%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN485-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.54s 0.73s
% Output : Proof 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN485-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:37:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.54/0.73 % SZS status Unsatisfiable
% 0.54/0.73 % SZS output start Proof
% 0.54/0.73 tff(c2_1_type, type, (
% 0.54/0.73 c2_1: $i > $o)).
% 0.54/0.73 tff(a2072_type, type, (
% 0.54/0.73 a2072: $i)).
% 0.54/0.73 tff(c3_1_type, type, (
% 0.54/0.73 c3_1: $i > $o)).
% 0.54/0.73 tff(c0_1_type, type, (
% 0.54/0.73 c0_1: $i > $o)).
% 0.54/0.73 tff(c1_1_type, type, (
% 0.54/0.73 c1_1: $i > $o)).
% 0.54/0.73 tff(ndr1_0_type, type, (
% 0.54/0.73 ndr1_0: $o)).
% 0.54/0.73 tff(a2070_type, type, (
% 0.54/0.73 a2070: $i)).
% 0.54/0.73 tff(hskp1_type, type, (
% 0.54/0.73 hskp1: $o)).
% 0.54/0.73 tff(a2076_type, type, (
% 0.54/0.73 a2076: $i)).
% 0.54/0.73 tff(hskp5_type, type, (
% 0.54/0.73 hskp5: $o)).
% 0.54/0.73 tff(hskp3_type, type, (
% 0.54/0.73 hskp3: $o)).
% 0.54/0.73 tff(hskp11_type, type, (
% 0.54/0.73 hskp11: $o)).
% 0.54/0.73 tff(a2082_type, type, (
% 0.54/0.73 a2082: $i)).
% 0.54/0.73 tff(hskp8_type, type, (
% 0.54/0.73 hskp8: $o)).
% 0.54/0.73 tff(a2087_type, type, (
% 0.54/0.73 a2087: $i)).
% 0.54/0.73 tff(hskp10_type, type, (
% 0.54/0.73 hskp10: $o)).
% 0.54/0.73 tff(a2110_type, type, (
% 0.54/0.73 a2110: $i)).
% 0.54/0.73 tff(hskp17_type, type, (
% 0.54/0.73 hskp17: $o)).
% 0.54/0.73 tff(hskp23_type, type, (
% 0.54/0.73 hskp23: $o)).
% 0.54/0.73 tff(a2149_type, type, (
% 0.54/0.73 a2149: $i)).
% 0.54/0.73 tff(hskp29_type, type, (
% 0.54/0.73 hskp29: $o)).
% 0.54/0.73 tff(a2074_type, type, (
% 0.54/0.73 a2074: $i)).
% 0.54/0.73 tff(hskp4_type, type, (
% 0.54/0.73 hskp4: $o)).
% 0.54/0.73 tff(a2068_type, type, (
% 0.54/0.73 a2068: $i)).
% 0.54/0.73 tff(hskp0_type, type, (
% 0.54/0.73 hskp0: $o)).
% 0.54/0.73 tff(a2077_type, type, (
% 0.54/0.73 a2077: $i)).
% 0.54/0.73 tff(a2093_type, type, (
% 0.54/0.73 a2093: $i)).
% 0.54/0.73 tff(a2069_type, type, (
% 0.54/0.73 a2069: $i)).
% 0.54/0.73 tff(hskp26_type, type, (
% 0.54/0.73 hskp26: $o)).
% 0.54/0.73 tff(a2073_type, type, (
% 0.54/0.73 a2073: $i)).
% 0.54/0.73 tff(hskp27_type, type, (
% 0.54/0.73 hskp27: $o)).
% 0.54/0.73 tff(a2075_type, type, (
% 0.54/0.73 a2075: $i)).
% 0.54/0.73 tff(hskp28_type, type, (
% 0.54/0.73 hskp28: $o)).
% 0.54/0.73 tff(a2079_type, type, (
% 0.54/0.73 a2079: $i)).
% 0.54/0.73 tff(hskp7_type, type, (
% 0.54/0.73 hskp7: $o)).
% 0.54/0.73 tff(hskp20_type, type, (
% 0.54/0.73 hskp20: $o)).
% 0.54/0.73 tff(a2130_type, type, (
% 0.54/0.73 a2130: $i)).
% 0.54/0.73 tff(hskp2_type, type, (
% 0.54/0.73 hskp2: $o)).
% 0.54/0.73 tff(a2140_type, type, (
% 0.54/0.73 a2140: $i)).
% 0.54/0.73 tff(hskp22_type, type, (
% 0.54/0.73 hskp22: $o)).
% 0.54/0.73 tff(a2071_type, type, (
% 0.54/0.73 a2071: $i)).
% 0.54/0.73 tff(a2116_type, type, (
% 0.54/0.73 a2116: $i)).
% 0.54/0.73 tff(hskp18_type, type, (
% 0.54/0.73 hskp18: $o)).
% 0.54/0.73 tff(a2104_type, type, (
% 0.54/0.73 a2104: $i)).
% 0.54/0.73 tff(hskp16_type, type, (
% 0.54/0.73 hskp16: $o)).
% 0.54/0.73 tff(a2099_type, type, (
% 0.54/0.73 a2099: $i)).
% 0.54/0.73 tff(hskp15_type, type, (
% 0.54/0.73 hskp15: $o)).
% 0.54/0.73 tff(a2097_type, type, (
% 0.54/0.73 a2097: $i)).
% 0.54/0.73 tff(hskp14_type, type, (
% 0.54/0.73 hskp14: $o)).
% 0.54/0.73 tff(a2095_type, type, (
% 0.54/0.73 a2095: $i)).
% 0.54/0.73 tff(hskp12_type, type, (
% 0.54/0.73 hskp12: $o)).
% 0.54/0.73 tff(a2160_type, type, (
% 0.54/0.73 a2160: $i)).
% 0.54/0.73 tff(hskp24_type, type, (
% 0.54/0.73 hskp24: $o)).
% 0.54/0.73 tff(a2122_type, type, (
% 0.54/0.73 a2122: $i)).
% 0.54/0.73 tff(hskp19_type, type, (
% 0.54/0.73 hskp19: $o)).
% 0.54/0.73 tff(1,plain,
% 0.54/0.73 (^[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) | 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) | c3_1(W) | (~c2_1(W))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(2,plain,
% 0.54/0.73 (![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) | c3_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) | c3_1(W) | (~c2_1(W)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.54/0.73 tff(3,plain,
% 0.54/0.73 (![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) | c3_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) | c3_1(W) | (~c2_1(W)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(4,plain,
% 0.54/0.73 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_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)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | 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)) | (~c2_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)) | (~c2_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) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | 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) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c0_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)))), rewrite((((~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) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c0_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) | c3_1(W) | (~c2_1(W)))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(5,plain,
% 0.54/0.73 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c0_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) | c3_1(W) | (~c2_1(W)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[4])).
% 0.54/0.73 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.54/0.73 tff(7,plain,
% 0.54/0.73 (![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) | c3_1(W) | (~c2_1(W)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.54/0.73 tff(8,plain,
% 0.54/0.73 (![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) | c3_1(W) | (~c2_1(W)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.54/0.73 tff(9,plain,(
% 0.54/0.73 ![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) | c3_1(W) | (~c2_1(W)))),
% 0.54/0.73 inference(skolemize,[status(sab)],[8])).
% 0.54/0.73 tff(10,plain,
% 0.54/0.73 (![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) | c3_1(W) | (~c2_1(W)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.54/0.73 tff(11,assumption,(~hskp1), introduced(assumption)).
% 0.54/0.73 tff(12,plain,
% 0.54/0.73 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(13,plain,
% 0.54/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[12])).
% 0.54/0.73 tff(14,plain,
% 0.54/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(15,plain,
% 0.54/0.73 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(16,plain,
% 0.54/0.73 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[15])).
% 0.54/0.73 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.54/0.73 tff(18,plain,
% 0.54/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.54/0.73 tff(19,plain,
% 0.54/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.54/0.73 tff(20,plain,(
% 0.54/0.73 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.54/0.73 inference(skolemize,[status(sab)],[19])).
% 0.54/0.73 tff(21,plain,
% 0.54/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.54/0.73 tff(22,assumption,(~hskp11), introduced(assumption)).
% 0.54/0.73 tff(23,plain,
% 0.54/0.73 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(24,plain,
% 0.54/0.73 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[23])).
% 0.54/0.73 tff(25,plain,
% 0.54/0.73 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(26,plain,
% 0.54/0.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp10) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp10) <=> (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(27,plain,
% 0.54/0.73 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp10) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[26])).
% 0.54/0.73 tff(28,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.54/0.73 tff(29,plain,
% 0.54/0.73 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.54/0.73 tff(30,plain,
% 0.54/0.73 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.54/0.73 tff(31,plain,(
% 0.54/0.73 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.54/0.73 inference(skolemize,[status(sab)],[30])).
% 0.54/0.73 tff(32,plain,
% 0.54/0.73 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.54/0.73 tff(33,assumption,(~hskp10), introduced(assumption)).
% 0.54/0.73 tff(34,assumption,(hskp23), introduced(assumption)).
% 0.54/0.73 tff(35,plain,
% 0.54/0.73 (((~hskp23) | (~c1_1(a2149))) <=> ((~hskp23) | (~c1_1(a2149)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(36,plain,
% 0.54/0.73 (((~c1_1(a2149)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a2149)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(37,axiom,((~c1_1(a2149)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.54/0.73 tff(38,plain,
% 0.54/0.73 ((~hskp23) | (~c1_1(a2149))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.54/0.73 tff(39,plain,
% 0.54/0.73 ((~hskp23) | (~c1_1(a2149))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.54/0.73 tff(40,plain,
% 0.54/0.73 (~c1_1(a2149)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.54/0.73 tff(41,plain,
% 0.54/0.73 (((~hskp23) | c3_1(a2149)) <=> ((~hskp23) | c3_1(a2149))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(42,axiom,((~hskp23) | c3_1(a2149)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.54/0.73 tff(43,plain,
% 0.54/0.73 ((~hskp23) | c3_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.54/0.73 tff(44,plain,
% 0.54/0.73 ((~hskp23) | c3_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.54/0.73 tff(45,plain,
% 0.54/0.73 ((~hskp23) | c3_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.54/0.73 tff(46,plain,
% 0.54/0.73 ((~hskp23) | c3_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.54/0.73 tff(47,plain,
% 0.54/0.73 ((~hskp23) | c3_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.54/0.73 tff(48,plain,
% 0.54/0.73 (c3_1(a2149)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[47, 34])).
% 0.54/0.73 tff(49,plain,
% 0.54/0.73 (((~hskp23) | c0_1(a2149)) <=> ((~hskp23) | c0_1(a2149))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(50,axiom,((~hskp23) | c0_1(a2149)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.54/0.73 tff(51,plain,
% 0.54/0.73 ((~hskp23) | c0_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.54/0.73 tff(52,plain,
% 0.54/0.73 ((~hskp23) | c0_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[51, 49])).
% 0.54/0.73 tff(53,plain,
% 0.54/0.73 ((~hskp23) | c0_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.54/0.73 tff(54,plain,
% 0.54/0.73 ((~hskp23) | c0_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.54/0.73 tff(55,plain,
% 0.54/0.73 ((~hskp23) | c0_1(a2149)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.54/0.73 tff(56,plain,
% 0.54/0.73 (c0_1(a2149)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[55, 34])).
% 0.54/0.73 tff(57,assumption,(~ndr1_0), introduced(assumption)).
% 0.54/0.73 tff(58,plain,
% 0.54/0.73 ((ndr1_0 | (~hskp3)) <=> (ndr1_0 | (~hskp3))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(59,plain,
% 0.54/0.73 (((~hskp3) | ndr1_0) <=> (ndr1_0 | (~hskp3))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(60,axiom,((~hskp3) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 0.54/0.73 tff(61,plain,
% 0.54/0.73 (ndr1_0 | (~hskp3)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.54/0.73 tff(62,plain,
% 0.54/0.73 (ndr1_0 | (~hskp3)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.54/0.73 tff(63,plain,
% 0.54/0.73 (~hskp3),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[62, 57])).
% 0.54/0.73 tff(64,plain,
% 0.54/0.73 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(65,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.54/0.73 tff(66,plain,
% 0.54/0.73 ((~hskp29) | ndr1_0),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.54/0.73 tff(67,plain,
% 0.54/0.73 ((~hskp29) | ndr1_0),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[66, 64])).
% 0.54/0.73 tff(68,plain,
% 0.54/0.73 ((~hskp29) | ndr1_0),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.54/0.73 tff(69,plain,
% 0.54/0.73 ((~hskp29) | ndr1_0),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.54/0.73 tff(70,plain,
% 0.54/0.73 ((~hskp29) | ndr1_0),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[69, 64])).
% 0.54/0.73 tff(71,plain,
% 0.54/0.73 (~hskp29),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[70, 57])).
% 0.54/0.73 tff(72,plain,
% 0.54/0.73 ((ndr1_0 | (~hskp5)) <=> (ndr1_0 | (~hskp5))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(73,plain,
% 0.54/0.73 (((~hskp5) | ndr1_0) <=> (ndr1_0 | (~hskp5))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(74,axiom,((~hskp5) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause26')).
% 0.54/0.73 tff(75,plain,
% 0.54/0.73 (ndr1_0 | (~hskp5)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.54/0.73 tff(76,plain,
% 0.54/0.73 (ndr1_0 | (~hskp5)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.54/0.73 tff(77,plain,
% 0.54/0.73 (~hskp5),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[76, 57])).
% 0.54/0.73 tff(78,plain,
% 0.54/0.73 ((hskp29 | hskp5 | hskp3) <=> (hskp29 | hskp5 | hskp3)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(79,plain,
% 0.54/0.73 (((hskp29 | hskp5) | hskp3) <=> (hskp29 | hskp5 | hskp3)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(80,axiom,((hskp29 | hskp5) | hskp3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.54/0.73 tff(81,plain,
% 0.54/0.73 (hskp29 | hskp5 | hskp3),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.54/0.73 tff(82,plain,
% 0.54/0.73 (hskp29 | hskp5 | hskp3),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.54/0.73 tff(83,plain,
% 0.54/0.73 (hskp29 | hskp5 | hskp3),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.54/0.73 tff(84,plain,
% 0.54/0.73 (hskp29 | hskp5 | hskp3),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[83, 78])).
% 0.54/0.73 tff(85,plain,
% 0.54/0.73 (hskp29 | hskp5 | hskp3),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.54/0.73 tff(86,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[85, 77, 71, 63])).
% 0.54/0.73 tff(87,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(88,plain,
% 0.54/0.73 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(89,plain,
% 0.54/0.73 ((hskp11 | hskp10 | (~ndr1_0) | c1_1(a2149) | (~c3_1(a2149)) | (~c0_1(a2149))) <=> (hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(90,plain,
% 0.54/0.73 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2149) | (~c3_1(a2149)) | (~c0_1(a2149)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[89])).
% 0.54/0.73 tff(91,plain,
% 0.54/0.73 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2149) | (~c3_1(a2149)) | (~c0_1(a2149)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[90, 88])).
% 0.54/0.73 tff(92,plain,
% 0.54/0.73 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2149) | (~c3_1(a2149)) | (~c0_1(a2149)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(93,plain,
% 0.54/0.73 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.54/0.73 tff(94,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[93, 87, 22, 33, 56, 48, 40, 32])).
% 0.54/0.73 tff(95,plain,((~hskp23) | hskp11 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(96,plain,
% 0.54/0.73 (~hskp23),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[95, 33, 22])).
% 0.54/0.73 tff(97,plain,
% 0.54/0.73 ((hskp17 | hskp23 | hskp1) <=> (hskp17 | hskp23 | hskp1)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(98,plain,
% 0.54/0.73 (((hskp17 | hskp23) | hskp1) <=> (hskp17 | hskp23 | hskp1)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(99,axiom,((hskp17 | hskp23) | hskp1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.54/0.73 tff(100,plain,
% 0.54/0.73 (hskp17 | hskp23 | hskp1),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.54/0.73 tff(101,plain,
% 0.54/0.73 (hskp17 | hskp23 | hskp1),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.54/0.73 tff(102,plain,
% 0.54/0.73 (hskp17 | hskp23 | hskp1),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.54/0.73 tff(103,plain,
% 0.54/0.73 (hskp17 | hskp23 | hskp1),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[102, 97])).
% 0.54/0.73 tff(104,plain,
% 0.54/0.73 (hskp17 | hskp23 | hskp1),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[103, 97])).
% 0.54/0.73 tff(105,plain,
% 0.54/0.73 (hskp17),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[104, 96, 11])).
% 0.54/0.74 tff(106,plain,
% 0.54/0.74 (((~hskp17) | (~c1_1(a2110))) <=> ((~hskp17) | (~c1_1(a2110)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(107,plain,
% 0.54/0.74 (((~c1_1(a2110)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2110)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(108,axiom,((~c1_1(a2110)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.54/0.74 tff(109,plain,
% 0.54/0.74 ((~hskp17) | (~c1_1(a2110))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.54/0.74 tff(110,plain,
% 0.54/0.74 ((~hskp17) | (~c1_1(a2110))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[109, 106])).
% 0.54/0.74 tff(111,plain,
% 0.54/0.74 (~c1_1(a2110)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[110, 105])).
% 0.54/0.74 tff(112,plain,
% 0.54/0.74 (((~hskp17) | c0_1(a2110)) <=> ((~hskp17) | c0_1(a2110))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(113,axiom,((~hskp17) | c0_1(a2110)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.54/0.74 tff(114,plain,
% 0.54/0.74 ((~hskp17) | c0_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.54/0.74 tff(115,plain,
% 0.54/0.74 ((~hskp17) | c0_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[114, 112])).
% 0.54/0.74 tff(116,plain,
% 0.54/0.74 ((~hskp17) | c0_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[115, 112])).
% 0.54/0.74 tff(117,plain,
% 0.54/0.74 ((~hskp17) | c0_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.54/0.74 tff(118,plain,
% 0.54/0.74 ((~hskp17) | c0_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[117, 112])).
% 0.54/0.74 tff(119,plain,
% 0.54/0.74 (c0_1(a2110)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[118, 105])).
% 0.54/0.74 tff(120,plain,
% 0.54/0.74 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(121,plain,
% 0.54/0.74 ((hskp11 | hskp10 | (~ndr1_0) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110))) <=> (hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(122,plain,
% 0.54/0.74 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[121])).
% 0.54/0.74 tff(123,plain,
% 0.54/0.74 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[122, 120])).
% 0.54/0.74 tff(124,plain,
% 0.54/0.74 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(125,plain,
% 0.54/0.74 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.54/0.74 tff(126,plain,
% 0.54/0.74 (~c3_1(a2110)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[125, 87, 22, 33, 119, 111, 32])).
% 0.54/0.74 tff(127,assumption,(hskp17), introduced(assumption)).
% 0.54/0.74 tff(128,plain,
% 0.54/0.74 (~c1_1(a2110)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[110, 127])).
% 0.54/0.74 tff(129,plain,
% 0.54/0.74 (c0_1(a2110)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[118, 127])).
% 0.54/0.74 tff(130,plain,
% 0.54/0.74 (~c3_1(a2110)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[125, 87, 22, 33, 129, 128, 32])).
% 0.54/0.74 tff(131,plain,
% 0.54/0.74 (^[U: $i] : refl((hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(132,plain,
% 0.54/0.74 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[131])).
% 0.54/0.74 tff(133,plain,
% 0.54/0.74 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(134,plain,
% 0.54/0.74 (^[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) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp8) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp8))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp8) <=> (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp8) <=> (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(135,plain,
% 0.54/0.74 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp8) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[134])).
% 0.54/0.74 tff(136,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.54/0.74 tff(137,plain,
% 0.54/0.74 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.54/0.74 tff(138,plain,
% 0.54/0.74 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.54/0.74 tff(139,plain,(
% 0.54/0.74 ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.54/0.74 inference(skolemize,[status(sab)],[138])).
% 0.54/0.74 tff(140,plain,
% 0.54/0.74 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.54/0.74 tff(141,assumption,(~hskp8), introduced(assumption)).
% 0.54/0.74 tff(142,plain,
% 0.54/0.74 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(143,plain,
% 0.54/0.74 ((hskp8 | hskp1 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c0_1(a2110))) <=> (hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(144,plain,
% 0.54/0.74 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[143])).
% 0.54/0.74 tff(145,plain,
% 0.54/0.74 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[144, 142])).
% 0.54/0.74 tff(146,plain,
% 0.54/0.74 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c0_1(a2110)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(147,plain,
% 0.54/0.74 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.54/0.74 tff(148,plain,
% 0.54/0.74 ($false),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[147, 87, 141, 11, 129, 128, 140, 130])).
% 0.54/0.74 tff(149,plain,((~hskp17) | hskp8 | hskp1 | hskp11 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(150,plain,
% 0.54/0.74 (hskp8),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[149, 105, 11, 22, 33])).
% 0.54/0.74 tff(151,plain,
% 0.54/0.74 (((~hskp8) | (~c0_1(a2082))) <=> ((~hskp8) | (~c0_1(a2082)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(152,plain,
% 0.54/0.74 (((~c0_1(a2082)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a2082)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(153,axiom,((~c0_1(a2082)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.54/0.74 tff(154,plain,
% 0.54/0.74 ((~hskp8) | (~c0_1(a2082))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.54/0.74 tff(155,plain,
% 0.54/0.74 ((~hskp8) | (~c0_1(a2082))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[154, 151])).
% 0.54/0.74 tff(156,plain,
% 0.54/0.74 (~c0_1(a2082)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[155, 150])).
% 0.54/0.74 tff(157,plain,
% 0.54/0.74 (((~hskp8) | c2_1(a2082)) <=> ((~hskp8) | c2_1(a2082))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(158,axiom,((~hskp8) | c2_1(a2082)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.54/0.74 tff(159,plain,
% 0.54/0.74 ((~hskp8) | c2_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.54/0.74 tff(160,plain,
% 0.54/0.74 ((~hskp8) | c2_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[159, 157])).
% 0.54/0.74 tff(161,plain,
% 0.54/0.74 ((~hskp8) | c2_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[160, 157])).
% 0.54/0.74 tff(162,plain,
% 0.54/0.74 ((~hskp8) | c2_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.54/0.74 tff(163,plain,
% 0.54/0.74 ((~hskp8) | c2_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[162, 157])).
% 0.54/0.74 tff(164,plain,
% 0.54/0.74 (c2_1(a2082)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[163, 150])).
% 0.54/0.74 tff(165,plain,
% 0.54/0.74 (((~hskp8) | c1_1(a2082)) <=> ((~hskp8) | c1_1(a2082))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(166,axiom,((~hskp8) | c1_1(a2082)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.54/0.74 tff(167,plain,
% 0.54/0.74 ((~hskp8) | c1_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.54/0.74 tff(168,plain,
% 0.54/0.74 ((~hskp8) | c1_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[167, 165])).
% 0.54/0.74 tff(169,plain,
% 0.54/0.74 ((~hskp8) | c1_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[168, 165])).
% 0.54/0.74 tff(170,plain,
% 0.54/0.74 ((~hskp8) | c1_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.54/0.74 tff(171,plain,
% 0.54/0.74 ((~hskp8) | c1_1(a2082)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[170, 165])).
% 0.54/0.74 tff(172,plain,
% 0.54/0.74 (c1_1(a2082)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[171, 150])).
% 0.54/0.74 tff(173,plain,
% 0.54/0.74 (((~hskp17) | c2_1(a2110)) <=> ((~hskp17) | c2_1(a2110))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(174,axiom,((~hskp17) | c2_1(a2110)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.54/0.74 tff(175,plain,
% 0.54/0.74 ((~hskp17) | c2_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.54/0.74 tff(176,plain,
% 0.54/0.74 ((~hskp17) | c2_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[175, 173])).
% 0.54/0.74 tff(177,plain,
% 0.54/0.74 ((~hskp17) | c2_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.54/0.74 tff(178,plain,
% 0.54/0.74 ((~hskp17) | c2_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.54/0.74 tff(179,plain,
% 0.54/0.74 ((~hskp17) | c2_1(a2110)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[178, 173])).
% 0.54/0.74 tff(180,plain,
% 0.54/0.74 (c2_1(a2110)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[179, 105])).
% 0.54/0.74 tff(181,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(182,plain,
% 0.54/0.74 ((hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082))) <=> (hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(183,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[182])).
% 0.54/0.74 tff(184,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[183, 181])).
% 0.54/0.74 tff(185,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(186,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.54/0.74 tff(187,plain,
% 0.54/0.74 ($false),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[186, 87, 22, 180, 172, 164, 111, 156, 21, 126])).
% 0.54/0.74 tff(188,plain,(hskp10 | hskp11 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(189,plain,
% 0.54/0.74 (hskp10),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[188, 22, 11])).
% 0.54/0.74 tff(190,plain,
% 0.54/0.74 (((~hskp10) | (~c3_1(a2087))) <=> ((~hskp10) | (~c3_1(a2087)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(191,plain,
% 0.54/0.74 (((~c3_1(a2087)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a2087)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(192,axiom,((~c3_1(a2087)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.54/0.74 tff(193,plain,
% 0.54/0.74 ((~hskp10) | (~c3_1(a2087))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.54/0.74 tff(194,plain,
% 0.54/0.74 ((~hskp10) | (~c3_1(a2087))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[193, 190])).
% 0.54/0.74 tff(195,plain,
% 0.54/0.74 (~c3_1(a2087)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[194, 189])).
% 0.54/0.74 tff(196,plain,
% 0.54/0.74 (((~hskp10) | (~c1_1(a2087))) <=> ((~hskp10) | (~c1_1(a2087)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(197,plain,
% 0.54/0.74 (((~c1_1(a2087)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a2087)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(198,axiom,((~c1_1(a2087)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.54/0.74 tff(199,plain,
% 0.54/0.74 ((~hskp10) | (~c1_1(a2087))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.54/0.74 tff(200,plain,
% 0.54/0.74 ((~hskp10) | (~c1_1(a2087))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[199, 196])).
% 0.54/0.74 tff(201,plain,
% 0.54/0.74 (~c1_1(a2087)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[200, 189])).
% 0.54/0.74 tff(202,plain,
% 0.54/0.74 (((~hskp10) | c2_1(a2087)) <=> ((~hskp10) | c2_1(a2087))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(203,axiom,((~hskp10) | c2_1(a2087)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.54/0.74 tff(204,plain,
% 0.54/0.74 ((~hskp10) | c2_1(a2087)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.54/0.74 tff(205,plain,
% 0.54/0.74 ((~hskp10) | c2_1(a2087)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[204, 202])).
% 0.54/0.74 tff(206,plain,
% 0.54/0.74 ((~hskp10) | c2_1(a2087)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[205, 202])).
% 0.54/0.74 tff(207,plain,
% 0.54/0.74 ((~hskp10) | c2_1(a2087)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.54/0.74 tff(208,plain,
% 0.54/0.74 ((~hskp10) | c2_1(a2087)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[207, 202])).
% 0.54/0.74 tff(209,plain,
% 0.54/0.74 (c2_1(a2087)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[208, 189])).
% 0.54/0.74 tff(210,assumption,(~c3_1(a2087)), introduced(assumption)).
% 0.54/0.74 tff(211,assumption,(~c1_1(a2087)), introduced(assumption)).
% 0.54/0.74 tff(212,plain,
% 0.54/0.74 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(213,plain,
% 0.54/0.74 ((hskp8 | hskp1 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087))) <=> (hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(214,plain,
% 0.54/0.74 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[213])).
% 0.54/0.74 tff(215,plain,
% 0.54/0.74 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[214, 212])).
% 0.54/0.74 tff(216,plain,
% 0.54/0.74 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(217,plain,
% 0.54/0.74 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.54/0.74 tff(218,plain,
% 0.54/0.74 (hskp8 | (~c0_1(a2087))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[217, 87, 11, 211, 210, 140])).
% 0.54/0.74 tff(219,plain,
% 0.54/0.74 (~c0_1(a2087)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[218, 141])).
% 0.54/0.74 tff(220,plain,
% 0.54/0.74 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(221,plain,
% 0.54/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[220])).
% 0.54/0.74 tff(222,plain,
% 0.54/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(223,plain,
% 0.54/0.74 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(224,plain,
% 0.54/0.74 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[223])).
% 0.54/0.74 tff(225,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.54/0.74 tff(226,plain,
% 0.54/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.54/0.74 tff(227,plain,
% 0.54/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.54/0.74 tff(228,plain,(
% 0.54/0.74 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.74 inference(skolemize,[status(sab)],[227])).
% 0.54/0.74 tff(229,plain,
% 0.54/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.54/0.74 tff(230,assumption,(c2_1(a2087)), introduced(assumption)).
% 0.54/0.74 tff(231,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(232,plain,
% 0.54/0.74 ((hskp4 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c3_1(a2087) | c1_1(a2087) | c0_1(a2087)) <=> (hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(233,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c3_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[232])).
% 0.54/0.74 tff(234,plain,
% 0.54/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c3_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[233, 231])).
% 0.54/0.74 tff(235,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c3_1(a2087) | c1_1(a2087) | c0_1(a2087))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(236,plain,
% 0.54/0.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.54/0.74 tff(237,plain,
% 0.54/0.74 (hskp4 | c0_1(a2087)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[236, 87, 230, 211, 210, 229])).
% 0.54/0.74 tff(238,plain,
% 0.54/0.74 (hskp4),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[237, 219])).
% 0.54/0.74 tff(239,plain,
% 0.54/0.74 (((~hskp4) | (~c2_1(a2074))) <=> ((~hskp4) | (~c2_1(a2074)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(240,plain,
% 0.54/0.74 (((~c2_1(a2074)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a2074)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(241,axiom,((~c2_1(a2074)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.54/0.74 tff(242,plain,
% 0.54/0.74 ((~hskp4) | (~c2_1(a2074))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.54/0.74 tff(243,plain,
% 0.54/0.74 ((~hskp4) | (~c2_1(a2074))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[242, 239])).
% 0.54/0.74 tff(244,plain,
% 0.54/0.74 (~c2_1(a2074)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[243, 238])).
% 0.54/0.74 tff(245,plain,
% 0.54/0.74 (((~hskp4) | c3_1(a2074)) <=> ((~hskp4) | c3_1(a2074))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(246,axiom,((~hskp4) | c3_1(a2074)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.54/0.74 tff(247,plain,
% 0.54/0.74 ((~hskp4) | c3_1(a2074)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.54/0.74 tff(248,plain,
% 0.54/0.74 ((~hskp4) | c3_1(a2074)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[247, 245])).
% 0.54/0.75 tff(249,plain,
% 0.54/0.75 ((~hskp4) | c3_1(a2074)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[248, 245])).
% 0.54/0.75 tff(250,plain,
% 0.54/0.75 ((~hskp4) | c3_1(a2074)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.54/0.75 tff(251,plain,
% 0.54/0.75 ((~hskp4) | c3_1(a2074)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[250, 245])).
% 0.54/0.75 tff(252,plain,
% 0.54/0.75 (c3_1(a2074)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[251, 238])).
% 0.54/0.75 tff(253,plain,
% 0.54/0.75 (((~hskp4) | c1_1(a2074)) <=> ((~hskp4) | c1_1(a2074))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(254,axiom,((~hskp4) | c1_1(a2074)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.54/0.75 tff(255,plain,
% 0.54/0.75 ((~hskp4) | c1_1(a2074)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.54/0.75 tff(256,plain,
% 0.54/0.75 ((~hskp4) | c1_1(a2074)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[255, 253])).
% 0.54/0.75 tff(257,plain,
% 0.54/0.75 ((~hskp4) | c1_1(a2074)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[256, 253])).
% 0.54/0.75 tff(258,plain,
% 0.54/0.75 ((~hskp4) | c1_1(a2074)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[257, 253])).
% 0.54/0.75 tff(259,plain,
% 0.54/0.75 ((~hskp4) | c1_1(a2074)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[258, 253])).
% 0.54/0.75 tff(260,plain,
% 0.54/0.75 (c1_1(a2074)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[259, 238])).
% 0.54/0.75 tff(261,plain,
% 0.54/0.75 (((~![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) | c3_1(W) | (~c2_1(W)))) | (c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(262,plain,
% 0.54/0.75 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087))) <=> (c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(263,plain,
% 0.54/0.75 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | (c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[262])).
% 0.54/0.75 tff(264,plain,
% 0.54/0.75 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[263, 261])).
% 0.54/0.75 tff(265,plain,
% 0.54/0.75 ((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(266,plain,
% 0.54/0.75 ((~![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) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.54/0.75 tff(267,plain,
% 0.54/0.75 (~c0_1(a2074)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[266, 87, 230, 260, 252, 210, 244, 10, 219])).
% 0.54/0.75 tff(268,plain,
% 0.54/0.75 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(269,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[268])).
% 0.54/0.75 tff(270,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(271,plain,
% 0.54/0.75 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(272,plain,
% 0.54/0.75 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[271])).
% 0.54/0.75 tff(273,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.54/0.75 tff(274,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.54/0.75 tff(275,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.54/0.75 tff(276,plain,(
% 0.54/0.75 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.54/0.75 inference(skolemize,[status(sab)],[275])).
% 0.54/0.75 tff(277,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.54/0.75 tff(278,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(279,plain,
% 0.54/0.75 ((hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074))) <=> (hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(280,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[279])).
% 0.54/0.75 tff(281,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[280, 278])).
% 0.54/0.75 tff(282,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(283,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.54/0.75 tff(284,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[283, 87, 141, 230, 260, 211, 210, 244, 277, 267])).
% 0.54/0.75 tff(285,plain,(hskp8 | (~c2_1(a2087)) | c1_1(a2087) | c3_1(a2087) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(286,plain,
% 0.54/0.75 (hskp8),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[285, 209, 201, 195, 11])).
% 0.54/0.75 tff(287,plain,
% 0.54/0.75 (~c0_1(a2082)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[155, 286])).
% 0.54/0.75 tff(288,plain,
% 0.54/0.75 (c2_1(a2082)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[163, 286])).
% 0.54/0.75 tff(289,plain,
% 0.54/0.75 (c1_1(a2082)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[171, 286])).
% 0.54/0.75 tff(290,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(291,plain,
% 0.54/0.75 ((hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082))) <=> (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(292,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[291])).
% 0.54/0.75 tff(293,plain,
% 0.54/0.75 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[292, 290])).
% 0.54/0.75 tff(294,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(295,plain,
% 0.54/0.75 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.54/0.75 tff(296,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[295, 87, 22, 209, 289, 288, 201, 195, 287, 21])).
% 0.54/0.75 tff(297,plain,(hskp11 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(298,plain,
% 0.54/0.75 (hskp11),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[297, 11])).
% 0.54/0.75 tff(299,plain,
% 0.54/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(300,plain,
% 0.54/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[299])).
% 0.54/0.75 tff(301,plain,
% 0.54/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(302,plain,
% 0.54/0.75 (^[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))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_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))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_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))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(303,plain,
% 0.54/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[302])).
% 0.54/0.75 tff(304,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.54/0.75 tff(305,plain,
% 0.54/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.54/0.75 tff(306,plain,
% 0.54/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.54/0.75 tff(307,plain,(
% 0.54/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.54/0.75 inference(skolemize,[status(sab)],[306])).
% 0.54/0.75 tff(308,plain,
% 0.54/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.54/0.75 tff(309,assumption,(hskp11), introduced(assumption)).
% 0.54/0.75 tff(310,plain,
% 0.54/0.75 (((~hskp11) | (~c3_1(a2093))) <=> ((~hskp11) | (~c3_1(a2093)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(311,plain,
% 0.54/0.75 (((~c3_1(a2093)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a2093)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(312,axiom,((~c3_1(a2093)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.54/0.75 tff(313,plain,
% 0.54/0.75 ((~hskp11) | (~c3_1(a2093))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.54/0.75 tff(314,plain,
% 0.54/0.75 ((~hskp11) | (~c3_1(a2093))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[313, 310])).
% 0.54/0.75 tff(315,plain,
% 0.54/0.75 (~c3_1(a2093)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[314, 309])).
% 0.54/0.75 tff(316,plain,
% 0.54/0.75 (((~hskp11) | (~c1_1(a2093))) <=> ((~hskp11) | (~c1_1(a2093)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(317,plain,
% 0.54/0.75 (((~c1_1(a2093)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a2093)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(318,axiom,((~c1_1(a2093)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.54/0.75 tff(319,plain,
% 0.54/0.75 ((~hskp11) | (~c1_1(a2093))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.54/0.75 tff(320,plain,
% 0.54/0.75 ((~hskp11) | (~c1_1(a2093))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[319, 316])).
% 0.54/0.75 tff(321,plain,
% 0.54/0.75 (~c1_1(a2093)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[320, 309])).
% 0.54/0.75 tff(322,plain,
% 0.54/0.75 (((~hskp11) | c0_1(a2093)) <=> ((~hskp11) | c0_1(a2093))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(323,axiom,((~hskp11) | c0_1(a2093)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.54/0.75 tff(324,plain,
% 0.54/0.75 ((~hskp11) | c0_1(a2093)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.54/0.75 tff(325,plain,
% 0.54/0.75 ((~hskp11) | c0_1(a2093)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[324, 322])).
% 0.54/0.75 tff(326,plain,
% 0.54/0.75 ((~hskp11) | c0_1(a2093)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[325, 322])).
% 0.54/0.75 tff(327,plain,
% 0.54/0.75 ((~hskp11) | c0_1(a2093)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.54/0.75 tff(328,plain,
% 0.54/0.75 ((~hskp11) | c0_1(a2093)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[327, 322])).
% 0.54/0.75 tff(329,plain,
% 0.54/0.75 (c0_1(a2093)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[328, 309])).
% 0.54/0.75 tff(330,assumption,(~hskp29), introduced(assumption)).
% 0.54/0.75 tff(331,plain,
% 0.54/0.75 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(332,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[331])).
% 0.54/0.75 tff(333,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(334,plain,
% 0.54/0.75 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_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)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(335,plain,
% 0.54/0.75 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[334])).
% 0.54/0.75 tff(336,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.54/0.75 tff(337,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.54/0.75 tff(338,plain,
% 0.54/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.54/0.75 tff(339,plain,(
% 0.54/0.75 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.54/0.76 inference(skolemize,[status(sab)],[338])).
% 0.54/0.76 tff(340,plain,
% 0.54/0.76 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[339, 332])).
% 0.54/0.76 tff(341,assumption,(~hskp5), introduced(assumption)).
% 0.54/0.76 tff(342,plain,
% 0.54/0.76 (hskp3),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[85, 341, 330])).
% 0.54/0.76 tff(343,plain,
% 0.54/0.76 (((~hskp3) | (~c3_1(a2072))) <=> ((~hskp3) | (~c3_1(a2072)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(344,plain,
% 0.54/0.76 (((~c3_1(a2072)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a2072)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(345,axiom,((~c3_1(a2072)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.54/0.76 tff(346,plain,
% 0.54/0.76 ((~hskp3) | (~c3_1(a2072))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.54/0.76 tff(347,plain,
% 0.54/0.76 ((~hskp3) | (~c3_1(a2072))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[346, 343])).
% 0.54/0.76 tff(348,plain,
% 0.54/0.76 (~c3_1(a2072)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[347, 342])).
% 0.54/0.76 tff(349,plain,
% 0.54/0.76 (((~hskp3) | (~c1_1(a2072))) <=> ((~hskp3) | (~c1_1(a2072)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(350,plain,
% 0.54/0.76 (((~c1_1(a2072)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a2072)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(351,axiom,((~c1_1(a2072)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.54/0.76 tff(352,plain,
% 0.54/0.76 ((~hskp3) | (~c1_1(a2072))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.54/0.76 tff(353,plain,
% 0.54/0.76 ((~hskp3) | (~c1_1(a2072))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[352, 349])).
% 0.54/0.76 tff(354,plain,
% 0.54/0.76 (~c1_1(a2072)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[353, 342])).
% 0.54/0.76 tff(355,plain,
% 0.54/0.76 (((~hskp3) | (~c0_1(a2072))) <=> ((~hskp3) | (~c0_1(a2072)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(356,plain,
% 0.54/0.76 (((~c0_1(a2072)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a2072)))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(357,axiom,((~c0_1(a2072)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.54/0.76 tff(358,plain,
% 0.54/0.76 ((~hskp3) | (~c0_1(a2072))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.54/0.76 tff(359,plain,
% 0.54/0.76 ((~hskp3) | (~c0_1(a2072))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[358, 355])).
% 0.54/0.76 tff(360,plain,
% 0.54/0.76 (~c0_1(a2072)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[359, 342])).
% 0.54/0.76 tff(361,assumption,(~c2_1(a2072)), introduced(assumption)).
% 0.54/0.76 tff(362,plain,
% 0.54/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(363,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[362])).
% 0.54/0.76 tff(364,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(365,plain,
% 0.54/0.76 (^[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))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(366,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[365])).
% 0.54/0.76 tff(367,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.54/0.76 tff(368,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.54/0.76 tff(369,plain,
% 0.54/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[368, 364])).
% 0.60/0.76 tff(370,plain,(
% 0.60/0.76 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.76 inference(skolemize,[status(sab)],[369])).
% 0.60/0.76 tff(371,plain,
% 0.60/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[370, 363])).
% 0.60/0.76 tff(372,assumption,(~c3_1(a2072)), introduced(assumption)).
% 0.60/0.76 tff(373,assumption,(~c1_1(a2072)), introduced(assumption)).
% 0.60/0.76 tff(374,assumption,(~c0_1(a2072)), introduced(assumption)).
% 0.60/0.76 tff(375,plain,
% 0.60/0.76 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(376,plain,
% 0.60/0.76 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[375])).
% 0.60/0.76 tff(377,plain,
% 0.60/0.76 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(378,plain,
% 0.60/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp4) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp4) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(379,plain,
% 0.60/0.76 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp4) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[378])).
% 0.60/0.76 tff(380,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.60/0.76 tff(381,plain,
% 0.60/0.76 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.60/0.76 tff(382,plain,
% 0.60/0.76 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[381, 377])).
% 0.60/0.76 tff(383,plain,(
% 0.60/0.76 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.60/0.76 inference(skolemize,[status(sab)],[382])).
% 0.60/0.76 tff(384,plain,
% 0.60/0.76 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[383, 376])).
% 0.60/0.76 tff(385,plain,
% 0.60/0.76 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(386,plain,
% 0.60/0.76 ((hskp5 | hskp4 | (~ndr1_0) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072)) <=> (hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(387,plain,
% 0.60/0.76 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072)))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[386])).
% 0.60/0.76 tff(388,plain,
% 0.60/0.76 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.60/0.76 inference(transitivity,[status(thm)],[387, 385])).
% 0.60/0.76 tff(389,plain,
% 0.60/0.76 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(390,plain,
% 0.60/0.76 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.60/0.76 tff(391,plain,
% 0.60/0.76 (hskp4 | c2_1(a2072)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[390, 87, 341, 374, 372, 384])).
% 0.60/0.76 tff(392,plain,
% 0.60/0.76 (hskp4),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[391, 361])).
% 0.60/0.76 tff(393,plain,
% 0.60/0.76 (~c2_1(a2074)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[243, 392])).
% 0.60/0.76 tff(394,plain,
% 0.60/0.76 (c1_1(a2074)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[259, 392])).
% 0.60/0.76 tff(395,plain,
% 0.60/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(396,plain,
% 0.60/0.76 (((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(397,plain,
% 0.60/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074)))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[396])).
% 0.60/0.76 tff(398,plain,
% 0.60/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.60/0.76 inference(transitivity,[status(thm)],[397, 395])).
% 0.60/0.76 tff(399,plain,
% 0.60/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(400,plain,
% 0.60/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.60/0.76 tff(401,plain,
% 0.60/0.76 (c0_1(a2074)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[400, 87, 394, 393, 374, 373, 372, 371, 361])).
% 0.60/0.76 tff(402,plain,
% 0.60/0.76 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(403,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[402])).
% 0.60/0.76 tff(404,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(405,plain,
% 0.60/0.76 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(406,plain,
% 0.60/0.76 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[405])).
% 0.60/0.76 tff(407,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.60/0.76 tff(408,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.60/0.76 tff(409,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[408, 404])).
% 0.60/0.76 tff(410,plain,(
% 0.60/0.76 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.76 inference(skolemize,[status(sab)],[409])).
% 0.60/0.76 tff(411,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[410, 403])).
% 0.60/0.76 tff(412,plain,
% 0.60/0.76 (c3_1(a2074)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[251, 392])).
% 0.60/0.76 tff(413,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(414,plain,
% 0.60/0.76 ((hskp5 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074))) <=> (hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(415,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[414])).
% 0.60/0.76 tff(416,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[415, 413])).
% 0.60/0.76 tff(417,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(418,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.60/0.76 tff(419,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[418, 87, 341, 394, 412, 393, 411, 401])).
% 0.60/0.76 tff(420,plain,(c2_1(a2072) | hskp5 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(421,plain,
% 0.60/0.76 (c2_1(a2072)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[420, 341, 360, 354, 348])).
% 0.60/0.76 tff(422,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(423,plain,
% 0.61/0.77 ((hskp4 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(424,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[423])).
% 0.61/0.77 tff(425,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.61/0.77 inference(transitivity,[status(thm)],[424, 422])).
% 0.61/0.77 tff(426,plain,
% 0.61/0.77 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(427,plain,
% 0.61/0.77 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.61/0.77 tff(428,plain,
% 0.61/0.77 (hskp4 | (~c2_1(a2072))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[427, 87, 360, 354, 348, 229])).
% 0.61/0.77 tff(429,plain,
% 0.61/0.77 (hskp4),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[428, 421])).
% 0.61/0.77 tff(430,plain,
% 0.61/0.77 (~c2_1(a2074)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[243, 429])).
% 0.61/0.77 tff(431,plain,
% 0.61/0.77 (c3_1(a2074)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[251, 429])).
% 0.61/0.77 tff(432,plain,
% 0.61/0.77 (c1_1(a2074)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[259, 429])).
% 0.61/0.77 tff(433,plain,
% 0.61/0.77 (((~![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) | c3_1(W) | (~c2_1(W)))) | (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(434,plain,
% 0.61/0.77 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072))) <=> (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(435,plain,
% 0.61/0.77 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[434])).
% 0.61/0.77 tff(436,plain,
% 0.61/0.77 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.61/0.77 inference(transitivity,[status(thm)],[435, 433])).
% 0.61/0.77 tff(437,plain,
% 0.61/0.77 ((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(438,plain,
% 0.61/0.77 ((~![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) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.61/0.77 tff(439,plain,
% 0.61/0.77 (~c0_1(a2074)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[438, 87, 432, 431, 430, 360, 348, 10, 421])).
% 0.61/0.77 tff(440,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(441,plain,
% 0.61/0.77 ((hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074))) <=> (hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(442,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074)))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[441])).
% 0.61/0.77 tff(443,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.61/0.77 inference(transitivity,[status(thm)],[442, 440])).
% 0.61/0.77 tff(444,plain,
% 0.61/0.77 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(445,plain,
% 0.61/0.77 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.61/0.77 tff(446,plain,
% 0.61/0.77 (hskp8),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[445, 87, 432, 430, 354, 348, 277, 421, 439])).
% 0.61/0.77 tff(447,plain,
% 0.61/0.77 (~c0_1(a2082)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[155, 446])).
% 0.61/0.77 tff(448,plain,
% 0.61/0.77 (c2_1(a2082)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[163, 446])).
% 0.61/0.77 tff(449,plain,
% 0.61/0.77 (c1_1(a2082)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[171, 446])).
% 0.61/0.77 tff(450,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(451,plain,
% 0.61/0.77 ((hskp11 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082))) <=> (hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(452,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[451])).
% 0.61/0.77 tff(453,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.61/0.77 inference(transitivity,[status(thm)],[452, 450])).
% 0.61/0.77 tff(454,plain,
% 0.61/0.77 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(455,plain,
% 0.61/0.77 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.61/0.77 tff(456,plain,
% 0.61/0.77 (hskp11),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[455, 87, 449, 448, 447, 354, 348, 21, 421])).
% 0.61/0.77 tff(457,plain,
% 0.61/0.77 (~c3_1(a2093)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[314, 456])).
% 0.61/0.77 tff(458,plain,
% 0.61/0.77 (~c1_1(a2093)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[320, 456])).
% 0.61/0.77 tff(459,plain,
% 0.61/0.77 (c0_1(a2093)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[328, 456])).
% 0.61/0.77 tff(460,plain,
% 0.61/0.77 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(461,plain,
% 0.61/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[460])).
% 0.61/0.77 tff(462,plain,
% 0.61/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(463,plain,
% 0.61/0.77 (^[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)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_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)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_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)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_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)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(464,plain,
% 0.61/0.77 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[463])).
% 0.61/0.77 tff(465,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.61/0.77 tff(466,plain,
% 0.61/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.61/0.77 tff(467,plain,
% 0.61/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[466, 462])).
% 0.61/0.77 tff(468,plain,(
% 0.61/0.77 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.61/0.77 inference(skolemize,[status(sab)],[467])).
% 0.61/0.77 tff(469,plain,
% 0.61/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[468, 461])).
% 0.61/0.77 tff(470,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(471,plain,
% 0.61/0.77 ((hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2072) | c0_1(a2072) | (~c2_1(a2072))) <=> (hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(472,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[471])).
% 0.61/0.77 tff(473,plain,
% 0.61/0.77 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.61/0.77 inference(transitivity,[status(thm)],[472, 470])).
% 0.61/0.77 tff(474,plain,
% 0.61/0.77 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(475,plain,
% 0.61/0.77 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.61/0.77 tff(476,plain,
% 0.61/0.77 (hskp1),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[475, 87, 449, 448, 447, 360, 348, 469, 421])).
% 0.61/0.77 tff(477,plain,
% 0.61/0.77 (^[U: $i] : refl((hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(478,plain,
% 0.61/0.77 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[477])).
% 0.61/0.77 tff(479,plain,
% 0.61/0.77 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(480,plain,
% 0.61/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp5) <=> ((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite(((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp5) <=> (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(481,plain,
% 0.61/0.77 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp5) <=> ![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[480])).
% 0.61/0.77 tff(482,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.61/0.77 tff(483,plain,
% 0.61/0.77 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.61/0.77 tff(484,plain,
% 0.61/0.77 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[483, 479])).
% 0.61/0.77 tff(485,plain,(
% 0.61/0.77 ![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.61/0.77 inference(skolemize,[status(sab)],[484])).
% 0.61/0.77 tff(486,plain,
% 0.61/0.77 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[485, 478])).
% 0.61/0.77 tff(487,assumption,(hskp1), introduced(assumption)).
% 0.61/0.77 tff(488,plain,
% 0.61/0.77 (((~hskp1) | c3_1(a2070)) <=> ((~hskp1) | c3_1(a2070))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(489,axiom,((~hskp1) | c3_1(a2070)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.61/0.77 tff(490,plain,
% 0.61/0.77 ((~hskp1) | c3_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.61/0.77 tff(491,plain,
% 0.61/0.77 ((~hskp1) | c3_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[490, 488])).
% 0.61/0.77 tff(492,plain,
% 0.61/0.77 ((~hskp1) | c3_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[491, 488])).
% 0.61/0.77 tff(493,plain,
% 0.61/0.77 ((~hskp1) | c3_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[492, 488])).
% 0.61/0.77 tff(494,plain,
% 0.61/0.77 ((~hskp1) | c3_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[493, 488])).
% 0.61/0.77 tff(495,plain,
% 0.61/0.77 (c3_1(a2070)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[494, 487])).
% 0.61/0.77 tff(496,plain,
% 0.61/0.77 (((~hskp1) | c0_1(a2070)) <=> ((~hskp1) | c0_1(a2070))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(497,axiom,((~hskp1) | c0_1(a2070)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.61/0.77 tff(498,plain,
% 0.61/0.77 ((~hskp1) | c0_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.61/0.77 tff(499,plain,
% 0.61/0.77 ((~hskp1) | c0_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[498, 496])).
% 0.61/0.77 tff(500,plain,
% 0.61/0.77 ((~hskp1) | c0_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[499, 496])).
% 0.61/0.77 tff(501,plain,
% 0.61/0.77 ((~hskp1) | c0_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[500, 496])).
% 0.61/0.77 tff(502,plain,
% 0.61/0.77 ((~hskp1) | c0_1(a2070)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[501, 496])).
% 0.61/0.77 tff(503,plain,
% 0.61/0.77 (c0_1(a2070)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[502, 487])).
% 0.61/0.77 tff(504,assumption,(~hskp26), introduced(assumption)).
% 0.61/0.77 tff(505,plain,
% 0.61/0.77 (((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(506,plain,
% 0.61/0.77 ((hskp26 | hskp5 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(507,plain,
% 0.61/0.77 (((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[506])).
% 0.61/0.77 tff(508,plain,
% 0.61/0.77 (((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.61/0.78 inference(transitivity,[status(thm)],[507, 505])).
% 0.61/0.78 tff(509,plain,
% 0.61/0.78 ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(510,plain,
% 0.61/0.78 ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.61/0.78 tff(511,plain,
% 0.61/0.78 (c1_1(a2070)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[510, 87, 504, 341, 503, 495, 486])).
% 0.61/0.78 tff(512,plain,
% 0.61/0.78 (((~hskp1) | (~c2_1(a2070))) <=> ((~hskp1) | (~c2_1(a2070)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(513,plain,
% 0.61/0.78 (((~c2_1(a2070)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2070)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(514,axiom,((~c2_1(a2070)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.61/0.78 tff(515,plain,
% 0.61/0.78 ((~hskp1) | (~c2_1(a2070))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.61/0.78 tff(516,plain,
% 0.61/0.78 ((~hskp1) | (~c2_1(a2070))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[515, 512])).
% 0.61/0.78 tff(517,plain,
% 0.61/0.78 (~c2_1(a2070)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[516, 487])).
% 0.61/0.78 tff(518,plain,
% 0.61/0.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(519,plain,
% 0.61/0.78 ((hskp5 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070))) <=> (hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(520,plain,
% 0.61/0.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[519])).
% 0.61/0.78 tff(521,plain,
% 0.61/0.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.61/0.78 inference(transitivity,[status(thm)],[520, 518])).
% 0.61/0.78 tff(522,plain,
% 0.61/0.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(523,plain,
% 0.61/0.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.61/0.78 tff(524,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[523, 87, 341, 503, 495, 517, 411, 511])).
% 0.61/0.78 tff(525,plain,((~hskp1) | hskp5 | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(526,plain,
% 0.61/0.78 (hskp26),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[525, 476, 341])).
% 0.61/0.78 tff(527,plain,
% 0.61/0.78 (((~hskp26) | c3_1(a2069)) <=> ((~hskp26) | c3_1(a2069))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(528,axiom,((~hskp26) | c3_1(a2069)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.61/0.78 tff(529,plain,
% 0.61/0.78 ((~hskp26) | c3_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.61/0.78 tff(530,plain,
% 0.61/0.78 ((~hskp26) | c3_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[529, 527])).
% 0.61/0.78 tff(531,plain,
% 0.61/0.78 ((~hskp26) | c3_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[530, 527])).
% 0.61/0.78 tff(532,plain,
% 0.61/0.78 ((~hskp26) | c3_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[531, 527])).
% 0.61/0.78 tff(533,plain,
% 0.61/0.78 ((~hskp26) | c3_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[532, 527])).
% 0.61/0.78 tff(534,plain,
% 0.61/0.78 (c3_1(a2069)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[533, 526])).
% 0.61/0.78 tff(535,plain,
% 0.61/0.78 (((~hskp26) | c2_1(a2069)) <=> ((~hskp26) | c2_1(a2069))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(536,axiom,((~hskp26) | c2_1(a2069)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.61/0.78 tff(537,plain,
% 0.61/0.78 ((~hskp26) | c2_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.61/0.78 tff(538,plain,
% 0.61/0.78 ((~hskp26) | c2_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[537, 535])).
% 0.61/0.78 tff(539,plain,
% 0.61/0.78 ((~hskp26) | c2_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[538, 535])).
% 0.61/0.78 tff(540,plain,
% 0.61/0.78 ((~hskp26) | c2_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[539, 535])).
% 0.61/0.78 tff(541,plain,
% 0.61/0.78 ((~hskp26) | c2_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[540, 535])).
% 0.61/0.78 tff(542,plain,
% 0.61/0.78 (c2_1(a2069)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[541, 526])).
% 0.61/0.78 tff(543,plain,
% 0.61/0.78 (((~hskp26) | c0_1(a2069)) <=> ((~hskp26) | c0_1(a2069))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(544,axiom,((~hskp26) | c0_1(a2069)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.61/0.78 tff(545,plain,
% 0.61/0.78 ((~hskp26) | c0_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.61/0.78 tff(546,plain,
% 0.61/0.78 ((~hskp26) | c0_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[545, 543])).
% 0.61/0.78 tff(547,plain,
% 0.61/0.78 ((~hskp26) | c0_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[546, 543])).
% 0.61/0.78 tff(548,plain,
% 0.61/0.78 ((~hskp26) | c0_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[547, 543])).
% 0.61/0.78 tff(549,plain,
% 0.61/0.78 ((~hskp26) | c0_1(a2069)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[548, 543])).
% 0.61/0.78 tff(550,plain,
% 0.61/0.78 (c0_1(a2069)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[549, 526])).
% 0.61/0.78 tff(551,plain,
% 0.61/0.78 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(552,plain,
% 0.61/0.78 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[551])).
% 0.61/0.78 tff(553,plain,
% 0.61/0.78 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(554,plain,
% 0.61/0.78 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | 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)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | 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))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_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)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | 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))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | 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)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(555,plain,
% 0.61/0.78 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[554])).
% 0.61/0.78 tff(556,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.61/0.78 tff(557,plain,
% 0.61/0.78 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.61/0.78 tff(558,plain,
% 0.61/0.78 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[557, 553])).
% 0.61/0.78 tff(559,plain,(
% 0.61/0.78 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.78 inference(skolemize,[status(sab)],[558])).
% 0.61/0.78 tff(560,plain,
% 0.61/0.78 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[559, 552])).
% 0.61/0.78 tff(561,plain,
% 0.61/0.78 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(562,plain,
% 0.61/0.78 ((hskp27 | (~ndr1_0) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(563,plain,
% 0.61/0.78 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[562])).
% 0.61/0.78 tff(564,plain,
% 0.61/0.78 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.61/0.78 inference(transitivity,[status(thm)],[563, 561])).
% 0.61/0.78 tff(565,plain,
% 0.61/0.78 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(566,plain,
% 0.61/0.78 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.61/0.78 tff(567,plain,
% 0.61/0.78 (hskp27 | (~c2_1(a2072))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[566, 87, 360, 354, 348, 560])).
% 0.61/0.78 tff(568,plain,
% 0.61/0.78 (hskp27),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[567, 421])).
% 0.61/0.78 tff(569,plain,
% 0.61/0.78 (((~hskp27) | c3_1(a2073)) <=> ((~hskp27) | c3_1(a2073))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(570,axiom,((~hskp27) | c3_1(a2073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.61/0.78 tff(571,plain,
% 0.61/0.78 ((~hskp27) | c3_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.61/0.78 tff(572,plain,
% 0.61/0.78 ((~hskp27) | c3_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[571, 569])).
% 0.61/0.78 tff(573,plain,
% 0.61/0.78 ((~hskp27) | c3_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[572, 569])).
% 0.61/0.78 tff(574,plain,
% 0.61/0.78 ((~hskp27) | c3_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[573, 569])).
% 0.61/0.78 tff(575,plain,
% 0.61/0.78 ((~hskp27) | c3_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[574, 569])).
% 0.61/0.78 tff(576,plain,
% 0.61/0.78 (c3_1(a2073)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[575, 568])).
% 0.61/0.78 tff(577,plain,
% 0.61/0.78 (((~hskp27) | c1_1(a2073)) <=> ((~hskp27) | c1_1(a2073))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(578,axiom,((~hskp27) | c1_1(a2073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.61/0.78 tff(579,plain,
% 0.61/0.78 ((~hskp27) | c1_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.61/0.78 tff(580,plain,
% 0.61/0.78 ((~hskp27) | c1_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[579, 577])).
% 0.61/0.78 tff(581,plain,
% 0.61/0.78 ((~hskp27) | c1_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[580, 577])).
% 0.61/0.78 tff(582,plain,
% 0.61/0.78 ((~hskp27) | c1_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[581, 577])).
% 0.61/0.78 tff(583,plain,
% 0.61/0.78 ((~hskp27) | c1_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[582, 577])).
% 0.61/0.78 tff(584,plain,
% 0.61/0.78 (c1_1(a2073)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[583, 568])).
% 0.61/0.78 tff(585,plain,
% 0.61/0.78 (((~hskp27) | c0_1(a2073)) <=> ((~hskp27) | c0_1(a2073))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(586,axiom,((~hskp27) | c0_1(a2073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.61/0.78 tff(587,plain,
% 0.61/0.78 ((~hskp27) | c0_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.61/0.78 tff(588,plain,
% 0.61/0.78 ((~hskp27) | c0_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[587, 585])).
% 0.61/0.78 tff(589,plain,
% 0.61/0.78 ((~hskp27) | c0_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[588, 585])).
% 0.61/0.78 tff(590,plain,
% 0.61/0.78 ((~hskp27) | c0_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[589, 585])).
% 0.61/0.78 tff(591,plain,
% 0.61/0.78 ((~hskp27) | c0_1(a2073)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[590, 585])).
% 0.61/0.78 tff(592,plain,
% 0.61/0.78 (c0_1(a2073)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[591, 568])).
% 0.61/0.78 tff(593,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(594,plain,
% 0.61/0.78 (((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093))) <=> (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(595,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[594])).
% 0.61/0.78 tff(596,plain,
% 0.61/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.61/0.78 inference(transitivity,[status(thm)],[595, 593])).
% 0.61/0.78 tff(597,plain,
% 0.61/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(598,plain,
% 0.61/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.61/0.78 tff(599,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[598, 87, 592, 584, 576, 550, 542, 534, 459, 458, 457, 308])).
% 0.61/0.78 tff(600,plain,(hskp5 | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(601,plain,
% 0.61/0.78 (hskp5),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[600, 330])).
% 0.61/0.78 tff(602,plain,
% 0.61/0.78 (((~hskp5) | c3_1(a2076)) <=> ((~hskp5) | c3_1(a2076))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(603,axiom,((~hskp5) | c3_1(a2076)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.61/0.78 tff(604,plain,
% 0.61/0.78 ((~hskp5) | c3_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.61/0.78 tff(605,plain,
% 0.61/0.78 ((~hskp5) | c3_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[604, 602])).
% 0.61/0.78 tff(606,plain,
% 0.61/0.78 ((~hskp5) | c3_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[605, 602])).
% 0.61/0.78 tff(607,plain,
% 0.61/0.78 ((~hskp5) | c3_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[606, 602])).
% 0.61/0.78 tff(608,plain,
% 0.61/0.78 ((~hskp5) | c3_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[607, 602])).
% 0.61/0.78 tff(609,plain,
% 0.61/0.78 (c3_1(a2076)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[608, 601])).
% 0.61/0.78 tff(610,plain,
% 0.61/0.78 (((~hskp5) | (~c0_1(a2076))) <=> ((~hskp5) | (~c0_1(a2076)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(611,plain,
% 0.61/0.78 (((~c0_1(a2076)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a2076)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(612,axiom,((~c0_1(a2076)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.61/0.78 tff(613,plain,
% 0.61/0.78 ((~hskp5) | (~c0_1(a2076))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.61/0.78 tff(614,plain,
% 0.61/0.78 ((~hskp5) | (~c0_1(a2076))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[613, 610])).
% 0.61/0.78 tff(615,plain,
% 0.61/0.78 (~c0_1(a2076)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[614, 601])).
% 0.61/0.78 tff(616,plain,
% 0.61/0.78 (((~hskp5) | c1_1(a2076)) <=> ((~hskp5) | c1_1(a2076))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(617,axiom,((~hskp5) | c1_1(a2076)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.61/0.78 tff(618,plain,
% 0.61/0.78 ((~hskp5) | c1_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.61/0.78 tff(619,plain,
% 0.61/0.78 ((~hskp5) | c1_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[618, 616])).
% 0.61/0.78 tff(620,plain,
% 0.61/0.78 ((~hskp5) | c1_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[619, 616])).
% 0.61/0.78 tff(621,plain,
% 0.61/0.78 ((~hskp5) | c1_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[620, 616])).
% 0.61/0.78 tff(622,plain,
% 0.61/0.78 ((~hskp5) | c1_1(a2076)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[621, 616])).
% 0.61/0.78 tff(623,plain,
% 0.61/0.78 (c1_1(a2076)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[622, 601])).
% 0.61/0.78 tff(624,assumption,(~hskp3), introduced(assumption)).
% 0.61/0.78 tff(625,plain,
% 0.61/0.78 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(626,plain,
% 0.61/0.78 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[625])).
% 0.61/0.78 tff(627,plain,
% 0.61/0.78 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(628,plain,
% 0.61/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(629,plain,
% 0.61/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[628])).
% 0.61/0.79 tff(630,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.61/0.79 tff(631,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.61/0.79 tff(632,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[631, 627])).
% 0.61/0.79 tff(633,plain,(
% 0.61/0.79 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[632])).
% 0.61/0.79 tff(634,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[633, 626])).
% 0.61/0.79 tff(635,plain,
% 0.61/0.79 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(636,plain,
% 0.61/0.79 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[635])).
% 0.61/0.79 tff(637,plain,
% 0.61/0.79 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(638,plain,
% 0.61/0.79 (^[U: $i] : 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)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(639,plain,
% 0.61/0.79 (![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[638])).
% 0.61/0.79 tff(640,axiom,(![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.61/0.79 tff(641,plain,
% 0.61/0.79 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.61/0.79 tff(642,plain,
% 0.61/0.79 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[641, 637])).
% 0.61/0.79 tff(643,plain,(
% 0.61/0.79 ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[642])).
% 0.61/0.79 tff(644,plain,
% 0.61/0.79 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[643, 636])).
% 0.61/0.79 tff(645,assumption,(~c0_1(a2076)), introduced(assumption)).
% 0.61/0.79 tff(646,assumption,(c3_1(a2076)), introduced(assumption)).
% 0.61/0.79 tff(647,assumption,(c1_1(a2076)), introduced(assumption)).
% 0.61/0.79 tff(648,plain,
% 0.61/0.79 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(649,plain,
% 0.61/0.79 ((hskp0 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076))) <=> (hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(650,plain,
% 0.61/0.79 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[649])).
% 0.61/0.79 tff(651,plain,
% 0.61/0.79 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[650, 648])).
% 0.61/0.79 tff(652,plain,
% 0.61/0.79 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(653,plain,
% 0.61/0.79 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.61/0.79 tff(654,plain,
% 0.61/0.79 (hskp0),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[653, 87, 647, 646, 645, 644])).
% 0.61/0.79 tff(655,plain,
% 0.61/0.79 (((~hskp0) | (~c2_1(a2068))) <=> ((~hskp0) | (~c2_1(a2068)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(656,plain,
% 0.61/0.79 (((~c2_1(a2068)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a2068)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(657,axiom,((~c2_1(a2068)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.61/0.79 tff(658,plain,
% 0.61/0.79 ((~hskp0) | (~c2_1(a2068))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.61/0.79 tff(659,plain,
% 0.61/0.79 ((~hskp0) | (~c2_1(a2068))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[658, 655])).
% 0.61/0.79 tff(660,plain,
% 0.61/0.79 (~c2_1(a2068)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[659, 654])).
% 0.61/0.79 tff(661,plain,
% 0.61/0.79 (((~hskp0) | (~c0_1(a2068))) <=> ((~hskp0) | (~c0_1(a2068)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(662,plain,
% 0.61/0.79 (((~c0_1(a2068)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2068)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(663,axiom,((~c0_1(a2068)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.61/0.79 tff(664,plain,
% 0.61/0.79 ((~hskp0) | (~c0_1(a2068))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.61/0.79 tff(665,plain,
% 0.61/0.79 ((~hskp0) | (~c0_1(a2068))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[664, 661])).
% 0.61/0.79 tff(666,plain,
% 0.61/0.79 (~c0_1(a2068)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[665, 654])).
% 0.61/0.79 tff(667,plain,
% 0.61/0.79 (((~hskp0) | c3_1(a2068)) <=> ((~hskp0) | c3_1(a2068))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(668,axiom,((~hskp0) | c3_1(a2068)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.61/0.79 tff(669,plain,
% 0.61/0.79 ((~hskp0) | c3_1(a2068)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.61/0.79 tff(670,plain,
% 0.61/0.79 ((~hskp0) | c3_1(a2068)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[669, 667])).
% 0.61/0.79 tff(671,plain,
% 0.61/0.79 ((~hskp0) | c3_1(a2068)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[670, 667])).
% 0.61/0.79 tff(672,plain,
% 0.61/0.79 ((~hskp0) | c3_1(a2068)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[671, 667])).
% 0.61/0.79 tff(673,plain,
% 0.61/0.79 ((~hskp0) | c3_1(a2068)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[672, 667])).
% 0.61/0.79 tff(674,plain,
% 0.61/0.79 (c3_1(a2068)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[673, 654])).
% 0.61/0.79 tff(675,assumption,(~hskp4), introduced(assumption)).
% 0.61/0.79 tff(676,plain,
% 0.61/0.79 (^[U: $i] : refl((hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(677,plain,
% 0.61/0.79 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[676])).
% 0.61/0.79 tff(678,plain,
% 0.61/0.79 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(679,plain,
% 0.61/0.79 (^[U: $i] : 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)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) | hskp4) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(680,plain,
% 0.61/0.79 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) | hskp4) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[679])).
% 0.61/0.79 tff(681,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.61/0.79 tff(682,plain,
% 0.61/0.79 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.61/0.79 tff(683,plain,
% 0.61/0.79 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[682, 678])).
% 0.61/0.79 tff(684,plain,(
% 0.61/0.79 ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[683])).
% 0.61/0.79 tff(685,plain,
% 0.61/0.79 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[684, 677])).
% 0.61/0.79 tff(686,plain,
% 0.61/0.79 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(687,plain,
% 0.61/0.79 ((hskp28 | hskp4 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076))) <=> (hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(688,plain,
% 0.61/0.79 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[687])).
% 0.61/0.79 tff(689,plain,
% 0.61/0.79 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[688, 686])).
% 0.61/0.79 tff(690,plain,
% 0.61/0.79 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(691,plain,
% 0.61/0.79 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.61/0.79 tff(692,plain,
% 0.61/0.79 (hskp28 | hskp4),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[691, 87, 647, 646, 645, 685])).
% 0.61/0.79 tff(693,plain,
% 0.61/0.79 (hskp28),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[692, 675])).
% 0.61/0.79 tff(694,plain,
% 0.61/0.79 (((~hskp28) | c2_1(a2075)) <=> ((~hskp28) | c2_1(a2075))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(695,axiom,((~hskp28) | c2_1(a2075)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.61/0.79 tff(696,plain,
% 0.61/0.79 ((~hskp28) | c2_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.61/0.79 tff(697,plain,
% 0.61/0.79 ((~hskp28) | c2_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[696, 694])).
% 0.61/0.79 tff(698,plain,
% 0.61/0.79 ((~hskp28) | c2_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[697, 694])).
% 0.61/0.79 tff(699,plain,
% 0.61/0.79 ((~hskp28) | c2_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[698, 694])).
% 0.61/0.79 tff(700,plain,
% 0.61/0.79 ((~hskp28) | c2_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[699, 694])).
% 0.61/0.79 tff(701,plain,
% 0.61/0.79 (c2_1(a2075)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[700, 693])).
% 0.61/0.79 tff(702,plain,
% 0.61/0.79 (((~hskp28) | c1_1(a2075)) <=> ((~hskp28) | c1_1(a2075))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(703,axiom,((~hskp28) | c1_1(a2075)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.61/0.79 tff(704,plain,
% 0.61/0.79 ((~hskp28) | c1_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.61/0.79 tff(705,plain,
% 0.61/0.79 ((~hskp28) | c1_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[704, 702])).
% 0.61/0.79 tff(706,plain,
% 0.61/0.79 ((~hskp28) | c1_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[705, 702])).
% 0.61/0.79 tff(707,plain,
% 0.61/0.79 ((~hskp28) | c1_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[706, 702])).
% 0.61/0.79 tff(708,plain,
% 0.61/0.79 ((~hskp28) | c1_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[707, 702])).
% 0.61/0.79 tff(709,plain,
% 0.61/0.79 (c1_1(a2075)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[708, 693])).
% 0.61/0.79 tff(710,plain,
% 0.61/0.79 (((~hskp28) | c0_1(a2075)) <=> ((~hskp28) | c0_1(a2075))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(711,axiom,((~hskp28) | c0_1(a2075)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.61/0.79 tff(712,plain,
% 0.61/0.79 ((~hskp28) | c0_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.61/0.79 tff(713,plain,
% 0.61/0.79 ((~hskp28) | c0_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[712, 710])).
% 0.61/0.79 tff(714,plain,
% 0.61/0.79 ((~hskp28) | c0_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[713, 710])).
% 0.61/0.79 tff(715,plain,
% 0.61/0.79 ((~hskp28) | c0_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[714, 710])).
% 0.61/0.79 tff(716,plain,
% 0.61/0.79 ((~hskp28) | c0_1(a2075)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[715, 710])).
% 0.61/0.79 tff(717,plain,
% 0.61/0.79 (c0_1(a2075)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[716, 693])).
% 0.61/0.79 tff(718,plain,
% 0.61/0.79 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(719,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[718])).
% 0.61/0.79 tff(720,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(721,plain,
% 0.61/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(722,plain,
% 0.61/0.79 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[721])).
% 0.61/0.79 tff(723,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.61/0.79 tff(724,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[723, 722])).
% 0.61/0.79 tff(725,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[724, 720])).
% 0.61/0.79 tff(726,plain,(
% 0.61/0.79 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[725])).
% 0.61/0.79 tff(727,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[726, 719])).
% 0.61/0.79 tff(728,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(729,plain,
% 0.61/0.79 ((hskp4 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068))) <=> (hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(730,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068)))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[729])).
% 0.61/0.79 tff(731,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.61/0.79 inference(transitivity,[status(thm)],[730, 728])).
% 0.61/0.79 tff(732,plain,
% 0.61/0.79 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(733,plain,
% 0.61/0.79 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.61/0.79 tff(734,plain,
% 0.61/0.79 (hskp4 | c1_1(a2068)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[733, 87, 674, 666, 660, 727])).
% 0.61/0.79 tff(735,plain,
% 0.61/0.79 (c1_1(a2068)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[734, 675])).
% 0.61/0.79 tff(736,assumption,(c1_1(a2068)), introduced(assumption)).
% 0.61/0.79 tff(737,assumption,(~c2_1(a2068)), introduced(assumption)).
% 0.61/0.79 tff(738,assumption,(c3_1(a2068)), introduced(assumption)).
% 0.61/0.79 tff(739,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(740,plain,
% 0.61/0.79 ((hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093))) <=> (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(741,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[740])).
% 0.61/0.79 tff(742,plain,
% 0.61/0.79 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[741, 739])).
% 0.61/0.79 tff(743,plain,
% 0.61/0.79 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(744,plain,
% 0.61/0.79 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.61/0.79 tff(745,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[744, 87, 624, 329, 738, 321, 315, 737, 340, 736])).
% 0.61/0.79 tff(746,plain,((~hskp11) | hskp3 | (~c3_1(a2068)) | c2_1(a2068) | (~c1_1(a2068))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(747,plain,
% 0.61/0.79 (~hskp11),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[746, 735, 674, 660, 624])).
% 0.61/0.79 tff(748,plain,
% 0.61/0.79 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(749,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[748])).
% 0.61/0.79 tff(750,plain,
% 0.61/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(751,plain,
% 0.61/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(752,plain,
% 0.61/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[751])).
% 0.61/0.80 tff(753,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.61/0.80 tff(754,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.61/0.80 tff(755,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[754, 750])).
% 0.61/0.80 tff(756,plain,(
% 0.61/0.80 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[755])).
% 0.61/0.80 tff(757,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[756, 749])).
% 0.61/0.80 tff(758,plain,
% 0.61/0.80 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(759,plain,
% 0.61/0.80 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[758])).
% 0.61/0.80 tff(760,plain,
% 0.61/0.80 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(761,plain,
% 0.61/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) | hskp4) <=> ((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) | hskp4) <=> (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(762,plain,
% 0.61/0.80 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) | hskp4) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[761])).
% 0.61/0.80 tff(763,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.61/0.80 tff(764,plain,
% 0.61/0.80 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.61/0.80 tff(765,plain,
% 0.61/0.80 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[764, 760])).
% 0.61/0.80 tff(766,plain,(
% 0.61/0.80 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[765])).
% 0.61/0.80 tff(767,plain,
% 0.61/0.80 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[766, 759])).
% 0.61/0.80 tff(768,plain,
% 0.61/0.80 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(769,plain,
% 0.61/0.80 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(770,plain,
% 0.61/0.80 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.61/0.80 tff(771,plain,
% 0.61/0.80 (hskp7),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[770, 87, 675, 717, 709, 701, 767])).
% 0.61/0.80 tff(772,plain,
% 0.61/0.80 (((~hskp7) | (~c3_1(a2079))) <=> ((~hskp7) | (~c3_1(a2079)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(773,plain,
% 0.61/0.80 (((~c3_1(a2079)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a2079)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(774,axiom,((~c3_1(a2079)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.61/0.80 tff(775,plain,
% 0.61/0.80 ((~hskp7) | (~c3_1(a2079))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[774, 773])).
% 0.61/0.80 tff(776,plain,
% 0.61/0.80 ((~hskp7) | (~c3_1(a2079))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[775, 772])).
% 0.61/0.80 tff(777,plain,
% 0.61/0.80 (~c3_1(a2079)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[776, 771])).
% 0.61/0.80 tff(778,plain,
% 0.61/0.80 (((~hskp7) | c0_1(a2079)) <=> ((~hskp7) | c0_1(a2079))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(779,axiom,((~hskp7) | c0_1(a2079)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.61/0.80 tff(780,plain,
% 0.61/0.80 ((~hskp7) | c0_1(a2079)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.61/0.80 tff(781,plain,
% 0.61/0.80 ((~hskp7) | c0_1(a2079)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[780, 778])).
% 0.61/0.80 tff(782,plain,
% 0.61/0.80 ((~hskp7) | c0_1(a2079)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[781, 778])).
% 0.61/0.80 tff(783,plain,
% 0.61/0.80 ((~hskp7) | c0_1(a2079)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[782, 778])).
% 0.61/0.80 tff(784,plain,
% 0.61/0.80 ((~hskp7) | c0_1(a2079)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[783, 778])).
% 0.61/0.80 tff(785,plain,
% 0.61/0.80 (c0_1(a2079)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[784, 771])).
% 0.61/0.80 tff(786,plain,
% 0.61/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(787,plain,
% 0.61/0.80 ((hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2079) | c2_1(a2079) | (~c0_1(a2079))) <=> (hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(788,plain,
% 0.61/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2079) | c2_1(a2079) | (~c0_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[787])).
% 0.61/0.80 tff(789,plain,
% 0.61/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2079) | c2_1(a2079) | (~c0_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079)))),
% 0.61/0.80 inference(transitivity,[status(thm)],[788, 786])).
% 0.61/0.80 tff(790,plain,
% 0.61/0.80 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2079) | c2_1(a2079) | (~c0_1(a2079)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(791,plain,
% 0.61/0.80 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.61/0.80 tff(792,plain,
% 0.61/0.80 (hskp11 | c2_1(a2079)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[791, 87, 717, 709, 701, 785, 777, 757])).
% 0.61/0.80 tff(793,plain,
% 0.61/0.80 (c2_1(a2079)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[792, 747])).
% 0.61/0.80 tff(794,assumption,(c2_1(a2079)), introduced(assumption)).
% 0.61/0.80 tff(795,plain,
% 0.61/0.80 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(796,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[795])).
% 0.61/0.80 tff(797,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(798,plain,
% 0.61/0.80 (^[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) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(799,plain,
% 0.61/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[798])).
% 0.61/0.80 tff(800,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.61/0.80 tff(801,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.61/0.80 tff(802,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[801, 797])).
% 0.61/0.80 tff(803,plain,(
% 0.61/0.80 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[802])).
% 0.61/0.80 tff(804,plain,
% 0.61/0.80 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[803, 796])).
% 0.61/0.80 tff(805,assumption,(~c3_1(a2079)), introduced(assumption)).
% 0.65/0.80 tff(806,assumption,(c0_1(a2079)), introduced(assumption)).
% 0.65/0.80 tff(807,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(808,plain,
% 0.65/0.80 ((hskp4 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c0_1(a2079)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(809,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c0_1(a2079)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[808])).
% 0.65/0.80 tff(810,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c0_1(a2079)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[809, 807])).
% 0.65/0.80 tff(811,plain,
% 0.65/0.80 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c0_1(a2079)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(812,plain,
% 0.65/0.80 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.65/0.80 tff(813,plain,
% 0.65/0.80 ($false),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[812, 87, 675, 806, 503, 495, 805, 517, 804, 794])).
% 0.65/0.80 tff(814,plain,((~hskp1) | hskp4 | (~c0_1(a2079)) | c3_1(a2079) | (~c2_1(a2079))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.80 tff(815,plain,
% 0.65/0.80 (~hskp1),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[814, 675, 785, 777, 793])).
% 0.65/0.80 tff(816,assumption,(c2_1(a2075)), introduced(assumption)).
% 0.65/0.80 tff(817,assumption,(c1_1(a2075)), introduced(assumption)).
% 0.65/0.80 tff(818,assumption,(c0_1(a2075)), introduced(assumption)).
% 0.65/0.80 tff(819,plain,
% 0.65/0.80 (~hskp11),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[746, 736, 674, 660, 624])).
% 0.65/0.80 tff(820,assumption,(~c0_1(a2068)), introduced(assumption)).
% 0.65/0.80 tff(821,assumption,(hskp20), introduced(assumption)).
% 0.65/0.80 tff(822,plain,
% 0.65/0.80 (((~hskp20) | (~c3_1(a2130))) <=> ((~hskp20) | (~c3_1(a2130)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(823,plain,
% 0.65/0.80 (((~c3_1(a2130)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a2130)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(824,axiom,((~c3_1(a2130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.65/0.80 tff(825,plain,
% 0.65/0.80 ((~hskp20) | (~c3_1(a2130))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.65/0.80 tff(826,plain,
% 0.65/0.80 ((~hskp20) | (~c3_1(a2130))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[825, 822])).
% 0.65/0.80 tff(827,plain,
% 0.65/0.80 (~c3_1(a2130)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[826, 821])).
% 0.65/0.80 tff(828,plain,
% 0.65/0.80 (((~hskp20) | (~c2_1(a2130))) <=> ((~hskp20) | (~c2_1(a2130)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(829,plain,
% 0.65/0.80 (((~c2_1(a2130)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a2130)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(830,axiom,((~c2_1(a2130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.65/0.80 tff(831,plain,
% 0.65/0.80 ((~hskp20) | (~c2_1(a2130))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[830, 829])).
% 0.65/0.80 tff(832,plain,
% 0.65/0.80 ((~hskp20) | (~c2_1(a2130))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[831, 828])).
% 0.65/0.80 tff(833,plain,
% 0.65/0.80 (~c2_1(a2130)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[832, 821])).
% 0.65/0.80 tff(834,plain,
% 0.65/0.80 (((~hskp20) | (~c1_1(a2130))) <=> ((~hskp20) | (~c1_1(a2130)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(835,plain,
% 0.65/0.80 (((~c1_1(a2130)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a2130)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(836,axiom,((~c1_1(a2130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.65/0.80 tff(837,plain,
% 0.65/0.80 ((~hskp20) | (~c1_1(a2130))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.65/0.80 tff(838,plain,
% 0.65/0.80 ((~hskp20) | (~c1_1(a2130))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[837, 834])).
% 0.65/0.80 tff(839,plain,
% 0.65/0.80 (~c1_1(a2130)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[838, 821])).
% 0.65/0.80 tff(840,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(841,plain,
% 0.65/0.80 (((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2130) | c1_1(a2130) | c2_1(a2130) | c2_1(a2130) | c1_1(a2130) | c0_1(a2130)) <=> (c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(842,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2130) | c1_1(a2130) | c2_1(a2130) | c2_1(a2130) | c1_1(a2130) | c0_1(a2130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130)))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[841])).
% 0.65/0.80 tff(843,plain,
% 0.65/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2130) | c1_1(a2130) | c2_1(a2130) | c2_1(a2130) | c1_1(a2130) | c0_1(a2130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130))),
% 0.65/0.80 inference(transitivity,[status(thm)],[842, 840])).
% 0.65/0.80 tff(844,plain,
% 0.65/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2130) | c1_1(a2130) | c2_1(a2130) | c2_1(a2130) | c1_1(a2130) | c0_1(a2130))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(845,plain,
% 0.65/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.65/0.80 tff(846,plain,
% 0.65/0.80 (c0_1(a2130)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[845, 87, 839, 833, 827, 820, 737, 371, 736])).
% 0.65/0.80 tff(847,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(848,plain,
% 0.65/0.80 ((hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2130) | c2_1(a2130) | (~c0_1(a2130))) <=> (hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(849,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2130) | c2_1(a2130) | (~c0_1(a2130)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[848])).
% 0.65/0.80 tff(850,plain,
% 0.65/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2130) | c2_1(a2130) | (~c0_1(a2130)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130)))),
% 0.65/0.80 inference(transitivity,[status(thm)],[849, 847])).
% 0.65/0.80 tff(851,plain,
% 0.65/0.80 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2130) | c2_1(a2130) | (~c0_1(a2130)))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(852,plain,
% 0.65/0.80 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[851, 850])).
% 0.65/0.80 tff(853,plain,
% 0.65/0.80 ($false),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[852, 87, 22, 818, 817, 816, 833, 827, 757, 846])).
% 0.65/0.80 tff(854,plain,((~hskp20) | hskp11 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.80 tff(855,plain,
% 0.65/0.80 (~hskp20),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[854, 819, 818, 817, 816, 666, 660, 736])).
% 0.65/0.80 tff(856,plain,
% 0.65/0.80 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(857,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[856])).
% 0.65/0.81 tff(858,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(859,plain,
% 0.65/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(860,plain,
% 0.65/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[859])).
% 0.65/0.81 tff(861,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.65/0.81 tff(862,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.65/0.81 tff(863,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[862, 858])).
% 0.65/0.81 tff(864,plain,(
% 0.65/0.81 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[863])).
% 0.65/0.81 tff(865,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[864, 857])).
% 0.65/0.81 tff(866,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(867,plain,
% 0.65/0.81 ((hskp26 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c0_1(a2076) | (~c3_1(a2076)) | (~c2_1(a2076))) <=> (hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(868,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c0_1(a2076) | (~c3_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[867])).
% 0.65/0.81 tff(869,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c0_1(a2076) | (~c3_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[868, 866])).
% 0.65/0.81 tff(870,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c0_1(a2076) | (~c3_1(a2076)) | (~c2_1(a2076)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(871,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.65/0.81 tff(872,plain,
% 0.65/0.81 (hskp26 | (~c2_1(a2076))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[871, 87, 818, 817, 816, 646, 645, 865])).
% 0.65/0.81 tff(873,plain,
% 0.65/0.81 (~c2_1(a2076)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[872, 504])).
% 0.65/0.81 tff(874,plain,
% 0.65/0.81 (~hskp11),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[746, 736, 738, 737, 624])).
% 0.65/0.81 tff(875,assumption,(~hskp20), introduced(assumption)).
% 0.65/0.81 tff(876,assumption,(~c2_1(a2076)), introduced(assumption)).
% 0.65/0.81 tff(877,assumption,(c3_1(a2087)), introduced(assumption)).
% 0.65/0.81 tff(878,plain,
% 0.65/0.81 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(879,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[878])).
% 0.65/0.81 tff(880,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(881,plain,
% 0.65/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(882,plain,
% 0.65/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[881])).
% 0.65/0.81 tff(883,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.65/0.81 tff(884,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.65/0.81 tff(885,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[884, 880])).
% 0.65/0.81 tff(886,plain,(
% 0.65/0.81 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(skolemize,[status(sab)],[885])).
% 0.65/0.81 tff(887,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[886, 879])).
% 0.65/0.81 tff(888,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(889,plain,
% 0.65/0.81 ((hskp20 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087))) <=> (hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(890,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[889])).
% 0.65/0.81 tff(891,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[890, 888])).
% 0.65/0.81 tff(892,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(893,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.65/0.81 tff(894,plain,
% 0.65/0.81 ((~c3_1(a2087)) | (~c2_1(a2087))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[893, 87, 875, 818, 817, 816, 211, 887])).
% 0.65/0.81 tff(895,plain,
% 0.65/0.81 (~c2_1(a2087)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[894, 877])).
% 0.65/0.81 tff(896,plain,
% 0.65/0.81 (~hskp10),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[194, 877])).
% 0.65/0.81 tff(897,plain,
% 0.65/0.81 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(898,plain,
% 0.65/0.81 ((hskp11 | hskp10 | (~ndr1_0) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087))) <=> (hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(899,plain,
% 0.65/0.81 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[898])).
% 0.65/0.81 tff(900,plain,
% 0.65/0.81 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[899, 897])).
% 0.65/0.81 tff(901,plain,
% 0.65/0.81 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(902,plain,
% 0.65/0.81 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.65/0.81 tff(903,plain,
% 0.65/0.81 (hskp10 | (~c3_1(a2087)) | (~c0_1(a2087))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[902, 87, 22, 211, 32])).
% 0.65/0.81 tff(904,plain,
% 0.65/0.81 (~c0_1(a2087)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[903, 896, 877])).
% 0.65/0.81 tff(905,plain,
% 0.65/0.81 (^[U: $i] : refl((hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(906,plain,
% 0.65/0.81 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[905])).
% 0.65/0.81 tff(907,plain,
% 0.65/0.81 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(908,plain,
% 0.65/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | 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))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | 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))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp1) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp1) <=> (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(909,plain,
% 0.65/0.81 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp1) <=> ![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[908])).
% 0.65/0.81 tff(910,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.65/0.81 tff(911,plain,
% 0.65/0.81 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.65/0.81 tff(912,plain,
% 0.65/0.81 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[911, 907])).
% 0.65/0.81 tff(913,plain,(
% 0.65/0.81 ![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.65/0.81 inference(skolemize,[status(sab)],[912])).
% 0.65/0.81 tff(914,plain,
% 0.65/0.81 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[913, 906])).
% 0.65/0.81 tff(915,plain,
% 0.65/0.81 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(916,plain,
% 0.65/0.81 ((hskp26 | hskp1 | (~ndr1_0) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087)) <=> (hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(917,plain,
% 0.65/0.81 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[916])).
% 0.65/0.81 tff(918,plain,
% 0.65/0.81 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087))),
% 0.65/0.81 inference(transitivity,[status(thm)],[917, 915])).
% 0.65/0.81 tff(919,plain,
% 0.65/0.81 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(920,plain,
% 0.65/0.81 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.65/0.81 tff(921,plain,
% 0.65/0.81 (c2_1(a2087) | c0_1(a2087)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[920, 87, 504, 11, 211, 914])).
% 0.65/0.81 tff(922,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[921, 904, 895])).
% 0.65/0.81 tff(923,plain,((~c3_1(a2087)) | hskp26 | hskp1 | c1_1(a2087) | hskp11 | hskp20 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(924,plain,
% 0.65/0.81 (~c3_1(a2087)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[923, 211, 11, 504, 874, 875, 818, 817, 816])).
% 0.65/0.81 tff(925,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(926,plain,
% 0.65/0.81 ((hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087))) <=> (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(927,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[926])).
% 0.65/0.81 tff(928,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[927, 925])).
% 0.65/0.81 tff(929,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(930,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.65/0.81 tff(931,plain,
% 0.65/0.81 (~c0_1(a2087)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[930, 87, 624, 738, 211, 924, 737, 340, 736])).
% 0.65/0.81 tff(932,plain,
% 0.65/0.81 (hskp8 | c3_1(a2087) | (~c0_1(a2087))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[217, 87, 11, 211, 140])).
% 0.65/0.81 tff(933,plain,
% 0.65/0.81 (~c0_1(a2087)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[932, 210, 141])).
% 0.65/0.81 tff(934,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(935,plain,
% 0.65/0.81 ((hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076))) <=> (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(936,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[935])).
% 0.65/0.81 tff(937,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[936, 934])).
% 0.65/0.81 tff(938,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(939,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.65/0.81 tff(940,plain,
% 0.65/0.81 (hskp8 | c3_1(a2087) | (~c2_1(a2087))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[939, 87, 647, 211, 645, 277, 876])).
% 0.65/0.81 tff(941,plain,
% 0.65/0.81 (~c2_1(a2087)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[940, 210, 141])).
% 0.65/0.81 tff(942,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[921, 941, 933])).
% 0.65/0.81 tff(943,plain,(c3_1(a2087) | hskp26 | hskp1 | c1_1(a2087) | hskp8 | (~c1_1(a2076)) | c0_1(a2076) | c2_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(944,plain,
% 0.65/0.81 (hskp8),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[943, 924, 11, 211, 504, 647, 645, 876])).
% 0.65/0.81 tff(945,plain,
% 0.65/0.81 (~c0_1(a2082)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[155, 944])).
% 0.65/0.81 tff(946,plain,
% 0.65/0.81 (c2_1(a2082)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[163, 944])).
% 0.65/0.81 tff(947,plain,
% 0.65/0.81 (c1_1(a2082)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[171, 944])).
% 0.65/0.81 tff(948,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(949,plain,
% 0.65/0.82 ((hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087))) <=> (hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(950,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[949])).
% 0.65/0.82 tff(951,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[950, 948])).
% 0.65/0.82 tff(952,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(953,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.65/0.82 tff(954,plain,
% 0.65/0.82 (~c2_1(a2087)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[953, 87, 11, 947, 946, 924, 945, 469, 931])).
% 0.65/0.82 tff(955,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[921, 954, 931])).
% 0.65/0.82 tff(956,plain,(c1_1(a2087) | hskp26 | hskp1 | hskp3 | (~c3_1(a2068)) | c2_1(a2068) | (~c1_1(a2068)) | (~c1_1(a2076)) | c0_1(a2076) | c2_1(a2076) | hskp20 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(957,plain,
% 0.65/0.82 (c1_1(a2087)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[956, 11, 504, 624, 738, 737, 736, 647, 645, 876, 875, 818, 817, 816])).
% 0.65/0.82 tff(958,plain,
% 0.65/0.82 (~hskp10),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[200, 957])).
% 0.65/0.82 tff(959,plain,
% 0.65/0.82 (~hskp23),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[95, 958, 874])).
% 0.65/0.82 tff(960,plain,
% 0.65/0.82 (hskp17),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[104, 959, 11])).
% 0.65/0.82 tff(961,plain,
% 0.65/0.82 (~c1_1(a2110)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[110, 960])).
% 0.65/0.82 tff(962,plain,
% 0.65/0.82 (c0_1(a2110)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[118, 960])).
% 0.65/0.82 tff(963,plain,
% 0.65/0.82 (~c3_1(a2110)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[125, 87, 874, 958, 962, 961, 32])).
% 0.65/0.82 tff(964,plain,
% 0.65/0.82 (hskp8),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[149, 960, 11, 874, 958])).
% 0.65/0.82 tff(965,plain,
% 0.65/0.82 (~c0_1(a2082)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[155, 964])).
% 0.65/0.82 tff(966,plain,
% 0.65/0.82 (c2_1(a2082)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[163, 964])).
% 0.65/0.82 tff(967,plain,
% 0.65/0.82 (c1_1(a2082)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[171, 964])).
% 0.65/0.82 tff(968,plain,
% 0.65/0.82 (c2_1(a2110)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[179, 960])).
% 0.65/0.82 tff(969,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[186, 87, 874, 968, 967, 966, 961, 965, 21, 963])).
% 0.65/0.82 tff(970,plain,(hskp1 | hskp26 | hskp3 | (~c3_1(a2068)) | c2_1(a2068) | (~c1_1(a2068)) | (~c1_1(a2076)) | c0_1(a2076) | c2_1(a2076) | hskp20 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(971,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[970, 873, 504, 624, 674, 660, 736, 647, 645, 11, 855, 818, 817, 816])).
% 0.65/0.82 tff(972,plain,(hskp26 | hskp3 | (~c1_1(a2068)) | (~c1_1(a2076)) | c0_1(a2076) | hskp1 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075)) | (~c3_1(a2076))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(973,plain,
% 0.65/0.82 (hskp26),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[972, 735, 624, 647, 645, 815, 717, 709, 701, 646])).
% 0.65/0.82 tff(974,plain,
% 0.65/0.82 (c3_1(a2069)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[533, 973])).
% 0.65/0.82 tff(975,plain,
% 0.65/0.82 (c2_1(a2069)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[541, 973])).
% 0.65/0.82 tff(976,plain,
% 0.65/0.82 (c0_1(a2069)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[549, 973])).
% 0.65/0.82 tff(977,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(978,plain,
% 0.65/0.82 ((hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068))) <=> (hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(979,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[978])).
% 0.65/0.82 tff(980,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[979, 977])).
% 0.65/0.82 tff(981,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(982,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[981, 980])).
% 0.65/0.82 tff(983,plain,
% 0.65/0.82 (hskp10),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[982, 87, 976, 975, 974, 674, 666, 660, 634])).
% 0.65/0.82 tff(984,plain,
% 0.65/0.82 (~c3_1(a2087)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[194, 983])).
% 0.65/0.82 tff(985,plain,
% 0.65/0.82 (~c1_1(a2087)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[200, 983])).
% 0.65/0.82 tff(986,plain,
% 0.65/0.82 (c2_1(a2087)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[208, 983])).
% 0.65/0.82 tff(987,plain,
% 0.65/0.82 (c0_1(a2087)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[236, 87, 675, 986, 985, 984, 229])).
% 0.65/0.82 tff(988,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[930, 87, 624, 674, 985, 984, 660, 340, 735, 987])).
% 0.65/0.82 tff(989,plain,(hskp4 | hskp3 | (~c1_1(a2076)) | c0_1(a2076) | (~c3_1(a2076))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(990,plain,
% 0.65/0.82 (hskp4),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[989, 624, 623, 615, 609])).
% 0.65/0.82 tff(991,plain,
% 0.65/0.82 (~c2_1(a2074)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[243, 990])).
% 0.65/0.82 tff(992,plain,
% 0.65/0.82 (hskp0),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[653, 87, 623, 609, 615, 644])).
% 0.65/0.82 tff(993,plain,
% 0.65/0.82 (~c2_1(a2068)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[659, 992])).
% 0.65/0.82 tff(994,plain,
% 0.65/0.82 (~c0_1(a2068)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[665, 992])).
% 0.65/0.82 tff(995,plain,
% 0.65/0.82 (c3_1(a2068)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[673, 992])).
% 0.65/0.82 tff(996,assumption,(c1_1(a2070)), introduced(assumption)).
% 0.65/0.82 tff(997,plain,
% 0.65/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(998,plain,
% 0.65/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[997])).
% 0.65/0.82 tff(999,plain,
% 0.65/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1000,plain,
% 0.65/0.82 (^[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))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(1001,plain,
% 0.65/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[1000])).
% 0.65/0.82 tff(1002,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.65/0.82 tff(1003,plain,
% 0.65/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 0.65/0.82 tff(1004,plain,
% 0.65/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1003, 999])).
% 0.65/0.82 tff(1005,plain,(
% 0.65/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[1004])).
% 0.65/0.82 tff(1006,plain,
% 0.65/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1005, 998])).
% 0.65/0.82 tff(1007,plain,
% 0.65/0.82 (hskp4),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[989, 624, 647, 645, 646])).
% 0.65/0.82 tff(1008,plain,
% 0.65/0.82 (~c2_1(a2074)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[243, 1007])).
% 0.65/0.82 tff(1009,plain,
% 0.65/0.82 (c3_1(a2074)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[251, 1007])).
% 0.65/0.82 tff(1010,plain,
% 0.65/0.82 (c1_1(a2074)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[259, 1007])).
% 0.65/0.82 tff(1011,assumption,(~c2_1(a2074)), introduced(assumption)).
% 0.65/0.82 tff(1012,assumption,(c3_1(a2074)), introduced(assumption)).
% 0.65/0.82 tff(1013,assumption,(c1_1(a2074)), introduced(assumption)).
% 0.65/0.82 tff(1014,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1015,plain,
% 0.65/0.82 ((hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093))) <=> (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1016,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1015])).
% 0.65/0.82 tff(1017,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1016, 1014])).
% 0.65/0.82 tff(1018,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1019,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.65/0.82 tff(1020,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1019, 87, 624, 329, 1013, 1012, 321, 315, 1011, 340])).
% 0.65/0.82 tff(1021,plain,((~hskp11) | hskp3 | (~c1_1(a2074)) | (~c3_1(a2074)) | c2_1(a2074)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(1022,plain,
% 0.65/0.82 (~hskp11),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1021, 624, 1010, 1009, 1008])).
% 0.65/0.82 tff(1023,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1024,plain,
% 0.65/0.82 ((hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076))) <=> (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1025,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1024])).
% 0.65/0.82 tff(1026,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1025, 1023])).
% 0.65/0.82 tff(1027,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1028,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 0.65/0.82 tff(1029,plain,
% 0.65/0.82 (~c2_1(a2076)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1028, 87, 22, 209, 647, 201, 195, 645, 21])).
% 0.65/0.82 tff(1030,plain,
% 0.65/0.82 (hskp8),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[939, 87, 209, 647, 201, 195, 645, 277, 1029])).
% 0.65/0.82 tff(1031,plain,
% 0.65/0.82 (~c0_1(a2082)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[155, 1030])).
% 0.65/0.82 tff(1032,plain,
% 0.65/0.82 (c2_1(a2082)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[163, 1030])).
% 0.65/0.82 tff(1033,plain,
% 0.65/0.82 (c1_1(a2082)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[171, 1030])).
% 0.65/0.82 tff(1034,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[295, 87, 22, 209, 1033, 1032, 201, 195, 1031, 21])).
% 0.65/0.82 tff(1035,plain,(hskp11 | (~c1_1(a2076)) | c0_1(a2076) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(1036,plain,
% 0.65/0.82 (hskp1),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1035, 1022, 645, 647])).
% 0.65/0.82 tff(1037,plain,
% 0.65/0.82 (~c2_1(a2070)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[516, 1036])).
% 0.65/0.82 tff(1038,plain,
% 0.65/0.82 (^[U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(1039,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[1038])).
% 0.65/0.82 tff(1040,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1041,plain,
% 0.65/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(1042,plain,
% 0.65/0.82 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[1041])).
% 0.65/0.82 tff(1043,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.65/0.82 tff(1044,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.65/0.82 tff(1045,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1044, 1040])).
% 0.65/0.82 tff(1046,plain,(
% 0.65/0.82 ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[1045])).
% 0.65/0.82 tff(1047,plain,
% 0.65/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1046, 1039])).
% 0.65/0.82 tff(1048,plain,
% 0.65/0.82 (c0_1(a2070)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[502, 1036])).
% 0.65/0.82 tff(1049,plain,
% 0.65/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1050,plain,
% 0.65/0.82 ((hskp22 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070))) <=> (hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1051,plain,
% 0.65/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1050])).
% 0.65/0.82 tff(1052,plain,
% 0.65/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1051, 1049])).
% 0.65/0.82 tff(1053,plain,
% 0.65/0.82 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1054,plain,
% 0.65/0.82 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.65/0.82 tff(1055,plain,
% 0.65/0.82 (hskp22 | (~c1_1(a2070))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1054, 87, 1048, 1037, 1047])).
% 0.65/0.82 tff(1056,plain,
% 0.65/0.82 (hskp22),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1055, 996])).
% 0.65/0.82 tff(1057,plain,
% 0.65/0.82 (((~hskp22) | (~c0_1(a2140))) <=> ((~hskp22) | (~c0_1(a2140)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1058,plain,
% 0.65/0.82 (((~c0_1(a2140)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a2140)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1059,axiom,((~c0_1(a2140)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.65/0.82 tff(1060,plain,
% 0.65/0.82 ((~hskp22) | (~c0_1(a2140))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.65/0.82 tff(1061,plain,
% 0.65/0.82 ((~hskp22) | (~c0_1(a2140))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1060, 1057])).
% 0.65/0.82 tff(1062,plain,
% 0.65/0.82 (~c0_1(a2140)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1061, 1056])).
% 0.65/0.82 tff(1063,plain,
% 0.65/0.82 (((~hskp22) | c3_1(a2140)) <=> ((~hskp22) | c3_1(a2140))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1064,axiom,((~hskp22) | c3_1(a2140)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.65/0.82 tff(1065,plain,
% 0.65/0.82 ((~hskp22) | c3_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.65/0.82 tff(1066,plain,
% 0.65/0.82 ((~hskp22) | c3_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1065, 1063])).
% 0.65/0.82 tff(1067,plain,
% 0.65/0.82 ((~hskp22) | c3_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1066, 1063])).
% 0.65/0.82 tff(1068,plain,
% 0.65/0.82 ((~hskp22) | c3_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1067, 1063])).
% 0.65/0.82 tff(1069,plain,
% 0.65/0.82 ((~hskp22) | c3_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1068, 1063])).
% 0.65/0.82 tff(1070,plain,
% 0.65/0.82 (c3_1(a2140)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1069, 1056])).
% 0.65/0.82 tff(1071,plain,
% 0.65/0.82 (((~hskp22) | c2_1(a2140)) <=> ((~hskp22) | c2_1(a2140))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1072,axiom,((~hskp22) | c2_1(a2140)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.65/0.82 tff(1073,plain,
% 0.65/0.82 ((~hskp22) | c2_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.65/0.82 tff(1074,plain,
% 0.65/0.82 ((~hskp22) | c2_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1073, 1071])).
% 0.65/0.82 tff(1075,plain,
% 0.65/0.82 ((~hskp22) | c2_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1074, 1071])).
% 0.65/0.82 tff(1076,plain,
% 0.65/0.82 ((~hskp22) | c2_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1075, 1071])).
% 0.65/0.82 tff(1077,plain,
% 0.65/0.82 ((~hskp22) | c2_1(a2140)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1076, 1071])).
% 0.65/0.82 tff(1078,plain,
% 0.65/0.82 (c2_1(a2140)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1077, 1056])).
% 0.65/0.82 tff(1079,assumption,(~c0_1(a2140)), introduced(assumption)).
% 0.65/0.82 tff(1080,assumption,(hskp2), introduced(assumption)).
% 0.65/0.82 tff(1081,plain,
% 0.65/0.82 (((~hskp2) | c2_1(a2071)) <=> ((~hskp2) | c2_1(a2071))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1082,axiom,((~hskp2) | c2_1(a2071)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.65/0.82 tff(1083,plain,
% 0.65/0.82 ((~hskp2) | c2_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.65/0.82 tff(1084,plain,
% 0.65/0.82 ((~hskp2) | c2_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1083, 1081])).
% 0.65/0.82 tff(1085,plain,
% 0.65/0.82 ((~hskp2) | c2_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1084, 1081])).
% 0.65/0.82 tff(1086,plain,
% 0.65/0.82 ((~hskp2) | c2_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1085, 1081])).
% 0.65/0.82 tff(1087,plain,
% 0.65/0.82 ((~hskp2) | c2_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1086, 1081])).
% 0.65/0.82 tff(1088,plain,
% 0.65/0.82 (c2_1(a2071)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1087, 1080])).
% 0.65/0.82 tff(1089,plain,
% 0.65/0.82 (((~hskp2) | c0_1(a2071)) <=> ((~hskp2) | c0_1(a2071))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1090,axiom,((~hskp2) | c0_1(a2071)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.65/0.82 tff(1091,plain,
% 0.65/0.82 ((~hskp2) | c0_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.65/0.82 tff(1092,plain,
% 0.65/0.82 ((~hskp2) | c0_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1091, 1089])).
% 0.65/0.82 tff(1093,plain,
% 0.65/0.82 ((~hskp2) | c0_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1092, 1089])).
% 0.65/0.82 tff(1094,plain,
% 0.65/0.82 ((~hskp2) | c0_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1093, 1089])).
% 0.65/0.82 tff(1095,plain,
% 0.65/0.82 ((~hskp2) | c0_1(a2071)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1094, 1089])).
% 0.65/0.82 tff(1096,plain,
% 0.65/0.82 (c0_1(a2071)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1095, 1080])).
% 0.65/0.82 tff(1097,assumption,(c3_1(a2140)), introduced(assumption)).
% 0.65/0.82 tff(1098,assumption,(c2_1(a2140)), introduced(assumption)).
% 0.65/0.82 tff(1099,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1100,plain,
% 0.65/0.82 ((hskp26 | (~ndr1_0) | (~c2_1(a2071)) | (~c1_1(a2071)) | (~c0_1(a2071)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140))) <=> (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1101,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2071)) | (~c1_1(a2071)) | (~c0_1(a2071)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1100])).
% 0.65/0.82 tff(1102,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2071)) | (~c1_1(a2071)) | (~c0_1(a2071)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1101, 1099])).
% 0.65/0.82 tff(1103,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2071)) | (~c1_1(a2071)) | (~c0_1(a2071)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1104,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 0.65/0.82 tff(1105,plain,
% 0.65/0.82 (~c1_1(a2071)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1104, 87, 504, 1098, 1097, 1096, 1088, 1079, 865])).
% 0.65/0.82 tff(1106,plain,
% 0.65/0.82 (((~hskp2) | (~c3_1(a2071))) <=> ((~hskp2) | (~c3_1(a2071)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1107,plain,
% 0.65/0.82 (((~c3_1(a2071)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2071)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1108,axiom,((~c3_1(a2071)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.65/0.82 tff(1109,plain,
% 0.65/0.82 ((~hskp2) | (~c3_1(a2071))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.65/0.82 tff(1110,plain,
% 0.65/0.82 ((~hskp2) | (~c3_1(a2071))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1109, 1106])).
% 0.65/0.82 tff(1111,plain,
% 0.65/0.82 (~c3_1(a2071)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1110, 1080])).
% 0.65/0.82 tff(1112,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1113,plain,
% 0.65/0.82 ((hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2071) | c1_1(a2071) | (~c0_1(a2071))) <=> (hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1114,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2071) | c1_1(a2071) | (~c0_1(a2071)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1113])).
% 0.65/0.82 tff(1115,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2071) | c1_1(a2071) | (~c0_1(a2071)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1114, 1112])).
% 0.65/0.82 tff(1116,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2071) | c1_1(a2071) | (~c0_1(a2071)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1117,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 0.65/0.83 tff(1118,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1117, 87, 624, 1013, 1012, 1096, 1011, 1111, 340, 1105])).
% 0.65/0.83 tff(1119,plain,((~hskp2) | hskp3 | (~c1_1(a2074)) | (~c3_1(a2074)) | c2_1(a2074) | hskp26 | (~c2_1(a2140)) | (~c3_1(a2140)) | c0_1(a2140)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(1120,plain,
% 0.65/0.83 (~hskp2),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1119, 1078, 1010, 1009, 1008, 504, 624, 1070, 1062])).
% 0.65/0.83 tff(1121,plain,
% 0.65/0.83 ((hskp17 | hskp2) <=> (hskp17 | hskp2)),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1122,axiom,(hskp17 | hskp2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.65/0.83 tff(1123,plain,
% 0.65/0.83 (hskp17 | hskp2),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.65/0.83 tff(1124,plain,
% 0.65/0.83 (hskp17),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1123, 1120])).
% 0.65/0.83 tff(1125,plain,
% 0.65/0.83 (~c1_1(a2110)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[110, 1124])).
% 0.65/0.83 tff(1126,plain,
% 0.65/0.83 (c0_1(a2110)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[118, 1124])).
% 0.65/0.83 tff(1127,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1128,plain,
% 0.65/0.83 (((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076))) <=> (c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1129,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1128])).
% 0.65/0.83 tff(1130,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1129, 1127])).
% 0.65/0.83 tff(1131,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1132,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.65/0.83 tff(1133,plain,
% 0.65/0.83 (~c3_1(a2110)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1132, 87, 1126, 647, 646, 1048, 1125, 645, 1037, 1006, 996])).
% 0.65/0.83 tff(1134,plain,
% 0.65/0.83 (c2_1(a2110)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[179, 1124])).
% 0.65/0.83 tff(1135,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1136,plain,
% 0.65/0.83 ((hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076))) <=> (hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1137,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1136])).
% 0.65/0.83 tff(1138,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1137, 1135])).
% 0.65/0.83 tff(1139,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1140,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 0.65/0.83 tff(1141,plain,
% 0.65/0.83 (~c2_1(a2076)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1140, 87, 1022, 1134, 647, 1125, 645, 21, 1133])).
% 0.65/0.83 tff(1142,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1143,plain,
% 0.65/0.83 ((hskp8 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076))) <=> (hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1144,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1143])).
% 0.65/0.83 tff(1145,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1144, 1142])).
% 0.65/0.83 tff(1146,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1147,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.65/0.83 tff(1148,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1147, 87, 141, 1134, 647, 1125, 645, 277, 1141, 1133])).
% 0.65/0.83 tff(1149,plain,((~c1_1(a2070)) | hskp8 | (~c1_1(a2076)) | c0_1(a2076) | (~c3_1(a2076)) | hskp26 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(1150,plain,
% 0.65/0.83 (~c1_1(a2070)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1149, 141, 647, 645, 646, 504, 624])).
% 0.65/0.83 tff(1151,plain,
% 0.65/0.83 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(1152,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[1151])).
% 0.65/0.83 tff(1153,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1154,plain,
% 0.65/0.83 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(1155,plain,
% 0.65/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[1154])).
% 0.65/0.83 tff(1156,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.65/0.83 tff(1157,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.65/0.83 tff(1158,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1157, 1153])).
% 0.65/0.83 tff(1159,plain,(
% 0.65/0.83 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[1158])).
% 0.65/0.83 tff(1160,plain,
% 0.65/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1159, 1152])).
% 0.65/0.83 tff(1161,plain,
% 0.65/0.83 (^[U: $i] : refl((hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(1162,plain,
% 0.65/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[1161])).
% 0.65/0.83 tff(1163,plain,
% 0.65/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1164,plain,
% 0.65/0.83 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp18) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18) <=> (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp18) <=> (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(1165,plain,
% 0.65/0.83 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp18) <=> ![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[1164])).
% 0.65/0.83 tff(1166,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.65/0.83 tff(1167,plain,
% 0.65/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.65/0.83 tff(1168,plain,
% 0.65/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1167, 1163])).
% 0.65/0.83 tff(1169,plain,(
% 0.65/0.83 ![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[1168])).
% 0.65/0.83 tff(1170,plain,
% 0.65/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1169, 1162])).
% 0.65/0.83 tff(1171,plain,
% 0.65/0.83 (c3_1(a2070)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[494, 1036])).
% 0.65/0.83 tff(1172,plain,
% 0.65/0.83 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1173,plain,
% 0.65/0.83 ((hskp26 | hskp18 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c3_1(a2070))) <=> (hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1174,plain,
% 0.65/0.83 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c3_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1173])).
% 0.65/0.83 tff(1175,plain,
% 0.65/0.83 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c3_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1174, 1172])).
% 0.65/0.83 tff(1176,plain,
% 0.65/0.83 ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c3_1(a2070)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1177,plain,
% 0.65/0.83 ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 0.65/0.83 tff(1178,plain,
% 0.65/0.83 (hskp26 | hskp18 | c1_1(a2070)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1177, 87, 1171, 1037, 1170])).
% 0.65/0.83 tff(1179,plain,
% 0.65/0.83 (hskp18),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1178, 1150, 504])).
% 0.65/0.83 tff(1180,plain,
% 0.65/0.83 (((~hskp18) | (~c3_1(a2116))) <=> ((~hskp18) | (~c3_1(a2116)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1181,plain,
% 0.65/0.83 (((~c3_1(a2116)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a2116)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1182,axiom,((~c3_1(a2116)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.65/0.83 tff(1183,plain,
% 0.65/0.83 ((~hskp18) | (~c3_1(a2116))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.65/0.83 tff(1184,plain,
% 0.65/0.83 ((~hskp18) | (~c3_1(a2116))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1183, 1180])).
% 0.65/0.83 tff(1185,plain,
% 0.65/0.83 (~c3_1(a2116)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1184, 1179])).
% 0.65/0.83 tff(1186,plain,
% 0.65/0.83 (((~hskp18) | (~c2_1(a2116))) <=> ((~hskp18) | (~c2_1(a2116)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1187,plain,
% 0.65/0.83 (((~c2_1(a2116)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2116)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1188,axiom,((~c2_1(a2116)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.65/0.83 tff(1189,plain,
% 0.65/0.83 ((~hskp18) | (~c2_1(a2116))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.65/0.83 tff(1190,plain,
% 0.65/0.83 ((~hskp18) | (~c2_1(a2116))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1189, 1186])).
% 0.65/0.83 tff(1191,plain,
% 0.65/0.83 (~c2_1(a2116)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1190, 1179])).
% 0.65/0.83 tff(1192,plain,
% 0.65/0.83 (((~hskp18) | c1_1(a2116)) <=> ((~hskp18) | c1_1(a2116))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1193,axiom,((~hskp18) | c1_1(a2116)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.65/0.83 tff(1194,plain,
% 0.65/0.83 ((~hskp18) | c1_1(a2116)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 0.65/0.83 tff(1195,plain,
% 0.65/0.83 ((~hskp18) | c1_1(a2116)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1194, 1192])).
% 0.65/0.83 tff(1196,plain,
% 0.65/0.83 ((~hskp18) | c1_1(a2116)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1195, 1192])).
% 0.65/0.83 tff(1197,plain,
% 0.65/0.83 ((~hskp18) | c1_1(a2116)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1196, 1192])).
% 0.65/0.83 tff(1198,plain,
% 0.65/0.83 ((~hskp18) | c1_1(a2116)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1197, 1192])).
% 0.65/0.83 tff(1199,plain,
% 0.65/0.83 (c1_1(a2116)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1198, 1179])).
% 0.65/0.83 tff(1200,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1201,plain,
% 0.65/0.83 ((hskp8 | (~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1202,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1201])).
% 0.65/0.83 tff(1203,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116)))),
% 0.68/0.83 inference(transitivity,[status(thm)],[1202, 1200])).
% 0.68/0.83 tff(1204,plain,
% 0.68/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.68/0.83 inference(quant_inst,[status(thm)],[])).
% 0.68/0.83 tff(1205,plain,
% 0.68/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.68/0.83 tff(1206,plain,
% 0.68/0.83 ($false),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1205, 87, 141, 1199, 1048, 1171, 1191, 1185, 1160, 1150])).
% 0.68/0.83 tff(1207,plain,(hskp8 | hskp26 | (~c1_1(a2076)) | c0_1(a2076) | (~c3_1(a2076)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(1208,plain,
% 0.68/0.83 (hskp8),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1207, 504, 647, 645, 646, 624])).
% 0.68/0.83 tff(1209,plain,
% 0.68/0.83 (~c0_1(a2082)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[155, 1208])).
% 0.68/0.83 tff(1210,plain,
% 0.68/0.83 (c2_1(a2082)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[163, 1208])).
% 0.68/0.83 tff(1211,plain,
% 0.68/0.83 (((~![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) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(1212,plain,
% 0.68/0.83 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082))) <=> (c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(1213,plain,
% 0.68/0.83 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082))))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[1212])).
% 0.68/0.83 tff(1214,plain,
% 0.68/0.83 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.68/0.83 inference(transitivity,[status(thm)],[1213, 1211])).
% 0.68/0.83 tff(1215,plain,
% 0.68/0.83 ((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.68/0.83 inference(quant_inst,[status(thm)],[])).
% 0.68/0.83 tff(1216,plain,
% 0.68/0.83 ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 0.68/0.83 tff(1217,plain,
% 0.68/0.83 (c3_1(a2082)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1216, 87, 1210, 1010, 1009, 1048, 1171, 1209, 1008, 1037, 10])).
% 0.68/0.83 tff(1218,plain,
% 0.68/0.83 (c1_1(a2082)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[171, 1208])).
% 0.68/0.83 tff(1219,assumption,(c3_1(a2082)), introduced(assumption)).
% 0.68/0.83 tff(1220,assumption,(~c2_1(a2070)), introduced(assumption)).
% 0.68/0.83 tff(1221,assumption,(~c0_1(a2082)), introduced(assumption)).
% 0.68/0.83 tff(1222,assumption,(c0_1(a2070)), introduced(assumption)).
% 0.68/0.83 tff(1223,plain,
% 0.68/0.83 (hskp22 | (~c1_1(a2070))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1054, 87, 1222, 1220, 1047])).
% 0.68/0.83 tff(1224,plain,
% 0.68/0.83 (hskp22),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1223, 996])).
% 0.68/0.83 tff(1225,plain,
% 0.68/0.83 (~c0_1(a2140)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1061, 1224])).
% 0.68/0.83 tff(1226,plain,
% 0.68/0.83 (c3_1(a2140)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1069, 1224])).
% 0.68/0.83 tff(1227,plain,
% 0.68/0.83 (c2_1(a2140)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1077, 1224])).
% 0.68/0.83 tff(1228,plain,
% 0.68/0.83 (~hskp2),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1119, 1227, 1013, 1012, 1011, 504, 624, 1226, 1225])).
% 0.68/0.83 tff(1229,plain,
% 0.68/0.83 (hskp17),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[1123, 1228])).
% 0.68/0.83 tff(1230,plain,
% 0.68/0.83 (~c1_1(a2110)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[110, 1229])).
% 0.68/0.83 tff(1231,assumption,(c1_1(a2082)), introduced(assumption)).
% 0.68/0.83 tff(1232,plain,
% 0.68/0.83 (c0_1(a2110)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[118, 1229])).
% 0.68/0.83 tff(1233,plain,
% 0.68/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(1234,plain,
% 0.68/0.83 (((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082))) <=> (c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(1235,plain,
% 0.68/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110))))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[1234])).
% 0.68/0.83 tff(1236,plain,
% 0.68/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[1235, 1233])).
% 0.68/0.84 tff(1237,plain,
% 0.68/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(1238,plain,
% 0.68/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 0.68/0.84 tff(1239,plain,
% 0.68/0.84 (~c3_1(a2110)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1238, 87, 1232, 1231, 1222, 1230, 1221, 1220, 1006, 1219, 996])).
% 0.68/0.84 tff(1240,assumption,(c2_1(a2082)), introduced(assumption)).
% 0.68/0.84 tff(1241,plain,
% 0.68/0.84 (c2_1(a2110)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[179, 1229])).
% 0.68/0.84 tff(1242,plain,
% 0.68/0.84 (~hskp11),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1021, 624, 1013, 1012, 1011])).
% 0.68/0.84 tff(1243,plain,
% 0.68/0.84 ($false),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[186, 87, 1242, 1241, 1231, 1240, 1230, 1221, 21, 1239])).
% 0.68/0.84 tff(1244,plain,((~c1_1(a2070)) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2082) | (~c0_1(a2070)) | c2_1(a2070) | (~c3_1(a2082)) | (~c1_1(a2074)) | (~c3_1(a2074)) | c2_1(a2074) | hskp26 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.68/0.84 tff(1245,plain,
% 0.68/0.84 (~c1_1(a2070)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1244, 1218, 1210, 1209, 1048, 1037, 1217, 1010, 1009, 1008, 504, 624])).
% 0.68/0.84 tff(1246,plain,
% 0.68/0.84 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1247,plain,
% 0.68/0.84 ((hskp11 | hskp10 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1248,plain,
% 0.68/0.84 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[1247])).
% 0.68/0.84 tff(1249,plain,
% 0.68/0.84 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[1248, 1246])).
% 0.68/0.84 tff(1250,plain,
% 0.68/0.84 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(1251,plain,
% 0.68/0.84 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.68/0.84 tff(1252,plain,
% 0.68/0.84 (hskp10 | c1_1(a2070)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1251, 87, 1022, 1048, 1171, 32])).
% 0.68/0.84 tff(1253,plain,
% 0.68/0.84 (hskp10),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1252, 1245])).
% 0.68/0.84 tff(1254,plain,
% 0.68/0.84 (~c3_1(a2087)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[194, 1253])).
% 0.68/0.84 tff(1255,plain,
% 0.68/0.84 (~c1_1(a2087)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[200, 1253])).
% 0.68/0.84 tff(1256,plain,
% 0.68/0.84 (c2_1(a2087)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[208, 1253])).
% 0.68/0.84 tff(1257,plain,
% 0.68/0.84 ($false),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[295, 87, 1022, 1256, 1218, 1210, 1255, 1254, 1209, 21])).
% 0.68/0.84 tff(1258,plain,(hskp26 | hskp3 | (~c1_1(a2076)) | c0_1(a2076) | (~c3_1(a2076))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.84 tff(1259,plain,
% 0.68/0.84 (hskp26),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1258, 624, 623, 615, 609])).
% 0.68/0.84 tff(1260,plain,
% 0.68/0.84 (c3_1(a2069)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[533, 1259])).
% 0.68/0.84 tff(1261,plain,
% 0.68/0.84 (c2_1(a2069)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[541, 1259])).
% 0.68/0.84 tff(1262,plain,
% 0.68/0.84 (c0_1(a2069)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[549, 1259])).
% 0.68/0.84 tff(1263,plain,
% 0.68/0.84 (hskp10),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[982, 87, 1262, 1261, 1260, 995, 994, 993, 634])).
% 0.68/0.84 tff(1264,plain,
% 0.68/0.84 (~c3_1(a2087)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[194, 1263])).
% 0.68/0.84 tff(1265,plain,
% 0.68/0.84 (~c1_1(a2087)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[200, 1263])).
% 0.68/0.84 tff(1266,plain,
% 0.68/0.84 (c3_1(a2074)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[251, 990])).
% 0.68/0.84 tff(1267,plain,
% 0.68/0.84 (c1_1(a2074)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[259, 990])).
% 0.68/0.84 tff(1268,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1269,plain,
% 0.68/0.84 ((hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087))) <=> (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1270,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[1269])).
% 0.68/0.84 tff(1271,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[1270, 1268])).
% 0.68/0.84 tff(1272,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(1273,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.68/0.84 tff(1274,plain,
% 0.68/0.84 (~c0_1(a2087)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1273, 87, 624, 1267, 1266, 1265, 1264, 991, 340])).
% 0.68/0.84 tff(1275,plain,
% 0.68/0.84 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(1276,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[1275])).
% 0.68/0.84 tff(1277,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1278,plain,
% 0.68/0.84 (^[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)) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(1279,plain,
% 0.68/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[1278])).
% 0.68/0.84 tff(1280,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.68/0.84 tff(1281,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.68/0.84 tff(1282,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1281, 1277])).
% 0.68/0.84 tff(1283,plain,(
% 0.68/0.84 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(skolemize,[status(sab)],[1282])).
% 0.68/0.84 tff(1284,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1283, 1276])).
% 0.68/0.84 tff(1285,plain,
% 0.68/0.84 (~hskp11),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1021, 624, 1267, 1266, 991])).
% 0.68/0.84 tff(1286,plain,
% 0.68/0.84 (hskp1),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1035, 1285, 615, 623])).
% 0.68/0.84 tff(1287,plain,
% 0.68/0.84 (~c2_1(a2070)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[516, 1286])).
% 0.68/0.84 tff(1288,plain,
% 0.68/0.84 (c0_1(a2070)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[502, 1286])).
% 0.68/0.84 tff(1289,plain,
% 0.68/0.84 (c2_1(a2087)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[208, 1263])).
% 0.68/0.84 tff(1290,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1291,plain,
% 0.68/0.84 ((hskp11 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c0_1(a2070)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087))) <=> (hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1292,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c0_1(a2070)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[1291])).
% 0.68/0.84 tff(1293,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c0_1(a2070)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[1292, 1290])).
% 0.68/0.84 tff(1294,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c0_1(a2070)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(1295,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 0.68/0.84 tff(1296,plain,
% 0.68/0.84 (c1_1(a2070)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1295, 87, 1285, 1289, 1288, 1264, 1287, 1284, 1274])).
% 0.68/0.84 tff(1297,plain,
% 0.68/0.84 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(1298,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[1297])).
% 0.68/0.84 tff(1299,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1300,plain,
% 0.68/0.84 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(1301,plain,
% 0.68/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[1300])).
% 0.68/0.84 tff(1302,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.68/0.84 tff(1303,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 0.68/0.84 tff(1304,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1303, 1299])).
% 0.68/0.84 tff(1305,plain,(
% 0.68/0.84 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(skolemize,[status(sab)],[1304])).
% 0.68/0.84 tff(1306,plain,
% 0.68/0.84 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1305, 1298])).
% 0.68/0.84 tff(1307,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1308,plain,
% 0.68/0.84 ((hskp29 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087))) <=> (hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1309,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[1308])).
% 0.68/0.84 tff(1310,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[1309, 1307])).
% 0.68/0.84 tff(1311,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(1312,plain,
% 0.68/0.84 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 0.68/0.84 tff(1313,plain,
% 0.68/0.84 ((~c1_1(a2070)) | c0_1(a2087)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1312, 330, 87, 1289, 1288, 1265, 1287, 1306])).
% 0.68/0.84 tff(1314,plain,
% 0.68/0.84 ($false),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1313, 1296, 1274])).
% 0.68/0.84 tff(1315,plain,(hskp3 | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.68/0.84 tff(1316,plain,
% 0.68/0.84 (hskp3),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1315, 330])).
% 0.68/0.84 tff(1317,plain,
% 0.68/0.84 (~c3_1(a2072)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[347, 1316])).
% 0.68/0.84 tff(1318,plain,
% 0.68/0.84 (~c0_1(a2072)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[359, 1316])).
% 0.68/0.84 tff(1319,plain,
% 0.68/0.84 (~c1_1(a2072)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[353, 1316])).
% 0.68/0.84 tff(1320,assumption,(~c1_1(a2068)), introduced(assumption)).
% 0.68/0.84 tff(1321,plain,
% 0.68/0.84 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1322,plain,
% 0.68/0.84 ((hskp26 | hskp1 | (~ndr1_0) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1323,plain,
% 0.68/0.84 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072)))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[1322])).
% 0.68/0.84 tff(1324,plain,
% 0.68/0.84 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.68/0.84 inference(transitivity,[status(thm)],[1323, 1321])).
% 0.68/0.84 tff(1325,plain,
% 0.68/0.84 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(1326,plain,
% 0.68/0.84 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 0.68/0.84 tff(1327,plain,
% 0.68/0.84 (hskp26 | hskp1 | c0_1(a2072) | c2_1(a2072)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1326, 87, 373, 914])).
% 0.68/0.84 tff(1328,plain,
% 0.68/0.84 (c2_1(a2072)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1327, 504, 374, 11])).
% 0.68/0.84 tff(1329,plain,
% 0.68/0.84 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1330,plain,
% 0.68/0.84 ((hskp26 | hskp1 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068)) <=> (hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1331,plain,
% 0.68/0.84 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068)))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[1330])).
% 0.68/0.84 tff(1332,plain,
% 0.68/0.84 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068))),
% 0.68/0.84 inference(transitivity,[status(thm)],[1331, 1329])).
% 0.68/0.84 tff(1333,plain,
% 0.68/0.84 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(1334,plain,
% 0.68/0.84 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068)),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 0.68/0.84 tff(1335,plain,
% 0.68/0.84 (hskp26 | hskp1 | c1_1(a2068)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1334, 87, 820, 737, 914])).
% 0.68/0.84 tff(1336,plain,
% 0.68/0.84 (c1_1(a2068)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[1335, 504, 11])).
% 0.68/0.84 tff(1337,plain,
% 0.68/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(1338,plain,
% 0.68/0.84 ((hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068))) <=> (hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1339,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072))))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[1338])).
% 0.68/0.85 tff(1340,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[1339, 1337])).
% 0.68/0.85 tff(1341,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(1342,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.68/0.85 tff(1343,plain,
% 0.68/0.85 (hskp8 | (~c1_1(a2068)) | (~c2_1(a2072))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1342, 87, 373, 372, 820, 737, 277])).
% 0.68/0.85 tff(1344,plain,
% 0.68/0.85 (hskp8),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1343, 1328, 1336])).
% 0.68/0.85 tff(1345,plain,
% 0.68/0.85 (~c0_1(a2082)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[155, 1344])).
% 0.68/0.85 tff(1346,plain,
% 0.68/0.85 (c2_1(a2082)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[163, 1344])).
% 0.68/0.85 tff(1347,plain,
% 0.68/0.85 (c1_1(a2082)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[171, 1344])).
% 0.68/0.85 tff(1348,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[475, 87, 11, 1347, 1346, 1345, 374, 372, 469, 1328])).
% 0.68/0.85 tff(1349,plain,(hskp26 | hskp1 | c0_1(a2072) | c3_1(a2072) | c1_1(a2072) | c0_1(a2068) | c2_1(a2068)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(1350,plain,
% 0.68/0.85 (hskp26),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1349, 11, 374, 372, 373, 666, 660])).
% 0.68/0.85 tff(1351,plain,
% 0.68/0.85 (c3_1(a2069)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[533, 1350])).
% 0.68/0.85 tff(1352,plain,
% 0.68/0.85 (c2_1(a2069)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[541, 1350])).
% 0.68/0.85 tff(1353,plain,
% 0.68/0.85 (c0_1(a2069)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[549, 1350])).
% 0.68/0.85 tff(1354,plain,
% 0.68/0.85 (hskp10),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[982, 87, 1353, 1352, 1351, 674, 666, 660, 634])).
% 0.68/0.85 tff(1355,plain,
% 0.68/0.85 (~c3_1(a2087)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[194, 1354])).
% 0.68/0.85 tff(1356,plain,
% 0.68/0.85 (~c1_1(a2087)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[200, 1354])).
% 0.68/0.85 tff(1357,plain,
% 0.68/0.85 (c2_1(a2087)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[208, 1354])).
% 0.68/0.85 tff(1358,plain,
% 0.68/0.85 (hskp8 | c2_1(a2076)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[939, 87, 230, 647, 211, 210, 645, 277])).
% 0.68/0.85 tff(1359,plain,
% 0.68/0.85 (c2_1(a2076)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1358, 141])).
% 0.68/0.85 tff(1360,plain,
% 0.68/0.85 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(1361,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[1360])).
% 0.68/0.85 tff(1362,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1363,plain,
% 0.68/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(1364,plain,
% 0.68/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[1363])).
% 0.68/0.85 tff(1365,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.68/0.85 tff(1366,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 0.68/0.85 tff(1367,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1366, 1362])).
% 0.68/0.85 tff(1368,plain,(
% 0.68/0.85 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.68/0.85 inference(skolemize,[status(sab)],[1367])).
% 0.68/0.85 tff(1369,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1368, 1361])).
% 0.68/0.85 tff(1370,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1371,plain,
% 0.68/0.85 ((hskp8 | (~ndr1_0) | (~c3_1(a2076)) | (~c2_1(a2076)) | (~c1_1(a2076)) | c1_1(a2068) | c2_1(a2068) | (~c3_1(a2068))) <=> (hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1372,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a2076)) | (~c2_1(a2076)) | (~c1_1(a2076)) | c1_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076))))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[1371])).
% 0.68/0.85 tff(1373,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a2076)) | (~c2_1(a2076)) | (~c1_1(a2076)) | c1_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[1372, 1370])).
% 0.68/0.85 tff(1374,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a2076)) | (~c2_1(a2076)) | (~c1_1(a2076)) | c1_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(1375,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 0.68/0.85 tff(1376,plain,
% 0.68/0.85 (hskp8 | (~c2_1(a2076))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1375, 87, 647, 646, 674, 660, 1369, 1320])).
% 0.68/0.85 tff(1377,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1376, 1359, 141])).
% 0.68/0.85 tff(1378,plain,(hskp8 | (~c1_1(a2076)) | (~c3_1(a2076)) | c1_1(a2068) | (~c2_1(a2087)) | c1_1(a2087) | c3_1(a2087) | c0_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(1379,plain,
% 0.68/0.85 (hskp8),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1378, 1320, 646, 647, 1357, 1356, 1355, 645])).
% 0.68/0.85 tff(1380,plain,
% 0.68/0.85 (~c0_1(a2082)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[155, 1379])).
% 0.68/0.85 tff(1381,plain,
% 0.68/0.85 (c2_1(a2082)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[163, 1379])).
% 0.68/0.85 tff(1382,plain,
% 0.68/0.85 (c1_1(a2082)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[171, 1379])).
% 0.68/0.85 tff(1383,plain,
% 0.68/0.85 (~c2_1(a2072)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[475, 87, 11, 1382, 1381, 1380, 374, 372, 469])).
% 0.68/0.85 tff(1384,plain,
% 0.68/0.85 (c0_1(a2087)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[953, 87, 11, 1357, 1382, 1381, 1355, 1380, 469])).
% 0.68/0.85 tff(1385,plain,
% 0.68/0.85 (hskp4 | c1_1(a2068)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[733, 87, 738, 820, 737, 727])).
% 0.68/0.85 tff(1386,plain,
% 0.68/0.85 (c1_1(a2068)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1385, 675])).
% 0.68/0.85 tff(1387,plain,
% 0.68/0.85 (hskp4 | c0_1(a2072) | (~c2_1(a2072))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[427, 87, 373, 372, 229])).
% 0.68/0.85 tff(1388,plain,
% 0.68/0.85 (~c2_1(a2072)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1387, 374, 675])).
% 0.68/0.85 tff(1389,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1390,plain,
% 0.68/0.85 (((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1391,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072)))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[1390])).
% 0.68/0.85 tff(1392,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072))),
% 0.68/0.85 inference(transitivity,[status(thm)],[1391, 1389])).
% 0.68/0.85 tff(1393,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(1394,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 0.68/0.85 tff(1395,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1394, 87, 374, 373, 372, 820, 737, 371, 1388, 736])).
% 0.68/0.85 tff(1396,plain,(c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(1397,plain,
% 0.68/0.85 (c0_1(a2072)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1396, 1386, 372, 820, 737, 373, 675])).
% 0.68/0.85 tff(1398,plain,
% 0.68/0.85 (~hskp3),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[359, 1397])).
% 0.68/0.85 tff(1399,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1400,plain,
% 0.68/0.85 ((hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | (~c0_1(a2072))) <=> (hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1401,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | (~c0_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068))))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[1400])).
% 0.68/0.85 tff(1402,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | (~c0_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[1401, 1399])).
% 0.68/0.85 tff(1403,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | (~c0_1(a2072)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(1404,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 0.68/0.85 tff(1405,plain,
% 0.68/0.85 (hskp3 | (~c0_1(a2072)) | c1_1(a2072) | (~c1_1(a2068))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1404, 87, 738, 372, 737, 340])).
% 0.68/0.85 tff(1406,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1405, 1398, 1397, 373, 1386])).
% 0.68/0.85 tff(1407,plain,(hskp4 | c1_1(a2072) | (~c3_1(a2068)) | c3_1(a2072) | c2_1(a2068) | c0_1(a2068)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(1408,plain,
% 0.68/0.85 (hskp4),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1407, 373, 674, 372, 660, 666])).
% 0.68/0.85 tff(1409,plain,
% 0.68/0.85 (c3_1(a2074)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[251, 1408])).
% 0.68/0.85 tff(1410,plain,
% 0.68/0.85 (c1_1(a2074)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[259, 1408])).
% 0.68/0.85 tff(1411,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1412,plain,
% 0.68/0.85 (((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2074)) | (~c3_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087))) <=> (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1413,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2074)) | (~c3_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[1412])).
% 0.68/0.85 tff(1414,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2074)) | (~c3_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[1413, 1411])).
% 0.68/0.85 tff(1415,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2074)) | (~c3_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(1416,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 0.68/0.85 tff(1417,plain,
% 0.68/0.85 ((~c0_1(a2074)) | (~c0_1(a2087))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1416, 87, 1353, 1352, 1351, 1410, 1409, 1356, 1355, 308])).
% 0.68/0.85 tff(1418,plain,
% 0.68/0.85 (~c0_1(a2074)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1417, 1384])).
% 0.68/0.85 tff(1419,plain,
% 0.68/0.85 (~c2_1(a2074)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[243, 1408])).
% 0.68/0.85 tff(1420,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1421,plain,
% 0.68/0.85 (((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068)) <=> (c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1422,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074)))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[1421])).
% 0.68/0.85 tff(1423,plain,
% 0.68/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.68/0.85 inference(transitivity,[status(thm)],[1422, 1420])).
% 0.68/0.85 tff(1424,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(1425,plain,
% 0.68/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 0.68/0.85 tff(1426,plain,
% 0.68/0.85 (c1_1(a2068) | c2_1(a2072) | c0_1(a2074)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1425, 87, 1410, 1419, 373, 372, 666, 660, 371])).
% 0.68/0.85 tff(1427,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1426, 1418, 1383, 1320])).
% 0.68/0.85 tff(1428,plain,(c1_1(a2068) | c1_1(a2072) | c3_1(a2072) | hskp1 | c0_1(a2072) | (~c3_1(a2076)) | (~c1_1(a2076)) | c0_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(1429,plain,
% 0.68/0.85 (c1_1(a2068)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1428, 11, 372, 373, 374, 646, 647, 645])).
% 0.68/0.85 tff(1430,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1431,plain,
% 0.68/0.85 ((hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068))) <=> (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(1432,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087))))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[1431])).
% 0.68/0.85 tff(1433,plain,
% 0.68/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[1432, 1430])).
% 0.68/0.85 tff(1434,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(1435,plain,
% 0.68/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 0.68/0.85 tff(1436,plain,
% 0.68/0.85 (hskp8 | (~c1_1(a2068))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[1435, 87, 1357, 1356, 1355, 666, 660, 277])).
% 0.68/0.85 tff(1437,plain,
% 0.68/0.85 (hskp8),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1436, 1429])).
% 0.68/0.86 tff(1438,plain,
% 0.68/0.86 (~c0_1(a2082)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[155, 1437])).
% 0.68/0.86 tff(1439,plain,
% 0.68/0.86 (c2_1(a2082)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[163, 1437])).
% 0.68/0.86 tff(1440,plain,
% 0.68/0.86 (c1_1(a2082)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[171, 1437])).
% 0.68/0.86 tff(1441,plain,
% 0.68/0.86 (~c2_1(a2072)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[475, 87, 11, 1440, 1439, 1438, 374, 372, 469])).
% 0.68/0.86 tff(1442,plain,
% 0.68/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(1443,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_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) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[1442])).
% 0.68/0.86 tff(1444,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_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) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1445,plain,
% 0.68/0.86 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(1446,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_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)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[1445])).
% 0.68/0.86 tff(1447,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.68/0.86 tff(1448,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 0.68/0.86 tff(1449,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1448, 1444])).
% 0.68/0.86 tff(1450,plain,(
% 0.68/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.68/0.86 inference(skolemize,[status(sab)],[1449])).
% 0.68/0.86 tff(1451,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1450, 1443])).
% 0.68/0.86 tff(1452,plain,
% 0.68/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1453,plain,
% 0.68/0.86 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c2_1(a2087)) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072)) <=> (c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1454,plain,
% 0.68/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c2_1(a2087)) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[1453])).
% 0.68/0.86 tff(1455,plain,
% 0.68/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c2_1(a2087)) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[1454, 1452])).
% 0.68/0.86 tff(1456,plain,
% 0.68/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c2_1(a2087)) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(1457,plain,
% 0.68/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 0.68/0.86 tff(1458,plain,
% 0.68/0.86 ($false),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1457, 87, 1357, 1410, 1409, 1356, 1355, 1419, 374, 372, 1451, 1441])).
% 0.68/0.86 tff(1459,plain,(hskp1 | c0_1(a2072) | c3_1(a2072) | c1_1(a2072) | (~c3_1(a2076)) | (~c1_1(a2076)) | c0_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.86 tff(1460,plain,
% 0.68/0.86 (hskp1),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1459, 374, 372, 373, 609, 623, 615])).
% 0.68/0.86 tff(1461,plain,
% 0.68/0.86 (~c2_1(a2070)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[516, 1460])).
% 0.68/0.86 tff(1462,plain,
% 0.68/0.86 (hskp4),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1407, 373, 995, 372, 993, 994])).
% 0.68/0.86 tff(1463,plain,
% 0.68/0.86 (~c2_1(a2074)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[243, 1462])).
% 0.68/0.86 tff(1464,plain,
% 0.68/0.86 (c3_1(a2070)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[494, 1460])).
% 0.68/0.86 tff(1465,plain,
% 0.68/0.86 (c0_1(a2070)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[502, 1460])).
% 0.68/0.86 tff(1466,plain,
% 0.68/0.86 (c3_1(a2074)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[251, 1462])).
% 0.68/0.86 tff(1467,plain,
% 0.68/0.86 (c1_1(a2074)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[259, 1462])).
% 0.68/0.86 tff(1468,plain,
% 0.68/0.86 (((~![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) | c3_1(W) | (~c2_1(W)))) | (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1469,plain,
% 0.68/0.86 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072))) <=> (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1470,plain,
% 0.68/0.86 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[1469])).
% 0.68/0.86 tff(1471,plain,
% 0.68/0.86 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[1470, 1468])).
% 0.68/0.86 tff(1472,plain,
% 0.68/0.86 ((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(1473,plain,
% 0.68/0.86 ((~![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) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 0.68/0.86 tff(1474,plain,
% 0.68/0.86 (~c2_1(a2072)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1473, 87, 1467, 1466, 1465, 1464, 1463, 374, 372, 1461, 10])).
% 0.68/0.86 tff(1475,plain,
% 0.68/0.86 (c0_1(a2074)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[400, 87, 1467, 1463, 374, 373, 372, 371, 1474])).
% 0.68/0.86 tff(1476,plain,
% 0.68/0.86 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(1477,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[1476])).
% 0.68/0.86 tff(1478,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1479,plain,
% 0.68/0.86 (^[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)) | (~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)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(1480,plain,
% 0.68/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[1479])).
% 0.68/0.86 tff(1481,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.68/0.86 tff(1482,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 0.68/0.86 tff(1483,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1482, 1478])).
% 0.68/0.86 tff(1484,plain,(
% 0.68/0.86 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(skolemize,[status(sab)],[1483])).
% 0.68/0.86 tff(1485,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1484, 1477])).
% 0.68/0.86 tff(1486,plain,
% 0.68/0.86 (~c1_1(a2068)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1394, 87, 374, 373, 372, 994, 993, 371, 1474])).
% 0.68/0.86 tff(1487,plain,
% 0.68/0.86 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(1488,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[1487])).
% 0.68/0.86 tff(1489,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1490,plain,
% 0.68/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(1491,plain,
% 0.68/0.86 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[1490])).
% 0.68/0.86 tff(1492,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.68/0.86 tff(1493,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.68/0.86 tff(1494,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 0.68/0.86 tff(1495,plain,(
% 0.68/0.86 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.68/0.86 inference(skolemize,[status(sab)],[1494])).
% 0.68/0.86 tff(1496,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1495, 1488])).
% 0.68/0.86 tff(1497,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1498,plain,
% 0.68/0.86 ((hskp15 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2076) | (~c1_1(a2076)) | (~c3_1(a2076))) <=> (hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1499,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2076) | (~c1_1(a2076)) | (~c3_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[1498])).
% 0.68/0.86 tff(1500,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2076) | (~c1_1(a2076)) | (~c3_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[1499, 1497])).
% 0.68/0.86 tff(1501,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2076) | (~c1_1(a2076)) | (~c3_1(a2076)))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(1502,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 0.68/0.86 tff(1503,plain,
% 0.68/0.86 (hskp15 | c1_1(a2068)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1502, 87, 623, 609, 995, 615, 993, 1496])).
% 0.68/0.86 tff(1504,plain,
% 0.68/0.86 (hskp15),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1503, 1486])).
% 0.68/0.86 tff(1505,plain,
% 0.68/0.86 (((~hskp15) | (~c3_1(a2099))) <=> ((~hskp15) | (~c3_1(a2099)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1506,plain,
% 0.68/0.86 (((~c3_1(a2099)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a2099)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1507,axiom,((~c3_1(a2099)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.68/0.86 tff(1508,plain,
% 0.68/0.86 ((~hskp15) | (~c3_1(a2099))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1507, 1506])).
% 0.68/0.86 tff(1509,plain,
% 0.68/0.86 ((~hskp15) | (~c3_1(a2099))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1508, 1505])).
% 0.68/0.86 tff(1510,plain,
% 0.68/0.86 (~c3_1(a2099)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1509, 1504])).
% 0.68/0.86 tff(1511,plain,
% 0.68/0.86 (((~hskp15) | (~c2_1(a2099))) <=> ((~hskp15) | (~c2_1(a2099)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1512,plain,
% 0.68/0.86 (((~c2_1(a2099)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a2099)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1513,axiom,((~c2_1(a2099)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.68/0.86 tff(1514,plain,
% 0.68/0.86 ((~hskp15) | (~c2_1(a2099))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.68/0.86 tff(1515,plain,
% 0.68/0.86 ((~hskp15) | (~c2_1(a2099))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1514, 1511])).
% 0.68/0.86 tff(1516,plain,
% 0.68/0.86 (~c2_1(a2099)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1515, 1504])).
% 0.68/0.86 tff(1517,plain,
% 0.68/0.86 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1518,plain,
% 0.68/0.86 ((hskp22 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074))) <=> (hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1519,plain,
% 0.68/0.86 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[1518])).
% 0.68/0.86 tff(1520,plain,
% 0.68/0.86 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[1519, 1517])).
% 0.68/0.86 tff(1521,plain,
% 0.68/0.86 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(1522,plain,
% 0.68/0.86 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 0.68/0.86 tff(1523,plain,
% 0.68/0.86 (hskp22 | (~c0_1(a2074))),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1522, 87, 1467, 1463, 1047])).
% 0.68/0.86 tff(1524,plain,
% 0.68/0.86 (hskp22),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1523, 1475])).
% 0.68/0.86 tff(1525,plain,
% 0.68/0.86 (~c0_1(a2140)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1061, 1524])).
% 0.68/0.86 tff(1526,plain,
% 0.68/0.86 (((~hskp15) | c0_1(a2099)) <=> ((~hskp15) | c0_1(a2099))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1527,axiom,((~hskp15) | c0_1(a2099)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.68/0.86 tff(1528,plain,
% 0.68/0.86 ((~hskp15) | c0_1(a2099)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 0.68/0.86 tff(1529,plain,
% 0.68/0.86 ((~hskp15) | c0_1(a2099)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1528, 1526])).
% 0.68/0.86 tff(1530,plain,
% 0.68/0.86 ((~hskp15) | c0_1(a2099)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1529, 1526])).
% 0.68/0.86 tff(1531,plain,
% 0.68/0.86 ((~hskp15) | c0_1(a2099)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1530, 1526])).
% 0.68/0.86 tff(1532,plain,
% 0.68/0.86 ((~hskp15) | c0_1(a2099)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[1531, 1526])).
% 0.68/0.86 tff(1533,plain,
% 0.68/0.86 (c0_1(a2099)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1532, 1504])).
% 0.68/0.86 tff(1534,plain,
% 0.68/0.86 (c3_1(a2140)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1069, 1524])).
% 0.68/0.86 tff(1535,plain,
% 0.68/0.86 (c2_1(a2140)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[1077, 1524])).
% 0.68/0.86 tff(1536,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1537,plain,
% 0.68/0.86 ((hskp16 | (~ndr1_0) | c2_1(a2099) | c3_1(a2099) | (~c0_1(a2099)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140))) <=> (hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(1538,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a2099) | c3_1(a2099) | (~c0_1(a2099)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[1537])).
% 0.68/0.87 tff(1539,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a2099) | c3_1(a2099) | (~c0_1(a2099)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[1538, 1536])).
% 0.68/0.87 tff(1540,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a2099) | c3_1(a2099) | (~c0_1(a2099)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(1541,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 0.68/0.87 tff(1542,plain,
% 0.68/0.87 (hskp16),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1541, 87, 1535, 1534, 1533, 1525, 1516, 1510, 1485])).
% 0.68/0.87 tff(1543,plain,
% 0.68/0.87 (((~hskp16) | (~c1_1(a2104))) <=> ((~hskp16) | (~c1_1(a2104)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1544,plain,
% 0.68/0.87 (((~c1_1(a2104)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a2104)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1545,axiom,((~c1_1(a2104)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.68/0.87 tff(1546,plain,
% 0.68/0.87 ((~hskp16) | (~c1_1(a2104))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.68/0.87 tff(1547,plain,
% 0.68/0.87 ((~hskp16) | (~c1_1(a2104))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1546, 1543])).
% 0.68/0.87 tff(1548,plain,
% 0.68/0.87 (~c1_1(a2104)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1547, 1542])).
% 0.68/0.87 tff(1549,plain,
% 0.68/0.87 (((~hskp16) | (~c0_1(a2104))) <=> ((~hskp16) | (~c0_1(a2104)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1550,plain,
% 0.68/0.87 (((~c0_1(a2104)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a2104)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1551,axiom,((~c0_1(a2104)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.68/0.87 tff(1552,plain,
% 0.68/0.87 ((~hskp16) | (~c0_1(a2104))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 0.68/0.87 tff(1553,plain,
% 0.68/0.87 ((~hskp16) | (~c0_1(a2104))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1552, 1549])).
% 0.68/0.87 tff(1554,plain,
% 0.68/0.87 (~c0_1(a2104)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1553, 1542])).
% 0.68/0.87 tff(1555,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1556,plain,
% 0.68/0.87 ((hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2104) | c0_1(a2104) | (~c2_1(a2104))) <=> (hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1557,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2104) | c0_1(a2104) | (~c2_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[1556])).
% 0.68/0.87 tff(1558,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2104) | c0_1(a2104) | (~c2_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[1557, 1555])).
% 0.68/0.87 tff(1559,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2104) | c0_1(a2104) | (~c2_1(a2104)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(1560,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 0.68/0.87 tff(1561,plain,
% 0.68/0.87 (~c2_1(a2104)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1560, 330, 87, 1467, 1554, 1548, 1463, 1306, 1475])).
% 0.68/0.87 tff(1562,plain,
% 0.68/0.87 (((~hskp16) | c3_1(a2104)) <=> ((~hskp16) | c3_1(a2104))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1563,axiom,((~hskp16) | c3_1(a2104)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.68/0.87 tff(1564,plain,
% 0.68/0.87 ((~hskp16) | c3_1(a2104)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 0.68/0.87 tff(1565,plain,
% 0.68/0.87 ((~hskp16) | c3_1(a2104)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1564, 1562])).
% 0.68/0.87 tff(1566,plain,
% 0.68/0.87 ((~hskp16) | c3_1(a2104)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1565, 1562])).
% 0.68/0.87 tff(1567,plain,
% 0.68/0.87 ((~hskp16) | c3_1(a2104)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1566, 1562])).
% 0.68/0.87 tff(1568,plain,
% 0.68/0.87 ((~hskp16) | c3_1(a2104)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1567, 1562])).
% 0.68/0.87 tff(1569,plain,
% 0.68/0.87 (c3_1(a2104)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1568, 1542])).
% 0.68/0.87 tff(1570,plain,
% 0.68/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1571,plain,
% 0.68/0.87 (((~ndr1_0) | c2_1(a2076) | c0_1(a2076) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068)) <=> (c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1572,plain,
% 0.68/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2076) | c0_1(a2076) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[1571])).
% 0.68/0.87 tff(1573,plain,
% 0.68/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2076) | c0_1(a2076) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[1572, 1570])).
% 0.68/0.87 tff(1574,plain,
% 0.68/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2076) | c0_1(a2076) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(1575,plain,
% 0.68/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 0.68/0.87 tff(1576,plain,
% 0.68/0.87 ($false),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1575, 87, 647, 645, 373, 372, 820, 737, 371, 361, 876, 1320])).
% 0.68/0.87 tff(1577,plain,(c2_1(a2076) | (~c1_1(a2076)) | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | c2_1(a2072) | c1_1(a2068)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.87 tff(1578,plain,
% 0.68/0.87 (c2_1(a2076)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1577, 1474, 615, 373, 372, 994, 993, 623, 1486])).
% 0.68/0.87 tff(1579,plain,
% 0.68/0.87 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(1580,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[1579])).
% 0.68/0.87 tff(1581,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1582,plain,
% 0.68/0.87 (^[V: $i, U: $i] : 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))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(1583,plain,
% 0.68/0.87 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[1582])).
% 0.68/0.87 tff(1584,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.68/0.87 tff(1585,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 0.68/0.87 tff(1586,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1585, 1581])).
% 0.68/0.87 tff(1587,plain,(
% 0.68/0.87 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.68/0.87 inference(skolemize,[status(sab)],[1586])).
% 0.68/0.87 tff(1588,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1587, 1580])).
% 0.68/0.87 tff(1589,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1590,plain,
% 0.68/0.87 ((hskp14 | (~ndr1_0) | c0_1(a2076) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072)) <=> (hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1591,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | (~ndr1_0) | c0_1(a2076) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[1590])).
% 0.68/0.87 tff(1592,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | (~ndr1_0) | c0_1(a2076) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[1591, 1589])).
% 0.68/0.87 tff(1593,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | (~ndr1_0) | c0_1(a2076) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(1594,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 0.68/0.87 tff(1595,plain,
% 0.68/0.87 (hskp14 | c1_1(a2072) | c2_1(a2072) | (~c2_1(a2076))),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1594, 87, 623, 615, 372, 1588])).
% 0.68/0.87 tff(1596,plain,
% 0.68/0.87 (hskp14),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1595, 1578, 373, 1474])).
% 0.68/0.87 tff(1597,plain,
% 0.68/0.87 (((~hskp14) | (~c0_1(a2097))) <=> ((~hskp14) | (~c0_1(a2097)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1598,plain,
% 0.68/0.87 (((~c0_1(a2097)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a2097)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1599,axiom,((~c0_1(a2097)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.68/0.87 tff(1600,plain,
% 0.68/0.87 ((~hskp14) | (~c0_1(a2097))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 0.68/0.87 tff(1601,plain,
% 0.68/0.87 ((~hskp14) | (~c0_1(a2097))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1600, 1597])).
% 0.68/0.87 tff(1602,plain,
% 0.68/0.87 (~c0_1(a2097)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1601, 1596])).
% 0.68/0.87 tff(1603,plain,
% 0.68/0.87 (((~hskp14) | (~c2_1(a2097))) <=> ((~hskp14) | (~c2_1(a2097)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1604,plain,
% 0.68/0.87 (((~c2_1(a2097)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a2097)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1605,axiom,((~c2_1(a2097)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.68/0.87 tff(1606,plain,
% 0.68/0.87 ((~hskp14) | (~c2_1(a2097))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 0.68/0.87 tff(1607,plain,
% 0.68/0.87 ((~hskp14) | (~c2_1(a2097))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1606, 1603])).
% 0.68/0.87 tff(1608,plain,
% 0.68/0.87 (~c2_1(a2097)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1607, 1596])).
% 0.68/0.87 tff(1609,plain,
% 0.68/0.87 (((~hskp14) | (~c1_1(a2097))) <=> ((~hskp14) | (~c1_1(a2097)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1610,plain,
% 0.68/0.87 (((~c1_1(a2097)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a2097)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1611,axiom,((~c1_1(a2097)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.68/0.87 tff(1612,plain,
% 0.68/0.87 ((~hskp14) | (~c1_1(a2097))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 0.68/0.87 tff(1613,plain,
% 0.68/0.87 ((~hskp14) | (~c1_1(a2097))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1612, 1609])).
% 0.68/0.87 tff(1614,plain,
% 0.68/0.87 (~c1_1(a2097)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1613, 1596])).
% 0.68/0.87 tff(1615,plain,
% 0.68/0.87 (hskp8 | (~c2_1(a2076))),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1375, 87, 623, 609, 995, 993, 1369, 1486])).
% 0.68/0.87 tff(1616,plain,
% 0.68/0.87 (hskp8),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1615, 1578])).
% 0.68/0.87 tff(1617,plain,
% 0.68/0.87 (~c0_1(a2082)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[155, 1616])).
% 0.68/0.87 tff(1618,plain,
% 0.68/0.87 (c2_1(a2082)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[163, 1616])).
% 0.68/0.87 tff(1619,plain,
% 0.68/0.87 (((~![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) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1620,plain,
% 0.68/0.87 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082))) <=> (c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1621,plain,
% 0.68/0.87 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[1620])).
% 0.68/0.87 tff(1622,plain,
% 0.68/0.87 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[1621, 1619])).
% 0.68/0.87 tff(1623,plain,
% 0.68/0.87 ((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(1624,plain,
% 0.68/0.87 ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 0.68/0.87 tff(1625,plain,
% 0.68/0.87 (c3_1(a2082)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1624, 87, 1618, 1467, 1466, 1617, 1463, 10, 1475])).
% 0.68/0.87 tff(1626,plain,
% 0.68/0.87 (c1_1(a2082)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[171, 1616])).
% 0.68/0.87 tff(1627,assumption,(~c0_1(a2097)), introduced(assumption)).
% 0.68/0.87 tff(1628,assumption,(~c2_1(a2097)), introduced(assumption)).
% 0.68/0.87 tff(1629,assumption,(~c1_1(a2097)), introduced(assumption)).
% 0.68/0.87 tff(1630,plain,
% 0.68/0.87 (hskp4),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1407, 373, 738, 372, 737, 820])).
% 0.68/0.87 tff(1631,plain,
% 0.68/0.87 (c3_1(a2074)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[251, 1630])).
% 0.68/0.87 tff(1632,plain,
% 0.68/0.87 (~c2_1(a2074)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[243, 1630])).
% 0.68/0.87 tff(1633,plain,
% 0.68/0.87 (c1_1(a2074)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[259, 1630])).
% 0.68/0.87 tff(1634,plain,
% 0.68/0.87 (c0_1(a2074)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[400, 87, 1633, 1632, 374, 373, 372, 371, 361])).
% 0.68/0.87 tff(1635,plain,
% 0.68/0.87 (~c1_1(a2068)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1394, 87, 374, 373, 372, 820, 737, 371, 361])).
% 0.68/0.87 tff(1636,plain,
% 0.68/0.87 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(1637,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[1636])).
% 0.68/0.87 tff(1638,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1639,plain,
% 0.68/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(1640,plain,
% 0.68/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[1639])).
% 0.68/0.87 tff(1641,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.68/0.87 tff(1642,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 0.68/0.87 tff(1643,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1642, 1638])).
% 0.68/0.87 tff(1644,plain,(
% 0.68/0.87 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.87 inference(skolemize,[status(sab)],[1643])).
% 0.68/0.87 tff(1645,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1644, 1637])).
% 0.68/0.87 tff(1646,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1647,plain,
% 0.68/0.87 ((hskp7 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2068) | c0_1(a2068) | (~c3_1(a2068))) <=> (hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1648,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[1647])).
% 0.68/0.87 tff(1649,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[1648, 1646])).
% 0.68/0.87 tff(1650,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(1651,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.68/0.87 tff(1652,plain,
% 0.68/0.87 (hskp7),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1651, 87, 1633, 1631, 738, 820, 1645, 1635, 1634])).
% 0.68/0.87 tff(1653,plain,
% 0.68/0.87 (((~hskp7) | c1_1(a2079)) <=> ((~hskp7) | c1_1(a2079))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1654,axiom,((~hskp7) | c1_1(a2079)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.68/0.87 tff(1655,plain,
% 0.68/0.87 ((~hskp7) | c1_1(a2079)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 0.68/0.87 tff(1656,plain,
% 0.68/0.87 ((~hskp7) | c1_1(a2079)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1655, 1653])).
% 0.68/0.87 tff(1657,plain,
% 0.68/0.87 ((~hskp7) | c1_1(a2079)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1656, 1653])).
% 0.68/0.87 tff(1658,plain,
% 0.68/0.87 ((~hskp7) | c1_1(a2079)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1657, 1653])).
% 0.68/0.87 tff(1659,plain,
% 0.68/0.87 ((~hskp7) | c1_1(a2079)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1658, 1653])).
% 0.68/0.87 tff(1660,plain,
% 0.68/0.87 (c1_1(a2079)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1659, 1652])).
% 0.68/0.87 tff(1661,plain,
% 0.68/0.87 (~c3_1(a2079)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[776, 1652])).
% 0.68/0.87 tff(1662,assumption,(c0_1(a2074)), introduced(assumption)).
% 0.68/0.87 tff(1663,assumption,(c1_1(a2079)), introduced(assumption)).
% 0.68/0.87 tff(1664,plain,
% 0.68/0.87 (~c2_1(a2087)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1457, 87, 1013, 1012, 211, 210, 1011, 374, 372, 1451, 361])).
% 0.68/0.87 tff(1665,plain,
% 0.68/0.87 (~hskp10),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[208, 1664])).
% 0.68/0.87 tff(1666,plain,
% 0.68/0.87 (hskp22 | (~c0_1(a2074))),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1522, 87, 1013, 1011, 1047])).
% 0.68/0.87 tff(1667,plain,
% 0.68/0.87 (hskp22),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1666, 1662])).
% 0.68/0.87 tff(1668,plain,
% 0.68/0.87 (~c0_1(a2140)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1061, 1667])).
% 0.68/0.87 tff(1669,plain,
% 0.68/0.87 (c3_1(a2140)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1069, 1667])).
% 0.68/0.87 tff(1670,plain,
% 0.68/0.87 (c2_1(a2140)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1077, 1667])).
% 0.68/0.87 tff(1671,assumption,(~hskp12), introduced(assumption)).
% 0.68/0.87 tff(1672,plain,
% 0.68/0.87 ((hskp24 | hskp12 | hskp10) <=> (hskp24 | hskp12 | hskp10)),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1673,plain,
% 0.68/0.87 (((hskp24 | hskp12) | hskp10) <=> (hskp24 | hskp12 | hskp10)),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1674,plain,
% 0.68/0.87 ((hskp24 | hskp12) <=> (hskp24 | hskp12)),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1675,plain,
% 0.68/0.87 (((hskp24 | hskp12) | hskp10) <=> ((hskp24 | hskp12) | hskp10)),
% 0.68/0.87 inference(monotonicity,[status(thm)],[1674])).
% 0.68/0.87 tff(1676,plain,
% 0.68/0.87 (((hskp24 | hskp12) | hskp10) <=> (hskp24 | hskp12 | hskp10)),
% 0.68/0.87 inference(transitivity,[status(thm)],[1675, 1673])).
% 0.68/0.87 tff(1677,axiom,((hskp24 | hskp12) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.68/0.87 tff(1678,plain,
% 0.68/0.87 (hskp24 | hskp12 | hskp10),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 0.68/0.87 tff(1679,plain,
% 0.68/0.87 (hskp24 | hskp12 | hskp10),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1678, 1672])).
% 0.68/0.87 tff(1680,plain,
% 0.68/0.87 (hskp24 | hskp12 | hskp10),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1679, 1672])).
% 0.68/0.87 tff(1681,plain,
% 0.68/0.87 (hskp24 | hskp12 | hskp10),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1680, 1672])).
% 0.68/0.87 tff(1682,plain,
% 0.68/0.87 (hskp24 | hskp12 | hskp10),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1681, 1672])).
% 0.68/0.87 tff(1683,plain,
% 0.68/0.87 (hskp24),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1682, 1671, 33])).
% 0.68/0.87 tff(1684,plain,
% 0.68/0.87 (((~hskp24) | c2_1(a2160)) <=> ((~hskp24) | c2_1(a2160))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1685,axiom,((~hskp24) | c2_1(a2160)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.68/0.87 tff(1686,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 0.68/0.87 tff(1687,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1686, 1684])).
% 0.68/0.87 tff(1688,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1687, 1684])).
% 0.68/0.87 tff(1689,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1688, 1684])).
% 0.68/0.87 tff(1690,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1689, 1684])).
% 0.68/0.87 tff(1691,plain,
% 0.68/0.87 (c2_1(a2160)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1690, 1683])).
% 0.68/0.87 tff(1692,plain,
% 0.68/0.87 (((~hskp24) | c1_1(a2160)) <=> ((~hskp24) | c1_1(a2160))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1693,axiom,((~hskp24) | c1_1(a2160)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.68/0.87 tff(1694,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 0.68/0.87 tff(1695,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1694, 1692])).
% 0.68/0.87 tff(1696,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1695, 1692])).
% 0.68/0.87 tff(1697,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1696, 1692])).
% 0.68/0.87 tff(1698,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a2160)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[1697, 1692])).
% 0.68/0.87 tff(1699,plain,
% 0.68/0.87 (c1_1(a2160)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[1698, 1683])).
% 0.68/0.87 tff(1700,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(1701,plain,
% 0.68/0.87 ((hskp26 | (~ndr1_0) | (~c2_1(a2160)) | (~c1_1(a2160)) | (~c0_1(a2160)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140))) <=> (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1702,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2160)) | (~c1_1(a2160)) | (~c0_1(a2160)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[1701])).
% 0.68/0.88 tff(1703,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2160)) | (~c1_1(a2160)) | (~c0_1(a2160)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[1702, 1700])).
% 0.68/0.88 tff(1704,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2160)) | (~c1_1(a2160)) | (~c0_1(a2160)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(1705,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 0.68/0.88 tff(1706,plain,
% 0.68/0.88 (~c0_1(a2160)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1705, 87, 504, 1699, 1691, 1670, 1669, 1668, 865])).
% 0.68/0.88 tff(1707,plain,
% 0.68/0.88 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.68/0.88 inference(bind,[status(th)],[])).
% 0.68/0.88 tff(1708,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[1707])).
% 0.68/0.88 tff(1709,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1710,plain,
% 0.68/0.88 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.68/0.88 inference(bind,[status(th)],[])).
% 0.68/0.88 tff(1711,plain,
% 0.68/0.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[1710])).
% 0.68/0.88 tff(1712,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.68/0.88 tff(1713,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 0.68/0.88 tff(1714,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1713, 1709])).
% 0.68/0.88 tff(1715,plain,(
% 0.68/0.88 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.68/0.88 inference(skolemize,[status(sab)],[1714])).
% 0.68/0.88 tff(1716,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1715, 1708])).
% 0.68/0.88 tff(1717,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1718,plain,
% 0.68/0.88 ((hskp12 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c1_1(a2079)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074))) <=> (hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1719,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c1_1(a2079)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[1718])).
% 0.68/0.88 tff(1720,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c1_1(a2079)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[1719, 1717])).
% 0.68/0.88 tff(1721,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c1_1(a2079)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(1722,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 0.68/0.88 tff(1723,plain,
% 0.68/0.88 (hskp12 | (~c2_1(a2079))),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1722, 87, 1663, 1013, 805, 1011, 1716, 1662])).
% 0.68/0.88 tff(1724,plain,
% 0.68/0.88 (~c2_1(a2079)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1723, 1671])).
% 0.68/0.88 tff(1725,plain,
% 0.68/0.88 (^[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)) | c2_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)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.68/0.88 inference(bind,[status(th)],[])).
% 0.68/0.88 tff(1726,plain,
% 0.68/0.88 (![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)) | c2_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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[1725])).
% 0.68/0.88 tff(1727,plain,
% 0.68/0.88 (![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)) | c2_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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1728,plain,
% 0.68/0.88 (^[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)) | c2_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))) | c2_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))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_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)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.68/0.88 inference(bind,[status(th)],[])).
% 0.68/0.88 tff(1729,plain,
% 0.68/0.88 (![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)) | c2_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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[1728])).
% 0.68/0.88 tff(1730,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)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.68/0.88 tff(1731,plain,
% 0.68/0.88 (![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 0.68/0.88 tff(1732,plain,
% 0.68/0.88 (![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1731, 1727])).
% 0.68/0.88 tff(1733,plain,(
% 0.68/0.88 ![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.88 inference(skolemize,[status(sab)],[1732])).
% 0.68/0.88 tff(1734,plain,
% 0.68/0.88 (![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1733, 1726])).
% 0.68/0.88 tff(1735,plain,
% 0.68/0.88 (((~hskp24) | (~c3_1(a2160))) <=> ((~hskp24) | (~c3_1(a2160)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1736,plain,
% 0.68/0.88 (((~c3_1(a2160)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a2160)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1737,axiom,((~c3_1(a2160)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.68/0.88 tff(1738,plain,
% 0.68/0.88 ((~hskp24) | (~c3_1(a2160))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 0.68/0.88 tff(1739,plain,
% 0.68/0.88 ((~hskp24) | (~c3_1(a2160))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1738, 1735])).
% 0.68/0.88 tff(1740,plain,
% 0.68/0.88 (~c3_1(a2160)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1739, 1683])).
% 0.68/0.88 tff(1741,plain,
% 0.68/0.88 (((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160)))) <=> ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1742,plain,
% 0.68/0.88 (((~ndr1_0) | c2_1(a2079) | c3_1(a2079) | (~c1_1(a2079)) | c3_1(a2160) | c0_1(a2160) | (~c1_1(a2160)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068))) <=> (c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1743,plain,
% 0.68/0.88 (((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2079) | c3_1(a2079) | (~c1_1(a2079)) | c3_1(a2160) | c0_1(a2160) | (~c1_1(a2160)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[1742])).
% 0.68/0.88 tff(1744,plain,
% 0.68/0.88 (((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2079) | c3_1(a2079) | (~c1_1(a2079)) | c3_1(a2160) | c0_1(a2160) | (~c1_1(a2160)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[1743, 1741])).
% 0.68/0.88 tff(1745,plain,
% 0.68/0.88 ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2079) | c3_1(a2079) | (~c1_1(a2079)) | c3_1(a2160) | c0_1(a2160) | (~c1_1(a2160)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(1746,plain,
% 0.68/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 0.68/0.88 tff(1747,plain,
% 0.68/0.88 ($false),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1746, 87, 1699, 1663, 738, 1740, 805, 820, 737, 1734, 1724, 1706])).
% 0.68/0.88 tff(1748,plain,(hskp12 | (~c1_1(a2079)) | (~c3_1(a2068)) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | hskp26 | hskp10 | (~c1_1(a2074)) | c2_1(a2074) | (~c0_1(a2074))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.88 tff(1749,plain,
% 0.68/0.88 (hskp12),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1748, 1665, 738, 805, 820, 737, 504, 1663, 1013, 1011, 1662])).
% 0.68/0.88 tff(1750,plain,
% 0.68/0.88 (((~hskp12) | (~c2_1(a2095))) <=> ((~hskp12) | (~c2_1(a2095)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1751,plain,
% 0.68/0.88 (((~c2_1(a2095)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a2095)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1752,axiom,((~c2_1(a2095)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.68/0.88 tff(1753,plain,
% 0.68/0.88 ((~hskp12) | (~c2_1(a2095))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 0.68/0.88 tff(1754,plain,
% 0.68/0.88 ((~hskp12) | (~c2_1(a2095))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1753, 1750])).
% 0.68/0.88 tff(1755,plain,
% 0.68/0.88 (~c2_1(a2095)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1754, 1749])).
% 0.68/0.88 tff(1756,plain,
% 0.68/0.88 (((~hskp12) | (~c0_1(a2095))) <=> ((~hskp12) | (~c0_1(a2095)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1757,plain,
% 0.68/0.88 (((~c0_1(a2095)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a2095)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1758,axiom,((~c0_1(a2095)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.68/0.88 tff(1759,plain,
% 0.68/0.88 ((~hskp12) | (~c0_1(a2095))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 0.68/0.88 tff(1760,plain,
% 0.68/0.88 ((~hskp12) | (~c0_1(a2095))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1759, 1756])).
% 0.68/0.88 tff(1761,plain,
% 0.68/0.88 (~c0_1(a2095)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1760, 1749])).
% 0.68/0.88 tff(1762,plain,
% 0.68/0.88 (((~hskp12) | c1_1(a2095)) <=> ((~hskp12) | c1_1(a2095))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1763,axiom,((~hskp12) | c1_1(a2095)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.68/0.88 tff(1764,plain,
% 0.68/0.88 ((~hskp12) | c1_1(a2095)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 0.68/0.88 tff(1765,plain,
% 0.68/0.88 ((~hskp12) | c1_1(a2095)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1764, 1762])).
% 0.68/0.88 tff(1766,plain,
% 0.68/0.88 ((~hskp12) | c1_1(a2095)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1765, 1762])).
% 0.68/0.88 tff(1767,plain,
% 0.68/0.88 ((~hskp12) | c1_1(a2095)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1766, 1762])).
% 0.68/0.88 tff(1768,plain,
% 0.68/0.88 ((~hskp12) | c1_1(a2095)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1767, 1762])).
% 0.68/0.88 tff(1769,plain,
% 0.68/0.88 (c1_1(a2095)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1768, 1749])).
% 0.68/0.88 tff(1770,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1771,plain,
% 0.68/0.88 (((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2087) | c1_1(a2087) | c2_1(a2087) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097)) <=> (c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1772,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2087) | c1_1(a2087) | c2_1(a2087) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[1771])).
% 0.68/0.88 tff(1773,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2087) | c1_1(a2087) | c2_1(a2087) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[1772, 1770])).
% 0.68/0.88 tff(1774,plain,
% 0.68/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2087) | c1_1(a2087) | c2_1(a2087) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(1775,plain,
% 0.68/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 0.68/0.88 tff(1776,plain,
% 0.68/0.88 ($false),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1775, 87, 1769, 1664, 1627, 1629, 1628, 1761, 1755, 211, 210, 371])).
% 0.68/0.88 tff(1777,plain,(c3_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c1_1(a2087) | (~c3_1(a2068)) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | hskp26 | (~c1_1(a2079)) | (~c1_1(a2074)) | c2_1(a2074) | (~c0_1(a2074)) | (~c3_1(a2074)) | c0_1(a2072) | c3_1(a2072) | c2_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.88 tff(1778,plain,
% 0.68/0.88 (c3_1(a2087)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1777, 211, 1629, 1628, 1627, 738, 1661, 820, 737, 504, 1660, 1633, 1632, 1634, 1631, 374, 372, 361])).
% 0.68/0.88 tff(1779,plain,
% 0.68/0.88 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1780,plain,
% 0.68/0.88 ((hskp26 | hskp18 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068))) <=> (hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1781,plain,
% 0.68/0.88 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068)))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[1780])).
% 0.68/0.88 tff(1782,plain,
% 0.68/0.88 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.68/0.88 inference(transitivity,[status(thm)],[1781, 1779])).
% 0.68/0.88 tff(1783,plain,
% 0.68/0.88 ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(1784,plain,
% 0.68/0.88 ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1783, 1782])).
% 0.68/0.88 tff(1785,plain,
% 0.68/0.88 (hskp26 | hskp18 | c1_1(a2068)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1784, 87, 738, 737, 1170])).
% 0.68/0.88 tff(1786,plain,
% 0.68/0.88 (hskp18),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1785, 504, 1635])).
% 0.68/0.88 tff(1787,plain,
% 0.68/0.88 (~c3_1(a2116)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1184, 1786])).
% 0.68/0.88 tff(1788,plain,
% 0.68/0.88 (~c2_1(a2116)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1190, 1786])).
% 0.68/0.88 tff(1789,plain,
% 0.68/0.88 (c1_1(a2116)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1198, 1786])).
% 0.68/0.88 tff(1790,plain,
% 0.68/0.88 (((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116)))) <=> ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1791,plain,
% 0.68/0.88 (((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c3_1(a2116) | c0_1(a2116) | (~c1_1(a2116)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068))) <=> (c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1792,plain,
% 0.68/0.88 (((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c3_1(a2116) | c0_1(a2116) | (~c1_1(a2116)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[1791])).
% 0.68/0.88 tff(1793,plain,
% 0.68/0.88 (((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c3_1(a2116) | c0_1(a2116) | (~c1_1(a2116)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[1792, 1790])).
% 0.68/0.88 tff(1794,plain,
% 0.68/0.88 ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c3_1(a2116) | c0_1(a2116) | (~c1_1(a2116)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(1795,plain,
% 0.68/0.88 ((~![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)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 0.68/0.88 tff(1796,plain,
% 0.68/0.88 (c0_1(a2116)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[1795, 87, 1789, 738, 1788, 1787, 820, 737, 1734])).
% 0.68/0.88 tff(1797,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(1798,plain,
% 0.68/0.88 (((~ndr1_0) | c2_1(a2116) | (~c1_1(a2116)) | (~c0_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082))) <=> (c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1799,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2116) | (~c1_1(a2116)) | (~c0_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[1798])).
% 0.68/0.89 tff(1800,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2116) | (~c1_1(a2116)) | (~c0_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[1799, 1797])).
% 0.68/0.89 tff(1801,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2116) | (~c1_1(a2116)) | (~c0_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(1802,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 0.68/0.89 tff(1803,plain,
% 0.68/0.89 ((~c3_1(a2087)) | (~c0_1(a2087))),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1802, 87, 1789, 1231, 1788, 211, 1221, 1006, 1219, 1796])).
% 0.68/0.89 tff(1804,plain,
% 0.68/0.89 (~c0_1(a2087)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1803, 1778])).
% 0.68/0.89 tff(1805,plain,
% 0.68/0.89 (~hskp10),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[194, 1778])).
% 0.68/0.89 tff(1806,plain,
% 0.68/0.89 (hskp12),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1748, 1805, 738, 1661, 820, 737, 504, 1660, 1633, 1632, 1634])).
% 0.68/0.89 tff(1807,plain,
% 0.68/0.89 (~c2_1(a2095)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1754, 1806])).
% 0.68/0.89 tff(1808,plain,
% 0.68/0.89 (~c0_1(a2095)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1760, 1806])).
% 0.68/0.89 tff(1809,plain,
% 0.68/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.68/0.89 inference(bind,[status(th)],[])).
% 0.68/0.89 tff(1810,plain,
% 0.68/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_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)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.89 inference(quant_intro,[status(thm)],[1809])).
% 0.68/0.89 tff(1811,plain,
% 0.68/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_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)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1812,plain,
% 0.68/0.89 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.68/0.89 inference(bind,[status(th)],[])).
% 0.68/0.89 tff(1813,plain,
% 0.68/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_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)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.89 inference(quant_intro,[status(thm)],[1812])).
% 0.68/0.89 tff(1814,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.68/0.89 tff(1815,plain,
% 0.68/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 0.68/0.89 tff(1816,plain,
% 0.68/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1815, 1811])).
% 0.68/0.89 tff(1817,plain,(
% 0.68/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.89 inference(skolemize,[status(sab)],[1816])).
% 0.68/0.89 tff(1818,plain,
% 0.68/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1817, 1810])).
% 0.68/0.89 tff(1819,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1820,plain,
% 0.68/0.89 (((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)) | c1_1(a2087) | c0_1(a2087) | (~c3_1(a2087))) <=> (c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1821,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)) | c1_1(a2087) | c0_1(a2087) | (~c3_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[1820])).
% 0.68/0.89 tff(1822,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)) | c1_1(a2087) | c0_1(a2087) | (~c3_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[1821, 1819])).
% 0.68/0.89 tff(1823,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)) | c1_1(a2087) | c0_1(a2087) | (~c3_1(a2087)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(1824,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 0.68/0.89 tff(1825,plain,
% 0.68/0.89 ((~c3_1(a2087)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1824, 87, 1789, 1788, 1787, 211, 1818])).
% 0.68/0.89 tff(1826,plain,
% 0.68/0.89 (~c2_1(a2087)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1825, 1778, 1804])).
% 0.68/0.89 tff(1827,plain,
% 0.68/0.89 (c1_1(a2095)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1768, 1806])).
% 0.68/0.89 tff(1828,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1829,plain,
% 0.68/0.89 (((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087)) <=> (c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1830,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[1829])).
% 0.68/0.89 tff(1831,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[1830, 1828])).
% 0.68/0.89 tff(1832,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(1833,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 0.68/0.89 tff(1834,plain,
% 0.68/0.89 ($false),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1833, 87, 1827, 1826, 1808, 1807, 211, 373, 372, 371, 361, 1804])).
% 0.68/0.89 tff(1835,plain,(c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | c2_1(a2072) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | hskp26 | (~c1_1(a2082)) | c0_1(a2082) | (~c3_1(a2082)) | c1_1(a2097) | c2_1(a2097) | c0_1(a2097) | c0_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.89 tff(1836,plain,
% 0.68/0.89 (c1_1(a2087)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1835, 504, 372, 361, 738, 820, 737, 373, 1231, 1221, 1219, 1629, 1628, 1627, 374])).
% 0.68/0.89 tff(1837,assumption,(hskp12), introduced(assumption)).
% 0.68/0.89 tff(1838,plain,
% 0.68/0.89 (~c2_1(a2095)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1754, 1837])).
% 0.68/0.89 tff(1839,plain,
% 0.68/0.89 (~c0_1(a2095)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1760, 1837])).
% 0.68/0.89 tff(1840,plain,
% 0.68/0.89 (c1_1(a2095)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1768, 1837])).
% 0.68/0.89 tff(1841,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1842,plain,
% 0.68/0.89 (((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097)) <=> (c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1843,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[1842])).
% 0.68/0.89 tff(1844,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[1843, 1841])).
% 0.68/0.89 tff(1845,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(1846,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 0.68/0.89 tff(1847,plain,
% 0.68/0.89 ($false),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1846, 87, 1840, 1627, 1629, 1628, 1839, 1838, 373, 372, 371, 361])).
% 0.68/0.89 tff(1848,plain,((~hskp12) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c1_1(a2072) | c3_1(a2072) | c2_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.89 tff(1849,plain,
% 0.68/0.89 (~hskp12),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1848, 1627, 1629, 1628, 373, 372, 361])).
% 0.68/0.89 tff(1850,plain,
% 0.68/0.89 (hskp10),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1748, 504, 738, 1661, 820, 737, 1849, 1660, 1633, 1632, 1634])).
% 0.68/0.89 tff(1851,plain,
% 0.68/0.89 ($false),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[200, 1850, 1836])).
% 0.68/0.89 tff(1852,plain,(hskp26 | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | c3_1(a2072) | c2_1(a2072) | c1_1(a2072) | (~c1_1(a2082)) | c0_1(a2082) | (~c3_1(a2082)) | c1_1(a2097) | c2_1(a2097) | c0_1(a2097) | c0_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.89 tff(1853,plain,
% 0.68/0.89 (hskp26),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1852, 1474, 994, 993, 372, 995, 373, 1626, 1617, 1625, 1614, 1608, 1602, 374])).
% 0.68/0.89 tff(1854,plain,
% 0.68/0.89 (c3_1(a2069)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[533, 1853])).
% 0.68/0.89 tff(1855,plain,
% 0.68/0.89 (c2_1(a2069)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[541, 1853])).
% 0.68/0.89 tff(1856,plain,
% 0.68/0.89 (c0_1(a2069)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[549, 1853])).
% 0.68/0.89 tff(1857,plain,
% 0.68/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1858,plain,
% 0.68/0.89 ((hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2104) | c2_1(a2104) | (~c3_1(a2104))) <=> (hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1859,plain,
% 0.68/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2104) | c2_1(a2104) | (~c3_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[1858])).
% 0.68/0.89 tff(1860,plain,
% 0.68/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2104) | c2_1(a2104) | (~c3_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[1859, 1857])).
% 0.68/0.89 tff(1861,plain,
% 0.68/0.89 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2104) | c2_1(a2104) | (~c3_1(a2104)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(1862,plain,
% 0.68/0.89 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 0.68/0.89 tff(1863,plain,
% 0.68/0.89 (hskp10),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1862, 87, 1856, 1855, 1854, 1569, 1554, 634, 1561])).
% 0.68/0.89 tff(1864,plain,
% 0.68/0.89 (~c3_1(a2087)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[194, 1863])).
% 0.68/0.89 tff(1865,plain,
% 0.68/0.89 (~c1_1(a2087)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[200, 1863])).
% 0.68/0.89 tff(1866,plain,
% 0.68/0.89 (^[U: $i] : refl((hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.68/0.89 inference(bind,[status(th)],[])).
% 0.68/0.89 tff(1867,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.68/0.89 inference(quant_intro,[status(thm)],[1866])).
% 0.68/0.89 tff(1868,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1869,plain,
% 0.68/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp29) <=> ((hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp29))), rewrite(((hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp29) <=> (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp29) <=> (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.68/0.89 inference(bind,[status(th)],[])).
% 0.68/0.89 tff(1870,plain,
% 0.68/0.89 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp29) <=> ![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.68/0.89 inference(quant_intro,[status(thm)],[1869])).
% 0.68/0.89 tff(1871,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.68/0.89 tff(1872,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 0.68/0.89 tff(1873,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1872, 1868])).
% 0.68/0.89 tff(1874,plain,(
% 0.68/0.89 ![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.68/0.89 inference(skolemize,[status(sab)],[1873])).
% 0.68/0.89 tff(1875,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1874, 1867])).
% 0.68/0.89 tff(1876,plain,
% 0.68/0.89 (((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1877,plain,
% 0.68/0.89 ((hskp29 | hskp27 | (~ndr1_0) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140))) <=> (hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1878,plain,
% 0.68/0.89 (((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | (~ndr1_0) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[1877])).
% 0.68/0.89 tff(1879,plain,
% 0.68/0.89 (((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | (~ndr1_0) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[1878, 1876])).
% 0.68/0.89 tff(1880,plain,
% 0.68/0.89 ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | (~ndr1_0) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(1881,plain,
% 0.68/0.89 ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 0.68/0.89 tff(1882,plain,
% 0.68/0.89 (hskp27),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[1881, 330, 87, 1535, 1534, 1525, 1875])).
% 0.68/0.89 tff(1883,plain,
% 0.68/0.89 (c3_1(a2073)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[575, 1882])).
% 0.68/0.89 tff(1884,plain,
% 0.68/0.89 (c1_1(a2073)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[583, 1882])).
% 0.68/0.89 tff(1885,plain,
% 0.68/0.89 (c0_1(a2073)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[591, 1882])).
% 0.68/0.89 tff(1886,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1887,plain,
% 0.68/0.89 (((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087))) <=> (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(1888,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[1887])).
% 0.68/0.89 tff(1889,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[1888, 1886])).
% 0.68/0.89 tff(1890,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(1891,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 0.68/0.90 tff(1892,plain,
% 0.68/0.90 (~c0_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1891, 87, 1885, 1884, 1883, 1856, 1855, 1854, 1865, 1864, 308])).
% 0.68/0.90 tff(1893,plain,
% 0.68/0.90 (c2_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[208, 1863])).
% 0.68/0.90 tff(1894,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1895,plain,
% 0.68/0.90 ((hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087))) <=> (hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1896,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[1895])).
% 0.68/0.90 tff(1897,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[1896, 1894])).
% 0.68/0.90 tff(1898,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(1899,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 0.68/0.90 tff(1900,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1899, 330, 87, 1893, 1467, 1865, 1463, 1306, 1475, 1892])).
% 0.68/0.90 tff(1901,plain,(c0_1(a2072) | hskp29 | c3_1(a2072) | c1_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(1902,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1901, 1319, 1318, 1317, 330])).
% 0.68/0.90 tff(1903,plain,(hskp29), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(1904,plain,
% 0.68/0.90 (((~hskp29) | c3_1(a2077)) <=> ((~hskp29) | c3_1(a2077))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1905,axiom,((~hskp29) | c3_1(a2077)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.68/0.90 tff(1906,plain,
% 0.68/0.90 ((~hskp29) | c3_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 0.68/0.90 tff(1907,plain,
% 0.68/0.90 ((~hskp29) | c3_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1906, 1904])).
% 0.68/0.90 tff(1908,plain,
% 0.68/0.90 ((~hskp29) | c3_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1907, 1904])).
% 0.68/0.90 tff(1909,plain,
% 0.68/0.90 ((~hskp29) | c3_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1908, 1904])).
% 0.68/0.90 tff(1910,plain,
% 0.68/0.90 ((~hskp29) | c3_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1909, 1904])).
% 0.68/0.90 tff(1911,plain,
% 0.68/0.90 (c3_1(a2077)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1910, 1903])).
% 0.68/0.90 tff(1912,plain,
% 0.68/0.90 (((~hskp29) | c2_1(a2077)) <=> ((~hskp29) | c2_1(a2077))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1913,axiom,((~hskp29) | c2_1(a2077)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.68/0.90 tff(1914,plain,
% 0.68/0.90 ((~hskp29) | c2_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 0.68/0.90 tff(1915,plain,
% 0.68/0.90 ((~hskp29) | c2_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1914, 1912])).
% 0.68/0.90 tff(1916,plain,
% 0.68/0.90 ((~hskp29) | c2_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1915, 1912])).
% 0.68/0.90 tff(1917,plain,
% 0.68/0.90 ((~hskp29) | c2_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1916, 1912])).
% 0.68/0.90 tff(1918,plain,
% 0.68/0.90 ((~hskp29) | c2_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1917, 1912])).
% 0.68/0.90 tff(1919,plain,
% 0.68/0.90 (c2_1(a2077)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1918, 1903])).
% 0.68/0.90 tff(1920,plain,
% 0.68/0.90 (((~hskp29) | c1_1(a2077)) <=> ((~hskp29) | c1_1(a2077))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1921,axiom,((~hskp29) | c1_1(a2077)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.68/0.90 tff(1922,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 0.68/0.90 tff(1923,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1922, 1920])).
% 0.68/0.90 tff(1924,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1923, 1920])).
% 0.68/0.90 tff(1925,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1924, 1920])).
% 0.68/0.90 tff(1926,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a2077)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1925, 1920])).
% 0.68/0.90 tff(1927,plain,
% 0.68/0.90 (c1_1(a2077)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1926, 1903])).
% 0.68/0.90 tff(1928,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1929,plain,
% 0.68/0.90 (((~ndr1_0) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2077)) | (~c1_1(a2077)) | (~c3_1(a2077)) | (~c0_1(a2077)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093))) <=> (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1930,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2077)) | (~c1_1(a2077)) | (~c3_1(a2077)) | (~c0_1(a2077)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[1929])).
% 0.68/0.90 tff(1931,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2077)) | (~c1_1(a2077)) | (~c3_1(a2077)) | (~c0_1(a2077)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[1930, 1928])).
% 0.68/0.90 tff(1932,plain,
% 0.68/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2077)) | (~c1_1(a2077)) | (~c3_1(a2077)) | (~c0_1(a2077)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(1933,plain,
% 0.68/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 0.68/0.90 tff(1934,plain,
% 0.68/0.90 (~c0_1(a2077)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1933, 87, 1927, 1919, 1911, 329, 321, 315, 308])).
% 0.68/0.90 tff(1935,plain,
% 0.68/0.90 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c1_1(a2077)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c1_1(a2077)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1936,plain,
% 0.68/0.90 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c1_1(a2077)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(1937,plain,
% 0.68/0.90 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c1_1(a2077))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 0.68/0.90 tff(1938,plain,
% 0.68/0.90 (hskp0 | c0_1(a2077)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1937, 87, 1927, 1911, 644])).
% 0.68/0.90 tff(1939,plain,
% 0.68/0.90 (hskp0),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1938, 1934])).
% 0.68/0.90 tff(1940,plain,
% 0.68/0.90 (c3_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[673, 1939])).
% 0.68/0.90 tff(1941,plain,
% 0.68/0.90 (~c2_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[659, 1939])).
% 0.68/0.90 tff(1942,plain,
% 0.68/0.90 (~c1_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[746, 624, 309, 1941, 1940])).
% 0.68/0.90 tff(1943,plain,
% 0.68/0.90 (~c0_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[665, 1939])).
% 0.68/0.90 tff(1944,plain,
% 0.68/0.90 (hskp4 | c1_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[733, 87, 1940, 1943, 1941, 727])).
% 0.68/0.90 tff(1945,plain,
% 0.68/0.90 (hskp4),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1944, 1942])).
% 0.68/0.90 tff(1946,plain,
% 0.68/0.90 (~c2_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[243, 1945])).
% 0.68/0.90 tff(1947,plain,
% 0.68/0.90 (c1_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[259, 1945])).
% 0.68/0.90 tff(1948,plain,
% 0.68/0.90 (c3_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[251, 1945])).
% 0.68/0.90 tff(1949,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1021, 1948, 1947, 624, 309, 1946])).
% 0.68/0.90 tff(1950,plain,(hskp3 | (~hskp11)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(1951,plain,
% 0.68/0.90 (hskp3),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1950, 298])).
% 0.68/0.90 tff(1952,plain,
% 0.68/0.90 (~c3_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[347, 1951])).
% 0.68/0.90 tff(1953,plain,
% 0.68/0.90 (~c1_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[353, 1951])).
% 0.68/0.90 tff(1954,plain,
% 0.68/0.90 (~c0_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[359, 1951])).
% 0.68/0.90 tff(1955,plain,
% 0.68/0.90 (~c3_1(a2093)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[314, 298])).
% 0.68/0.90 tff(1956,plain,
% 0.68/0.90 (~c1_1(a2093)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[320, 298])).
% 0.68/0.90 tff(1957,plain,
% 0.68/0.90 (c0_1(a2093)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[328, 298])).
% 0.68/0.90 tff(1958,plain,
% 0.68/0.90 (~c0_1(a2077)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1933, 87, 1927, 1919, 1911, 1957, 1956, 1955, 308])).
% 0.68/0.90 tff(1959,plain,
% 0.68/0.90 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1960,plain,
% 0.68/0.90 ((hskp8 | hskp1 | (~ndr1_0) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093))) <=> (hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1961,plain,
% 0.68/0.90 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[1960])).
% 0.68/0.90 tff(1962,plain,
% 0.68/0.90 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[1961, 1959])).
% 0.68/0.90 tff(1963,plain,
% 0.68/0.90 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(1964,plain,
% 0.68/0.90 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 0.68/0.90 tff(1965,plain,
% 0.68/0.90 (hskp8),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1964, 87, 11, 1957, 1956, 1955, 140])).
% 0.68/0.90 tff(1966,plain,
% 0.68/0.90 (~c0_1(a2082)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[155, 1965])).
% 0.68/0.90 tff(1967,plain,
% 0.68/0.90 (hskp0),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1938, 1958])).
% 0.68/0.90 tff(1968,plain,
% 0.68/0.90 (~c2_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[659, 1967])).
% 0.68/0.90 tff(1969,plain,
% 0.68/0.90 (~c0_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[665, 1967])).
% 0.68/0.90 tff(1970,plain,
% 0.68/0.90 (c3_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[673, 1967])).
% 0.68/0.90 tff(1971,plain,
% 0.68/0.90 (~c1_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[746, 1970, 298, 1968, 624])).
% 0.68/0.90 tff(1972,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1334, 87, 504, 11, 1969, 1968, 914, 1971])).
% 0.68/0.90 tff(1973,plain,(hskp1 | hskp26 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(1974,plain,
% 0.68/0.90 (hskp1),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1973, 624, 504])).
% 0.68/0.90 tff(1975,plain,
% 0.68/0.90 (hskp5),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[525, 1974, 504])).
% 0.68/0.90 tff(1976,plain,
% 0.68/0.90 (~c0_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[614, 1975])).
% 0.68/0.90 tff(1977,plain,
% 0.68/0.90 (c1_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[622, 1975])).
% 0.68/0.90 tff(1978,plain,
% 0.68/0.90 (c3_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[608, 1975])).
% 0.68/0.90 tff(1979,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1258, 1978, 1977, 504, 624, 1976])).
% 0.68/0.90 tff(1980,plain,(hskp3 | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(1981,plain,
% 0.68/0.90 (hskp3),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1980, 504])).
% 0.68/0.90 tff(1982,plain,
% 0.68/0.90 (~c3_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[347, 1981])).
% 0.68/0.90 tff(1983,plain,
% 0.68/0.90 (~c1_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[353, 1981])).
% 0.68/0.90 tff(1984,plain,
% 0.68/0.90 (~c0_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[359, 1981])).
% 0.68/0.90 tff(1985,plain,
% 0.68/0.90 (hskp1 | c2_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1326, 87, 504, 1984, 1983, 914])).
% 0.68/0.90 tff(1986,plain,
% 0.68/0.90 (c2_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1985, 11])).
% 0.68/0.90 tff(1987,assumption,(c2_1(a2072)), introduced(assumption)).
% 0.68/0.90 tff(1988,plain,
% 0.68/0.90 (hskp4 | (~c2_1(a2072))),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[427, 87, 374, 373, 372, 229])).
% 0.68/0.90 tff(1989,plain,
% 0.68/0.90 (hskp4),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1988, 1987])).
% 0.68/0.90 tff(1990,plain,
% 0.68/0.90 (~c2_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[243, 1989])).
% 0.68/0.90 tff(1991,plain,
% 0.68/0.90 (c3_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[251, 1989])).
% 0.68/0.90 tff(1992,plain,
% 0.68/0.90 (c1_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[259, 1989])).
% 0.68/0.90 tff(1993,plain,
% 0.68/0.90 (~c0_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[438, 87, 1992, 1991, 1990, 374, 372, 10, 1987])).
% 0.68/0.90 tff(1994,assumption,(~hskp0), introduced(assumption)).
% 0.68/0.90 tff(1995,plain,
% 0.68/0.90 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1996,plain,
% 0.68/0.90 ((hskp0 | (~ndr1_0) | c0_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074))) <=> (hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(1997,plain,
% 0.68/0.90 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074)))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[1996])).
% 0.68/0.90 tff(1998,plain,
% 0.68/0.90 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.68/0.90 inference(transitivity,[status(thm)],[1997, 1995])).
% 0.68/0.90 tff(1999,plain,
% 0.68/0.90 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(2000,plain,
% 0.68/0.90 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 0.68/0.90 tff(2001,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2000, 87, 1994, 1992, 1991, 644, 1993])).
% 0.68/0.90 tff(2002,plain,((~c2_1(a2072)) | hskp0 | c0_1(a2072) | c3_1(a2072) | c1_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(2003,plain,
% 0.68/0.90 (hskp0),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2002, 1986, 1984, 1982, 1983])).
% 0.68/0.90 tff(2004,plain,
% 0.68/0.90 (~c0_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[665, 2003])).
% 0.68/0.90 tff(2005,plain,
% 0.68/0.90 (~c2_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[659, 2003])).
% 0.68/0.90 tff(2006,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1349, 2005, 2004, 504, 1984, 1983, 1982, 11])).
% 0.68/0.90 tff(2007,plain,(hskp1 | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(2008,plain,
% 0.68/0.90 (hskp1),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2007, 504])).
% 0.68/0.90 tff(2009,plain,
% 0.68/0.90 (~c2_1(a2070)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[516, 2008])).
% 0.68/0.90 tff(2010,plain,
% 0.68/0.90 (hskp5),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[525, 2008, 504])).
% 0.68/0.90 tff(2011,plain,
% 0.68/0.90 (~c0_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[614, 2010])).
% 0.68/0.90 tff(2012,plain,
% 0.68/0.90 (c3_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[608, 2010])).
% 0.68/0.90 tff(2013,plain,
% 0.68/0.90 (c1_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[622, 2010])).
% 0.68/0.90 tff(2014,plain,
% 0.68/0.90 (hskp0),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[653, 87, 2013, 2012, 2011, 644])).
% 0.68/0.90 tff(2015,plain,
% 0.68/0.90 (~c0_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[665, 2014])).
% 0.68/0.90 tff(2016,plain,
% 0.68/0.90 (~c2_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[659, 2014])).
% 0.68/0.90 tff(2017,plain,
% 0.68/0.90 (c3_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[673, 2014])).
% 0.68/0.90 tff(2018,plain,
% 0.68/0.90 (hskp4),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1407, 2017, 1983, 1982, 2016, 2015])).
% 0.68/0.90 tff(2019,plain,
% 0.68/0.90 (~c2_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[243, 2018])).
% 0.68/0.90 tff(2020,plain,
% 0.68/0.90 (c3_1(a2070)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[494, 2008])).
% 0.68/0.90 tff(2021,plain,
% 0.68/0.90 (c0_1(a2070)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[502, 2008])).
% 0.68/0.90 tff(2022,plain,
% 0.68/0.90 (c3_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[251, 2018])).
% 0.68/0.90 tff(2023,plain,
% 0.68/0.90 (c1_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[259, 2018])).
% 0.68/0.90 tff(2024,plain,
% 0.68/0.90 (~c2_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1473, 87, 2023, 2022, 2021, 2020, 2019, 1984, 1982, 2009, 10])).
% 0.68/0.90 tff(2025,plain,
% 0.68/0.90 (~c1_1(a2068)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1394, 87, 1984, 1983, 1982, 2015, 2016, 371, 2024])).
% 0.68/0.90 tff(2026,plain,
% 0.68/0.90 (c2_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1577, 2025, 2011, 1983, 1982, 2015, 2016, 2024, 2013])).
% 0.68/0.90 tff(2027,plain,
% 0.68/0.90 (hskp14 | c2_1(a2072) | (~c2_1(a2076))),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1594, 87, 2013, 2011, 1983, 1982, 1588])).
% 0.68/0.90 tff(2028,plain,
% 0.68/0.90 (hskp14),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2027, 2026, 2024])).
% 0.68/0.90 tff(2029,plain,
% 0.68/0.90 (~c0_1(a2097)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1601, 2028])).
% 0.68/0.90 tff(2030,plain,
% 0.68/0.90 (c0_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[400, 87, 2023, 2019, 1984, 1983, 1982, 371, 2024])).
% 0.68/0.90 tff(2031,plain,
% 0.68/0.90 (hskp7),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1651, 87, 2023, 2022, 2017, 2015, 1645, 2025, 2030])).
% 0.68/0.90 tff(2032,plain,
% 0.68/0.90 (c1_1(a2079)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1659, 2031])).
% 0.68/0.90 tff(2033,plain,
% 0.68/0.90 (~c3_1(a2079)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[776, 2031])).
% 0.68/0.90 tff(2034,plain,
% 0.68/0.90 (~c1_1(a2097)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1613, 2028])).
% 0.68/0.90 tff(2035,plain,
% 0.68/0.90 (~c2_1(a2097)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1607, 2028])).
% 0.68/0.90 tff(2036,plain,
% 0.68/0.90 (~hskp12),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1848, 2034, 2024, 2035, 1983, 1982, 2029])).
% 0.68/0.90 tff(2037,plain,
% 0.68/0.90 (hskp10),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1748, 2033, 2017, 2030, 2015, 2016, 504, 2036, 2023, 2019, 2032])).
% 0.68/0.90 tff(2038,plain,
% 0.68/0.90 (~c1_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[200, 2037])).
% 0.68/0.90 tff(2039,plain,
% 0.68/0.90 (~c3_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[194, 2037])).
% 0.68/0.90 tff(2040,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1777, 2039, 2038, 2024, 2035, 2034, 2017, 2033, 2015, 2016, 504, 2032, 2023, 2019, 2030, 2022, 1984, 1982, 2029])).
% 0.68/0.90 tff(2041,plain,(hskp26), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(2042,plain,
% 0.68/0.90 (c3_1(a2069)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[533, 2041])).
% 0.68/0.90 tff(2043,plain,
% 0.68/0.90 (c2_1(a2069)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[541, 2041])).
% 0.68/0.90 tff(2044,plain,
% 0.68/0.90 (c0_1(a2069)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[549, 2041])).
% 0.68/0.90 tff(2045,plain,
% 0.68/0.90 (hskp10),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[982, 87, 2044, 2043, 2042, 1970, 1969, 1968, 634])).
% 0.68/0.90 tff(2046,plain,
% 0.68/0.90 (~c3_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[194, 2045])).
% 0.68/0.90 tff(2047,plain,
% 0.68/0.90 (c2_1(a2082)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[163, 1965])).
% 0.68/0.90 tff(2048,plain,
% 0.68/0.90 (c1_1(a2082)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[171, 1965])).
% 0.68/0.90 tff(2049,plain,
% 0.68/0.90 (c2_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[208, 2045])).
% 0.68/0.90 tff(2050,plain,
% 0.68/0.90 (c0_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[953, 87, 11, 2049, 2048, 2047, 2046, 1966, 469])).
% 0.68/0.90 tff(2051,plain,
% 0.68/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.68/0.90 inference(bind,[status(th)],[])).
% 0.68/0.90 tff(2052,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.90 inference(quant_intro,[status(thm)],[2051])).
% 0.68/0.90 tff(2053,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2054,plain,
% 0.68/0.90 (^[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) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.68/0.90 inference(bind,[status(th)],[])).
% 0.68/0.90 tff(2055,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.90 inference(quant_intro,[status(thm)],[2054])).
% 0.68/0.90 tff(2056,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.68/0.90 tff(2057,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 0.68/0.90 tff(2058,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2057, 2053])).
% 0.68/0.90 tff(2059,plain,(
% 0.68/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.90 inference(skolemize,[status(sab)],[2058])).
% 0.68/0.90 tff(2060,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2059, 2052])).
% 0.68/0.90 tff(2061,plain,
% 0.68/0.90 (~c1_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[200, 2045])).
% 0.68/0.90 tff(2062,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2063,plain,
% 0.68/0.90 (((~ndr1_0) | c1_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072))) <=> (c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2064,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[2063])).
% 0.68/0.90 tff(2065,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[2064, 2062])).
% 0.68/0.90 tff(2066,plain,
% 0.68/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(2067,plain,
% 0.68/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 0.68/0.90 tff(2068,plain,
% 0.68/0.90 (~c2_1(a2072)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2067, 87, 1919, 1911, 2049, 2061, 1954, 1953, 2060, 2050, 1958])).
% 0.68/0.90 tff(2069,plain,
% 0.68/0.90 (hskp5),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[420, 2068, 1954, 1953, 1952])).
% 0.68/0.90 tff(2070,plain,
% 0.68/0.90 (~c0_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[614, 2069])).
% 0.68/0.90 tff(2071,plain,
% 0.68/0.90 (c1_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[622, 2069])).
% 0.68/0.90 tff(2072,plain,
% 0.68/0.90 (c3_1(a2076)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[608, 2069])).
% 0.68/0.90 tff(2073,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1459, 2072, 2071, 11, 1954, 1952, 1953, 2070])).
% 0.68/0.90 tff(2074,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(2075,plain,
% 0.68/0.90 (~c2_1(a2070)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[516, 2074])).
% 0.68/0.90 tff(2076,plain,
% 0.68/0.90 (~hskp11),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1950, 624])).
% 0.68/0.90 tff(2077,assumption,(~c1_1(a2070)), introduced(assumption)).
% 0.68/0.90 tff(2078,plain,
% 0.68/0.90 (c3_1(a2070)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[494, 2074])).
% 0.68/0.90 tff(2079,plain,
% 0.68/0.90 (c0_1(a2070)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[502, 2074])).
% 0.68/0.90 tff(2080,plain,
% 0.68/0.90 (hskp11 | hskp10 | c1_1(a2070)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1251, 87, 2079, 2078, 32])).
% 0.68/0.90 tff(2081,plain,
% 0.68/0.90 (hskp10),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2080, 2077, 22])).
% 0.68/0.90 tff(2082,plain,
% 0.68/0.90 (c2_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[208, 2081])).
% 0.68/0.90 tff(2083,plain,
% 0.68/0.90 (c1_1(a2070) | c0_1(a2087) | (~c2_1(a2087))),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[1295, 87, 22, 2079, 210, 2075, 1284])).
% 0.68/0.90 tff(2084,plain,
% 0.68/0.90 (c0_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2083, 2082, 2077])).
% 0.68/0.90 tff(2085,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2086,plain,
% 0.68/0.90 ((hskp4 | (~ndr1_0) | c3_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2087,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[2086])).
% 0.68/0.90 tff(2088,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[2087, 2085])).
% 0.68/0.90 tff(2089,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(2090,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 0.68/0.90 tff(2091,plain,
% 0.68/0.90 (hskp4 | (~c2_1(a2087)) | (~c0_1(a2087))),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2090, 87, 2079, 2078, 210, 2075, 804])).
% 0.68/0.90 tff(2092,plain,
% 0.68/0.90 (hskp4),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2091, 2084, 2082])).
% 0.68/0.90 tff(2093,plain,
% 0.68/0.90 (~c2_1(a2074)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[243, 2092])).
% 0.68/0.90 tff(2094,plain,
% 0.68/0.90 (~c1_1(a2087)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[200, 2081])).
% 0.68/0.90 tff(2095,plain,
% 0.68/0.90 (^[U: $i] : refl((hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.68/0.90 inference(bind,[status(th)],[])).
% 0.68/0.90 tff(2096,plain,
% 0.68/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.68/0.90 inference(quant_intro,[status(thm)],[2095])).
% 0.68/0.90 tff(2097,plain,
% 0.68/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2098,plain,
% 0.68/0.90 (^[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) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp19) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp19) <=> (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.68/0.90 inference(bind,[status(th)],[])).
% 0.68/0.90 tff(2099,plain,
% 0.68/0.90 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp19) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.68/0.90 inference(quant_intro,[status(thm)],[2098])).
% 0.68/0.90 tff(2100,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.68/0.90 tff(2101,plain,
% 0.68/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 0.68/0.90 tff(2102,plain,
% 0.68/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2101, 2097])).
% 0.68/0.90 tff(2103,plain,(
% 0.68/0.90 ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.68/0.90 inference(skolemize,[status(sab)],[2102])).
% 0.68/0.90 tff(2104,plain,
% 0.68/0.90 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2103, 2096])).
% 0.68/0.90 tff(2105,plain,
% 0.68/0.90 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2106,plain,
% 0.68/0.90 ((hskp19 | hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087))) <=> (hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2107,plain,
% 0.68/0.90 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[2106])).
% 0.68/0.90 tff(2108,plain,
% 0.68/0.90 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[2107, 2105])).
% 0.68/0.90 tff(2109,plain,
% 0.68/0.90 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(2110,plain,
% 0.68/0.90 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 0.68/0.90 tff(2111,plain,
% 0.68/0.90 (hskp19 | c1_1(a2087) | (~c0_1(a2087))),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2110, 87, 22, 210, 2104])).
% 0.68/0.90 tff(2112,plain,
% 0.68/0.90 (hskp19),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2111, 2094, 2084])).
% 0.68/0.90 tff(2113,plain,
% 0.68/0.90 (((~hskp19) | (~c3_1(a2122))) <=> ((~hskp19) | (~c3_1(a2122)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2114,plain,
% 0.68/0.90 (((~c3_1(a2122)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a2122)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2115,axiom,((~c3_1(a2122)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.68/0.90 tff(2116,plain,
% 0.68/0.90 ((~hskp19) | (~c3_1(a2122))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 0.68/0.90 tff(2117,plain,
% 0.68/0.90 ((~hskp19) | (~c3_1(a2122))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2116, 2113])).
% 0.68/0.90 tff(2118,plain,
% 0.68/0.90 (~c3_1(a2122)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2117, 2112])).
% 0.68/0.90 tff(2119,plain,
% 0.68/0.90 (((~hskp19) | (~c0_1(a2122))) <=> ((~hskp19) | (~c0_1(a2122)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2120,plain,
% 0.68/0.90 (((~c0_1(a2122)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a2122)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(2121,axiom,((~c0_1(a2122)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.68/0.90 tff(2122,plain,
% 0.68/0.90 ((~hskp19) | (~c0_1(a2122))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 0.68/0.90 tff(2123,plain,
% 0.68/0.90 ((~hskp19) | (~c0_1(a2122))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[2122, 2119])).
% 0.68/0.90 tff(2124,plain,
% 0.68/0.90 (~c0_1(a2122)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[2123, 2112])).
% 0.68/0.90 tff(2125,plain,
% 0.68/0.90 (c3_1(a2074)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[251, 2092])).
% 0.68/0.91 tff(2126,plain,
% 0.68/0.91 (c1_1(a2074)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[259, 2092])).
% 0.68/0.91 tff(2127,plain,
% 0.68/0.91 (((~hskp19) | c2_1(a2122)) <=> ((~hskp19) | c2_1(a2122))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2128,axiom,((~hskp19) | c2_1(a2122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.68/0.91 tff(2129,plain,
% 0.68/0.91 ((~hskp19) | c2_1(a2122)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.68/0.91 tff(2130,plain,
% 0.68/0.91 ((~hskp19) | c2_1(a2122)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2129, 2127])).
% 0.68/0.91 tff(2131,plain,
% 0.68/0.91 ((~hskp19) | c2_1(a2122)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2130, 2127])).
% 0.68/0.91 tff(2132,plain,
% 0.68/0.91 ((~hskp19) | c2_1(a2122)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2131, 2127])).
% 0.68/0.91 tff(2133,plain,
% 0.68/0.91 ((~hskp19) | c2_1(a2122)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2132, 2127])).
% 0.68/0.91 tff(2134,plain,
% 0.68/0.91 (c2_1(a2122)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2133, 2112])).
% 0.68/0.91 tff(2135,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2136,plain,
% 0.68/0.91 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2122) | c3_1(a2122) | (~c2_1(a2122))) <=> (c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2137,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2122) | c3_1(a2122) | (~c2_1(a2122)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[2136])).
% 0.68/0.91 tff(2138,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2122) | c3_1(a2122) | (~c2_1(a2122)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[2137, 2135])).
% 0.68/0.91 tff(2139,plain,
% 0.68/0.91 ((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2122) | c3_1(a2122) | (~c2_1(a2122)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(2140,plain,
% 0.68/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 0.68/0.91 tff(2141,plain,
% 0.68/0.91 ($false),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2140, 87, 2134, 2126, 2125, 2079, 2078, 2124, 2118, 2093, 2075, 10])).
% 0.68/0.91 tff(2142,plain,(c1_1(a2070) | c3_1(a2087) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.68/0.91 tff(2143,plain,
% 0.68/0.91 (c3_1(a2087)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2142, 2077, 22])).
% 0.68/0.91 tff(2144,plain,
% 0.68/0.91 ($false),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[194, 2143, 2081])).
% 0.68/0.91 tff(2145,plain,(c1_1(a2070) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.68/0.91 tff(2146,plain,
% 0.68/0.91 (c1_1(a2070)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2145, 2076])).
% 0.68/0.91 tff(2147,plain,
% 0.68/0.91 (hskp5 | (~c1_1(a2070))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[523, 87, 2079, 2078, 2075, 411])).
% 0.68/0.91 tff(2148,plain,
% 0.68/0.91 (hskp5),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2147, 2146])).
% 0.68/0.91 tff(2149,plain,
% 0.68/0.91 (~c0_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[614, 2148])).
% 0.68/0.91 tff(2150,plain,
% 0.68/0.91 (c3_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[608, 2148])).
% 0.68/0.91 tff(2151,plain,
% 0.68/0.91 (c1_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[622, 2148])).
% 0.68/0.91 tff(2152,plain,
% 0.68/0.91 (c1_1(a2070)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2142, 210, 2076])).
% 0.68/0.91 tff(2153,plain,
% 0.68/0.91 (hskp5),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2147, 2152])).
% 0.68/0.91 tff(2154,plain,
% 0.68/0.91 (c3_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[608, 2153])).
% 0.68/0.91 tff(2155,plain,
% 0.68/0.91 (c1_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[622, 2153])).
% 0.68/0.91 tff(2156,plain,
% 0.68/0.91 (hskp0 | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[653, 87, 645, 644])).
% 0.68/0.91 tff(2157,plain,
% 0.68/0.91 (hskp0),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2156, 2155, 2154])).
% 0.68/0.91 tff(2158,plain,
% 0.68/0.91 (~c0_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[665, 2157])).
% 0.68/0.91 tff(2159,plain,
% 0.68/0.91 (c3_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[673, 2157])).
% 0.68/0.91 tff(2160,plain,
% 0.68/0.91 (hskp10),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[982, 87, 2044, 2043, 2042, 2159, 2158, 737, 634])).
% 0.68/0.91 tff(2161,plain,
% 0.68/0.91 (~c1_1(a2087)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[200, 2160])).
% 0.68/0.91 tff(2162,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2163,plain,
% 0.68/0.91 ((hskp3 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087))) <=> (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2164,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[2163])).
% 0.68/0.91 tff(2165,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[2164, 2162])).
% 0.68/0.91 tff(2166,plain,
% 0.68/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(2167,plain,
% 0.68/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 0.68/0.91 tff(2168,plain,
% 0.68/0.91 (c1_1(a2087) | (~c1_1(a2070)) | (~c0_1(a2087))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2167, 87, 624, 2078, 210, 2075, 340])).
% 0.68/0.91 tff(2169,plain,
% 0.68/0.91 (~c0_1(a2087)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2168, 2161, 2152])).
% 0.68/0.91 tff(2170,plain,
% 0.68/0.91 (hskp4),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[989, 2155, 624, 645, 2154])).
% 0.68/0.91 tff(2171,plain,
% 0.68/0.91 (~c2_1(a2074)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[243, 2170])).
% 0.68/0.91 tff(2172,plain,
% 0.68/0.91 (c3_1(a2074)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[251, 2170])).
% 0.68/0.91 tff(2173,plain,
% 0.68/0.91 (c1_1(a2074)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[259, 2170])).
% 0.68/0.91 tff(2174,plain,
% 0.68/0.91 (c2_1(a2087)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[208, 2160])).
% 0.68/0.91 tff(2175,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | (c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2176,plain,
% 0.68/0.91 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087))) <=> (c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2177,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | (c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[2176])).
% 0.68/0.91 tff(2178,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[2177, 2175])).
% 0.68/0.91 tff(2179,plain,
% 0.68/0.91 ((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(2180,plain,
% 0.68/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 0.68/0.91 tff(2181,plain,
% 0.68/0.91 ($false),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2180, 87, 2174, 2173, 2172, 2079, 2078, 210, 2171, 2075, 10, 2169])).
% 0.68/0.91 tff(2182,plain,(c3_1(a2087) | hskp3 | c2_1(a2068) | c0_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.91 tff(2183,plain,
% 0.68/0.91 (c3_1(a2087)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2182, 645, 737, 624])).
% 0.68/0.91 tff(2184,plain,
% 0.68/0.91 (~hskp10),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[194, 2183])).
% 0.68/0.91 tff(2185,plain,
% 0.68/0.91 (c1_1(a2070)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2080, 2184, 2076])).
% 0.68/0.91 tff(2186,plain,
% 0.68/0.91 (hskp5),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2147, 2185])).
% 0.68/0.91 tff(2187,plain,
% 0.68/0.91 (c3_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[608, 2186])).
% 0.68/0.91 tff(2188,plain,
% 0.68/0.91 (c1_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[622, 2186])).
% 0.68/0.91 tff(2189,plain,
% 0.68/0.91 (hskp0),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2156, 2188, 2187])).
% 0.68/0.91 tff(2190,plain,
% 0.68/0.91 (~c0_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[665, 2189])).
% 0.68/0.91 tff(2191,plain,
% 0.68/0.91 (c3_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[673, 2189])).
% 0.68/0.91 tff(2192,plain,
% 0.68/0.91 ($false),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[982, 87, 2184, 2044, 2043, 2042, 2191, 2190, 737, 634])).
% 0.68/0.91 tff(2193,plain,(c0_1(a2076) | c2_1(a2068) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.68/0.91 tff(2194,plain,
% 0.68/0.91 (c2_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2193, 2149, 624])).
% 0.68/0.91 tff(2195,plain,
% 0.68/0.91 (~hskp0),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[659, 2194])).
% 0.68/0.91 tff(2196,plain,
% 0.68/0.91 ($false),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[653, 87, 2195, 2151, 2150, 2149, 644])).
% 0.68/0.91 tff(2197,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 0.68/0.91 tff(2198,plain,
% 0.68/0.91 (~c3_1(a2072)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[347, 2197])).
% 0.68/0.91 tff(2199,plain,
% 0.68/0.91 (~c0_1(a2072)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[359, 2197])).
% 0.68/0.91 tff(2200,plain,
% 0.68/0.91 (c1_1(a2070)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2145, 22])).
% 0.68/0.91 tff(2201,plain,
% 0.68/0.91 (hskp5),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2147, 2200])).
% 0.68/0.91 tff(2202,plain,
% 0.68/0.91 (c1_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[622, 2201])).
% 0.68/0.91 tff(2203,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2204,plain,
% 0.68/0.91 (((~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072))) <=> (c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2205,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[2204])).
% 0.68/0.91 tff(2206,plain,
% 0.68/0.91 (((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[2205, 2203])).
% 0.68/0.91 tff(2207,plain,
% 0.68/0.91 ((~![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) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(2208,plain,
% 0.68/0.91 ((~![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) | c3_1(W) | (~c2_1(W)))) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 0.68/0.91 tff(2209,plain,
% 0.68/0.91 ((~c1_1(a2070)) | (~c2_1(a2072))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2208, 87, 2079, 2078, 2199, 2198, 2075, 10])).
% 0.68/0.91 tff(2210,plain,
% 0.68/0.91 (~c2_1(a2072)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2209, 2200])).
% 0.68/0.91 tff(2211,plain,
% 0.68/0.91 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(2212,plain,
% 0.68/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[2211])).
% 0.68/0.91 tff(2213,plain,
% 0.68/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2214,plain,
% 0.68/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_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)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(2215,plain,
% 0.68/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[2214])).
% 0.68/0.91 tff(2216,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.68/0.91 tff(2217,plain,
% 0.68/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 0.68/0.91 tff(2218,plain,
% 0.68/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2217, 2213])).
% 0.68/0.91 tff(2219,plain,(
% 0.68/0.91 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.68/0.91 inference(skolemize,[status(sab)],[2218])).
% 0.68/0.91 tff(2220,plain,
% 0.68/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2219, 2212])).
% 0.68/0.91 tff(2221,plain,
% 0.68/0.91 (~c1_1(a2072)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[353, 2197])).
% 0.68/0.91 tff(2222,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2223,plain,
% 0.68/0.91 ((hskp0 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c1_1(a2072) | c0_1(a2072) | c2_1(a2072)) <=> (hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(2224,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c1_1(a2072) | c0_1(a2072) | c2_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[2223])).
% 0.68/0.91 tff(2225,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c1_1(a2072) | c0_1(a2072) | c2_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[2224, 2222])).
% 0.68/0.91 tff(2226,plain,
% 0.68/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c1_1(a2072) | c0_1(a2072) | c2_1(a2072))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(2227,plain,
% 0.68/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 0.68/0.91 tff(2228,plain,
% 0.68/0.91 (hskp0 | c2_1(a2072)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2227, 87, 2044, 2043, 2042, 2199, 2221, 2220])).
% 0.68/0.91 tff(2229,plain,
% 0.68/0.91 (hskp0),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[2228, 2210])).
% 0.68/0.91 tff(2230,plain,
% 0.68/0.91 (~c2_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[659, 2229])).
% 0.68/0.91 tff(2231,plain,
% 0.68/0.91 (~c0_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[665, 2229])).
% 0.68/0.91 tff(2232,plain,
% 0.68/0.91 (c3_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[673, 2229])).
% 0.68/0.91 tff(2233,plain,
% 0.68/0.91 (hskp10),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[982, 87, 2044, 2043, 2042, 2232, 2231, 2230, 634])).
% 0.68/0.91 tff(2234,plain,
% 0.68/0.91 (~c3_1(a2087)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[194, 2233])).
% 0.68/0.91 tff(2235,plain,
% 0.68/0.91 (~c1_1(a2087)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[200, 2233])).
% 0.68/0.91 tff(2236,plain,
% 0.68/0.91 (~c1_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[1394, 87, 2199, 2221, 2198, 2231, 2230, 371, 2210])).
% 0.68/0.91 tff(2237,plain,
% 0.68/0.91 (~c0_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[614, 2201])).
% 0.68/0.91 tff(2238,plain,
% 0.68/0.91 (c3_1(a2076)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[608, 2201])).
% 0.68/0.91 tff(2239,plain,
% 0.68/0.91 (c2_1(a2087)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[208, 2233])).
% 0.68/0.91 tff(2240,plain,
% 0.68/0.91 (hskp8),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[1378, 2239, 2238, 2237, 2236, 2235, 2234, 2202])).
% 0.68/0.91 tff(2241,plain,
% 0.68/0.91 (~c0_1(a2082)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[155, 2240])).
% 0.68/0.91 tff(2242,plain,
% 0.68/0.91 (c2_1(a2082)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[163, 2240])).
% 0.68/0.91 tff(2243,plain,
% 0.68/0.91 (c1_1(a2082)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[171, 2240])).
% 0.68/0.91 tff(2244,plain,
% 0.68/0.91 ($false),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[295, 87, 22, 2239, 2243, 2242, 2235, 2234, 2241, 21])).
% 0.68/0.91 tff(2245,plain,(hskp11), inference(lemma,lemma(discharge,[]))).
% 0.68/0.91 tff(2246,plain,
% 0.68/0.91 (~c3_1(a2093)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[314, 2245])).
% 0.68/0.91 tff(2247,plain,
% 0.68/0.91 (~c1_1(a2093)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[320, 2245])).
% 0.68/0.91 tff(2248,plain,
% 0.68/0.91 (c0_1(a2093)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[328, 2245])).
% 0.68/0.91 tff(2249,plain,
% 0.68/0.91 (~c0_1(a2077)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[1933, 87, 1927, 1919, 1911, 2248, 2247, 2246, 308])).
% 0.68/0.91 tff(2250,plain,
% 0.68/0.91 (hskp0),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[1938, 2249])).
% 0.68/0.91 tff(2251,plain,
% 0.68/0.91 (~c0_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[665, 2250])).
% 0.68/0.91 tff(2252,plain,
% 0.68/0.91 (~c2_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[659, 2250])).
% 0.68/0.91 tff(2253,plain,
% 0.68/0.91 (c3_1(a2068)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[673, 2250])).
% 0.68/0.91 tff(2254,plain,
% 0.68/0.91 (hskp4),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[1407, 2253, 2221, 2198, 2252, 2251])).
% 0.68/0.91 tff(2255,plain,
% 0.68/0.91 (~c2_1(a2074)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[243, 2254])).
% 0.68/0.91 tff(2256,plain,
% 0.68/0.91 (c3_1(a2074)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[251, 2254])).
% 0.68/0.91 tff(2257,plain,
% 0.68/0.91 (c1_1(a2074)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[259, 2254])).
% 0.68/0.91 tff(2258,plain,
% 0.68/0.91 (~c2_1(a2072)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[1473, 87, 2257, 2256, 2079, 2078, 2255, 2199, 2198, 2075, 10])).
% 0.68/0.91 tff(2259,plain,
% 0.68/0.91 (hskp10),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[982, 87, 2044, 2043, 2042, 2253, 2251, 2252, 634])).
% 0.68/0.91 tff(2260,plain,
% 0.68/0.92 (~c3_1(a2087)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[194, 2259])).
% 0.68/0.92 tff(2261,plain,
% 0.68/0.92 (~c1_1(a2087)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[200, 2259])).
% 0.68/0.92 tff(2262,plain,
% 0.68/0.92 (c2_1(a2087)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[208, 2259])).
% 0.68/0.92 tff(2263,plain,
% 0.68/0.92 ($false),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[1457, 87, 2262, 2257, 2256, 2261, 2260, 2255, 2199, 2198, 1451, 2258])).
% 0.68/0.92 % SZS output end Proof
% 0.68/0.92 % E exiting
%------------------------------------------------------------------------------