp11 | hskp1 | (~c3_1(a2188))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[681, 102, 1860, 1858, 675])).
% 1.03/1.22 tff(1864,plain,
% 1.03/1.22 (hskp1),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1863, 263, 1862])).
% 1.03/1.22 tff(1865,plain,
% 1.03/1.22 (~c3_1(a2175)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[549, 1864])).
% 1.03/1.22 tff(1866,plain,
% 1.03/1.22 (c2_1(a2175)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[563, 1864])).
% 1.03/1.22 tff(1867,plain,
% 1.03/1.22 (~c0_1(a2175)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[555, 1864])).
% 1.03/1.22 tff(1868,plain,
% 1.03/1.22 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1869,plain,
% 1.03/1.22 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(1870,plain,
% 1.03/1.22 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 1.03/1.22 tff(1871,plain,
% 1.03/1.22 (hskp19 | hskp13 | (~c3_1(a2188))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1870, 102, 491, 1282, 1686])).
% 1.03/1.22 tff(1872,plain,
% 1.03/1.22 (hskp19),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1871, 1083, 1451])).
% 1.03/1.22 tff(1873,plain,
% 1.03/1.22 (~c2_1(a2211)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1387, 1872])).
% 1.03/1.22 tff(1874,assumption,(~hskp14), introduced(assumption)).
% 1.03/1.22 tff(1875,plain,
% 1.03/1.22 (~c0_1(a2211)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1354, 1872])).
% 1.03/1.22 tff(1876,plain,
% 1.03/1.22 (~c3_1(a2211)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1348, 1872])).
% 1.03/1.22 tff(1877,assumption,(~c3_1(a2211)), introduced(assumption)).
% 1.03/1.22 tff(1878,assumption,(~c2_1(a2211)), introduced(assumption)).
% 1.03/1.22 tff(1879,assumption,(~c0_1(a2211)), introduced(assumption)).
% 1.03/1.22 tff(1880,plain,
% 1.03/1.22 (hskp14 | (~c1_1(a2211))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1394, 102, 1879, 1878, 1877, 1382])).
% 1.03/1.22 tff(1881,plain,
% 1.03/1.22 (~c1_1(a2211)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1880, 1874])).
% 1.03/1.22 tff(1882,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1883,plain,
% 1.03/1.22 (((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211)) <=> (c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1884,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1883])).
% 1.03/1.22 tff(1885,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211))),
% 1.03/1.22 inference(transitivity,[status(thm)],[1884, 1882])).
% 1.03/1.22 tff(1886,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2175) | c0_1(a2175) | (~c2_1(a2175)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(1887,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2211) | c3_1(a2211) | c0_1(a2175) | c3_1(a2175) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2175)) | c1_1(a2211)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 1.03/1.22 tff(1888,plain,
% 1.03/1.22 ((~c3_1(a2174)) | c1_1(a2211)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1887, 102, 1523, 1045, 1879, 1877, 1522, 1521, 138, 695])).
% 1.03/1.22 tff(1889,plain,
% 1.03/1.22 (~c3_1(a2174)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1888, 1881])).
% 1.03/1.22 tff(1890,plain,
% 1.03/1.22 ((hskp24 | hskp14 | hskp13) <=> (hskp24 | hskp14 | hskp13)),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1891,plain,
% 1.03/1.22 (((hskp13 | hskp24) | hskp14) <=> (hskp24 | hskp14 | hskp13)),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1892,axiom,((hskp13 | hskp24) | hskp14), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 1.03/1.22 tff(1893,plain,
% 1.03/1.22 (hskp24 | hskp14 | hskp13),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1892, 1891])).
% 1.03/1.22 tff(1894,plain,
% 1.03/1.22 (hskp24 | hskp14 | hskp13),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1893, 1890])).
% 1.03/1.22 tff(1895,plain,
% 1.03/1.22 (hskp24 | hskp14 | hskp13),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1894, 1890])).
% 1.03/1.22 tff(1896,plain,
% 1.03/1.22 (hskp24 | hskp14 | hskp13),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1895, 1890])).
% 1.03/1.22 tff(1897,plain,
% 1.03/1.22 (hskp24 | hskp14 | hskp13),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1896, 1890])).
% 1.03/1.22 tff(1898,plain,
% 1.03/1.22 (hskp24),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1897, 1874, 1083])).
% 1.03/1.22 tff(1899,plain,
% 1.03/1.22 (((~hskp24) | (~c0_1(a2262))) <=> ((~hskp24) | (~c0_1(a2262)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1900,plain,
% 1.03/1.22 (((~c0_1(a2262)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a2262)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1901,axiom,((~c0_1(a2262)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.03/1.22 tff(1902,plain,
% 1.03/1.22 ((~hskp24) | (~c0_1(a2262))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 1.03/1.22 tff(1903,plain,
% 1.03/1.22 ((~hskp24) | (~c0_1(a2262))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1902, 1899])).
% 1.03/1.22 tff(1904,plain,
% 1.03/1.22 (~c0_1(a2262)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1903, 1898])).
% 1.03/1.22 tff(1905,plain,
% 1.03/1.22 (((~hskp24) | c3_1(a2262)) <=> ((~hskp24) | c3_1(a2262))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1906,axiom,((~hskp24) | c3_1(a2262)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.03/1.22 tff(1907,plain,
% 1.03/1.22 ((~hskp24) | c3_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 1.03/1.22 tff(1908,plain,
% 1.03/1.22 ((~hskp24) | c3_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1907, 1905])).
% 1.03/1.22 tff(1909,plain,
% 1.03/1.22 ((~hskp24) | c3_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1908, 1905])).
% 1.03/1.22 tff(1910,plain,
% 1.03/1.22 ((~hskp24) | c3_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1909, 1905])).
% 1.03/1.22 tff(1911,plain,
% 1.03/1.22 ((~hskp24) | c3_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1910, 1905])).
% 1.03/1.22 tff(1912,plain,
% 1.03/1.22 (c3_1(a2262)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1911, 1898])).
% 1.03/1.22 tff(1913,plain,
% 1.03/1.22 (((~hskp24) | c1_1(a2262)) <=> ((~hskp24) | c1_1(a2262))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1914,axiom,((~hskp24) | c1_1(a2262)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.03/1.22 tff(1915,plain,
% 1.03/1.22 ((~hskp24) | c1_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.03/1.22 tff(1916,plain,
% 1.03/1.22 ((~hskp24) | c1_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1915, 1913])).
% 1.03/1.22 tff(1917,plain,
% 1.03/1.22 ((~hskp24) | c1_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1916, 1913])).
% 1.03/1.22 tff(1918,plain,
% 1.03/1.22 ((~hskp24) | c1_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1917, 1913])).
% 1.03/1.22 tff(1919,plain,
% 1.03/1.22 ((~hskp24) | c1_1(a2262)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1918, 1913])).
% 1.03/1.22 tff(1920,plain,
% 1.03/1.22 (c1_1(a2262)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1919, 1898])).
% 1.03/1.22 tff(1921,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1922,plain,
% 1.03/1.22 (((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211)) <=> (c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(1923,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[1922])).
% 1.03/1.22 tff(1924,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.03/1.22 inference(transitivity,[status(thm)],[1923, 1921])).
% 1.03/1.22 tff(1925,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2211) | c1_1(a2211) | c0_1(a2211))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(1926,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2211) | (~c3_1(a2262)) | (~c1_1(a2262))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.03/1.22 tff(1927,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1926, 102, 1920, 1912, 1044, 1904, 1879, 1877, 138, 695, 1889, 1881])).
% 1.03/1.22 tff(1928,plain,(hskp14 | (~c2_1(a2174)) | c0_1(a2211) | c3_1(a2211) | c0_1(a2174) | (~c2_1(a2175)) | (~c1_1(a2174)) | c0_1(a2175) | c3_1(a2175) | c2_1(a2211) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(1929,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1928, 1876, 1875, 1044, 1874, 138, 1523, 1045, 1522, 1521, 1873, 1083])).
% 1.03/1.22 tff(1930,plain,(hskp13 | (~c2_1(a2174)) | hskp14 | c0_1(a2174) | (~c2_1(a2175)) | (~c1_1(a2174)) | c0_1(a2175) | c3_1(a2175) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2188))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(1931,plain,
% 1.03/1.22 (hskp14),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1930, 1867, 1083, 630, 638, 646, 1866, 1865, 1862, 1859, 1858])).
% 1.03/1.23 tff(1932,plain,
% 1.03/1.23 (~c1_1(a2193)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1400, 1931])).
% 1.03/1.23 tff(1933,plain,
% 1.03/1.23 (c3_1(a2193)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1408, 1931])).
% 1.03/1.23 tff(1934,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1935,plain,
% 1.03/1.23 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193))) <=> (hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1936,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[1935])).
% 1.03/1.23 tff(1937,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.03/1.23 inference(transitivity,[status(thm)],[1936, 1934])).
% 1.03/1.23 tff(1938,plain,
% 1.03/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2193) | (~c0_1(a2193)) | (~c3_1(a2193)))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(1939,plain,
% 1.03/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2193) | (~ndr1_0) | (~c0_1(a2193)) | (~c3_1(a2193))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 1.03/1.23 tff(1940,plain,
% 1.03/1.23 (~c0_1(a2193)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1939, 102, 11, 1083, 1933, 1932, 1082])).
% 1.03/1.23 tff(1941,plain,
% 1.03/1.23 (c1_1(a2175)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1551, 1866, 1859, 1862, 646, 638, 1867, 630, 1860])).
% 1.03/1.23 tff(1942,plain,
% 1.03/1.23 (~hskp9),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1582, 1941, 1859, 1866, 1867, 1862, 1860])).
% 1.03/1.23 tff(1943,plain,
% 1.03/1.23 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1944,plain,
% 1.03/1.23 ((hskp10 | hskp9 | (~ndr1_0) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193))) <=> (hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1945,plain,
% 1.03/1.23 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[1944])).
% 1.03/1.23 tff(1946,plain,
% 1.03/1.23 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.03/1.23 inference(transitivity,[status(thm)],[1945, 1943])).
% 1.03/1.23 tff(1947,plain,
% 1.03/1.23 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp9 | (~ndr1_0) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(1948,plain,
% 1.03/1.23 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp9 | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 1.03/1.23 tff(1949,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1948, 102, 176, 1942, 1933, 1932, 1542, 1940])).
% 1.03/1.23 tff(1950,plain,(hskp11 | hskp10 | hskp16 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(1951,plain,
% 1.03/1.23 (hskp11),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1950, 11, 176, 1083])).
% 1.03/1.23 tff(1952,plain,
% 1.03/1.23 (~c1_1(a2187)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[209, 1951])).
% 1.03/1.23 tff(1953,plain,
% 1.03/1.23 (c0_1(a2187)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[225, 1951])).
% 1.03/1.23 tff(1954,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1955,plain,
% 1.03/1.23 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c3_1(a2187))) <=> (hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1956,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c3_1(a2187)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[1955])).
% 1.03/1.23 tff(1957,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c3_1(a2187)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187)))),
% 1.03/1.23 inference(transitivity,[status(thm)],[1956, 1954])).
% 1.03/1.23 tff(1958,plain,
% 1.03/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2187) | (~c0_1(a2187)) | (~c3_1(a2187)))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(1959,plain,
% 1.03/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2187) | (~ndr1_0) | (~c0_1(a2187)) | (~c3_1(a2187))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 1.03/1.23 tff(1960,plain,
% 1.03/1.23 (~c3_1(a2187)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1959, 102, 11, 1083, 1953, 1952, 1082])).
% 1.03/1.23 tff(1961,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1225, 102, 111, 1953, 646, 638, 1952, 630, 1146, 1960])).
% 1.03/1.23 tff(1962,plain,(hskp16 | hskp13 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(1963,plain,
% 1.03/1.23 (hskp16),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1962, 1672, 176])).
% 1.03/1.23 tff(1964,plain,
% 1.03/1.23 (~c2_1(a2195)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[384, 1963])).
% 1.03/1.23 tff(1965,plain,
% 1.03/1.23 (~c3_1(a2195)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[378, 1963])).
% 1.03/1.23 tff(1966,plain,
% 1.03/1.23 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.03/1.23 inference(bind,[status(th)],[])).
% 1.03/1.23 tff(1967,plain,
% 1.03/1.23 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.23 inference(quant_intro,[status(thm)],[1966])).
% 1.03/1.23 tff(1968,plain,
% 1.03/1.23 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1969,plain,
% 1.03/1.23 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp16) <=> ((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.03/1.23 inference(bind,[status(th)],[])).
% 1.03/1.23 tff(1970,plain,
% 1.03/1.23 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp16) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.23 inference(quant_intro,[status(thm)],[1969])).
% 1.03/1.23 tff(1971,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.03/1.23 tff(1972,plain,
% 1.03/1.23 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[1971, 1970])).
% 1.03/1.23 tff(1973,plain,
% 1.03/1.23 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[1972, 1968])).
% 1.03/1.23 tff(1974,plain,(
% 1.03/1.23 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.23 inference(skolemize,[status(sab)],[1973])).
% 1.03/1.23 tff(1975,plain,
% 1.03/1.23 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[1974, 1967])).
% 1.03/1.23 tff(1976,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1977,plain,
% 1.03/1.23 ((hskp16 | hskp13 | (~ndr1_0) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2195))) <=> (hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(1978,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2195)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0)))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[1977])).
% 1.03/1.23 tff(1979,plain,
% 1.03/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2195)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0))),
% 1.03/1.23 inference(transitivity,[status(thm)],[1978, 1976])).
% 1.03/1.23 tff(1980,plain,
% 1.03/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2195) | c3_1(a2195) | (~c1_1(a2195)))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(1981,plain,
% 1.03/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2195)) | c2_1(a2195) | c3_1(a2195) | (~ndr1_0)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 1.08/1.23 tff(1982,plain,
% 1.08/1.23 (hskp16 | (~c1_1(a2195)) | c2_1(a2195)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1981, 102, 1672, 1460, 1975])).
% 1.08/1.23 tff(1983,plain,
% 1.08/1.23 (~c1_1(a2195)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1982, 11, 1461])).
% 1.08/1.23 tff(1984,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1985,plain,
% 1.08/1.23 ((hskp16 | (~ndr1_0) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195))) <=> (hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(1986,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195))))),
% 1.08/1.23 inference(monotonicity,[status(thm)],[1985])).
% 1.08/1.23 tff(1987,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195)))),
% 1.08/1.23 inference(transitivity,[status(thm)],[1986, 1984])).
% 1.08/1.23 tff(1988,plain,
% 1.08/1.23 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)))),
% 1.08/1.23 inference(quant_inst,[status(thm)],[])).
% 1.08/1.23 tff(1989,plain,
% 1.08/1.23 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | (~c0_1(a2195))),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 1.08/1.23 tff(1990,plain,
% 1.08/1.23 (hskp16 | c1_1(a2195) | (~c0_1(a2195))),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1989, 102, 1461, 52])).
% 1.08/1.23 tff(1991,plain,
% 1.08/1.23 (~c0_1(a2195)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1990, 1983, 11])).
% 1.08/1.23 tff(1992,plain,
% 1.08/1.23 (hskp28),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1856, 1672, 176])).
% 1.08/1.23 tff(1993,plain,
% 1.08/1.23 (c1_1(a2188)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[444, 1992])).
% 1.08/1.23 tff(1994,plain,
% 1.08/1.23 (c0_1(a2188)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[261, 1992])).
% 1.08/1.23 tff(1995,plain,
% 1.08/1.23 (c2_1(a2188)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[253, 1992])).
% 1.08/1.23 tff(1996,plain,
% 1.08/1.23 (hskp11 | c3_1(a2188)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[269, 102, 176, 1994, 1995, 245])).
% 1.08/1.23 tff(1997,plain,
% 1.08/1.23 (c3_1(a2188)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1996, 263])).
% 1.08/1.23 tff(1998,plain,
% 1.08/1.23 (~hskp17),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1471, 1997, 1995, 1994, 1461, 1460, 1983, 1993, 646, 638, 630])).
% 1.08/1.23 tff(1999,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(2000,plain,
% 1.08/1.23 ((hskp16 | hskp13 | (~ndr1_0) | c2_1(a2191) | c3_1(a2191) | (~c1_1(a2191))) <=> (hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(2001,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191)))),
% 1.08/1.23 inference(monotonicity,[status(thm)],[2000])).
% 1.08/1.23 tff(2002,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191))),
% 1.08/1.23 inference(transitivity,[status(thm)],[2001, 1999])).
% 1.08/1.23 tff(2003,plain,
% 1.08/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))),
% 1.08/1.23 inference(quant_inst,[status(thm)],[])).
% 1.08/1.23 tff(2004,plain,
% 1.08/1.23 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0) | c2_1(a2191)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 1.08/1.23 tff(2005,plain,
% 1.08/1.23 (hskp16 | hskp13 | (~c1_1(a2191)) | c2_1(a2191)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2004, 102, 177, 1975])).
% 1.08/1.23 tff(2006,plain,
% 1.08/1.23 (c2_1(a2191)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2005, 11, 1672, 1671])).
% 1.08/1.23 tff(2007,plain,
% 1.08/1.23 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(2008,plain,
% 1.08/1.23 ((hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2191)) | (~c2_1(a2191)) | c3_1(a2191)) <=> (hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(2009,plain,
% 1.08/1.23 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2191)) | (~c2_1(a2191)) | c3_1(a2191))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191))))),
% 1.08/1.23 inference(monotonicity,[status(thm)],[2008])).
% 1.08/1.23 tff(2010,plain,
% 1.08/1.23 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2191)) | (~c2_1(a2191)) | c3_1(a2191))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191)))),
% 1.08/1.23 inference(transitivity,[status(thm)],[2009, 2007])).
% 1.08/1.23 tff(2011,plain,
% 1.08/1.23 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(a2191)) | (~c2_1(a2191)) | c3_1(a2191))),
% 1.08/1.23 inference(quant_inst,[status(thm)],[])).
% 1.08/1.23 tff(2012,plain,
% 1.08/1.23 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U))) | hskp11 | hskp10 | c3_1(a2191) | (~ndr1_0) | (~c2_1(a2191)) | (~c0_1(a2191))),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 1.08/1.23 tff(2013,plain,
% 1.08/1.23 (hskp11 | (~c2_1(a2191)) | (~c0_1(a2191))),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2012, 102, 176, 177, 245])).
% 1.08/1.23 tff(2014,plain,
% 1.08/1.23 (~c0_1(a2191)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2013, 263, 2006])).
% 1.08/1.23 tff(2015,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(2016,plain,
% 1.08/1.23 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a2191) | c3_1(a2191) | (~c1_1(a2191))) <=> (hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(2017,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0)))),
% 1.08/1.23 inference(monotonicity,[status(thm)],[2016])).
% 1.08/1.23 tff(2018,plain,
% 1.08/1.23 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0))),
% 1.08/1.23 inference(transitivity,[status(thm)],[2017, 2015])).
% 1.08/1.23 tff(2019,plain,
% 1.08/1.23 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2191) | c3_1(a2191) | (~c1_1(a2191)))),
% 1.08/1.23 inference(quant_inst,[status(thm)],[])).
% 1.08/1.23 tff(2020,plain,
% 1.08/1.23 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191)) | c3_1(a2191) | (~ndr1_0)),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 1.08/1.23 tff(2021,plain,
% 1.08/1.23 (hskp16 | hskp15 | c0_1(a2191) | (~c1_1(a2191))),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2020, 102, 177, 1731])).
% 1.08/1.23 tff(2022,plain,
% 1.08/1.23 (hskp15),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2021, 2014, 1671, 11])).
% 1.08/1.23 tff(2023,plain,
% 1.08/1.23 ($false),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1479, 2022, 1997, 1995, 1994, 1461, 1460, 1983, 1998, 176])).
% 1.08/1.23 tff(2024,plain,(hskp11 | c2_1(a2195) | c3_1(a2195) | hskp10 | hskp16 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.23 tff(2025,plain,
% 1.08/1.23 (hskp11),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2024, 11, 1460, 176, 1461, 177])).
% 1.08/1.23 tff(2026,plain,
% 1.08/1.23 (~c1_1(a2187)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[209, 2025])).
% 1.08/1.23 tff(2027,plain,
% 1.08/1.23 (c2_1(a2187)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[217, 2025])).
% 1.08/1.23 tff(2028,plain,
% 1.08/1.23 (c0_1(a2187)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[225, 2025])).
% 1.08/1.23 tff(2029,plain,
% 1.08/1.23 ($false),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1325, 102, 2028, 2027, 1983, 1461, 1460, 2026, 188, 1991])).
% 1.08/1.23 tff(2030,plain,(hskp16 | c2_1(a2195) | c3_1(a2195) | hskp10 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.23 tff(2031,plain,
% 1.08/1.23 (hskp16),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2030, 1461, 1460, 176, 177])).
% 1.08/1.23 tff(2032,plain,
% 1.08/1.23 (~c1_1(a2195)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[390, 2031])).
% 1.08/1.23 tff(2033,plain,
% 1.08/1.23 (hskp1),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1863, 1862, 263])).
% 1.08/1.23 tff(2034,plain,
% 1.08/1.23 (~c3_1(a2175)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[549, 2033])).
% 1.08/1.23 tff(2035,plain,
% 1.08/1.23 (~hskp14),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1661, 1862, 638, 646, 1860, 1460, 630, 1461, 1858, 1462])).
% 1.08/1.23 tff(2036,plain,
% 1.08/1.23 (c2_1(a2175)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[563, 2033])).
% 1.08/1.23 tff(2037,plain,
% 1.08/1.23 (~c0_1(a2175)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[555, 2033])).
% 1.08/1.23 tff(2038,plain,
% 1.08/1.23 ($false),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1930, 2037, 2036, 1083, 630, 638, 646, 2035, 2034, 1862, 1859, 1858])).
% 1.08/1.23 tff(2039,plain,(hskp11 | hskp13 | c3_1(a2195) | c2_1(a2195) | c1_1(a2195) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.08/1.23 tff(2040,plain,
% 1.08/1.23 (hskp11),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2039, 1461, 1460, 1672, 2032, 176])).
% 1.08/1.23 tff(2041,plain,
% 1.08/1.23 (~c1_1(a2187)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[209, 2040])).
% 1.08/1.23 tff(2042,plain,
% 1.08/1.23 (c2_1(a2187)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[217, 2040])).
% 1.08/1.23 tff(2043,plain,
% 1.08/1.23 (c0_1(a2187)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[225, 2040])).
% 1.08/1.23 tff(2044,plain,
% 1.08/1.23 (c0_1(a2195)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1325, 102, 2043, 2042, 2032, 1461, 1460, 2041, 188])).
% 1.08/1.23 tff(2045,plain,
% 1.08/1.23 (~c3_1(a2187)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1433, 102, 2043, 2042, 2032, 1461, 1460, 2041, 175])).
% 1.08/1.23 tff(2046,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(2047,plain,
% 1.08/1.23 (((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174))) <=> (c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.08/1.23 inference(rewrite,[status(thm)],[])).
% 1.08/1.23 tff(2048,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195))))),
% 1.08/1.23 inference(monotonicity,[status(thm)],[2047])).
% 1.08/1.23 tff(2049,plain,
% 1.08/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195)))),
% 1.08/1.23 inference(transitivity,[status(thm)],[2048, 2046])).
% 1.08/1.23 tff(2050,plain,
% 1.08/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2187)) | (~c2_1(a2187)) | c3_1(a2187) | c2_1(a2195) | c1_1(a2195) | (~c0_1(a2195)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))),
% 1.08/1.23 inference(quant_inst,[status(thm)],[])).
% 1.08/1.23 tff(2051,plain,
% 1.08/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | c3_1(U) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2195) | c2_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2187)) | c3_1(a2187) | (~c2_1(a2187)) | (~c0_1(a2195))),
% 1.08/1.23 inference(modus_ponens,[status(thm)],[2050, 2049])).
% 1.08/1.23 tff(2052,plain,
% 1.08/1.23 ((~c3_1(a2174)) | (~c0_1(a2195))),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2051, 102, 2043, 2042, 638, 2032, 1461, 630, 1295, 2045])).
% 1.08/1.23 tff(2053,plain,
% 1.08/1.23 (~c3_1(a2174)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[2052, 2044])).
% 1.08/1.23 tff(2054,plain,
% 1.08/1.23 (hskp18),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1225, 102, 2043, 646, 638, 2041, 630, 1146, 2045])).
% 1.08/1.23 tff(2055,plain,
% 1.08/1.23 (~c1_1(a2198)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[64, 2054])).
% 1.08/1.23 tff(2056,plain,
% 1.08/1.23 (c0_1(a2198)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[72, 2054])).
% 1.08/1.23 tff(2057,plain,
% 1.08/1.23 (~c2_1(a2198)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[58, 2054])).
% 1.08/1.23 tff(2058,plain,
% 1.08/1.23 (c3_1(a2188)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1424, 2057, 1994, 2056, 176, 2055, 1995])).
% 1.08/1.23 tff(2059,plain,
% 1.08/1.23 (~hskp17),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1471, 2058, 1995, 1994, 1461, 1460, 2032, 1993, 646, 638, 630])).
% 1.08/1.23 tff(2060,plain,
% 1.08/1.23 (~hskp15),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1479, 2058, 1995, 1994, 1461, 1460, 2032, 2059, 176])).
% 1.08/1.23 tff(2061,plain,
% 1.08/1.23 (hskp3),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1497, 2060])).
% 1.08/1.23 tff(2062,plain,
% 1.08/1.23 (~c3_1(a2177)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1611, 2061])).
% 1.08/1.23 tff(2063,plain,
% 1.08/1.23 (~c1_1(a2177)),
% 1.08/1.23 inference(unit_resolution,[status(thm)],[1506, 2061])).
% 1.08/1.23 tff(2064,plain,
% 1.08/1.23 (~c0_1(a2177)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1512, 2061])).
% 1.08/1.24 tff(2065,plain,
% 1.08/1.24 (~hskp14),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1661, 2058, 638, 646, 1994, 1460, 630, 1461, 1995, 2032])).
% 1.08/1.24 tff(2066,plain,
% 1.08/1.24 (hskp24),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1897, 2065, 1672])).
% 1.08/1.24 tff(2067,plain,
% 1.08/1.24 (~c0_1(a2262)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1903, 2066])).
% 1.08/1.24 tff(2068,plain,
% 1.08/1.24 (c3_1(a2262)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1911, 2066])).
% 1.08/1.24 tff(2069,plain,
% 1.08/1.24 (c1_1(a2262)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1919, 2066])).
% 1.08/1.24 tff(2070,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2071,plain,
% 1.08/1.24 (((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177)) <=> (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2072,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[2071])).
% 1.08/1.24 tff(2073,plain,
% 1.08/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.08/1.24 inference(transitivity,[status(thm)],[2072, 2070])).
% 1.08/1.24 tff(2074,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2174) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(2075,plain,
% 1.08/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2262)) | (~c1_1(a2262))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 1.08/1.24 tff(2076,plain,
% 1.08/1.24 ($false),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2075, 102, 2069, 2068, 638, 2067, 2064, 2063, 2062, 630, 695, 2053])).
% 1.08/1.24 tff(2077,plain,(c2_1(a2195) | c3_1(a2195) | hskp10 | c3_1(a2191)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.24 tff(2078,plain,
% 1.08/1.24 ($false),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2077, 1965, 1964, 176, 177])).
% 1.08/1.24 tff(2079,plain,(c3_1(a2191) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.08/1.24 tff(2080,plain,
% 1.08/1.24 (c3_1(a2191)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2079, 176])).
% 1.08/1.24 tff(2081,plain,
% 1.08/1.24 (~hskp13),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[329, 2080])).
% 1.08/1.24 tff(2082,plain,
% 1.08/1.24 (hskp16),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1962, 2081, 176])).
% 1.08/1.24 tff(2083,plain,
% 1.08/1.24 (~c1_1(a2195)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[390, 2082])).
% 1.08/1.24 tff(2084,plain,
% 1.08/1.24 (~c3_1(a2195)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[378, 2082])).
% 1.08/1.24 tff(2085,plain,
% 1.08/1.24 (~c2_1(a2195)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[384, 2082])).
% 1.08/1.24 tff(2086,plain,
% 1.08/1.24 (hskp11),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2039, 2085, 2084, 2081, 2083, 176])).
% 1.08/1.24 tff(2087,plain,
% 1.08/1.24 (~c1_1(a2187)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[209, 2086])).
% 1.08/1.24 tff(2088,plain,
% 1.08/1.24 (c2_1(a2187)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[217, 2086])).
% 1.08/1.24 tff(2089,plain,
% 1.08/1.24 (c0_1(a2187)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[225, 2086])).
% 1.08/1.24 tff(2090,plain,
% 1.08/1.24 (~c3_1(a2187)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1433, 102, 2089, 2088, 2083, 2085, 2084, 2087, 175])).
% 1.08/1.24 tff(2091,plain,
% 1.08/1.24 (c0_1(a2195)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1325, 102, 2089, 2088, 2083, 2085, 2084, 2087, 188])).
% 1.08/1.24 tff(2092,plain,
% 1.08/1.24 (~c3_1(a2174)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2051, 102, 2089, 2088, 638, 2083, 2085, 630, 1295, 2091, 2090])).
% 1.08/1.24 tff(2093,plain,
% 1.08/1.24 (hskp28),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1856, 2081, 176])).
% 1.08/1.24 tff(2094,plain,
% 1.08/1.24 (c1_1(a2188)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[444, 2093])).
% 1.08/1.24 tff(2095,plain,
% 1.08/1.24 (c0_1(a2188)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[261, 2093])).
% 1.08/1.24 tff(2096,plain,
% 1.08/1.24 (c2_1(a2188)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[253, 2093])).
% 1.08/1.24 tff(2097,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2098,plain,
% 1.08/1.24 ((hskp18 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174))) <=> (hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2099,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[2098])).
% 1.08/1.24 tff(2100,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195)))),
% 1.08/1.24 inference(transitivity,[status(thm)],[2099, 2097])).
% 1.08/1.24 tff(2101,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(2102,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | c3_1(U) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c1_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2195))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 1.08/1.24 tff(2103,plain,
% 1.08/1.24 (hskp18),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2102, 102, 646, 638, 2083, 2084, 630, 1146, 2091])).
% 1.08/1.24 tff(2104,plain,
% 1.08/1.24 (~c1_1(a2198)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[64, 2103])).
% 1.08/1.24 tff(2105,plain,
% 1.08/1.24 (c0_1(a2198)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[72, 2103])).
% 1.08/1.24 tff(2106,plain,
% 1.08/1.24 (~c2_1(a2198)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[58, 2103])).
% 1.08/1.24 tff(2107,plain,
% 1.08/1.24 (c3_1(a2188)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1424, 2106, 2095, 2105, 176, 2104, 2096])).
% 1.08/1.24 tff(2108,plain,
% 1.08/1.24 (~hskp17),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1471, 2107, 2096, 2095, 2085, 2084, 2083, 2094, 646, 638, 630])).
% 1.08/1.24 tff(2109,plain,
% 1.08/1.24 (~hskp15),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1479, 2107, 2096, 2095, 2085, 2084, 2083, 2108, 176])).
% 1.08/1.24 tff(2110,plain,
% 1.08/1.24 (hskp3),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1497, 2109])).
% 1.08/1.24 tff(2111,plain,
% 1.08/1.24 (~c3_1(a2177)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1611, 2110])).
% 1.08/1.24 tff(2112,plain,
% 1.08/1.24 (~c1_1(a2177)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1506, 2110])).
% 1.08/1.24 tff(2113,plain,
% 1.08/1.24 (~c0_1(a2177)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1512, 2110])).
% 1.08/1.24 tff(2114,plain,
% 1.08/1.24 (~hskp14),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1661, 2107, 638, 646, 2095, 2084, 630, 2085, 2096, 2083])).
% 1.08/1.24 tff(2115,plain,
% 1.08/1.24 (hskp24),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1897, 2114, 2081])).
% 1.08/1.24 tff(2116,plain,
% 1.08/1.24 (~c0_1(a2262)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1903, 2115])).
% 1.08/1.24 tff(2117,plain,
% 1.08/1.24 (c3_1(a2262)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1911, 2115])).
% 1.08/1.24 tff(2118,plain,
% 1.08/1.24 (c1_1(a2262)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1919, 2115])).
% 1.08/1.24 tff(2119,plain,
% 1.08/1.24 ($false),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2075, 102, 2118, 2117, 638, 2116, 2113, 2112, 2111, 630, 695, 2092])).
% 1.08/1.24 tff(2120,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 1.08/1.24 tff(2121,plain,
% 1.08/1.24 (((~hskp10) | (~c1_1(a2186))) <=> ((~hskp10) | (~c1_1(a2186)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2122,plain,
% 1.08/1.24 (((~c1_1(a2186)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a2186)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2123,axiom,((~c1_1(a2186)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.08/1.24 tff(2124,plain,
% 1.08/1.24 ((~hskp10) | (~c1_1(a2186))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 1.08/1.24 tff(2125,plain,
% 1.08/1.24 ((~hskp10) | (~c1_1(a2186))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2124, 2121])).
% 1.08/1.24 tff(2126,plain,
% 1.08/1.24 (~c1_1(a2186)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2125, 2120])).
% 1.08/1.24 tff(2127,plain,
% 1.08/1.24 (((~hskp10) | (~c0_1(a2186))) <=> ((~hskp10) | (~c0_1(a2186)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2128,plain,
% 1.08/1.24 (((~c0_1(a2186)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a2186)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2129,axiom,((~c0_1(a2186)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.08/1.24 tff(2130,plain,
% 1.08/1.24 ((~hskp10) | (~c0_1(a2186))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 1.08/1.24 tff(2131,plain,
% 1.08/1.24 ((~hskp10) | (~c0_1(a2186))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2130, 2127])).
% 1.08/1.24 tff(2132,plain,
% 1.08/1.24 (~c0_1(a2186)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2131, 2120])).
% 1.08/1.24 tff(2133,assumption,(~c1_1(a2174)), introduced(assumption)).
% 1.08/1.24 tff(2134,plain,
% 1.08/1.24 (~hskp0),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[645, 2133])).
% 1.08/1.24 tff(2135,plain,
% 1.08/1.24 (~c0_1(a2193)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1939, 102, 11, 1083, 1652, 1651, 1082])).
% 1.08/1.24 tff(2136,plain,
% 1.08/1.24 (((~hskp14) | (~c2_1(a2193))) <=> ((~hskp14) | (~c2_1(a2193)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2137,plain,
% 1.08/1.24 (((~c2_1(a2193)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a2193)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2138,axiom,((~c2_1(a2193)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.08/1.24 tff(2139,plain,
% 1.08/1.24 ((~hskp14) | (~c2_1(a2193))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 1.08/1.24 tff(2140,plain,
% 1.08/1.24 ((~hskp14) | (~c2_1(a2193))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2139, 2136])).
% 1.08/1.24 tff(2141,plain,
% 1.08/1.24 (~c2_1(a2193)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2140, 1650])).
% 1.08/1.24 tff(2142,plain,
% 1.08/1.24 ((hskp17 | hskp16 | hskp3) <=> (hskp17 | hskp16 | hskp3)),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2143,plain,
% 1.08/1.24 (((hskp17 | hskp3) | hskp16) <=> (hskp17 | hskp16 | hskp3)),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2144,axiom,((hskp17 | hskp3) | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.08/1.24 tff(2145,plain,
% 1.08/1.24 (hskp17 | hskp16 | hskp3),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2144, 2143])).
% 1.08/1.24 tff(2146,plain,
% 1.08/1.24 (hskp17 | hskp16 | hskp3),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2145, 2142])).
% 1.08/1.24 tff(2147,plain,
% 1.08/1.24 (hskp17 | hskp16 | hskp3),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2146, 2142])).
% 1.08/1.24 tff(2148,plain,
% 1.08/1.24 (hskp17 | hskp16 | hskp3),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2147, 2142])).
% 1.08/1.24 tff(2149,plain,
% 1.08/1.24 (hskp17 | hskp16 | hskp3),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2148, 2142])).
% 1.08/1.24 tff(2150,plain,
% 1.08/1.24 (hskp3),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2149, 781, 11])).
% 1.08/1.24 tff(2151,plain,
% 1.08/1.24 (~c0_1(a2177)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[1512, 2150])).
% 1.08/1.24 tff(2152,assumption,(hskp26), introduced(assumption)).
% 1.08/1.24 tff(2153,plain,
% 1.08/1.24 (((~hskp26) | (~c2_1(a2268))) <=> ((~hskp26) | (~c2_1(a2268)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2154,plain,
% 1.08/1.24 (((~c2_1(a2268)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a2268)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2155,axiom,((~c2_1(a2268)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.08/1.24 tff(2156,plain,
% 1.08/1.24 ((~hskp26) | (~c2_1(a2268))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 1.08/1.24 tff(2157,plain,
% 1.08/1.24 ((~hskp26) | (~c2_1(a2268))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2156, 2153])).
% 1.08/1.24 tff(2158,plain,
% 1.08/1.24 (~c2_1(a2268)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2157, 2152])).
% 1.08/1.24 tff(2159,plain,
% 1.08/1.24 (((~hskp10) | c3_1(a2186)) <=> ((~hskp10) | c3_1(a2186))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2160,axiom,((~hskp10) | c3_1(a2186)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.08/1.24 tff(2161,plain,
% 1.08/1.24 ((~hskp10) | c3_1(a2186)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2160, 2159])).
% 1.08/1.24 tff(2162,plain,
% 1.08/1.24 ((~hskp10) | c3_1(a2186)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2161, 2159])).
% 1.08/1.24 tff(2163,plain,
% 1.08/1.24 ((~hskp10) | c3_1(a2186)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2162, 2159])).
% 1.08/1.24 tff(2164,plain,
% 1.08/1.24 ((~hskp10) | c3_1(a2186)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2163, 2159])).
% 1.08/1.24 tff(2165,plain,
% 1.08/1.24 ((~hskp10) | c3_1(a2186)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2164, 2159])).
% 1.08/1.24 tff(2166,plain,
% 1.08/1.24 (c3_1(a2186)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2165, 2120])).
% 1.08/1.24 tff(2167,plain,
% 1.08/1.24 (((~hskp26) | c1_1(a2268)) <=> ((~hskp26) | c1_1(a2268))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2168,axiom,((~hskp26) | c1_1(a2268)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.08/1.24 tff(2169,plain,
% 1.08/1.24 ((~hskp26) | c1_1(a2268)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2168, 2167])).
% 1.08/1.24 tff(2170,plain,
% 1.08/1.24 ((~hskp26) | c1_1(a2268)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2169, 2167])).
% 1.08/1.24 tff(2171,plain,
% 1.08/1.24 ((~hskp26) | c1_1(a2268)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2170, 2167])).
% 1.08/1.24 tff(2172,plain,
% 1.08/1.24 ((~hskp26) | c1_1(a2268)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2171, 2167])).
% 1.08/1.24 tff(2173,plain,
% 1.08/1.24 ((~hskp26) | c1_1(a2268)),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2172, 2167])).
% 1.08/1.24 tff(2174,plain,
% 1.08/1.24 (c1_1(a2268)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2173, 2152])).
% 1.08/1.24 tff(2175,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2176,plain,
% 1.08/1.24 ((hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2177,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[2176])).
% 1.08/1.24 tff(2178,plain,
% 1.08/1.24 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.08/1.24 inference(transitivity,[status(thm)],[2177, 2175])).
% 1.08/1.24 tff(2179,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(2180,plain,
% 1.08/1.24 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2268)) | (~c1_1(a2268))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 1.08/1.24 tff(2181,plain,
% 1.08/1.24 (~c3_1(a2268)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[2180, 102, 291, 2174, 2166, 2158, 2132, 2126, 165])).
% 1.08/1.24 tff(2182,plain,
% 1.08/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.08/1.24 inference(bind,[status(th)],[])).
% 1.08/1.24 tff(2183,plain,
% 1.08/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/1.24 inference(quant_intro,[status(thm)],[2182])).
% 1.08/1.24 tff(2184,plain,
% 1.08/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(2185,plain,
% 1.08/1.24 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.09/1.24 inference(bind,[status(th)],[])).
% 1.09/1.24 tff(2186,plain,
% 1.09/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.09/1.24 inference(quant_intro,[status(thm)],[2185])).
% 1.09/1.24 tff(2187,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.09/1.24 tff(2188,plain,
% 1.09/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 1.09/1.24 tff(2189,plain,
% 1.09/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[2188, 2184])).
% 1.09/1.24 tff(2190,plain,(
% 1.09/1.24 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.09/1.24 inference(skolemize,[status(sab)],[2189])).
% 1.09/1.24 tff(2191,plain,
% 1.09/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[2190, 2183])).
% 1.09/1.24 tff(2192,plain,
% 1.09/1.24 (((~hskp26) | (~c0_1(a2268))) <=> ((~hskp26) | (~c0_1(a2268)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(2193,plain,
% 1.09/1.24 (((~c0_1(a2268)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a2268)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(2194,axiom,((~c0_1(a2268)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.09/1.24 tff(2195,plain,
% 1.09/1.24 ((~hskp26) | (~c0_1(a2268))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 1.09/1.24 tff(2196,plain,
% 1.09/1.24 ((~hskp26) | (~c0_1(a2268))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[2195, 2192])).
% 1.09/1.24 tff(2197,plain,
% 1.09/1.24 (~c0_1(a2268)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[2196, 2152])).
% 1.09/1.24 tff(2198,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(2199,plain,
% 1.09/1.24 (((~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)) | c3_1(a2268) | c0_1(a2268) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(2200,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)) | c3_1(a2268) | c0_1(a2268) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268))))),
% 1.09/1.24 inference(monotonicity,[status(thm)],[2199])).
% 1.09/1.24 tff(2201,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)) | c3_1(a2268) | c0_1(a2268) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.24 inference(transitivity,[status(thm)],[2200, 2198])).
% 1.09/1.24 tff(2202,plain,
% 1.09/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)) | c3_1(a2268) | c0_1(a2268) | (~c1_1(a2268)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.09/1.24 inference(quant_inst,[status(thm)],[])).
% 1.09/1.24 tff(2203,plain,
% 1.09/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a2268) | c2_1(a2268) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | c3_1(a2268) | (~c1_1(a2268))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[2202, 2201])).
% 1.09/1.24 tff(2204,plain,
% 1.09/1.24 ($false),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[2203, 102, 2174, 2166, 2197, 2158, 2132, 2126, 2191, 2181])).
% 1.09/1.24 tff(2205,plain,((~hskp26) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.09/1.24 tff(2206,plain,
% 1.09/1.24 (~hskp26),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[2205, 291])).
% 1.09/1.24 tff(2207,plain,
% 1.09/1.24 (hskp24),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[100, 781, 2206])).
% 1.09/1.24 tff(2208,plain,
% 1.09/1.24 (~c1_1(a2177)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[1506, 2150])).
% 1.09/1.24 tff(2209,plain,
% 1.09/1.24 (~c3_1(a2177)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[1611, 2150])).
% 1.09/1.24 tff(2210,assumption,(~c3_1(a2177)), introduced(assumption)).
% 1.09/1.24 tff(2211,assumption,(~c1_1(a2177)), introduced(assumption)).
% 1.09/1.24 tff(2212,assumption,(~c0_1(a2177)), introduced(assumption)).
% 1.09/1.24 tff(2213,assumption,(hskp24), introduced(assumption)).
% 1.09/1.24 tff(2214,plain,
% 1.09/1.24 (~c0_1(a2262)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[1903, 2213])).
% 1.09/1.24 tff(2215,plain,
% 1.09/1.24 (c3_1(a2262)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[1911, 2213])).
% 1.09/1.24 tff(2216,plain,
% 1.09/1.24 (c1_1(a2262)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[1919, 2213])).
% 1.09/1.24 tff(2217,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(2218,plain,
% 1.09/1.24 (((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177)) <=> (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(2219,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262))))),
% 1.09/1.24 inference(monotonicity,[status(thm)],[2218])).
% 1.09/1.24 tff(2220,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.24 inference(transitivity,[status(thm)],[2219, 2217])).
% 1.09/1.24 tff(2221,plain,
% 1.09/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))),
% 1.09/1.24 inference(quant_inst,[status(thm)],[])).
% 1.09/1.24 tff(2222,plain,
% 1.09/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2262) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | (~c2_1(a2177)) | (~c3_1(a2262)) | (~c1_1(a2262))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.09/1.25 tff(2223,plain,
% 1.09/1.25 (~c2_1(a2177)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2222, 102, 2216, 2215, 2214, 2212, 2211, 2210, 695])).
% 1.09/1.25 tff(2224,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2225,plain,
% 1.09/1.25 (((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177)) <=> (c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2226,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[2225])).
% 1.09/1.25 tff(2227,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[2226, 2224])).
% 1.09/1.25 tff(2228,plain,
% 1.09/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(2229,plain,
% 1.09/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | (~ndr1_0) | c2_1(a2177) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 1.09/1.25 tff(2230,plain,
% 1.09/1.25 (c2_1(a2177) | (~c2_1(a2262))),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2229, 102, 2216, 2166, 2214, 2132, 2126, 2211, 2210, 148])).
% 1.09/1.25 tff(2231,plain,
% 1.09/1.25 (~c2_1(a2262)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2230, 2223])).
% 1.09/1.25 tff(2232,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2233,plain,
% 1.09/1.25 ((hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2234,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[2233])).
% 1.09/1.25 tff(2235,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[2234, 2232])).
% 1.09/1.25 tff(2236,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(2237,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.09/1.25 tff(2238,plain,
% 1.09/1.25 ($false),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2237, 102, 291, 2216, 2215, 2166, 2132, 2126, 165, 2231])).
% 1.09/1.25 tff(2239,plain,((~hskp24) | hskp0 | c1_1(a2177) | c3_1(a2177) | c0_1(a2177)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.25 tff(2240,plain,
% 1.09/1.25 ($false),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2239, 2209, 2208, 291, 2207, 2151])).
% 1.09/1.25 tff(2241,plain,(hskp17 | hskp0 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.09/1.25 tff(2242,plain,
% 1.09/1.25 (hskp17),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2241, 291, 11])).
% 1.09/1.25 tff(2243,plain,
% 1.09/1.25 (~c1_1(a2197)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[154, 2242])).
% 1.09/1.25 tff(2244,plain,
% 1.09/1.25 (c3_1(a2197)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[599, 2242])).
% 1.09/1.25 tff(2245,plain,
% 1.09/1.25 (c2_1(a2197)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[607, 2242])).
% 1.09/1.25 tff(2246,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2247,plain,
% 1.09/1.25 ((hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2193) | c1_1(a2193) | c0_1(a2193)) <=> (hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2248,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2193) | c1_1(a2193) | c0_1(a2193))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[2247])).
% 1.09/1.25 tff(2249,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2193) | c1_1(a2193) | c0_1(a2193))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[2248, 2246])).
% 1.09/1.25 tff(2250,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2193) | c1_1(a2193) | c0_1(a2193))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(2251,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2193) | c2_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 1.09/1.25 tff(2252,plain,
% 1.09/1.25 ($false),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2251, 102, 291, 2245, 2244, 2243, 1651, 2141, 10, 2135])).
% 1.09/1.25 tff(2253,plain,((~hskp14) | hskp0 | hskp16 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.09/1.25 tff(2254,plain,
% 1.09/1.25 (~hskp14),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2253, 1083, 11, 2134])).
% 1.09/1.25 tff(2255,plain,
% 1.09/1.25 (hskp24),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1897, 2254, 1083])).
% 1.09/1.25 tff(2256,plain,
% 1.09/1.25 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2257,plain,
% 1.09/1.25 ((hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2262)) | (~c3_1(a2262)) | (~c1_1(a2262))) <=> (hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2258,plain,
% 1.09/1.25 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2262)) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[2257])).
% 1.09/1.25 tff(2259,plain,
% 1.09/1.25 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2262)) | (~c3_1(a2262)) | (~c1_1(a2262)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[2258, 2256])).
% 1.09/1.25 tff(2260,plain,
% 1.09/1.25 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(a2262)) | (~c3_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(2261,plain,
% 1.09/1.25 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp16 | (~ndr1_0) | (~c3_1(a2262)) | (~c2_1(a2262)) | (~c1_1(a2262))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 1.09/1.25 tff(2262,plain,
% 1.09/1.25 (~c2_1(a2262)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2261, 102, 1167, 11, 2216, 2215, 1713])).
% 1.09/1.25 tff(2263,plain,
% 1.09/1.25 ($false),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2237, 102, 291, 2216, 2215, 2166, 2132, 2126, 165, 2262])).
% 1.09/1.25 tff(2264,plain,((~hskp24) | hskp0 | hskp27 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.09/1.25 tff(2265,plain,
% 1.09/1.25 (hskp27),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2264, 2255, 11, 2134])).
% 1.09/1.25 tff(2266,plain,
% 1.09/1.25 (c3_1(a2178)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[842, 2265])).
% 1.09/1.25 tff(2267,plain,
% 1.09/1.25 (c0_1(a2178)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[858, 2265])).
% 1.09/1.25 tff(2268,plain,
% 1.09/1.25 (c1_1(a2178)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1089, 102, 11, 1083, 2267, 2266, 1082])).
% 1.09/1.25 tff(2269,plain,
% 1.09/1.25 (~c0_1(a2262)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1903, 2255])).
% 1.09/1.25 tff(2270,assumption,(~c2_1(a2174)), introduced(assumption)).
% 1.09/1.25 tff(2271,plain,
% 1.09/1.25 (~hskp0),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[637, 2270])).
% 1.09/1.25 tff(2272,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2273,plain,
% 1.09/1.25 ((hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2274,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[2273])).
% 1.09/1.25 tff(2275,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[2274, 2272])).
% 1.09/1.25 tff(2276,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(2277,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2186))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2276, 2275])).
% 1.09/1.25 tff(2278,plain,
% 1.09/1.25 ((~c1_1(a2174)) | (~c3_1(a2174))),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2277, 102, 2271, 2166, 2270, 2132, 2126, 165])).
% 1.09/1.25 tff(2279,plain,
% 1.09/1.25 (~c3_1(a2174)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2278, 1045])).
% 1.09/1.25 tff(2280,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2281,plain,
% 1.09/1.25 (((~ndr1_0) | c2_1(a2174) | c3_1(a2174) | (~c1_1(a2174)) | c3_1(a2174) | c0_1(a2174) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2282,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2174) | c3_1(a2174) | (~c1_1(a2174)) | c3_1(a2174) | c0_1(a2174) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[2281])).
% 1.09/1.25 tff(2283,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2174) | c3_1(a2174) | (~c1_1(a2174)) | c3_1(a2174) | c0_1(a2174) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[2282, 2280])).
% 1.09/1.25 tff(2284,plain,
% 1.09/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2174) | c3_1(a2174) | (~c1_1(a2174)) | c3_1(a2174) | c0_1(a2174) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(2285,plain,
% 1.09/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2174) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c3_1(a2186))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 1.09/1.25 tff(2286,plain,
% 1.09/1.25 ($false),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2285, 102, 2166, 1045, 2270, 2132, 2126, 138, 2191, 2279])).
% 1.09/1.25 tff(2287,plain,((~c1_1(a2174)) | c2_1(a2174) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.25 tff(2288,plain,
% 1.09/1.25 (~c1_1(a2174)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2287, 2270, 138])).
% 1.09/1.25 tff(2289,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2290,plain,
% 1.09/1.25 ((hskp0 | (~ndr1_0) | c1_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174)) <=> (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2291,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[2290])).
% 1.09/1.25 tff(2292,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[2291, 2289])).
% 1.09/1.25 tff(2293,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(2294,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 1.09/1.25 tff(2295,plain,
% 1.09/1.25 (c1_1(a2174) | (~c2_1(a2186))),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2294, 102, 2271, 2166, 2270, 2126, 138, 10])).
% 1.09/1.25 tff(2296,plain,
% 1.09/1.25 (~c2_1(a2186)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2295, 2133])).
% 1.09/1.25 tff(2297,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2298,plain,
% 1.09/1.25 ((hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174)) <=> (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2299,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[2298])).
% 1.09/1.25 tff(2300,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[2299, 2297])).
% 1.09/1.25 tff(2301,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2174) | c1_1(a2174) | c0_1(a2174))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(2302,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2174) | c2_1(a2174) | c1_1(a2197) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 1.09/1.25 tff(2303,plain,
% 1.09/1.25 ($false),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2302, 102, 2271, 1452, 1463, 2133, 2270, 155, 138, 10])).
% 1.09/1.25 tff(2304,plain,((~hskp17) | c1_1(a2174) | c2_1(a2174) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.25 tff(2305,plain,
% 1.09/1.25 (~hskp17),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2304, 2133, 2270, 138])).
% 1.09/1.25 tff(2306,assumption,(~c2_1(a2186)), introduced(assumption)).
% 1.09/1.25 tff(2307,plain,
% 1.09/1.25 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.09/1.25 inference(bind,[status(th)],[])).
% 1.09/1.25 tff(2308,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.09/1.25 inference(quant_intro,[status(thm)],[2307])).
% 1.09/1.25 tff(2309,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2310,plain,
% 1.09/1.25 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.09/1.25 inference(bind,[status(th)],[])).
% 1.09/1.25 tff(2311,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.09/1.25 inference(quant_intro,[status(thm)],[2310])).
% 1.09/1.25 tff(2312,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.09/1.25 tff(2313,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 1.09/1.25 tff(2314,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2313, 2309])).
% 1.09/1.25 tff(2315,plain,(
% 1.09/1.25 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.09/1.25 inference(skolemize,[status(sab)],[2314])).
% 1.09/1.25 tff(2316,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[2315, 2308])).
% 1.09/1.25 tff(2317,plain,
% 1.09/1.25 (hskp3),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2149, 11, 781])).
% 1.09/1.25 tff(2318,plain,
% 1.09/1.25 (~c0_1(a2177)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1512, 2317])).
% 1.09/1.25 tff(2319,plain,
% 1.09/1.25 (~c3_1(a2177)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1611, 2317])).
% 1.09/1.25 tff(2320,plain,
% 1.09/1.25 (~c1_1(a2177)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1506, 2317])).
% 1.09/1.25 tff(2321,plain,
% 1.09/1.25 (~hskp24),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[2239, 2320, 291, 2319, 2318])).
% 1.09/1.25 tff(2322,assumption,(~hskp24), introduced(assumption)).
% 1.09/1.25 tff(2323,plain,
% 1.09/1.25 (hskp14),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1897, 2322, 1083])).
% 1.09/1.25 tff(2324,plain,
% 1.09/1.25 (~c1_1(a2193)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1400, 2323])).
% 1.09/1.25 tff(2325,plain,
% 1.09/1.25 (hskp26),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[100, 2322, 781])).
% 1.09/1.25 tff(2326,plain,
% 1.09/1.25 (c3_1(a2193)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[1408, 2323])).
% 1.09/1.25 tff(2327,plain,
% 1.09/1.25 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2328,plain,
% 1.09/1.25 ((hskp16 | hskp13 | (~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268))) <=> (hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(2329,plain,
% 1.09/1.25 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2328])).
% 1.09/1.26 tff(2330,plain,
% 1.09/1.26 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[2329, 2327])).
% 1.09/1.26 tff(2331,plain,
% 1.09/1.26 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c2_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(2332,plain,
% 1.09/1.26 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 1.09/1.26 tff(2333,plain,
% 1.09/1.26 (c3_1(a2268)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2332, 102, 11, 1083, 2174, 2158, 1975])).
% 1.09/1.26 tff(2334,assumption,(~c1_1(a2193)), introduced(assumption)).
% 1.09/1.26 tff(2335,assumption,(c3_1(a2193)), introduced(assumption)).
% 1.09/1.26 tff(2336,plain,
% 1.09/1.26 (~c0_1(a2193)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[1939, 102, 11, 1083, 2335, 2334, 1082])).
% 1.09/1.26 tff(2337,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2338,plain,
% 1.09/1.26 ((hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193))) <=> (hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2339,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2338])).
% 1.09/1.26 tff(2340,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[2339, 2337])).
% 1.09/1.26 tff(2341,plain,
% 1.09/1.26 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2268) | (~c3_1(a2268)) | (~c1_1(a2268)) | c1_1(a2193) | c0_1(a2193) | (~c3_1(a2193)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(2342,plain,
% 1.09/1.26 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2268) | c1_1(a2193) | (~ndr1_0) | c0_1(a2193) | (~c3_1(a2193)) | (~c3_1(a2268)) | (~c1_1(a2268))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2341, 2340])).
% 1.09/1.26 tff(2343,plain,
% 1.09/1.26 ($false),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2342, 102, 291, 2174, 2335, 2158, 2334, 165, 2336, 2333])).
% 1.09/1.26 tff(2344,plain,((~hskp26) | hskp0 | (~c3_1(a2193)) | c1_1(a2193) | hskp16 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.09/1.26 tff(2345,plain,
% 1.09/1.26 ($false),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2344, 2326, 2325, 291, 2324, 11, 1083])).
% 1.09/1.26 tff(2346,plain,(hskp24 | hskp0 | hskp16 | hskp13 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.09/1.26 tff(2347,plain,
% 1.09/1.26 (hskp13),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2346, 2321, 11, 291, 781])).
% 1.09/1.26 tff(2348,plain,
% 1.09/1.26 (~c3_1(a2191)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[329, 2347])).
% 1.09/1.26 tff(2349,plain,
% 1.09/1.26 (~c1_1(a2191)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[335, 2347])).
% 1.09/1.26 tff(2350,plain,
% 1.09/1.26 (c0_1(a2191)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[343, 2347])).
% 1.09/1.26 tff(2351,plain,
% 1.09/1.26 (hskp15),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[350, 102, 291, 2350, 2349, 2348, 312])).
% 1.09/1.26 tff(2352,plain,
% 1.09/1.26 (~c2_1(a2194)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[356, 2351])).
% 1.09/1.26 tff(2353,plain,
% 1.09/1.26 (c3_1(a2194)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[398, 2351])).
% 1.09/1.26 tff(2354,plain,
% 1.09/1.26 (c0_1(a2194)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[364, 2351])).
% 1.09/1.26 tff(2355,plain,
% 1.09/1.26 (hskp26),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[100, 2321, 781])).
% 1.09/1.26 tff(2356,plain,
% 1.09/1.26 (~c2_1(a2268)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2157, 2355])).
% 1.09/1.26 tff(2357,plain,
% 1.09/1.26 (c1_1(a2268)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2173, 2355])).
% 1.09/1.26 tff(2358,plain,
% 1.09/1.26 (~c3_1(a2268)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2180, 102, 291, 2357, 2166, 2356, 2132, 2126, 165])).
% 1.09/1.26 tff(2359,plain,
% 1.09/1.26 (^[U: $i] : refl((hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.09/1.26 inference(bind,[status(th)],[])).
% 1.09/1.26 tff(2360,plain,
% 1.09/1.26 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.09/1.26 inference(quant_intro,[status(thm)],[2359])).
% 1.09/1.26 tff(2361,plain,
% 1.09/1.26 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2362,plain,
% 1.09/1.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp17) <=> ((hskp29 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp17))), rewrite(((hskp29 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp17) <=> (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp17) <=> (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.09/1.26 inference(bind,[status(th)],[])).
% 1.09/1.26 tff(2363,plain,
% 1.09/1.26 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp17) <=> ![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.09/1.26 inference(quant_intro,[status(thm)],[2362])).
% 1.09/1.26 tff(2364,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.09/1.26 tff(2365,plain,
% 1.09/1.26 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 1.09/1.26 tff(2366,plain,
% 1.09/1.26 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2365, 2361])).
% 1.09/1.26 tff(2367,plain,(
% 1.09/1.26 ![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.09/1.26 inference(skolemize,[status(sab)],[2366])).
% 1.09/1.26 tff(2368,plain,
% 1.09/1.26 (![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2367, 2360])).
% 1.09/1.26 tff(2369,plain,
% 1.09/1.26 (~c0_1(a2268)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2196, 2355])).
% 1.09/1.26 tff(2370,plain,
% 1.09/1.26 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2371,plain,
% 1.09/1.26 ((hskp29 | hskp17 | (~ndr1_0) | c0_1(a2268) | c3_1(a2268) | (~c1_1(a2268))) <=> (hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2372,plain,
% 1.09/1.26 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2371])).
% 1.09/1.26 tff(2373,plain,
% 1.09/1.26 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[2372, 2370])).
% 1.09/1.26 tff(2374,plain,
% 1.09/1.26 ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2268) | c3_1(a2268) | (~c1_1(a2268)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(2375,plain,
% 1.09/1.26 ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2268) | (~ndr1_0) | c3_1(a2268) | (~c1_1(a2268))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 1.09/1.26 tff(2376,plain,
% 1.09/1.26 (hskp29 | c3_1(a2268)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2375, 102, 781, 2357, 2369, 2368])).
% 1.09/1.26 tff(2377,plain,
% 1.09/1.26 (hskp29),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2376, 2358])).
% 1.09/1.26 tff(2378,plain,
% 1.09/1.26 (((~hskp29) | c3_1(a2196)) <=> ((~hskp29) | c3_1(a2196))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2379,axiom,((~hskp29) | c3_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.09/1.26 tff(2380,plain,
% 1.09/1.26 ((~hskp29) | c3_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2379, 2378])).
% 1.09/1.26 tff(2381,plain,
% 1.09/1.26 ((~hskp29) | c3_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2380, 2378])).
% 1.09/1.26 tff(2382,plain,
% 1.09/1.26 ((~hskp29) | c3_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2381, 2378])).
% 1.09/1.26 tff(2383,plain,
% 1.09/1.26 ((~hskp29) | c3_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2382, 2378])).
% 1.09/1.26 tff(2384,plain,
% 1.09/1.26 ((~hskp29) | c3_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2383, 2378])).
% 1.09/1.26 tff(2385,plain,
% 1.09/1.26 (c3_1(a2196)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2384, 2377])).
% 1.09/1.26 tff(2386,plain,
% 1.09/1.26 (((~hskp29) | c2_1(a2196)) <=> ((~hskp29) | c2_1(a2196))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2387,axiom,((~hskp29) | c2_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.09/1.26 tff(2388,plain,
% 1.09/1.26 ((~hskp29) | c2_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 1.09/1.26 tff(2389,plain,
% 1.09/1.26 ((~hskp29) | c2_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2388, 2386])).
% 1.09/1.26 tff(2390,plain,
% 1.09/1.26 ((~hskp29) | c2_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2389, 2386])).
% 1.09/1.26 tff(2391,plain,
% 1.09/1.26 ((~hskp29) | c2_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2390, 2386])).
% 1.09/1.26 tff(2392,plain,
% 1.09/1.26 ((~hskp29) | c2_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2391, 2386])).
% 1.09/1.26 tff(2393,plain,
% 1.09/1.26 (c2_1(a2196)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2392, 2377])).
% 1.09/1.26 tff(2394,plain,
% 1.09/1.26 (((~hskp29) | c1_1(a2196)) <=> ((~hskp29) | c1_1(a2196))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2395,axiom,((~hskp29) | c1_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.09/1.26 tff(2396,plain,
% 1.09/1.26 ((~hskp29) | c1_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 1.09/1.26 tff(2397,plain,
% 1.09/1.26 ((~hskp29) | c1_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2396, 2394])).
% 1.09/1.26 tff(2398,plain,
% 1.09/1.26 ((~hskp29) | c1_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2397, 2394])).
% 1.09/1.26 tff(2399,plain,
% 1.09/1.26 ((~hskp29) | c1_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2398, 2394])).
% 1.09/1.26 tff(2400,plain,
% 1.09/1.26 ((~hskp29) | c1_1(a2196)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2399, 2394])).
% 1.09/1.26 tff(2401,plain,
% 1.09/1.26 (c1_1(a2196)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2400, 2377])).
% 1.09/1.26 tff(2402,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2403,plain,
% 1.09/1.26 (((~ndr1_0) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c1_1(a2196)) | c2_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c0_1(a2186) | c2_1(a2186) | (~c3_1(a2186))) <=> (c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2404,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c1_1(a2196)) | c2_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c0_1(a2186) | c2_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2403])).
% 1.09/1.26 tff(2405,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c1_1(a2196)) | c2_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c0_1(a2186) | c2_1(a2186) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[2404, 2402])).
% 1.09/1.26 tff(2406,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c1_1(a2196)) | c2_1(a2194) | (~c3_1(a2194)) | (~c0_1(a2194)) | c0_1(a2186) | c2_1(a2186) | (~c3_1(a2186)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(2407,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2194) | c0_1(a2186) | (~ndr1_0) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2196)) | (~c3_1(a2186)) | c2_1(a2186) | (~c0_1(a2194)) | (~c3_1(a2194))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.09/1.26 tff(2408,plain,
% 1.09/1.26 ($false),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2407, 102, 2401, 2393, 2385, 2354, 2353, 2166, 2352, 2132, 2316, 2306])).
% 1.09/1.26 tff(2409,plain,(hskp16 | c2_1(a2186) | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.09/1.26 tff(2410,plain,
% 1.09/1.26 ($false),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2409, 2305, 2296, 11, 2271])).
% 1.09/1.26 tff(2411,plain,(c1_1(a2174) | hskp16 | c2_1(a2174) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.26 tff(2412,plain,
% 1.09/1.26 (hskp16),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2411, 2288, 2270, 138])).
% 1.09/1.26 tff(2413,plain,
% 1.09/1.26 (~c3_1(a2195)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[378, 2412])).
% 1.09/1.26 tff(2414,plain,
% 1.09/1.26 (~c2_1(a2195)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[384, 2412])).
% 1.09/1.26 tff(2415,plain,
% 1.09/1.26 (~hskp26),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2205, 2271])).
% 1.09/1.26 tff(2416,plain,
% 1.09/1.26 (~hskp17),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2304, 2288, 2270, 138])).
% 1.09/1.26 tff(2417,plain,
% 1.09/1.26 (hskp24),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[100, 2416, 2415])).
% 1.09/1.26 tff(2418,plain,
% 1.09/1.26 (~c1_1(a2195)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[390, 2412])).
% 1.09/1.26 tff(2419,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2420,plain,
% 1.09/1.26 (((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2421,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2420])).
% 1.09/1.26 tff(2422,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[2421, 2419])).
% 1.09/1.26 tff(2423,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(2424,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2262) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2262)) | (~c1_1(a2262))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 1.09/1.26 tff(2425,plain,
% 1.09/1.26 (~c2_1(a2262)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2424, 102, 2216, 2166, 2214, 1462, 1461, 1460, 2132, 2126, 148])).
% 1.09/1.26 tff(2426,plain,
% 1.09/1.26 ($false),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2237, 102, 291, 2216, 2215, 2166, 2132, 2126, 165, 2425])).
% 1.09/1.26 tff(2427,plain,((~hskp24) | hskp0 | c1_1(a2195) | c2_1(a2195) | c3_1(a2195)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.26 tff(2428,plain,
% 1.09/1.26 ($false),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2427, 2418, 2417, 2271, 2414, 2413])).
% 1.09/1.26 tff(2429,plain,(c2_1(a2174) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.26 tff(2430,plain,
% 1.09/1.26 (c2_1(a2174)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2429, 138])).
% 1.09/1.26 tff(2431,plain,
% 1.09/1.26 (c1_1(a2262)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[1919, 2255])).
% 1.09/1.26 tff(2432,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2433,plain,
% 1.09/1.26 (((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2174) | c0_1(a2174) | (~c2_1(a2174))) <=> (c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2434,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2433])).
% 1.09/1.26 tff(2435,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[2434, 2432])).
% 1.09/1.26 tff(2436,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | c0_1(a2262) | (~c2_1(a2262)) | (~c1_1(a2262)) | c1_1(a2174) | c0_1(a2174) | (~c2_1(a2174)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(2437,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2174) | c0_1(a2262) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c0_1(a2178)) | (~c3_1(a2178)) | (~c1_1(a2178)) | (~c2_1(a2262)) | (~c1_1(a2262))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 1.09/1.26 tff(2438,plain,
% 1.09/1.26 (~c2_1(a2262)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2437, 102, 2267, 2266, 2431, 2133, 2430, 2269, 138, 280, 2268])).
% 1.09/1.26 tff(2439,plain,
% 1.09/1.26 (hskp17),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2241, 2134, 11])).
% 1.09/1.26 tff(2440,plain,
% 1.09/1.26 (~c1_1(a2197)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[154, 2439])).
% 1.09/1.26 tff(2441,plain,
% 1.09/1.26 (c3_1(a2197)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[599, 2439])).
% 1.09/1.26 tff(2442,plain,
% 1.09/1.26 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2443,plain,
% 1.09/1.26 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c3_1(a2197))) <=> (hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2444,plain,
% 1.09/1.26 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c3_1(a2197)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2443])).
% 1.09/1.26 tff(2445,plain,
% 1.09/1.26 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c3_1(a2197)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[2444, 2442])).
% 1.09/1.26 tff(2446,plain,
% 1.09/1.26 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a2197) | (~c0_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(2447,plain,
% 1.09/1.26 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp13 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | (~c0_1(a2197))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 1.09/1.26 tff(2448,plain,
% 1.09/1.26 (hskp13 | (~c0_1(a2197))),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2447, 102, 11, 2441, 2440, 1082])).
% 1.09/1.26 tff(2449,plain,
% 1.09/1.26 (~c0_1(a2197)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2448, 1083])).
% 1.09/1.26 tff(2450,plain,
% 1.09/1.26 (c3_1(a2262)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[1911, 2255])).
% 1.09/1.26 tff(2451,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2452,plain,
% 1.09/1.26 ((hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197))) <=> (hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2453,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2452])).
% 1.09/1.26 tff(2454,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[2453, 2451])).
% 1.09/1.26 tff(2455,plain,
% 1.09/1.26 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2262) | (~c3_1(a2262)) | (~c1_1(a2262)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(2456,plain,
% 1.09/1.26 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a2197) | (~ndr1_0) | (~c3_1(a2197)) | c0_1(a2197) | (~c3_1(a2262)) | c2_1(a2262) | (~c1_1(a2262))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 1.09/1.26 tff(2457,plain,
% 1.09/1.26 ($false),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2456, 102, 2134, 2431, 2450, 2441, 2440, 165, 2449, 2438])).
% 1.09/1.26 tff(2458,plain,(hskp13 | c1_1(a2174) | c0_1(a2174) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.09/1.26 tff(2459,plain,
% 1.09/1.26 (hskp13),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[2458, 2133, 138, 11])).
% 1.09/1.26 tff(2460,plain,
% 1.09/1.26 (~c3_1(a2191)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[329, 2459])).
% 1.09/1.26 tff(2461,plain,
% 1.09/1.26 (~c1_1(a2191)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[335, 2459])).
% 1.09/1.26 tff(2462,plain,
% 1.09/1.26 (c0_1(a2191)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[343, 2459])).
% 1.09/1.26 tff(2463,plain,
% 1.09/1.26 (hskp15),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[350, 102, 2134, 2462, 2461, 2460, 312])).
% 1.09/1.26 tff(2464,plain,
% 1.09/1.26 (~c2_1(a2194)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[356, 2463])).
% 1.09/1.26 tff(2465,plain,
% 1.09/1.26 (c3_1(a2194)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[398, 2463])).
% 1.09/1.26 tff(2466,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2467,plain,
% 1.09/1.26 ((hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(2468,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[2467])).
% 1.09/1.26 tff(2469,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[2468, 2466])).
% 1.09/1.27 tff(2470,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2194) | (~c3_1(a2194)) | (~c1_1(a2194)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(2471,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2194) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c3_1(a2194)) | (~c1_1(a2194))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 1.09/1.27 tff(2472,plain,
% 1.09/1.27 (~c1_1(a2194)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2471, 102, 2134, 2465, 2166, 2464, 2132, 2126, 165])).
% 1.09/1.27 tff(2473,plain,
% 1.09/1.27 (c0_1(a2194)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[364, 2463])).
% 1.09/1.27 tff(2474,plain,
% 1.09/1.27 ($false),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[371, 102, 11, 2473, 2464, 52, 2472])).
% 1.09/1.27 tff(2475,plain,(c1_1(a2174) | hskp16 | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.27 tff(2476,plain,
% 1.09/1.27 (c1_1(a2174)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2475, 11, 138])).
% 1.09/1.27 tff(2477,assumption,(hskp13), introduced(assumption)).
% 1.09/1.27 tff(2478,plain,
% 1.09/1.27 (~c3_1(a2191)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[329, 2477])).
% 1.09/1.27 tff(2479,plain,
% 1.09/1.27 (~c1_1(a2191)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[335, 2477])).
% 1.09/1.27 tff(2480,plain,
% 1.09/1.27 (c0_1(a2191)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[343, 2477])).
% 1.09/1.27 tff(2481,assumption,(~hskp18), introduced(assumption)).
% 1.09/1.27 tff(2482,plain,
% 1.09/1.27 ($false),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[1266, 102, 2481, 2480, 1045, 2430, 2479, 2478, 138, 1146])).
% 1.09/1.27 tff(2483,plain,((~hskp13) | hskp18 | (~c1_1(a2174)) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.27 tff(2484,plain,
% 1.09/1.27 (~hskp13),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2483, 111, 2476, 138])).
% 1.09/1.27 tff(2485,assumption,(~c1_1(a2197)), introduced(assumption)).
% 1.09/1.27 tff(2486,assumption,(c3_1(a2197)), introduced(assumption)).
% 1.09/1.27 tff(2487,plain,
% 1.09/1.27 (hskp13 | (~c0_1(a2197))),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2447, 102, 11, 2486, 2485, 1082])).
% 1.09/1.27 tff(2488,plain,
% 1.09/1.27 (~c0_1(a2197)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2487, 1083])).
% 1.09/1.27 tff(2489,assumption,(c2_1(a2197)), introduced(assumption)).
% 1.09/1.27 tff(2490,plain,
% 1.09/1.27 (hskp28),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[1751, 1083, 2430, 138, 11, 2476])).
% 1.09/1.27 tff(2491,plain,
% 1.09/1.27 (c1_1(a2188)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[444, 2490])).
% 1.09/1.27 tff(2492,plain,
% 1.09/1.27 (c0_1(a2188)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[261, 2490])).
% 1.09/1.27 tff(2493,plain,
% 1.09/1.27 (~c3_1(a2188)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[1458, 102, 2492, 2491, 2489, 2476, 2430, 2485, 138, 280, 2488])).
% 1.09/1.27 tff(2494,plain,
% 1.09/1.27 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.09/1.27 inference(bind,[status(th)],[])).
% 1.09/1.27 tff(2495,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.09/1.27 inference(quant_intro,[status(thm)],[2494])).
% 1.09/1.27 tff(2496,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2497,plain,
% 1.09/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.09/1.27 inference(bind,[status(th)],[])).
% 1.09/1.27 tff(2498,plain,
% 1.09/1.27 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.09/1.27 inference(quant_intro,[status(thm)],[2497])).
% 1.09/1.27 tff(2499,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.09/1.27 tff(2500,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2499, 2498])).
% 1.09/1.27 tff(2501,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2500, 2496])).
% 1.09/1.27 tff(2502,plain,(
% 1.09/1.27 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.09/1.27 inference(skolemize,[status(sab)],[2501])).
% 1.09/1.27 tff(2503,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2502, 2495])).
% 1.09/1.27 tff(2504,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2505,plain,
% 1.09/1.27 ((hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197))) <=> (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2506,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[2505])).
% 1.09/1.27 tff(2507,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.27 inference(transitivity,[status(thm)],[2506, 2504])).
% 1.09/1.27 tff(2508,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(2509,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2508, 2507])).
% 1.09/1.27 tff(2510,plain,
% 1.09/1.27 ($false),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2509, 102, 11, 2492, 2491, 2489, 2486, 2503, 2493, 2488])).
% 1.09/1.27 tff(2511,plain,(hskp13 | hskp16 | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.27 tff(2512,plain,
% 1.09/1.27 ($false),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2511, 1463, 1452, 11, 2484, 155, 138])).
% 1.09/1.27 tff(2513,plain,((~hskp17) | hskp16 | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.27 tff(2514,plain,
% 1.09/1.27 (~hskp17),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2513, 11, 138])).
% 1.09/1.27 tff(2515,plain,
% 1.09/1.27 (hskp3),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2149, 2514, 11])).
% 1.09/1.27 tff(2516,plain,
% 1.09/1.27 (~c3_1(a2177)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[1611, 2515])).
% 1.09/1.27 tff(2517,plain,
% 1.09/1.27 (~c1_1(a2177)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[1506, 2515])).
% 1.09/1.27 tff(2518,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2519,plain,
% 1.09/1.27 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177)) <=> (c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2520,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[2519])).
% 1.09/1.27 tff(2521,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[2520, 2518])).
% 1.09/1.27 tff(2522,plain,
% 1.09/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2177) | c1_1(a2177) | c2_1(a2177))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(2523,plain,
% 1.09/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a2186) | c1_1(a2186) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | c2_1(a2177) | (~c3_1(a2186))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 1.09/1.27 tff(2524,plain,
% 1.09/1.27 (c2_1(a2177)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2523, 102, 2166, 2476, 2430, 2132, 2126, 2517, 2516, 138, 148])).
% 1.09/1.27 tff(2525,plain,
% 1.09/1.27 (~c0_1(a2177)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[1512, 2515])).
% 1.09/1.27 tff(2526,plain,
% 1.09/1.27 (hskp28),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[1751, 2484, 2430, 138, 11, 2476])).
% 1.09/1.27 tff(2527,plain,
% 1.09/1.27 (c1_1(a2188)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[444, 2526])).
% 1.09/1.27 tff(2528,plain,
% 1.09/1.27 (c0_1(a2188)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[261, 2526])).
% 1.09/1.27 tff(2529,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2530,plain,
% 1.09/1.27 (((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177))) <=> (c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2531,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[2530])).
% 1.09/1.27 tff(2532,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[2531, 2529])).
% 1.09/1.27 tff(2533,plain,
% 1.09/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2177) | c0_1(a2177) | (~c2_1(a2177)))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(2534,plain,
% 1.09/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2177) | c1_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c0_1(a2188)) | (~c3_1(a2188)) | (~c1_1(a2188)) | (~c2_1(a2177))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 1.09/1.27 tff(2535,plain,
% 1.09/1.27 ((~c3_1(a2188)) | (~c2_1(a2177))),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2534, 102, 2528, 2527, 2476, 2430, 2525, 2517, 138, 280])).
% 1.09/1.27 tff(2536,plain,
% 1.09/1.27 (~c3_1(a2188)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2535, 2524])).
% 1.09/1.27 tff(2537,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2538,plain,
% 1.09/1.27 ((hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186))) <=> (hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2539,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[2538])).
% 1.09/1.27 tff(2540,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[2539, 2537])).
% 1.09/1.27 tff(2541,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | c0_1(a2186) | (~c2_1(a2186)) | (~c3_1(a2186)))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(2542,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a2186) | (~ndr1_0) | (~c0_1(a2188)) | c3_1(a2188) | (~c1_1(a2188)) | (~c3_1(a2186)) | (~c2_1(a2186))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 1.09/1.27 tff(2543,plain,
% 1.09/1.27 (c3_1(a2188) | (~c2_1(a2186))),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2542, 102, 11, 2528, 2527, 2166, 2132, 2503])).
% 1.09/1.27 tff(2544,plain,
% 1.09/1.27 (~c2_1(a2186)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2543, 2536])).
% 1.09/1.27 tff(2545,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2546,plain,
% 1.09/1.27 (((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177)) <=> (c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2547,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[2546])).
% 1.09/1.27 tff(2548,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[2547, 2545])).
% 1.09/1.27 tff(2549,plain,
% 1.09/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c3_1(a2177) | c0_1(a2177) | (~c2_1(a2177)) | c3_1(a2177) | c1_1(a2177) | c0_1(a2177))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(2550,plain,
% 1.09/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2177) | c1_1(a2177) | c3_1(a2177) | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2177))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 1.09/1.27 tff(2551,plain,
% 1.09/1.27 (~c3_1(a2174)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2550, 102, 2476, 2525, 2517, 2516, 138, 695, 2524])).
% 1.09/1.27 tff(2552,plain,
% 1.09/1.27 (hskp16 | hskp15 | (~c1_1(a2174)) | c3_1(a2174)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[1737, 102, 138, 1731])).
% 1.09/1.27 tff(2553,plain,
% 1.09/1.27 (hskp15),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2552, 2551, 11, 2476])).
% 1.09/1.27 tff(2554,plain,
% 1.09/1.27 (~c2_1(a2194)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[356, 2553])).
% 1.09/1.27 tff(2555,plain,
% 1.09/1.27 (c3_1(a2194)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[398, 2553])).
% 1.09/1.27 tff(2556,plain,
% 1.09/1.27 (c0_1(a2194)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[364, 2553])).
% 1.09/1.27 tff(2557,plain,
% 1.09/1.27 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2558,plain,
% 1.09/1.27 ((hskp29 | hskp17 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174))) <=> (hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2559,plain,
% 1.09/1.27 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174)))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[2558])).
% 1.09/1.27 tff(2560,plain,
% 1.09/1.27 (((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))) <=> ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174))),
% 1.09/1.27 inference(transitivity,[status(thm)],[2559, 2557])).
% 1.09/1.27 tff(2561,plain,
% 1.09/1.27 ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp29 | hskp17 | (~ndr1_0) | c0_1(a2174) | c3_1(a2174) | (~c1_1(a2174)))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(2562,plain,
% 1.09/1.27 ((~![U: $i] : (hskp29 | hskp17 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp29 | hskp17 | c0_1(a2174) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 1.09/1.27 tff(2563,plain,
% 1.09/1.27 (hskp29 | hskp17 | (~c1_1(a2174)) | c3_1(a2174)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2562, 102, 138, 2368])).
% 1.09/1.27 tff(2564,plain,
% 1.09/1.27 (hskp29),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2563, 2551, 2476, 2514])).
% 1.09/1.27 tff(2565,plain,
% 1.09/1.27 (c3_1(a2196)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2384, 2564])).
% 1.09/1.27 tff(2566,plain,
% 1.09/1.27 (c2_1(a2196)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2392, 2564])).
% 1.09/1.27 tff(2567,plain,
% 1.09/1.27 (c1_1(a2196)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2400, 2564])).
% 1.09/1.27 tff(2568,plain,
% 1.09/1.27 ($false),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2407, 102, 2567, 2566, 2565, 2556, 2555, 2166, 2554, 2132, 2316, 2544])).
% 1.09/1.27 tff(2569,plain,(hskp16 | c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.27 tff(2570,plain,
% 1.09/1.27 (hskp16),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[2569, 138])).
% 1.09/1.27 tff(2571,plain,
% 1.09/1.27 (~c2_1(a2195)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[384, 2570])).
% 1.09/1.27 tff(2572,plain,
% 1.09/1.27 (~c1_1(a2195)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[390, 2570])).
% 1.09/1.27 tff(2573,plain,
% 1.09/1.27 (~c3_1(a2195)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[378, 2570])).
% 1.09/1.27 tff(2574,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2575,plain,
% 1.09/1.27 (((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195)) <=> (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(2576,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[2575])).
% 1.09/1.27 tff(2577,plain,
% 1.09/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2576, 2574])).
% 1.09/1.28 tff(2578,plain,
% 1.09/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | (~c1_1(a2174)) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)) | c3_1(a2195) | c1_1(a2195) | c2_1(a2195))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2579,plain,
% 1.09/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a2195) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2186))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.09/1.28 tff(2580,plain,
% 1.09/1.28 (~c1_1(a2174)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2579, 102, 2166, 2430, 2572, 2571, 2573, 2132, 2126, 138, 148])).
% 1.09/1.28 tff(2581,plain,
% 1.09/1.28 (~hskp0),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[645, 2580])).
% 1.09/1.28 tff(2582,plain,
% 1.09/1.28 (~hskp26),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2205, 2581])).
% 1.09/1.28 tff(2583,plain,
% 1.09/1.28 (~hskp24),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2427, 2581, 2572, 2571, 2573])).
% 1.09/1.28 tff(2584,plain,
% 1.09/1.28 (hskp17),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[100, 2583, 2582])).
% 1.09/1.28 tff(2585,plain,
% 1.09/1.28 (~c1_1(a2197)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[154, 2584])).
% 1.09/1.28 tff(2586,plain,
% 1.09/1.28 (c3_1(a2197)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[599, 2584])).
% 1.09/1.28 tff(2587,plain,
% 1.09/1.28 (c2_1(a2197)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[607, 2584])).
% 1.09/1.28 tff(2588,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2589,plain,
% 1.09/1.28 ((hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2195) | c1_1(a2195) | c0_1(a2195)) <=> (hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2590,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2195) | c1_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[2589])).
% 1.09/1.28 tff(2591,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2195) | c1_1(a2195) | c0_1(a2195))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2590, 2588])).
% 1.09/1.28 tff(2592,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2195) | c1_1(a2195) | c0_1(a2195))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2593,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c1_1(a2195) | c2_1(a2195) | (~ndr1_0) | c0_1(a2195) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2592, 2591])).
% 1.09/1.28 tff(2594,plain,
% 1.09/1.28 (c0_1(a2195)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2593, 102, 2581, 2587, 2586, 2585, 2572, 2571, 10])).
% 1.09/1.28 tff(2595,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2596,plain,
% 1.09/1.28 (((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2174) | (~c2_1(a2174)) | (~c3_1(a2174)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174))) <=> (c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2597,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2174) | (~c2_1(a2174)) | (~c3_1(a2174)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[2596])).
% 1.09/1.28 tff(2598,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2174) | (~c2_1(a2174)) | (~c3_1(a2174)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2597, 2595])).
% 1.09/1.28 tff(2599,plain,
% 1.09/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2174) | (~c2_1(a2174)) | (~c3_1(a2174)) | c0_1(a2174) | (~c3_1(a2174)) | (~c2_1(a2174)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2600,plain,
% 1.09/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2174) | c2_1(a2195) | c3_1(a2195) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c0_1(a2195))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2599, 2598])).
% 1.09/1.28 tff(2601,plain,
% 1.09/1.28 ((~c3_1(a2174)) | (~c0_1(a2195))),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2600, 102, 2580, 2430, 2571, 2573, 138, 970])).
% 1.09/1.28 tff(2602,plain,
% 1.09/1.28 (~c3_1(a2174)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2601, 2594])).
% 1.09/1.28 tff(2603,plain,
% 1.09/1.28 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.09/1.28 inference(bind,[status(th)],[])).
% 1.09/1.28 tff(2604,plain,
% 1.09/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.09/1.28 inference(quant_intro,[status(thm)],[2603])).
% 1.09/1.28 tff(2605,plain,
% 1.09/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2606,plain,
% 1.09/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.09/1.28 inference(bind,[status(th)],[])).
% 1.09/1.28 tff(2607,plain,
% 1.09/1.28 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.09/1.28 inference(quant_intro,[status(thm)],[2606])).
% 1.09/1.28 tff(2608,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.09/1.28 tff(2609,plain,
% 1.09/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2608, 2607])).
% 1.09/1.28 tff(2610,plain,
% 1.09/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2609, 2605])).
% 1.09/1.28 tff(2611,plain,(
% 1.09/1.28 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.09/1.28 inference(skolemize,[status(sab)],[2610])).
% 1.09/1.28 tff(2612,plain,
% 1.09/1.28 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2611, 2604])).
% 1.09/1.28 tff(2613,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2614,plain,
% 1.09/1.28 ((hskp7 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186))) <=> (hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2615,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[2614])).
% 1.09/1.28 tff(2616,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2615, 2613])).
% 1.09/1.28 tff(2617,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a2174) | (~c2_1(a2174)) | c3_1(a2174) | c1_1(a2186) | c0_1(a2186) | (~c3_1(a2186)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2618,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2186) | c1_1(a2186) | c0_1(a2174) | (~ndr1_0) | (~c2_1(a2174)) | c3_1(a2174) | (~c3_1(a2186))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 1.09/1.28 tff(2619,plain,
% 1.09/1.28 (hskp7 | (~c2_1(a2174)) | c3_1(a2174)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2618, 102, 2166, 2132, 2126, 138, 2612])).
% 1.09/1.28 tff(2620,plain,
% 1.09/1.28 (hskp7),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2619, 2602, 2430])).
% 1.09/1.28 tff(2621,plain,
% 1.09/1.28 (~c0_1(a2182)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[725, 2620])).
% 1.09/1.28 tff(2622,plain,
% 1.09/1.28 (c3_1(a2182)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[733, 2620])).
% 1.09/1.28 tff(2623,plain,
% 1.09/1.28 (c2_1(a2182)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[741, 2620])).
% 1.09/1.28 tff(2624,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2625,plain,
% 1.09/1.28 (((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182))) <=> (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2626,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[2625])).
% 1.09/1.28 tff(2627,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2626, 2624])).
% 1.09/1.28 tff(2628,plain,
% 1.09/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2182) | (~c3_1(a2182)) | (~c2_1(a2182)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2629,plain,
% 1.09/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2182) | (~ndr1_0) | (~c2_1(a2182)) | (~c3_1(a2182)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 1.09/1.28 tff(2630,plain,
% 1.09/1.28 ($false),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2629, 102, 2587, 2586, 2623, 2622, 2585, 2571, 2573, 2621, 970, 2594])).
% 1.09/1.28 tff(2631,plain,(c0_1(a2174)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.28 tff(2632,plain,
% 1.09/1.28 (~hskp0),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[629, 2631])).
% 1.09/1.28 tff(2633,plain,
% 1.09/1.28 (hskp17),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2241, 11, 2632])).
% 1.09/1.28 tff(2634,plain,
% 1.09/1.28 (~c1_1(a2197)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[154, 2633])).
% 1.09/1.28 tff(2635,plain,
% 1.09/1.28 (c3_1(a2197)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[599, 2633])).
% 1.09/1.28 tff(2636,plain,
% 1.09/1.28 (c2_1(a2197)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[607, 2633])).
% 1.09/1.28 tff(2637,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2638,plain,
% 1.09/1.28 ((hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197))) <=> (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2639,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[2638])).
% 1.09/1.28 tff(2640,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2639, 2637])).
% 1.09/1.28 tff(2641,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2197) | (~c2_1(a2197)) | (~c0_1(a2197)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2642,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c3_1(a2197)) | (~c0_1(a2197))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2641, 2640])).
% 1.09/1.28 tff(2643,plain,
% 1.09/1.28 (hskp21 | (~c0_1(a2197))),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2642, 102, 2636, 2635, 2634, 137])).
% 1.09/1.28 tff(2644,plain,
% 1.09/1.28 (~c0_1(a2197)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2643, 127])).
% 1.09/1.28 tff(2645,plain,
% 1.09/1.28 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2646,plain,
% 1.09/1.28 ((hskp16 | (~ndr1_0) | c2_1(a2174) | c1_1(a2174) | (~c0_1(a2174))) <=> (hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2647,plain,
% 1.09/1.28 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2174) | c1_1(a2174) | (~c0_1(a2174)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0)))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[2646])).
% 1.09/1.28 tff(2648,plain,
% 1.09/1.28 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2174) | c1_1(a2174) | (~c0_1(a2174)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2647, 2645])).
% 1.09/1.28 tff(2649,plain,
% 1.09/1.28 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a2174) | c1_1(a2174) | (~c0_1(a2174)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2650,plain,
% 1.09/1.28 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp16 | c1_1(a2174) | c2_1(a2174) | (~c0_1(a2174)) | (~ndr1_0)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2649, 2648])).
% 1.09/1.28 tff(2651,plain,
% 1.09/1.28 (hskp16 | c1_1(a2174) | c2_1(a2174)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2650, 102, 2631, 52])).
% 1.09/1.28 tff(2652,plain,
% 1.09/1.28 (c2_1(a2174)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2651, 2133, 11])).
% 1.09/1.28 tff(2653,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2654,plain,
% 1.09/1.28 ((hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2174) | (~c2_1(a2174)) | (~c0_1(a2174))) <=> (hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2655,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2174) | (~c2_1(a2174)) | (~c0_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[2654])).
% 1.09/1.28 tff(2656,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2174) | (~c2_1(a2174)) | (~c0_1(a2174)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2655, 2653])).
% 1.09/1.28 tff(2657,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2174) | (~c2_1(a2174)) | (~c0_1(a2174)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2658,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2174) | c1_1(a2197) | (~c0_1(a2174)) | (~ndr1_0) | (~c2_1(a2174)) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 1.09/1.28 tff(2659,plain,
% 1.09/1.28 ($false),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2658, 102, 127, 2636, 2635, 2133, 2652, 2634, 2631, 137])).
% 1.09/1.28 tff(2660,plain,(c1_1(a2174) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.09/1.28 tff(2661,plain,
% 1.09/1.28 (c1_1(a2174)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2660, 11])).
% 1.09/1.28 tff(2662,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2663,plain,
% 1.09/1.28 ((hskp16 | (~ndr1_0) | (~c0_1(a2174)) | c3_1(a2174) | (~c1_1(a2174)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197))) <=> (hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2664,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2174)) | c3_1(a2174) | (~c1_1(a2174)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[2663])).
% 1.09/1.28 tff(2665,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2174)) | c3_1(a2174) | (~c1_1(a2174)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.28 inference(transitivity,[status(thm)],[2664, 2662])).
% 1.09/1.28 tff(2666,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2174)) | c3_1(a2174) | (~c1_1(a2174)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(2667,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | (~c0_1(a2174)) | (~ndr1_0) | (~c1_1(a2174)) | c3_1(a2174) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[2666, 2665])).
% 1.09/1.28 tff(2668,plain,
% 1.09/1.28 ((~c1_1(a2174)) | c3_1(a2174)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2667, 102, 11, 2636, 2635, 2631, 2503, 2644])).
% 1.09/1.28 tff(2669,plain,
% 1.09/1.28 (c3_1(a2174)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[2668, 2661])).
% 1.09/1.28 tff(2670,plain,
% 1.09/1.28 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.09/1.28 inference(bind,[status(th)],[])).
% 1.09/1.28 tff(2671,plain,
% 1.09/1.28 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.09/1.28 inference(quant_intro,[status(thm)],[2670])).
% 1.09/1.28 tff(2672,plain,
% 1.09/1.28 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(2673,plain,
% 1.09/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.09/1.29 inference(bind,[status(th)],[])).
% 1.09/1.29 tff(2674,plain,
% 1.09/1.29 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.09/1.29 inference(quant_intro,[status(thm)],[2673])).
% 1.09/1.29 tff(2675,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.09/1.29 tff(2676,plain,
% 1.09/1.29 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2675, 2674])).
% 1.09/1.29 tff(2677,plain,
% 1.09/1.29 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2676, 2672])).
% 1.09/1.29 tff(2678,plain,(
% 1.09/1.29 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.09/1.29 inference(skolemize,[status(sab)],[2677])).
% 1.09/1.29 tff(2679,plain,
% 1.09/1.29 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2678, 2671])).
% 1.09/1.29 tff(2680,assumption,(~c0_1(a2197)), introduced(assumption)).
% 1.09/1.29 tff(2681,assumption,(c3_1(a2174)), introduced(assumption)).
% 1.09/1.29 tff(2682,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2683,plain,
% 1.09/1.29 ((hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197))) <=> (hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2684,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[2683])).
% 1.09/1.29 tff(2685,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(transitivity,[status(thm)],[2684, 2682])).
% 1.09/1.29 tff(2686,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a2174) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c3_1(a2197)))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(2687,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a2174) | c1_1(a2197) | (~ndr1_0) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2686, 2685])).
% 1.09/1.29 tff(2688,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2687, 102, 2632, 2486, 1045, 2270, 2485, 165, 2681, 2680])).
% 1.09/1.29 tff(2689,plain,(c2_1(a2174) | (~c3_1(a2197)) | (~c1_1(a2174)) | c1_1(a2197) | (~c3_1(a2174)) | c0_1(a2197)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(2690,plain,
% 1.09/1.29 (c2_1(a2174)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2689, 2635, 2661, 2634, 2669, 2644])).
% 1.09/1.29 tff(2691,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2692,plain,
% 1.09/1.29 ((hskp4 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197))) <=> (hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2693,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197)))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[2692])).
% 1.09/1.29 tff(2694,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(transitivity,[status(thm)],[2693, 2691])).
% 1.09/1.29 tff(2695,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a2174)) | (~c3_1(a2174)) | (~c1_1(a2174)) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(2696,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2174)) | (~c1_1(a2174)) | (~c3_1(a2174)) | (~c2_1(a2197)) | c0_1(a2197)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2695, 2694])).
% 1.09/1.29 tff(2697,plain,
% 1.09/1.29 (hskp4),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2696, 102, 2636, 2661, 2690, 2634, 2679, 2669, 2644])).
% 1.09/1.29 tff(2698,plain,
% 1.09/1.29 (((~hskp4) | (~c3_1(a2179))) <=> ((~hskp4) | (~c3_1(a2179)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2699,plain,
% 1.09/1.29 (((~c3_1(a2179)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a2179)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2700,axiom,((~c3_1(a2179)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.09/1.29 tff(2701,plain,
% 1.09/1.29 ((~hskp4) | (~c3_1(a2179))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2700, 2699])).
% 1.09/1.29 tff(2702,plain,
% 1.09/1.29 ((~hskp4) | (~c3_1(a2179))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2701, 2698])).
% 1.09/1.29 tff(2703,plain,
% 1.09/1.29 (~c3_1(a2179)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2702, 2697])).
% 1.09/1.29 tff(2704,plain,
% 1.09/1.29 (((~hskp4) | c0_1(a2179)) <=> ((~hskp4) | c0_1(a2179))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2705,axiom,((~hskp4) | c0_1(a2179)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.09/1.29 tff(2706,plain,
% 1.09/1.29 ((~hskp4) | c0_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2705, 2704])).
% 1.09/1.29 tff(2707,plain,
% 1.09/1.29 ((~hskp4) | c0_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2706, 2704])).
% 1.09/1.29 tff(2708,plain,
% 1.09/1.29 ((~hskp4) | c0_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2707, 2704])).
% 1.09/1.29 tff(2709,plain,
% 1.09/1.29 ((~hskp4) | c0_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2708, 2704])).
% 1.09/1.29 tff(2710,plain,
% 1.09/1.29 ((~hskp4) | c0_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2709, 2704])).
% 1.09/1.29 tff(2711,plain,
% 1.09/1.29 (c0_1(a2179)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2710, 2697])).
% 1.09/1.29 tff(2712,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2713,plain,
% 1.09/1.29 ((hskp16 | (~ndr1_0) | (~c0_1(a2179)) | c3_1(a2179) | (~c1_1(a2179)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197))) <=> (hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2714,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2179)) | c3_1(a2179) | (~c1_1(a2179)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[2713])).
% 1.09/1.29 tff(2715,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2179)) | c3_1(a2179) | (~c1_1(a2179)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197))),
% 1.09/1.29 inference(transitivity,[status(thm)],[2714, 2712])).
% 1.09/1.29 tff(2716,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a2179)) | c3_1(a2179) | (~c1_1(a2179)) | c0_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(2717,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a2179) | (~ndr1_0) | (~c1_1(a2179)) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2197)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 1.09/1.29 tff(2718,plain,
% 1.09/1.29 (~c1_1(a2179)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2717, 102, 11, 2636, 2635, 2711, 2703, 2503, 2644])).
% 1.09/1.29 tff(2719,plain,
% 1.09/1.29 (((~hskp4) | c2_1(a2179)) <=> ((~hskp4) | c2_1(a2179))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2720,axiom,((~hskp4) | c2_1(a2179)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.09/1.29 tff(2721,plain,
% 1.09/1.29 ((~hskp4) | c2_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2720, 2719])).
% 1.09/1.29 tff(2722,plain,
% 1.09/1.29 ((~hskp4) | c2_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2721, 2719])).
% 1.09/1.29 tff(2723,plain,
% 1.09/1.29 ((~hskp4) | c2_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2722, 2719])).
% 1.09/1.29 tff(2724,plain,
% 1.09/1.29 ((~hskp4) | c2_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2723, 2719])).
% 1.09/1.29 tff(2725,plain,
% 1.09/1.29 ((~hskp4) | c2_1(a2179)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2724, 2719])).
% 1.09/1.29 tff(2726,plain,
% 1.09/1.29 (c2_1(a2179)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2725, 2697])).
% 1.09/1.29 tff(2727,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2728,plain,
% 1.09/1.29 ((hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2179) | (~c2_1(a2179)) | (~c0_1(a2179))) <=> (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2729,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2179) | (~c2_1(a2179)) | (~c0_1(a2179)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[2728])).
% 1.09/1.29 tff(2730,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2179) | (~c2_1(a2179)) | (~c0_1(a2179)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.29 inference(transitivity,[status(thm)],[2729, 2727])).
% 1.09/1.29 tff(2731,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c1_1(a2179) | (~c2_1(a2179)) | (~c0_1(a2179)))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(2732,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2179)) | c1_1(a2179) | (~c0_1(a2179)) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.09/1.29 tff(2733,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2732, 102, 127, 2636, 2635, 2711, 2726, 2634, 137, 2718])).
% 1.09/1.29 tff(2734,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(2735,plain,
% 1.09/1.29 (~c2_1(a2195)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[384, 2734])).
% 1.09/1.29 tff(2736,plain,
% 1.09/1.29 (~c1_1(a2195)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[390, 2734])).
% 1.09/1.29 tff(2737,plain,
% 1.09/1.29 (~hskp26),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2205, 2632])).
% 1.09/1.29 tff(2738,plain,
% 1.09/1.29 (~c3_1(a2195)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[378, 2734])).
% 1.09/1.29 tff(2739,plain,
% 1.09/1.29 (~hskp24),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2427, 2736, 2632, 2735, 2738])).
% 1.09/1.29 tff(2740,plain,
% 1.09/1.29 (hskp17),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[100, 2739, 2737])).
% 1.09/1.29 tff(2741,plain,
% 1.09/1.29 (~c1_1(a2197)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[154, 2740])).
% 1.09/1.29 tff(2742,plain,
% 1.09/1.29 (c3_1(a2197)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[599, 2740])).
% 1.09/1.29 tff(2743,plain,
% 1.09/1.29 (c2_1(a2197)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[607, 2740])).
% 1.09/1.29 tff(2744,plain,
% 1.09/1.29 (c0_1(a2195)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2593, 102, 2632, 2743, 2742, 2741, 2736, 2735, 10])).
% 1.09/1.29 tff(2745,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2746,plain,
% 1.09/1.29 (((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2186) | (~c3_1(a2186)) | (~c2_1(a2186))) <=> (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(2747,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2186) | (~c3_1(a2186)) | (~c2_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[2746])).
% 1.09/1.29 tff(2748,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2186) | (~c3_1(a2186)) | (~c2_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.29 inference(transitivity,[status(thm)],[2747, 2745])).
% 1.09/1.29 tff(2749,plain,
% 1.09/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2195) | (~c0_1(a2195)) | c3_1(a2195) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c0_1(a2186) | (~c3_1(a2186)) | (~c2_1(a2186)))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(2750,plain,
% 1.09/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | c3_1(U) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a2197) | c2_1(a2195) | c3_1(a2195) | c0_1(a2186) | (~ndr1_0) | (~c3_1(a2186)) | (~c2_1(a2186)) | (~c0_1(a2195)) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 1.09/1.29 tff(2751,plain,
% 1.09/1.29 ((~c2_1(a2186)) | (~c0_1(a2195))),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2750, 102, 2743, 2742, 2166, 2741, 2735, 2738, 2132, 970])).
% 1.09/1.29 tff(2752,plain,
% 1.09/1.29 (~c2_1(a2186)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[2751, 2744])).
% 1.09/1.29 tff(2753,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(2754,plain,
% 1.09/1.30 ((hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2186) | c1_1(a2186) | c0_1(a2186)) <=> (hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(2755,plain,
% 1.09/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2186) | c1_1(a2186) | c0_1(a2186))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197))))),
% 1.09/1.30 inference(monotonicity,[status(thm)],[2754])).
% 1.09/1.30 tff(2756,plain,
% 1.09/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2186) | c1_1(a2186) | c0_1(a2186))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197)))),
% 1.09/1.30 inference(transitivity,[status(thm)],[2755, 2753])).
% 1.09/1.30 tff(2757,plain,
% 1.09/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2197) | (~c2_1(a2197)) | (~c3_1(a2197)) | c2_1(a2186) | c1_1(a2186) | c0_1(a2186))),
% 1.09/1.30 inference(quant_inst,[status(thm)],[])).
% 1.09/1.30 tff(2758,plain,
% 1.09/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a2197) | c0_1(a2186) | c1_1(a2186) | (~ndr1_0) | c2_1(a2186) | (~c2_1(a2197)) | (~c3_1(a2197))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[2757, 2756])).
% 1.09/1.30 tff(2759,plain,
% 1.09/1.30 ($false),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[2758, 102, 2632, 2743, 2742, 2741, 2132, 2126, 10, 2752])).
% 1.09/1.30 % SZS output end Proof
% 1.09/1.30 % E exiting
%------------------------------------------------------------------------------