%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN502-1 : 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 05:39:22 AM UTC 2025
% Result : Unsatisfiable 0.49s 0.68s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN502-1 : TPTP v9.0.0. Released v2.1.0.
% 0.02/0.11 % 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 12:37:24 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.49/0.68 % SZS status Unsatisfiable
% 0.49/0.68 % SZS output start Proof
% 0.49/0.68 tff(c3_1_type, type, (
% 0.49/0.68 c3_1: $i > $o)).
% 0.49/0.68 tff(a271_type, type, (
% 0.49/0.68 a271: $i)).
% 0.49/0.68 tff(c1_1_type, type, (
% 0.49/0.68 c1_1: $i > $o)).
% 0.49/0.68 tff(c0_1_type, type, (
% 0.49/0.68 c0_1: $i > $o)).
% 0.49/0.68 tff(ndr1_0_type, type, (
% 0.49/0.68 ndr1_0: $o)).
% 0.49/0.68 tff(hskp4_type, type, (
% 0.49/0.68 hskp4: $o)).
% 0.49/0.68 tff(hskp20_type, type, (
% 0.49/0.68 hskp20: $o)).
% 0.49/0.68 tff(a238_type, type, (
% 0.49/0.68 a238: $i)).
% 0.49/0.68 tff(a249_type, type, (
% 0.49/0.68 a249: $i)).
% 0.49/0.68 tff(c2_1_type, type, (
% 0.49/0.68 c2_1: $i > $o)).
% 0.49/0.68 tff(hskp3_type, type, (
% 0.49/0.68 hskp3: $o)).
% 0.49/0.68 tff(hskp10_type, type, (
% 0.49/0.68 hskp10: $o)).
% 0.49/0.68 tff(a246_type, type, (
% 0.49/0.68 a246: $i)).
% 0.49/0.68 tff(hskp31_type, type, (
% 0.49/0.68 hskp31: $o)).
% 0.49/0.68 tff(a241_type, type, (
% 0.49/0.68 a241: $i)).
% 0.49/0.68 tff(hskp5_type, type, (
% 0.49/0.68 hskp5: $o)).
% 0.49/0.68 tff(a251_type, type, (
% 0.49/0.68 a251: $i)).
% 0.49/0.68 tff(hskp11_type, type, (
% 0.49/0.68 hskp11: $o)).
% 0.49/0.68 tff(a237_type, type, (
% 0.49/0.68 a237: $i)).
% 0.49/0.68 tff(hskp28_type, type, (
% 0.49/0.68 hskp28: $o)).
% 0.49/0.68 tff(a239_type, type, (
% 0.49/0.68 a239: $i)).
% 0.49/0.68 tff(a258_type, type, (
% 0.49/0.68 a258: $i)).
% 0.49/0.68 tff(hskp18_type, type, (
% 0.49/0.68 hskp18: $o)).
% 0.49/0.68 tff(a265_type, type, (
% 0.49/0.68 a265: $i)).
% 0.49/0.68 tff(a269_type, type, (
% 0.49/0.68 a269: $i)).
% 0.49/0.68 tff(hskp19_type, type, (
% 0.49/0.68 hskp19: $o)).
% 0.49/0.68 tff(hskp2_type, type, (
% 0.49/0.68 hskp2: $o)).
% 0.49/0.68 tff(hskp22_type, type, (
% 0.49/0.68 hskp22: $o)).
% 0.49/0.68 tff(a252_type, type, (
% 0.49/0.68 a252: $i)).
% 0.49/0.68 tff(hskp12_type, type, (
% 0.49/0.68 hskp12: $o)).
% 0.49/0.68 tff(a240_type, type, (
% 0.49/0.68 a240: $i)).
% 0.49/0.68 tff(hskp29_type, type, (
% 0.49/0.68 hskp29: $o)).
% 0.49/0.68 tff(a259_type, type, (
% 0.49/0.68 a259: $i)).
% 0.49/0.68 tff(hskp16_type, type, (
% 0.49/0.68 hskp16: $o)).
% 0.49/0.68 tff(a236_type, type, (
% 0.49/0.68 a236: $i)).
% 0.49/0.68 tff(a294_type, type, (
% 0.49/0.68 a294: $i)).
% 0.49/0.68 tff(hskp25_type, type, (
% 0.49/0.68 hskp25: $o)).
% 0.49/0.68 tff(hskp15_type, type, (
% 0.49/0.68 hskp15: $o)).
% 0.49/0.68 tff(a244_type, type, (
% 0.49/0.68 a244: $i)).
% 0.49/0.68 tff(hskp7_type, type, (
% 0.49/0.68 hskp7: $o)).
% 0.49/0.68 tff(1,plain,
% 0.49/0.68 (^[U: $i] : refl((hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(2,plain,
% 0.49/0.68 (![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[1])).
% 0.49/0.68 tff(3,plain,
% 0.49/0.68 (![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(4,plain,
% 0.49/0.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(5,plain,
% 0.49/0.68 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4) <=> ![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[4])).
% 0.49/0.68 tff(6,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.49/0.68 tff(7,plain,
% 0.49/0.68 (![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.49/0.68 tff(8,plain,
% 0.49/0.68 (![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.49/0.68 tff(9,plain,(
% 0.49/0.68 ![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(skolemize,[status(sab)],[8])).
% 0.49/0.68 tff(10,plain,
% 0.49/0.68 (![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.49/0.68 tff(11,plain,
% 0.49/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(12,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[11])).
% 0.49/0.68 tff(13,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(14,plain,
% 0.49/0.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(15,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[14])).
% 0.49/0.68 tff(16,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause206')).
% 0.49/0.68 tff(17,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.49/0.68 tff(18,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.49/0.68 tff(19,plain,(
% 0.49/0.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.68 inference(skolemize,[status(sab)],[18])).
% 0.49/0.68 tff(20,plain,
% 0.49/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.49/0.68 tff(21,plain,
% 0.49/0.68 (^[U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.49/0.68 inference(bind,[status(th)],[])).
% 0.49/0.68 tff(22,plain,
% 0.49/0.68 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.68 inference(quant_intro,[status(thm)],[21])).
% 0.49/0.68 tff(23,plain,
% 0.49/0.68 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(24,plain,
% 0.49/0.68 (^[U: $i] : 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)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(25,plain,
% 0.49/0.69 (![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp10) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[24])).
% 0.49/0.69 tff(26,axiom,(![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.49/0.69 tff(27,plain,
% 0.49/0.69 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.49/0.69 tff(28,plain,
% 0.49/0.69 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.49/0.69 tff(29,plain,(
% 0.49/0.69 ![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.69 inference(skolemize,[status(sab)],[28])).
% 0.49/0.69 tff(30,plain,
% 0.49/0.69 (![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.49/0.69 tff(31,assumption,(~hskp10), introduced(assumption)).
% 0.49/0.69 tff(32,assumption,(~hskp11), introduced(assumption)).
% 0.49/0.69 tff(33,plain,
% 0.49/0.69 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(34,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[33])).
% 0.49/0.69 tff(35,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(36,plain,
% 0.49/0.69 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_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)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_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)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_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)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(37,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_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)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[36])).
% 0.49/0.69 tff(38,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 0.49/0.69 tff(39,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.49/0.69 tff(40,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.49/0.69 tff(41,plain,(
% 0.49/0.69 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.49/0.69 inference(skolemize,[status(sab)],[40])).
% 0.49/0.69 tff(42,plain,
% 0.49/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.49/0.69 tff(43,assumption,(~c2_1(a239)), introduced(assumption)).
% 0.49/0.69 tff(44,assumption,(~c1_1(a239)), introduced(assumption)).
% 0.49/0.69 tff(45,assumption,(~hskp3), introduced(assumption)).
% 0.49/0.69 tff(46,assumption,(~hskp18), introduced(assumption)).
% 0.49/0.69 tff(47,plain,
% 0.49/0.69 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(48,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[47])).
% 0.49/0.69 tff(49,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(50,plain,
% 0.49/0.69 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(51,plain,
% 0.49/0.69 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[50])).
% 0.49/0.69 tff(52,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.49/0.69 tff(53,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.49/0.69 tff(54,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.49/0.69 tff(55,plain,(
% 0.49/0.69 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.69 inference(skolemize,[status(sab)],[54])).
% 0.49/0.69 tff(56,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.49/0.69 tff(57,plain,
% 0.49/0.69 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(58,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[57])).
% 0.49/0.69 tff(59,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(60,plain,
% 0.49/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(61,plain,
% 0.49/0.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[60])).
% 0.49/0.69 tff(62,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.49/0.69 tff(63,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.49/0.69 tff(64,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.49/0.69 tff(65,plain,(
% 0.49/0.69 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.49/0.69 inference(skolemize,[status(sab)],[64])).
% 0.49/0.69 tff(66,plain,
% 0.49/0.69 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.49/0.69 tff(67,plain,
% 0.49/0.69 (^[U: $i] : refl((hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(68,plain,
% 0.49/0.69 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[67])).
% 0.49/0.69 tff(69,plain,
% 0.49/0.69 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(70,plain,
% 0.49/0.69 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp5) <=> ((hskp10 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp5))), rewrite(((hskp10 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp5) <=> (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp5) <=> (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(71,plain,
% 0.49/0.69 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp5) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[70])).
% 0.49/0.69 tff(72,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.49/0.69 tff(73,plain,
% 0.49/0.69 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.49/0.69 tff(74,plain,
% 0.49/0.69 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.49/0.69 tff(75,plain,(
% 0.49/0.69 ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.69 inference(skolemize,[status(sab)],[74])).
% 0.49/0.69 tff(76,plain,
% 0.49/0.69 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.49/0.69 tff(77,plain,
% 0.49/0.69 ((hskp19 | hskp18 | hskp11) <=> (hskp19 | hskp18 | hskp11)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(78,plain,
% 0.49/0.69 (((hskp19 | hskp18) | hskp11) <=> (hskp19 | hskp18 | hskp11)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(79,plain,
% 0.49/0.69 ((hskp19 | hskp18) <=> (hskp19 | hskp18)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(80,plain,
% 0.49/0.69 (((hskp19 | hskp18) | hskp11) <=> ((hskp19 | hskp18) | hskp11)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[79])).
% 0.49/0.69 tff(81,plain,
% 0.49/0.69 (((hskp19 | hskp18) | hskp11) <=> (hskp19 | hskp18 | hskp11)),
% 0.49/0.69 inference(transitivity,[status(thm)],[80, 78])).
% 0.49/0.69 tff(82,axiom,((hskp19 | hskp18) | hskp11), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.49/0.69 tff(83,plain,
% 0.49/0.69 (hskp19 | hskp18 | hskp11),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.49/0.69 tff(84,plain,
% 0.49/0.69 (hskp19 | hskp18 | hskp11),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[83, 77])).
% 0.49/0.69 tff(85,plain,
% 0.49/0.69 (hskp19 | hskp18 | hskp11),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.49/0.69 tff(86,plain,
% 0.49/0.69 (hskp19 | hskp18 | hskp11),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[85, 77])).
% 0.49/0.69 tff(87,plain,
% 0.49/0.69 (hskp19 | hskp18 | hskp11),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[86, 77])).
% 0.49/0.69 tff(88,plain,
% 0.49/0.69 (hskp19),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[87, 32, 46])).
% 0.49/0.69 tff(89,plain,
% 0.49/0.69 (((~hskp19) | (~c1_1(a269))) <=> ((~hskp19) | (~c1_1(a269)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(90,plain,
% 0.49/0.69 (((~c1_1(a269)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a269)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(91,axiom,((~c1_1(a269)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.49/0.69 tff(92,plain,
% 0.49/0.69 ((~hskp19) | (~c1_1(a269))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.49/0.69 tff(93,plain,
% 0.49/0.69 ((~hskp19) | (~c1_1(a269))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.49/0.69 tff(94,plain,
% 0.49/0.69 (~c1_1(a269)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[93, 88])).
% 0.49/0.69 tff(95,plain,
% 0.49/0.69 (((~hskp19) | c3_1(a269)) <=> ((~hskp19) | c3_1(a269))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(96,axiom,((~hskp19) | c3_1(a269)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.49/0.69 tff(97,plain,
% 0.49/0.69 ((~hskp19) | c3_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.49/0.69 tff(98,plain,
% 0.49/0.69 ((~hskp19) | c3_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[97, 95])).
% 0.49/0.69 tff(99,plain,
% 0.49/0.69 ((~hskp19) | c3_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.49/0.69 tff(100,plain,
% 0.49/0.69 ((~hskp19) | c3_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.49/0.69 tff(101,plain,
% 0.49/0.69 ((~hskp19) | c3_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[100, 95])).
% 0.49/0.69 tff(102,plain,
% 0.49/0.69 (c3_1(a269)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[101, 88])).
% 0.49/0.69 tff(103,plain,
% 0.49/0.69 (((~hskp19) | c0_1(a269)) <=> ((~hskp19) | c0_1(a269))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(104,axiom,((~hskp19) | c0_1(a269)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.49/0.69 tff(105,plain,
% 0.49/0.69 ((~hskp19) | c0_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.49/0.69 tff(106,plain,
% 0.49/0.69 ((~hskp19) | c0_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[105, 103])).
% 0.49/0.69 tff(107,plain,
% 0.49/0.69 ((~hskp19) | c0_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[106, 103])).
% 0.49/0.69 tff(108,plain,
% 0.49/0.69 ((~hskp19) | c0_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.49/0.69 tff(109,plain,
% 0.49/0.69 ((~hskp19) | c0_1(a269)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[108, 103])).
% 0.49/0.69 tff(110,plain,
% 0.49/0.69 (c0_1(a269)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[109, 88])).
% 0.49/0.69 tff(111,assumption,(~ndr1_0), introduced(assumption)).
% 0.49/0.69 tff(112,plain,
% 0.49/0.69 ((ndr1_0 | (~hskp2)) <=> (ndr1_0 | (~hskp2))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(113,plain,
% 0.49/0.69 (((~hskp2) | ndr1_0) <=> (ndr1_0 | (~hskp2))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(114,axiom,((~hskp2) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 0.49/0.69 tff(115,plain,
% 0.49/0.69 (ndr1_0 | (~hskp2)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.49/0.69 tff(116,plain,
% 0.49/0.69 (ndr1_0 | (~hskp2)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[115, 112])).
% 0.49/0.69 tff(117,plain,
% 0.49/0.69 (~hskp2),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[116, 111])).
% 0.49/0.69 tff(118,plain,
% 0.49/0.69 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(119,plain,
% 0.49/0.69 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(120,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.49/0.69 tff(121,plain,
% 0.49/0.69 (ndr1_0 | (~hskp28)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.49/0.69 tff(122,plain,
% 0.49/0.69 (ndr1_0 | (~hskp28)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.49/0.69 tff(123,plain,
% 0.49/0.69 (~hskp28),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[122, 111])).
% 0.49/0.69 tff(124,plain,
% 0.49/0.69 ((ndr1_0 | (~hskp22)) <=> (ndr1_0 | (~hskp22))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(125,plain,
% 0.49/0.69 (((~hskp22) | ndr1_0) <=> (ndr1_0 | (~hskp22))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(126,axiom,((~hskp22) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause10')).
% 0.49/0.69 tff(127,plain,
% 0.49/0.69 (ndr1_0 | (~hskp22)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.49/0.69 tff(128,plain,
% 0.49/0.69 (ndr1_0 | (~hskp22)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[127, 124])).
% 0.49/0.69 tff(129,plain,
% 0.49/0.69 (~hskp22),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[128, 111])).
% 0.49/0.69 tff(130,plain,
% 0.49/0.69 ((hskp28 | hskp22 | hskp2) <=> (hskp28 | hskp22 | hskp2)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(131,plain,
% 0.49/0.69 (((hskp28 | hskp22) | hskp2) <=> (hskp28 | hskp22 | hskp2)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(132,plain,
% 0.49/0.69 ((hskp28 | hskp22) <=> (hskp28 | hskp22)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(133,plain,
% 0.49/0.69 (((hskp28 | hskp22) | hskp2) <=> ((hskp28 | hskp22) | hskp2)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[132])).
% 0.49/0.69 tff(134,plain,
% 0.49/0.69 (((hskp28 | hskp22) | hskp2) <=> (hskp28 | hskp22 | hskp2)),
% 0.49/0.69 inference(transitivity,[status(thm)],[133, 131])).
% 0.49/0.69 tff(135,axiom,((hskp28 | hskp22) | hskp2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.49/0.69 tff(136,plain,
% 0.49/0.69 (hskp28 | hskp22 | hskp2),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.49/0.69 tff(137,plain,
% 0.49/0.69 (hskp28 | hskp22 | hskp2),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[136, 130])).
% 0.49/0.69 tff(138,plain,
% 0.49/0.69 (hskp28 | hskp22 | hskp2),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.49/0.69 tff(139,plain,
% 0.49/0.69 (hskp28 | hskp22 | hskp2),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[138, 130])).
% 0.49/0.69 tff(140,plain,
% 0.49/0.69 (hskp28 | hskp22 | hskp2),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[139, 130])).
% 0.49/0.69 tff(141,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[140, 129, 123, 117])).
% 0.49/0.69 tff(142,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(143,plain,
% 0.49/0.69 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | c1_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp10 | hskp5 | c1_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(144,plain,
% 0.49/0.69 ((hskp10 | hskp5 | (~ndr1_0) | c1_1(a269) | (~c0_1(a269)) | (~c3_1(a269))) <=> (hskp10 | hskp5 | c1_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(145,plain,
% 0.49/0.69 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c1_1(a269) | (~c0_1(a269)) | (~c3_1(a269)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | c1_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[144])).
% 0.49/0.69 tff(146,plain,
% 0.49/0.69 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c1_1(a269) | (~c0_1(a269)) | (~c3_1(a269)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp10 | hskp5 | c1_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[145, 143])).
% 0.49/0.69 tff(147,plain,
% 0.49/0.69 ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c1_1(a269) | (~c0_1(a269)) | (~c3_1(a269)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(148,plain,
% 0.49/0.69 ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp10 | hskp5 | c1_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.49/0.69 tff(149,plain,
% 0.49/0.69 (hskp5),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[148, 142, 31, 110, 102, 94, 76])).
% 0.49/0.69 tff(150,plain,
% 0.49/0.69 (((~hskp5) | (~c0_1(a241))) <=> ((~hskp5) | (~c0_1(a241)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(151,plain,
% 0.49/0.69 (((~c0_1(a241)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a241)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(152,axiom,((~c0_1(a241)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.49/0.69 tff(153,plain,
% 0.49/0.69 ((~hskp5) | (~c0_1(a241))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.49/0.69 tff(154,plain,
% 0.49/0.69 ((~hskp5) | (~c0_1(a241))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[153, 150])).
% 0.49/0.69 tff(155,plain,
% 0.49/0.69 (~c0_1(a241)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[154, 149])).
% 0.49/0.69 tff(156,plain,
% 0.49/0.69 (((~hskp5) | c3_1(a241)) <=> ((~hskp5) | c3_1(a241))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(157,axiom,((~hskp5) | c3_1(a241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.49/0.69 tff(158,plain,
% 0.49/0.69 ((~hskp5) | c3_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.49/0.69 tff(159,plain,
% 0.49/0.69 ((~hskp5) | c3_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[158, 156])).
% 0.49/0.69 tff(160,plain,
% 0.49/0.69 ((~hskp5) | c3_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[159, 156])).
% 0.49/0.69 tff(161,plain,
% 0.49/0.69 ((~hskp5) | c3_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.49/0.69 tff(162,plain,
% 0.49/0.69 ((~hskp5) | c3_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[161, 156])).
% 0.49/0.69 tff(163,plain,
% 0.49/0.69 (c3_1(a241)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[162, 149])).
% 0.49/0.69 tff(164,plain,
% 0.49/0.69 (((~hskp5) | c2_1(a241)) <=> ((~hskp5) | c2_1(a241))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(165,axiom,((~hskp5) | c2_1(a241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.49/0.69 tff(166,plain,
% 0.49/0.69 ((~hskp5) | c2_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.49/0.69 tff(167,plain,
% 0.49/0.69 ((~hskp5) | c2_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[166, 164])).
% 0.49/0.69 tff(168,plain,
% 0.49/0.69 ((~hskp5) | c2_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[167, 164])).
% 0.49/0.69 tff(169,plain,
% 0.49/0.69 ((~hskp5) | c2_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.49/0.69 tff(170,plain,
% 0.49/0.69 ((~hskp5) | c2_1(a241)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[169, 164])).
% 0.49/0.69 tff(171,plain,
% 0.49/0.69 (c2_1(a241)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[170, 149])).
% 0.49/0.69 tff(172,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c3_1(a241)) | (~c2_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(173,plain,
% 0.49/0.69 ((hskp11 | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a241)) | (~c1_1(a241)) | c0_1(a241) | (~c1_1(a241)) | (~c3_1(a241))) <=> (hskp11 | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(174,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a241)) | (~c1_1(a241)) | c0_1(a241) | (~c1_1(a241)) | (~c3_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c3_1(a241)) | (~c2_1(a241))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[173])).
% 0.49/0.69 tff(175,plain,
% 0.49/0.69 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a241)) | (~c1_1(a241)) | c0_1(a241) | (~c1_1(a241)) | (~c3_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[174, 172])).
% 0.49/0.69 tff(176,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a241)) | (~c3_1(a241)) | (~c1_1(a241)) | c0_1(a241) | (~c1_1(a241)) | (~c3_1(a241)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(177,plain,
% 0.49/0.69 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c3_1(a241)) | (~c2_1(a241))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.49/0.69 tff(178,plain,
% 0.49/0.69 (~c1_1(a241)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[177, 142, 32, 171, 163, 155, 66])).
% 0.49/0.69 tff(179,plain,
% 0.49/0.69 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | c0_1(a241) | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp10 | c0_1(a241) | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(180,plain,
% 0.49/0.69 ((hskp10 | (~ndr1_0) | c1_1(a241) | c0_1(a241) | (~c2_1(a241))) <=> (hskp10 | c0_1(a241) | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(181,plain,
% 0.49/0.69 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a241) | c0_1(a241) | (~c2_1(a241)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | c0_1(a241) | (~ndr1_0) | c1_1(a241) | (~c2_1(a241))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[180])).
% 0.49/0.69 tff(182,plain,
% 0.49/0.69 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a241) | c0_1(a241) | (~c2_1(a241)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp10 | c0_1(a241) | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)))),
% 0.49/0.69 inference(transitivity,[status(thm)],[181, 179])).
% 0.49/0.69 tff(183,plain,
% 0.49/0.69 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a241) | c0_1(a241) | (~c2_1(a241)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(184,plain,
% 0.49/0.69 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp10 | c0_1(a241) | (~ndr1_0) | c1_1(a241) | (~c2_1(a241))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.49/0.69 tff(185,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[184, 142, 31, 171, 155, 30, 178])).
% 0.49/0.69 tff(186,plain,(hskp11 | hskp10 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(187,plain,
% 0.49/0.69 (hskp18),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[186, 32, 31])).
% 0.49/0.69 tff(188,plain,
% 0.49/0.69 (((~hskp18) | (~c0_1(a265))) <=> ((~hskp18) | (~c0_1(a265)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(189,plain,
% 0.49/0.69 (((~c0_1(a265)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a265)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(190,axiom,((~c0_1(a265)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.49/0.70 tff(191,plain,
% 0.49/0.70 ((~hskp18) | (~c0_1(a265))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.49/0.70 tff(192,plain,
% 0.49/0.70 ((~hskp18) | (~c0_1(a265))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[191, 188])).
% 0.49/0.70 tff(193,plain,
% 0.49/0.70 (~c0_1(a265)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[192, 187])).
% 0.49/0.70 tff(194,plain,
% 0.49/0.70 (^[U: $i] : refl((hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(195,plain,
% 0.49/0.70 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[194])).
% 0.49/0.70 tff(196,plain,
% 0.49/0.70 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(197,plain,
% 0.49/0.70 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp4) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)) | hskp4))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U)) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(198,plain,
% 0.49/0.70 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp4) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[197])).
% 0.49/0.70 tff(199,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.49/0.70 tff(200,plain,
% 0.49/0.70 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.49/0.70 tff(201,plain,
% 0.49/0.70 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.49/0.70 tff(202,plain,(
% 0.49/0.70 ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))),
% 0.49/0.70 inference(skolemize,[status(sab)],[201])).
% 0.49/0.70 tff(203,plain,
% 0.49/0.70 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.49/0.70 tff(204,assumption,(~hskp4), introduced(assumption)).
% 0.49/0.70 tff(205,assumption,(hskp10), introduced(assumption)).
% 0.49/0.70 tff(206,plain,
% 0.49/0.70 (((~hskp10) | c3_1(a249)) <=> ((~hskp10) | c3_1(a249))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(207,axiom,((~hskp10) | c3_1(a249)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.49/0.70 tff(208,plain,
% 0.49/0.70 ((~hskp10) | c3_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.49/0.70 tff(209,plain,
% 0.49/0.70 ((~hskp10) | c3_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[208, 206])).
% 0.49/0.70 tff(210,plain,
% 0.49/0.70 ((~hskp10) | c3_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[209, 206])).
% 0.49/0.70 tff(211,plain,
% 0.49/0.70 ((~hskp10) | c3_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.49/0.70 tff(212,plain,
% 0.49/0.70 ((~hskp10) | c3_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[211, 206])).
% 0.49/0.70 tff(213,plain,
% 0.49/0.70 (c3_1(a249)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[212, 205])).
% 0.49/0.70 tff(214,plain,
% 0.49/0.70 (((~hskp10) | c0_1(a249)) <=> ((~hskp10) | c0_1(a249))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(215,axiom,((~hskp10) | c0_1(a249)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.49/0.70 tff(216,plain,
% 0.49/0.70 ((~hskp10) | c0_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.49/0.70 tff(217,plain,
% 0.49/0.70 ((~hskp10) | c0_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[216, 214])).
% 0.49/0.70 tff(218,plain,
% 0.49/0.70 ((~hskp10) | c0_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[217, 214])).
% 0.49/0.70 tff(219,plain,
% 0.49/0.70 ((~hskp10) | c0_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.49/0.70 tff(220,plain,
% 0.49/0.70 ((~hskp10) | c0_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[219, 214])).
% 0.49/0.70 tff(221,plain,
% 0.49/0.70 (c0_1(a249)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[220, 205])).
% 0.49/0.70 tff(222,plain,
% 0.49/0.70 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(223,plain,
% 0.49/0.70 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(224,plain,
% 0.49/0.70 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.49/0.70 tff(225,plain,
% 0.49/0.70 (~c1_1(a249)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[224, 142, 204, 221, 213, 10])).
% 0.49/0.70 tff(226,plain,
% 0.49/0.70 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(227,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[226])).
% 0.49/0.70 tff(228,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(229,plain,
% 0.49/0.70 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(230,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[229])).
% 0.49/0.70 tff(231,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 0.49/0.70 tff(232,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.49/0.70 tff(233,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.49/0.70 tff(234,plain,(
% 0.49/0.70 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.70 inference(skolemize,[status(sab)],[233])).
% 0.49/0.70 tff(235,plain,
% 0.49/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.49/0.70 tff(236,plain,
% 0.49/0.70 (((~hskp10) | (~c2_1(a249))) <=> ((~hskp10) | (~c2_1(a249)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(237,plain,
% 0.49/0.70 (((~c2_1(a249)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a249)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(238,axiom,((~c2_1(a249)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.49/0.70 tff(239,plain,
% 0.49/0.70 ((~hskp10) | (~c2_1(a249))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.49/0.70 tff(240,plain,
% 0.49/0.70 ((~hskp10) | (~c2_1(a249))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[239, 236])).
% 0.49/0.70 tff(241,plain,
% 0.49/0.70 (~c2_1(a249)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[240, 205])).
% 0.49/0.70 tff(242,plain,
% 0.49/0.70 (^[U: $i] : refl((hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(243,plain,
% 0.49/0.70 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[242])).
% 0.49/0.70 tff(244,plain,
% 0.49/0.70 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(245,plain,
% 0.49/0.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp12) | hskp3) <=> ((hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp3))), rewrite(((hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp3) <=> (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp12) | hskp3) <=> (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(246,plain,
% 0.49/0.70 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp12) | hskp3) <=> ![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[245])).
% 0.49/0.70 tff(247,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp12) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.49/0.70 tff(248,plain,
% 0.49/0.70 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.49/0.70 tff(249,plain,
% 0.49/0.70 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.49/0.70 tff(250,plain,(
% 0.49/0.70 ![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.70 inference(skolemize,[status(sab)],[249])).
% 0.49/0.70 tff(251,plain,
% 0.49/0.70 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[250, 243])).
% 0.49/0.70 tff(252,plain,
% 0.49/0.70 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(253,plain,
% 0.49/0.70 ((hskp12 | hskp3 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249))) <=> (hskp12 | hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(254,plain,
% 0.49/0.70 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[253])).
% 0.49/0.70 tff(255,plain,
% 0.49/0.70 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.49/0.70 inference(transitivity,[status(thm)],[254, 252])).
% 0.49/0.70 tff(256,plain,
% 0.49/0.70 ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(257,plain,
% 0.49/0.70 ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.49/0.70 tff(258,plain,
% 0.49/0.70 (hskp12),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[257, 142, 45, 221, 213, 251, 225])).
% 0.49/0.70 tff(259,plain,
% 0.49/0.70 (((~hskp12) | (~c3_1(a252))) <=> ((~hskp12) | (~c3_1(a252)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(260,plain,
% 0.49/0.70 (((~c3_1(a252)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a252)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(261,axiom,((~c3_1(a252)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.49/0.70 tff(262,plain,
% 0.49/0.70 ((~hskp12) | (~c3_1(a252))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.49/0.70 tff(263,plain,
% 0.49/0.70 ((~hskp12) | (~c3_1(a252))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[262, 259])).
% 0.49/0.70 tff(264,plain,
% 0.49/0.70 (~c3_1(a252)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[263, 258])).
% 0.49/0.70 tff(265,plain,
% 0.49/0.70 (((~hskp12) | (~c1_1(a252))) <=> ((~hskp12) | (~c1_1(a252)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(266,plain,
% 0.49/0.70 (((~c1_1(a252)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a252)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(267,axiom,((~c1_1(a252)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.49/0.70 tff(268,plain,
% 0.49/0.70 ((~hskp12) | (~c1_1(a252))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.49/0.70 tff(269,plain,
% 0.49/0.70 ((~hskp12) | (~c1_1(a252))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[268, 265])).
% 0.49/0.70 tff(270,plain,
% 0.49/0.70 (~c1_1(a252)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[269, 258])).
% 0.49/0.70 tff(271,plain,
% 0.49/0.70 (((~hskp12) | c0_1(a252)) <=> ((~hskp12) | c0_1(a252))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(272,axiom,((~hskp12) | c0_1(a252)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.49/0.70 tff(273,plain,
% 0.49/0.70 ((~hskp12) | c0_1(a252)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.49/0.70 tff(274,plain,
% 0.49/0.70 ((~hskp12) | c0_1(a252)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[273, 271])).
% 0.49/0.70 tff(275,plain,
% 0.49/0.70 ((~hskp12) | c0_1(a252)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[274, 271])).
% 0.49/0.70 tff(276,plain,
% 0.49/0.70 ((~hskp12) | c0_1(a252)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.49/0.70 tff(277,plain,
% 0.49/0.70 ((~hskp12) | c0_1(a252)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[276, 271])).
% 0.49/0.70 tff(278,plain,
% 0.49/0.70 (c0_1(a252)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[277, 258])).
% 0.49/0.70 tff(279,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a252) | c3_1(a252) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a252)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(280,plain,
% 0.49/0.70 (((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c3_1(a252) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a252)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(281,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a252) | c3_1(a252) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a252))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[280])).
% 0.49/0.70 tff(282,plain,
% 0.49/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a252)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[281, 279])).
% 0.49/0.70 tff(283,plain,
% 0.49/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(284,plain,
% 0.49/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c0_1(a252))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.49/0.70 tff(285,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[284, 142, 278, 221, 213, 270, 264, 241, 235, 225])).
% 0.49/0.70 tff(286,plain,((~hskp10) | hskp3 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(287,plain,
% 0.49/0.70 (~hskp10),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[286, 45, 204])).
% 0.49/0.70 tff(288,assumption,(~hskp28), introduced(assumption)).
% 0.49/0.70 tff(289,plain,
% 0.49/0.70 (((~hskp18) | c2_1(a265)) <=> ((~hskp18) | c2_1(a265))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(290,axiom,((~hskp18) | c2_1(a265)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.49/0.70 tff(291,plain,
% 0.49/0.70 ((~hskp18) | c2_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.49/0.70 tff(292,plain,
% 0.49/0.70 ((~hskp18) | c2_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[291, 289])).
% 0.49/0.70 tff(293,plain,
% 0.49/0.70 ((~hskp18) | c2_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[292, 289])).
% 0.49/0.70 tff(294,plain,
% 0.49/0.70 ((~hskp18) | c2_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.49/0.70 tff(295,plain,
% 0.49/0.70 ((~hskp18) | c2_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[294, 289])).
% 0.49/0.70 tff(296,plain,
% 0.49/0.70 (c2_1(a265)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[295, 187])).
% 0.49/0.70 tff(297,plain,
% 0.49/0.70 (((~hskp18) | c1_1(a265)) <=> ((~hskp18) | c1_1(a265))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(298,axiom,((~hskp18) | c1_1(a265)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.49/0.70 tff(299,plain,
% 0.49/0.70 ((~hskp18) | c1_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.49/0.70 tff(300,plain,
% 0.49/0.70 ((~hskp18) | c1_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[299, 297])).
% 0.49/0.70 tff(301,plain,
% 0.49/0.70 ((~hskp18) | c1_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[300, 297])).
% 0.49/0.70 tff(302,plain,
% 0.49/0.70 ((~hskp18) | c1_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.49/0.70 tff(303,plain,
% 0.49/0.70 ((~hskp18) | c1_1(a265)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[302, 297])).
% 0.49/0.70 tff(304,plain,
% 0.49/0.70 (c1_1(a265)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[303, 187])).
% 0.49/0.70 tff(305,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a265) | (~ndr1_0) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a265) | (~ndr1_0) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(306,plain,
% 0.49/0.70 ((hskp11 | (~ndr1_0) | (~c2_1(a265)) | (~c3_1(a265)) | (~c1_1(a265)) | c0_1(a265) | (~c1_1(a265)) | (~c3_1(a265))) <=> (hskp11 | c0_1(a265) | (~ndr1_0) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(307,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a265)) | (~c3_1(a265)) | (~c1_1(a265)) | c0_1(a265) | (~c1_1(a265)) | (~c3_1(a265)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a265) | (~ndr1_0) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[306])).
% 0.49/0.70 tff(308,plain,
% 0.49/0.70 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a265)) | (~c3_1(a265)) | (~c1_1(a265)) | c0_1(a265) | (~c1_1(a265)) | (~c3_1(a265)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a265) | (~ndr1_0) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[307, 305])).
% 0.49/0.70 tff(309,plain,
% 0.49/0.70 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a265)) | (~c3_1(a265)) | (~c1_1(a265)) | c0_1(a265) | (~c1_1(a265)) | (~c3_1(a265)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(310,plain,
% 0.49/0.70 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a265) | (~ndr1_0) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.49/0.70 tff(311,plain,
% 0.49/0.70 (~c3_1(a265)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[310, 142, 32, 304, 296, 193, 66])).
% 0.49/0.70 tff(312,plain,
% 0.49/0.70 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | c0_1(a265) | (~ndr1_0) | c3_1(a265) | (~c2_1(a265)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | hskp28 | hskp4 | c0_1(a265) | (~ndr1_0) | c3_1(a265) | (~c2_1(a265)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(313,plain,
% 0.49/0.70 ((hskp28 | hskp4 | (~ndr1_0) | c0_1(a265) | (~c2_1(a265)) | c3_1(a265)) <=> (hskp28 | hskp4 | c0_1(a265) | (~ndr1_0) | c3_1(a265) | (~c2_1(a265)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(314,plain,
% 0.49/0.70 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a265) | (~c2_1(a265)) | c3_1(a265))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | c0_1(a265) | (~ndr1_0) | c3_1(a265) | (~c2_1(a265))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[313])).
% 0.49/0.70 tff(315,plain,
% 0.49/0.70 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a265) | (~c2_1(a265)) | c3_1(a265))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | hskp28 | hskp4 | c0_1(a265) | (~ndr1_0) | c3_1(a265) | (~c2_1(a265)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[314, 312])).
% 0.49/0.70 tff(316,plain,
% 0.49/0.70 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a265) | (~c2_1(a265)) | c3_1(a265))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(317,plain,
% 0.49/0.70 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | hskp28 | hskp4 | c0_1(a265) | (~ndr1_0) | c3_1(a265) | (~c2_1(a265))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.49/0.70 tff(318,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[317, 142, 288, 204, 296, 193, 203, 311])).
% 0.49/0.70 tff(319,plain,(hskp11 | hskp28 | hskp4 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(320,plain,
% 0.49/0.70 (hskp11),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[319, 288, 204, 31])).
% 0.49/0.70 tff(321,assumption,(hskp11), introduced(assumption)).
% 0.49/0.70 tff(322,plain,
% 0.49/0.70 (((~hskp11) | (~c3_1(a251))) <=> ((~hskp11) | (~c3_1(a251)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(323,plain,
% 0.49/0.70 (((~c3_1(a251)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a251)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(324,axiom,((~c3_1(a251)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.49/0.70 tff(325,plain,
% 0.49/0.70 ((~hskp11) | (~c3_1(a251))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.49/0.70 tff(326,plain,
% 0.49/0.70 ((~hskp11) | (~c3_1(a251))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[325, 322])).
% 0.49/0.70 tff(327,plain,
% 0.49/0.70 (~c3_1(a251)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[326, 321])).
% 0.49/0.70 tff(328,plain,
% 0.49/0.70 (((~hskp11) | c2_1(a251)) <=> ((~hskp11) | c2_1(a251))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(329,axiom,((~hskp11) | c2_1(a251)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.49/0.70 tff(330,plain,
% 0.49/0.70 ((~hskp11) | c2_1(a251)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.49/0.70 tff(331,plain,
% 0.49/0.70 ((~hskp11) | c2_1(a251)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[330, 328])).
% 0.49/0.70 tff(332,plain,
% 0.49/0.70 ((~hskp11) | c2_1(a251)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[331, 328])).
% 0.49/0.70 tff(333,plain,
% 0.49/0.70 ((~hskp11) | c2_1(a251)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[332, 328])).
% 0.49/0.70 tff(334,plain,
% 0.49/0.70 ((~hskp11) | c2_1(a251)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[333, 328])).
% 0.49/0.70 tff(335,plain,
% 0.49/0.70 (c2_1(a251)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[334, 321])).
% 0.49/0.70 tff(336,plain,
% 0.49/0.70 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | hskp28 | hskp4 | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(337,plain,
% 0.49/0.70 ((hskp28 | hskp4 | (~ndr1_0) | c0_1(a251) | (~c2_1(a251)) | c3_1(a251)) <=> (hskp28 | hskp4 | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(338,plain,
% 0.49/0.70 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a251) | (~c2_1(a251)) | c3_1(a251))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251)))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[337])).
% 0.49/0.70 tff(339,plain,
% 0.49/0.70 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a251) | (~c2_1(a251)) | c3_1(a251))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | hskp28 | hskp4 | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251))),
% 0.49/0.70 inference(transitivity,[status(thm)],[338, 336])).
% 0.49/0.70 tff(340,plain,
% 0.49/0.70 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a251) | (~c2_1(a251)) | c3_1(a251))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(341,plain,
% 0.49/0.70 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(U))) | hskp28 | hskp4 | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.49/0.70 tff(342,plain,
% 0.49/0.70 (c0_1(a251)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[341, 142, 288, 204, 335, 327, 203])).
% 0.49/0.70 tff(343,plain,
% 0.49/0.70 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(344,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[343])).
% 0.49/0.70 tff(345,plain,
% 0.49/0.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(346,plain,
% 0.49/0.70 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(347,plain,
% 0.49/0.71 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[346])).
% 0.49/0.71 tff(348,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.49/0.71 tff(349,plain,
% 0.49/0.71 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.49/0.71 tff(350,plain,
% 0.49/0.71 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[349, 345])).
% 0.49/0.71 tff(351,plain,(
% 0.49/0.71 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.49/0.71 inference(skolemize,[status(sab)],[350])).
% 0.49/0.71 tff(352,plain,
% 0.49/0.71 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[351, 344])).
% 0.49/0.71 tff(353,plain,
% 0.49/0.71 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(354,plain,
% 0.49/0.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[353])).
% 0.49/0.71 tff(355,plain,
% 0.49/0.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(356,plain,
% 0.49/0.71 (^[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)) | (~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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(357,plain,
% 0.49/0.71 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[356])).
% 0.49/0.71 tff(358,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.49/0.71 tff(359,plain,
% 0.49/0.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.49/0.71 tff(360,plain,
% 0.49/0.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[359, 355])).
% 0.49/0.71 tff(361,plain,(
% 0.49/0.71 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.49/0.71 inference(skolemize,[status(sab)],[360])).
% 0.49/0.71 tff(362,plain,
% 0.49/0.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[361, 354])).
% 0.49/0.71 tff(363,plain,
% 0.49/0.71 (((~hskp11) | (~c1_1(a251))) <=> ((~hskp11) | (~c1_1(a251)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(364,plain,
% 0.49/0.71 (((~c1_1(a251)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a251)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(365,axiom,((~c1_1(a251)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.49/0.71 tff(366,plain,
% 0.49/0.71 ((~hskp11) | (~c1_1(a251))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.49/0.71 tff(367,plain,
% 0.49/0.71 ((~hskp11) | (~c1_1(a251))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[366, 363])).
% 0.49/0.71 tff(368,plain,
% 0.49/0.71 (~c1_1(a251)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[367, 321])).
% 0.49/0.71 tff(369,plain,
% 0.49/0.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | (~c0_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | (~c0_1(a251)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(370,plain,
% 0.49/0.71 ((hskp5 | (~ndr1_0) | (~c2_1(a251)) | c3_1(a251) | (~c0_1(a251)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251))) <=> (hskp5 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | (~c0_1(a251)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(371,plain,
% 0.49/0.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a251)) | c3_1(a251) | (~c0_1(a251)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | (~c0_1(a251))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[370])).
% 0.49/0.71 tff(372,plain,
% 0.49/0.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a251)) | c3_1(a251) | (~c0_1(a251)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | (~c0_1(a251)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[371, 369])).
% 0.49/0.71 tff(373,plain,
% 0.49/0.71 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a251)) | c3_1(a251) | (~c0_1(a251)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(374,plain,
% 0.49/0.71 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c2_1(a251)) | (~c0_1(a251))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.49/0.71 tff(375,plain,
% 0.49/0.71 (hskp5 | (~c0_1(a251))),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[374, 142, 335, 368, 327, 362])).
% 0.49/0.71 tff(376,plain,
% 0.49/0.71 (hskp5),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[375, 342])).
% 0.49/0.71 tff(377,plain,
% 0.49/0.71 (~c0_1(a241)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[154, 376])).
% 0.49/0.71 tff(378,plain,
% 0.49/0.71 (c2_1(a241)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[170, 376])).
% 0.49/0.71 tff(379,assumption,(~hskp20), introduced(assumption)).
% 0.49/0.71 tff(380,plain,
% 0.49/0.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a251) | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c2_1(a241)) | (~c2_1(a251)) | (~c0_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a251) | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c2_1(a241)) | (~c2_1(a251)) | (~c0_1(a251)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(381,plain,
% 0.49/0.71 ((hskp20 | (~ndr1_0) | (~c2_1(a251)) | c3_1(a251) | (~c0_1(a251)) | c0_1(a241) | (~c1_1(a241)) | (~c2_1(a241))) <=> (hskp20 | c3_1(a251) | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c2_1(a241)) | (~c2_1(a251)) | (~c0_1(a251)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(382,plain,
% 0.49/0.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a251)) | c3_1(a251) | (~c0_1(a251)) | c0_1(a241) | (~c1_1(a241)) | (~c2_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a251) | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c2_1(a241)) | (~c2_1(a251)) | (~c0_1(a251))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[381])).
% 0.49/0.71 tff(383,plain,
% 0.49/0.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a251)) | c3_1(a251) | (~c0_1(a251)) | c0_1(a241) | (~c1_1(a241)) | (~c2_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a251) | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c2_1(a241)) | (~c2_1(a251)) | (~c0_1(a251)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[382, 380])).
% 0.49/0.71 tff(384,plain,
% 0.49/0.71 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a251)) | c3_1(a251) | (~c0_1(a251)) | c0_1(a241) | (~c1_1(a241)) | (~c2_1(a241)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(385,plain,
% 0.49/0.71 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a251) | c0_1(a241) | (~ndr1_0) | (~c1_1(a241)) | (~c2_1(a241)) | (~c2_1(a251)) | (~c0_1(a251))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.49/0.71 tff(386,plain,
% 0.49/0.71 (~c1_1(a241)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[385, 142, 379, 335, 378, 327, 377, 352, 342])).
% 0.49/0.71 tff(387,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[184, 142, 31, 378, 377, 30, 386])).
% 0.49/0.71 tff(388,plain,((~hskp11) | hskp10 | hskp20 | hskp28 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(389,plain,
% 0.49/0.71 (hskp20),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[388, 320, 31, 288, 204])).
% 0.49/0.71 tff(390,plain,
% 0.49/0.71 (((~hskp20) | c1_1(a271)) <=> ((~hskp20) | c1_1(a271))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(391,axiom,((~hskp20) | c1_1(a271)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.49/0.71 tff(392,plain,
% 0.49/0.71 ((~hskp20) | c1_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.49/0.71 tff(393,plain,
% 0.49/0.71 ((~hskp20) | c1_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[392, 390])).
% 0.49/0.71 tff(394,plain,
% 0.49/0.71 ((~hskp20) | c1_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[393, 390])).
% 0.49/0.71 tff(395,plain,
% 0.49/0.71 ((~hskp20) | c1_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[394, 390])).
% 0.49/0.71 tff(396,plain,
% 0.49/0.71 ((~hskp20) | c1_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[395, 390])).
% 0.49/0.71 tff(397,plain,
% 0.49/0.71 (c1_1(a271)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[396, 389])).
% 0.49/0.71 tff(398,plain,
% 0.49/0.71 (((~hskp20) | c0_1(a271)) <=> ((~hskp20) | c0_1(a271))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(399,axiom,((~hskp20) | c0_1(a271)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.49/0.71 tff(400,plain,
% 0.49/0.71 ((~hskp20) | c0_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.49/0.71 tff(401,plain,
% 0.49/0.71 ((~hskp20) | c0_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[400, 398])).
% 0.49/0.71 tff(402,plain,
% 0.49/0.71 ((~hskp20) | c0_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[401, 398])).
% 0.49/0.71 tff(403,plain,
% 0.49/0.71 ((~hskp20) | c0_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[402, 398])).
% 0.49/0.71 tff(404,plain,
% 0.49/0.71 ((~hskp20) | c0_1(a271)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[403, 398])).
% 0.49/0.71 tff(405,plain,
% 0.49/0.71 (c0_1(a271)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[404, 389])).
% 0.49/0.71 tff(406,plain,
% 0.49/0.71 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(407,plain,
% 0.49/0.71 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(408,plain,
% 0.49/0.71 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.49/0.71 tff(409,plain,
% 0.49/0.71 (~c3_1(a271)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[408, 142, 204, 405, 397, 10])).
% 0.49/0.71 tff(410,plain,
% 0.49/0.71 (^[U: $i] : refl((hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(411,plain,
% 0.49/0.71 (![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[410])).
% 0.49/0.71 tff(412,plain,
% 0.49/0.71 (![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(413,plain,
% 0.49/0.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp31) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp31))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp31) <=> (hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp31) | hskp4) <=> ((hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp4))), rewrite(((hskp31 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp4) <=> (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp31) | hskp4) <=> (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(414,plain,
% 0.49/0.71 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp31) | hskp4) <=> ![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[413])).
% 0.49/0.71 tff(415,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp31) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.49/0.71 tff(416,plain,
% 0.49/0.71 (![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.49/0.71 tff(417,plain,
% 0.49/0.71 (![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[416, 412])).
% 0.49/0.71 tff(418,plain,(
% 0.49/0.71 ![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.49/0.71 inference(skolemize,[status(sab)],[417])).
% 0.49/0.71 tff(419,plain,
% 0.49/0.71 (![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[418, 411])).
% 0.49/0.71 tff(420,plain,
% 0.49/0.71 (((~hskp20) | (~c2_1(a271))) <=> ((~hskp20) | (~c2_1(a271)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(421,plain,
% 0.49/0.71 (((~c2_1(a271)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a271)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(422,axiom,((~c2_1(a271)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.49/0.71 tff(423,plain,
% 0.49/0.71 ((~hskp20) | (~c2_1(a271))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.49/0.71 tff(424,plain,
% 0.49/0.71 ((~hskp20) | (~c2_1(a271))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[423, 420])).
% 0.49/0.71 tff(425,plain,
% 0.49/0.71 (~c2_1(a271)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[424, 389])).
% 0.49/0.71 tff(426,plain,
% 0.49/0.71 (((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | c2_1(a271) | (~ndr1_0) | c3_1(a271) | (~c1_1(a271)))) <=> ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp31 | hskp4 | c2_1(a271) | (~ndr1_0) | c3_1(a271) | (~c1_1(a271)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(427,plain,
% 0.49/0.71 ((hskp31 | hskp4 | (~ndr1_0) | c2_1(a271) | c3_1(a271) | (~c1_1(a271))) <=> (hskp31 | hskp4 | c2_1(a271) | (~ndr1_0) | c3_1(a271) | (~c1_1(a271)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(428,plain,
% 0.49/0.71 (((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | (~ndr1_0) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)))) <=> ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | c2_1(a271) | (~ndr1_0) | c3_1(a271) | (~c1_1(a271))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[427])).
% 0.49/0.71 tff(429,plain,
% 0.49/0.71 (((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | (~ndr1_0) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)))) <=> ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp31 | hskp4 | c2_1(a271) | (~ndr1_0) | c3_1(a271) | (~c1_1(a271)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[428, 426])).
% 0.49/0.71 tff(430,plain,
% 0.49/0.71 ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | (~ndr1_0) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(431,plain,
% 0.49/0.71 ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp31 | hskp4 | c2_1(a271) | (~ndr1_0) | c3_1(a271) | (~c1_1(a271))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.49/0.71 tff(432,plain,
% 0.49/0.71 (hskp31 | c3_1(a271)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[431, 142, 204, 397, 425, 419])).
% 0.49/0.71 tff(433,plain,
% 0.49/0.71 (hskp31),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[432, 409])).
% 0.49/0.71 tff(434,plain,
% 0.49/0.71 (((~hskp31) | c3_1(a246)) <=> ((~hskp31) | c3_1(a246))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(435,axiom,((~hskp31) | c3_1(a246)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.49/0.71 tff(436,plain,
% 0.49/0.71 ((~hskp31) | c3_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.49/0.71 tff(437,plain,
% 0.49/0.71 ((~hskp31) | c3_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[436, 434])).
% 0.49/0.71 tff(438,plain,
% 0.49/0.71 ((~hskp31) | c3_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[437, 434])).
% 0.49/0.71 tff(439,plain,
% 0.49/0.71 ((~hskp31) | c3_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[438, 434])).
% 0.49/0.71 tff(440,plain,
% 0.49/0.71 ((~hskp31) | c3_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[439, 434])).
% 0.49/0.71 tff(441,plain,
% 0.49/0.71 (c3_1(a246)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[440, 433])).
% 0.49/0.71 tff(442,plain,
% 0.49/0.71 (((~hskp31) | c0_1(a246)) <=> ((~hskp31) | c0_1(a246))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(443,axiom,((~hskp31) | c0_1(a246)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.49/0.71 tff(444,plain,
% 0.49/0.71 ((~hskp31) | c0_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.49/0.71 tff(445,plain,
% 0.49/0.71 ((~hskp31) | c0_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[444, 442])).
% 0.49/0.71 tff(446,plain,
% 0.49/0.71 ((~hskp31) | c0_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[445, 442])).
% 0.49/0.71 tff(447,plain,
% 0.49/0.71 ((~hskp31) | c0_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[446, 442])).
% 0.49/0.71 tff(448,plain,
% 0.49/0.71 ((~hskp31) | c0_1(a246)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[447, 442])).
% 0.49/0.71 tff(449,plain,
% 0.49/0.71 (c0_1(a246)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[448, 433])).
% 0.49/0.71 tff(450,plain,
% 0.49/0.71 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c1_1(a246)) | (~c3_1(a246)) | (~c0_1(a246)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c1_1(a246)) | (~c3_1(a246)) | (~c0_1(a246)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(451,plain,
% 0.49/0.71 ((hskp4 | (~ndr1_0) | (~c0_1(a246)) | (~c3_1(a246)) | (~c1_1(a246))) <=> (hskp4 | (~ndr1_0) | (~c1_1(a246)) | (~c3_1(a246)) | (~c0_1(a246)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(452,plain,
% 0.49/0.71 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a246)) | (~c3_1(a246)) | (~c1_1(a246)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c1_1(a246)) | (~c3_1(a246)) | (~c0_1(a246))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[451])).
% 0.49/0.71 tff(453,plain,
% 0.49/0.71 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a246)) | (~c3_1(a246)) | (~c1_1(a246)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c1_1(a246)) | (~c3_1(a246)) | (~c0_1(a246)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[452, 450])).
% 0.49/0.71 tff(454,plain,
% 0.49/0.71 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a246)) | (~c3_1(a246)) | (~c1_1(a246)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(455,plain,
% 0.49/0.71 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c1_1(a246)) | (~c3_1(a246)) | (~c0_1(a246))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.49/0.71 tff(456,plain,
% 0.49/0.71 (~c1_1(a246)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[455, 142, 204, 449, 441, 10])).
% 0.49/0.71 tff(457,plain,
% 0.49/0.71 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(458,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[457])).
% 0.55/0.71 tff(459,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(460,plain,
% 0.55/0.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(461,plain,
% 0.55/0.71 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[460])).
% 0.55/0.71 tff(462,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.55/0.71 tff(463,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.55/0.71 tff(464,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[463, 459])).
% 0.55/0.71 tff(465,plain,(
% 0.55/0.71 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.71 inference(skolemize,[status(sab)],[464])).
% 0.55/0.71 tff(466,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[465, 458])).
% 0.55/0.71 tff(467,plain,
% 0.55/0.71 (~c3_1(a251)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[326, 320])).
% 0.55/0.71 tff(468,plain,
% 0.55/0.71 (c2_1(a251)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[334, 320])).
% 0.55/0.71 tff(469,plain,
% 0.55/0.71 (c0_1(a251)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[341, 142, 288, 204, 468, 467, 203])).
% 0.55/0.71 tff(470,plain,
% 0.55/0.71 (^[U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(471,plain,
% 0.55/0.71 (![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[470])).
% 0.55/0.71 tff(472,plain,
% 0.55/0.71 (![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(473,plain,
% 0.55/0.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | 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)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(474,plain,
% 0.55/0.71 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) <=> ![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[473])).
% 0.55/0.71 tff(475,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.55/0.71 tff(476,plain,
% 0.55/0.71 (![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.55/0.71 tff(477,plain,
% 0.55/0.71 (![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[476, 472])).
% 0.55/0.71 tff(478,plain,(
% 0.55/0.71 ![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.55/0.71 inference(skolemize,[status(sab)],[477])).
% 0.55/0.71 tff(479,plain,
% 0.55/0.71 (![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[478, 471])).
% 0.55/0.71 tff(480,plain,
% 0.55/0.71 (~c1_1(a251)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[367, 320])).
% 0.55/0.71 tff(481,plain,
% 0.55/0.71 (((~![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a251)))) <=> ((~![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a251)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(482,plain,
% 0.55/0.71 ((hskp29 | (~ndr1_0) | c1_1(a251) | c3_1(a251) | (~c0_1(a251))) <=> (hskp29 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a251)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(483,plain,
% 0.55/0.71 (((~![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | (~ndr1_0) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))) <=> ((~![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a251))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[482])).
% 0.55/0.71 tff(484,plain,
% 0.55/0.71 (((~![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | (~ndr1_0) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))) <=> ((~![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a251)))),
% 0.55/0.71 inference(transitivity,[status(thm)],[483, 481])).
% 0.55/0.71 tff(485,plain,
% 0.55/0.71 ((~![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp29 | (~ndr1_0) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(486,plain,
% 0.55/0.71 ((~![U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp29 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a251))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.55/0.71 tff(487,plain,
% 0.55/0.71 (hskp29),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[486, 142, 480, 467, 479, 469])).
% 0.55/0.71 tff(488,plain,
% 0.55/0.71 (((~hskp29) | c3_1(a240)) <=> ((~hskp29) | c3_1(a240))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(489,axiom,((~hskp29) | c3_1(a240)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.55/0.71 tff(490,plain,
% 0.55/0.71 ((~hskp29) | c3_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.55/0.71 tff(491,plain,
% 0.55/0.71 ((~hskp29) | c3_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[490, 488])).
% 0.55/0.71 tff(492,plain,
% 0.55/0.71 ((~hskp29) | c3_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[491, 488])).
% 0.55/0.71 tff(493,plain,
% 0.55/0.71 ((~hskp29) | c3_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[492, 488])).
% 0.55/0.71 tff(494,plain,
% 0.55/0.71 ((~hskp29) | c3_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[493, 488])).
% 0.55/0.71 tff(495,plain,
% 0.55/0.71 (c3_1(a240)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[494, 487])).
% 0.55/0.71 tff(496,plain,
% 0.55/0.71 (((~hskp29) | c2_1(a240)) <=> ((~hskp29) | c2_1(a240))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(497,axiom,((~hskp29) | c2_1(a240)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.55/0.71 tff(498,plain,
% 0.55/0.71 ((~hskp29) | c2_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.55/0.71 tff(499,plain,
% 0.55/0.71 ((~hskp29) | c2_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[498, 496])).
% 0.55/0.71 tff(500,plain,
% 0.55/0.71 ((~hskp29) | c2_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[499, 496])).
% 0.55/0.71 tff(501,plain,
% 0.55/0.71 ((~hskp29) | c2_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[500, 496])).
% 0.55/0.71 tff(502,plain,
% 0.55/0.71 ((~hskp29) | c2_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[501, 496])).
% 0.55/0.71 tff(503,plain,
% 0.55/0.71 (c2_1(a240)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[502, 487])).
% 0.55/0.71 tff(504,plain,
% 0.55/0.71 (((~hskp29) | c1_1(a240)) <=> ((~hskp29) | c1_1(a240))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(505,axiom,((~hskp29) | c1_1(a240)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.55/0.71 tff(506,plain,
% 0.55/0.71 ((~hskp29) | c1_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.55/0.71 tff(507,plain,
% 0.55/0.71 ((~hskp29) | c1_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[506, 504])).
% 0.55/0.71 tff(508,plain,
% 0.55/0.71 ((~hskp29) | c1_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[507, 504])).
% 0.55/0.71 tff(509,plain,
% 0.55/0.71 ((~hskp29) | c1_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[508, 504])).
% 0.55/0.71 tff(510,plain,
% 0.55/0.71 ((~hskp29) | c1_1(a240)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[509, 504])).
% 0.55/0.71 tff(511,plain,
% 0.55/0.71 (c1_1(a240)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[510, 487])).
% 0.55/0.71 tff(512,plain,
% 0.55/0.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(513,plain,
% 0.55/0.72 ((hskp4 | (~ndr1_0) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240)) | c2_1(a239) | c1_1(a239) | c0_1(a239)) <=> (hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(514,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[513])).
% 0.55/0.72 tff(515,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[514, 512])).
% 0.55/0.72 tff(516,plain,
% 0.55/0.72 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240)) | c2_1(a239) | c1_1(a239) | c0_1(a239))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(517,plain,
% 0.55/0.72 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c2_1(a240)) | (~c3_1(a240)) | (~c1_1(a240))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.55/0.72 tff(518,plain,
% 0.55/0.72 (c0_1(a239)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[517, 142, 204, 511, 503, 495, 44, 43, 466])).
% 0.55/0.72 tff(519,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(520,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[519])).
% 0.55/0.72 tff(521,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(522,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(523,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[522])).
% 0.55/0.72 tff(524,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 0.55/0.72 tff(525,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.55/0.72 tff(526,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[525, 521])).
% 0.55/0.72 tff(527,plain,(
% 0.55/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.55/0.72 inference(skolemize,[status(sab)],[526])).
% 0.55/0.72 tff(528,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[527, 520])).
% 0.55/0.72 tff(529,plain,
% 0.55/0.72 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(530,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[529])).
% 0.55/0.72 tff(531,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(532,plain,
% 0.55/0.72 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~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))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~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))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(533,plain,
% 0.55/0.72 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[532])).
% 0.55/0.72 tff(534,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.55/0.72 tff(535,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.55/0.72 tff(536,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[535, 531])).
% 0.55/0.72 tff(537,plain,(
% 0.55/0.72 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.72 inference(skolemize,[status(sab)],[536])).
% 0.55/0.72 tff(538,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[537, 530])).
% 0.55/0.72 tff(539,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a271) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a271) | (~c1_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a271) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a271) | (~c1_1(a271)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(540,plain,
% 0.55/0.72 ((hskp10 | (~ndr1_0) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239))) <=> (hskp10 | c2_1(a271) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a271) | (~c1_1(a271)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(541,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a271) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a271) | (~c1_1(a271))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[540])).
% 0.55/0.72 tff(542,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a271) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a271) | (~c1_1(a271)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[541, 539])).
% 0.55/0.72 tff(543,plain,
% 0.55/0.72 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(544,plain,
% 0.55/0.72 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a271) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a271) | (~c1_1(a271))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.55/0.72 tff(545,plain,
% 0.55/0.72 ((~c3_1(a239)) | c3_1(a271)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[544, 142, 31, 397, 425, 44, 43, 538])).
% 0.55/0.72 tff(546,plain,
% 0.55/0.72 (~c3_1(a239)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[545, 409])).
% 0.55/0.72 tff(547,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(548,plain,
% 0.55/0.72 (((~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c2_1(a239) | c1_1(a239) | (~c0_1(a239)) | c2_1(a239) | c1_1(a239) | c3_1(a239)) <=> (c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(549,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c2_1(a239) | c1_1(a239) | (~c0_1(a239)) | c2_1(a239) | c1_1(a239) | c3_1(a239))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[548])).
% 0.55/0.72 tff(550,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c2_1(a239) | c1_1(a239) | (~c0_1(a239)) | c2_1(a239) | c1_1(a239) | c3_1(a239))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[549, 547])).
% 0.55/0.72 tff(551,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c2_1(a239) | c1_1(a239) | (~c0_1(a239)) | c2_1(a239) | c1_1(a239) | c3_1(a239))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(552,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.55/0.72 tff(553,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[552, 142, 449, 441, 546, 44, 43, 528, 518, 456])).
% 0.55/0.72 tff(554,plain,(hskp28 | c1_1(a239) | c2_1(a239) | hskp4 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(555,plain,
% 0.55/0.72 (hskp28),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[554, 287, 43, 204, 44])).
% 0.55/0.72 tff(556,plain,
% 0.55/0.72 (((~hskp28) | c2_1(a237)) <=> ((~hskp28) | c2_1(a237))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(557,axiom,((~hskp28) | c2_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.55/0.72 tff(558,plain,
% 0.55/0.72 ((~hskp28) | c2_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[557, 556])).
% 0.55/0.72 tff(559,plain,
% 0.55/0.72 ((~hskp28) | c2_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[558, 556])).
% 0.55/0.72 tff(560,plain,
% 0.55/0.72 ((~hskp28) | c2_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[559, 556])).
% 0.55/0.72 tff(561,plain,
% 0.55/0.72 ((~hskp28) | c2_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[560, 556])).
% 0.55/0.72 tff(562,plain,
% 0.55/0.72 ((~hskp28) | c2_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[561, 556])).
% 0.55/0.72 tff(563,plain,
% 0.55/0.72 (c2_1(a237)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[562, 555])).
% 0.55/0.72 tff(564,plain,
% 0.55/0.72 (((~hskp28) | c0_1(a237)) <=> ((~hskp28) | c0_1(a237))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(565,axiom,((~hskp28) | c0_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.55/0.72 tff(566,plain,
% 0.55/0.72 ((~hskp28) | c0_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.55/0.72 tff(567,plain,
% 0.55/0.72 ((~hskp28) | c0_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[566, 564])).
% 0.55/0.72 tff(568,plain,
% 0.55/0.72 ((~hskp28) | c0_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[567, 564])).
% 0.55/0.72 tff(569,plain,
% 0.55/0.72 ((~hskp28) | c0_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[568, 564])).
% 0.55/0.72 tff(570,plain,
% 0.55/0.72 ((~hskp28) | c0_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[569, 564])).
% 0.55/0.72 tff(571,plain,
% 0.55/0.72 (c0_1(a237)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[570, 555])).
% 0.55/0.72 tff(572,plain,
% 0.55/0.72 (((~hskp28) | c1_1(a237)) <=> ((~hskp28) | c1_1(a237))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(573,axiom,((~hskp28) | c1_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.55/0.72 tff(574,plain,
% 0.55/0.72 ((~hskp28) | c1_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.55/0.72 tff(575,plain,
% 0.55/0.72 ((~hskp28) | c1_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[574, 572])).
% 0.55/0.72 tff(576,plain,
% 0.55/0.72 ((~hskp28) | c1_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[575, 572])).
% 0.55/0.72 tff(577,plain,
% 0.55/0.72 ((~hskp28) | c1_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[576, 572])).
% 0.55/0.72 tff(578,plain,
% 0.55/0.72 ((~hskp28) | c1_1(a237)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[577, 572])).
% 0.55/0.72 tff(579,plain,
% 0.55/0.72 (c1_1(a237)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[578, 555])).
% 0.55/0.72 tff(580,assumption,(c1_1(a237)), introduced(assumption)).
% 0.55/0.72 tff(581,assumption,(c2_1(a237)), introduced(assumption)).
% 0.55/0.72 tff(582,assumption,(c0_1(a237)), introduced(assumption)).
% 0.55/0.72 tff(583,assumption,(~c3_1(a239)), introduced(assumption)).
% 0.55/0.72 tff(584,plain,
% 0.55/0.72 (((~hskp4) | c3_1(a239)) <=> ((~hskp4) | c3_1(a239))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(585,axiom,((~hskp4) | c3_1(a239)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.55/0.72 tff(586,plain,
% 0.55/0.72 ((~hskp4) | c3_1(a239)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.55/0.72 tff(587,plain,
% 0.55/0.72 ((~hskp4) | c3_1(a239)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[586, 584])).
% 0.55/0.72 tff(588,plain,
% 0.55/0.72 ((~hskp4) | c3_1(a239)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[587, 584])).
% 0.55/0.72 tff(589,plain,
% 0.55/0.72 ((~hskp4) | c3_1(a239)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[588, 584])).
% 0.55/0.72 tff(590,plain,
% 0.55/0.72 ((~hskp4) | c3_1(a239)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[589, 584])).
% 0.55/0.72 tff(591,plain,
% 0.55/0.72 (~hskp4),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[590, 583])).
% 0.55/0.72 tff(592,plain,
% 0.55/0.72 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(593,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[592])).
% 0.55/0.72 tff(594,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(595,plain,
% 0.55/0.72 (^[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)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(596,plain,
% 0.55/0.72 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[595])).
% 0.55/0.72 tff(597,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.55/0.72 tff(598,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.55/0.72 tff(599,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[598, 594])).
% 0.55/0.72 tff(600,plain,(
% 0.55/0.72 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.55/0.72 inference(skolemize,[status(sab)],[599])).
% 0.55/0.72 tff(601,plain,
% 0.55/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[600, 593])).
% 0.55/0.72 tff(602,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(603,plain,
% 0.55/0.72 ((hskp4 | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | c3_1(a239)) <=> (hskp4 | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(604,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | c3_1(a239))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[603])).
% 0.55/0.72 tff(605,plain,
% 0.55/0.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | c3_1(a239))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[604, 602])).
% 0.55/0.72 tff(606,plain,
% 0.55/0.72 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | c3_1(a239))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(607,plain,
% 0.55/0.72 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c3_1(a239) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[606, 605])).
% 0.55/0.72 tff(608,plain,
% 0.55/0.72 (hskp4 | c3_1(a239) | c1_1(a239)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[607, 142, 582, 580, 581, 43, 601])).
% 0.55/0.72 tff(609,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[608, 591, 583, 44])).
% 0.55/0.72 tff(610,plain,(c3_1(a239) | c1_1(a239) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a237)) | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(611,plain,
% 0.55/0.72 (c3_1(a239)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[610, 44, 582, 580, 581, 43])).
% 0.55/0.72 tff(612,assumption,(~c3_1(a237)), introduced(assumption)).
% 0.55/0.72 tff(613,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(614,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_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) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[613])).
% 0.55/0.72 tff(615,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_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) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(616,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~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)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | 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)) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_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) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(617,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_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) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[616])).
% 0.55/0.72 tff(618,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 0.55/0.72 tff(619,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.55/0.72 tff(620,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[619, 615])).
% 0.55/0.72 tff(621,plain,(
% 0.55/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(skolemize,[status(sab)],[620])).
% 0.55/0.72 tff(622,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[621, 614])).
% 0.55/0.73 tff(623,assumption,(c3_1(a239)), introduced(assumption)).
% 0.55/0.73 tff(624,plain,
% 0.55/0.73 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(625,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[624])).
% 0.55/0.73 tff(626,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(627,plain,
% 0.55/0.73 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(628,plain,
% 0.55/0.73 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[627])).
% 0.55/0.73 tff(629,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.55/0.73 tff(630,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.55/0.73 tff(631,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[630, 626])).
% 0.55/0.73 tff(632,plain,(
% 0.55/0.73 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(skolemize,[status(sab)],[631])).
% 0.55/0.73 tff(633,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[632, 625])).
% 0.55/0.73 tff(634,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(635,plain,
% 0.55/0.73 ((hskp11 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239))) <=> (hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(636,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[635])).
% 0.55/0.73 tff(637,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[636, 634])).
% 0.55/0.73 tff(638,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(639,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.55/0.73 tff(640,plain,
% 0.55/0.73 (hskp11 | c1_1(a239) | c3_1(a237) | (~c3_1(a239))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[639, 142, 580, 581, 43, 633])).
% 0.55/0.73 tff(641,plain,
% 0.55/0.73 (hskp11),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[640, 612, 44, 623])).
% 0.55/0.73 tff(642,plain,
% 0.55/0.73 (~c3_1(a251)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[326, 641])).
% 0.55/0.73 tff(643,plain,
% 0.55/0.73 (~c1_1(a251)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[367, 641])).
% 0.55/0.73 tff(644,plain,
% 0.55/0.73 (c2_1(a251)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[334, 641])).
% 0.55/0.73 tff(645,assumption,(c0_1(a239)), introduced(assumption)).
% 0.55/0.73 tff(646,assumption,(~c3_1(a251)), introduced(assumption)).
% 0.55/0.73 tff(647,assumption,(~c1_1(a251)), introduced(assumption)).
% 0.55/0.73 tff(648,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a251) | c3_1(a251) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a251)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(649,plain,
% 0.55/0.73 (((~ndr1_0) | c2_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251))) <=> (c1_1(a251) | c3_1(a251) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a251)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(650,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a251) | c3_1(a251) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a251))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[649])).
% 0.55/0.73 tff(651,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a251)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[650, 648])).
% 0.55/0.73 tff(652,plain,
% 0.55/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(653,plain,
% 0.55/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a251))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.55/0.73 tff(654,plain,
% 0.55/0.73 ((~c0_1(a239)) | (~c0_1(a251))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[653, 142, 623, 647, 646, 44, 43, 235])).
% 0.55/0.73 tff(655,plain,
% 0.55/0.73 (~c0_1(a251)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[654, 645])).
% 0.55/0.73 tff(656,assumption,(c2_1(a251)), introduced(assumption)).
% 0.55/0.73 tff(657,plain,
% 0.55/0.73 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | c1_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp10 | c1_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(658,plain,
% 0.55/0.73 ((hskp10 | (~ndr1_0) | c1_1(a251) | c0_1(a251) | (~c2_1(a251))) <=> (hskp10 | c1_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(659,plain,
% 0.55/0.73 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a251) | c0_1(a251) | (~c2_1(a251)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | c1_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[658])).
% 0.55/0.73 tff(660,plain,
% 0.55/0.73 (((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a251) | c0_1(a251) | (~c2_1(a251)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp10 | c1_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251))),
% 0.55/0.73 inference(transitivity,[status(thm)],[659, 657])).
% 0.55/0.73 tff(661,plain,
% 0.55/0.73 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp10 | (~ndr1_0) | c1_1(a251) | c0_1(a251) | (~c2_1(a251)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(662,plain,
% 0.55/0.73 ((~![U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp10 | c1_1(a251) | (~ndr1_0) | (~c2_1(a251)) | c0_1(a251)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.55/0.73 tff(663,plain,
% 0.55/0.73 (hskp10 | c0_1(a251)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[662, 142, 656, 647, 30])).
% 0.55/0.73 tff(664,plain,
% 0.55/0.73 (hskp10),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[663, 655])).
% 0.55/0.73 tff(665,plain,
% 0.55/0.73 (~c2_1(a249)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[240, 664])).
% 0.55/0.73 tff(666,plain,
% 0.55/0.73 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(667,plain,
% 0.55/0.73 ((hskp12 | hskp3 | (~ndr1_0) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239))) <=> (hskp12 | hskp3 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(668,plain,
% 0.55/0.73 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[667])).
% 0.55/0.73 tff(669,plain,
% 0.55/0.73 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[668, 666])).
% 0.55/0.73 tff(670,plain,
% 0.55/0.73 ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(671,plain,
% 0.55/0.73 ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.55/0.73 tff(672,plain,
% 0.55/0.73 (hskp12 | (~c0_1(a239))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[671, 142, 45, 623, 44, 251])).
% 0.55/0.73 tff(673,plain,
% 0.55/0.73 (hskp12),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[672, 645])).
% 0.55/0.73 tff(674,plain,
% 0.55/0.73 (~c3_1(a252)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[263, 673])).
% 0.55/0.73 tff(675,plain,
% 0.55/0.73 (~c1_1(a252)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[269, 673])).
% 0.55/0.73 tff(676,plain,
% 0.55/0.73 (c3_1(a249)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[212, 664])).
% 0.55/0.73 tff(677,plain,
% 0.55/0.73 (c0_1(a249)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[220, 664])).
% 0.55/0.73 tff(678,plain,
% 0.55/0.73 (c0_1(a252)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[277, 673])).
% 0.55/0.73 tff(679,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a252) | c3_1(a252) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a252)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(680,plain,
% 0.55/0.73 (((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c3_1(a252) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a252)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(681,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a252) | c3_1(a252) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a252))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[680])).
% 0.55/0.73 tff(682,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a252)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[681, 679])).
% 0.55/0.73 tff(683,plain,
% 0.55/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(684,plain,
% 0.55/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a252))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.55/0.73 tff(685,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[684, 142, 678, 677, 676, 623, 675, 674, 665, 44, 235, 645])).
% 0.55/0.73 tff(686,plain,((~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c2_1(a251)) | c1_1(a251) | c3_1(a251) | c2_1(a239) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(687,plain,
% 0.55/0.73 (~c0_1(a239)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[686, 644, 45, 44, 643, 642, 43, 623])).
% 0.55/0.73 tff(688,plain,
% 0.55/0.73 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(689,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[688])).
% 0.55/0.73 tff(690,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(691,plain,
% 0.55/0.73 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(692,plain,
% 0.55/0.73 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[691])).
% 0.55/0.73 tff(693,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.55/0.73 tff(694,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.55/0.73 tff(695,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[694, 690])).
% 0.55/0.73 tff(696,plain,(
% 0.55/0.73 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(skolemize,[status(sab)],[695])).
% 0.55/0.73 tff(697,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[696, 689])).
% 0.55/0.73 tff(698,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | c0_1(a239))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(699,plain,
% 0.55/0.73 ((hskp16 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a239) | c0_1(a239) | (~c3_1(a239))) <=> (hskp16 | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | c0_1(a239))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(700,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a239) | c0_1(a239) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | c0_1(a239)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[699])).
% 0.55/0.73 tff(701,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a239) | c0_1(a239) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | c0_1(a239))),
% 0.55/0.73 inference(transitivity,[status(thm)],[700, 698])).
% 0.55/0.73 tff(702,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a239) | c0_1(a239) | (~c3_1(a239)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(703,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp16 | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | c0_1(a239)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.55/0.73 tff(704,plain,
% 0.55/0.73 (hskp16 | c3_1(a237) | (~c3_1(a239)) | c0_1(a239)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[703, 142, 580, 581, 43, 697])).
% 0.55/0.73 tff(705,plain,
% 0.55/0.73 (hskp16),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[704, 687, 623, 612])).
% 0.55/0.73 tff(706,plain,
% 0.55/0.73 (((~hskp16) | (~c3_1(a259))) <=> ((~hskp16) | (~c3_1(a259)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(707,plain,
% 0.55/0.73 (((~c3_1(a259)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a259)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(708,axiom,((~c3_1(a259)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.55/0.73 tff(709,plain,
% 0.55/0.73 ((~hskp16) | (~c3_1(a259))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.55/0.73 tff(710,plain,
% 0.55/0.73 ((~hskp16) | (~c3_1(a259))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[709, 706])).
% 0.55/0.73 tff(711,plain,
% 0.55/0.73 (~c3_1(a259)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[710, 705])).
% 0.55/0.73 tff(712,plain,
% 0.55/0.73 (((~hskp16) | (~c2_1(a259))) <=> ((~hskp16) | (~c2_1(a259)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(713,plain,
% 0.55/0.73 (((~c2_1(a259)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a259)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(714,axiom,((~c2_1(a259)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.55/0.73 tff(715,plain,
% 0.55/0.73 ((~hskp16) | (~c2_1(a259))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.55/0.73 tff(716,plain,
% 0.55/0.73 ((~hskp16) | (~c2_1(a259))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[715, 712])).
% 0.55/0.73 tff(717,plain,
% 0.55/0.73 (~c2_1(a259)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[716, 705])).
% 0.55/0.73 tff(718,plain,
% 0.55/0.73 (((~hskp16) | c1_1(a259)) <=> ((~hskp16) | c1_1(a259))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(719,axiom,((~hskp16) | c1_1(a259)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.55/0.73 tff(720,plain,
% 0.55/0.73 ((~hskp16) | c1_1(a259)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.55/0.73 tff(721,plain,
% 0.55/0.73 ((~hskp16) | c1_1(a259)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[720, 718])).
% 0.55/0.73 tff(722,plain,
% 0.55/0.73 ((~hskp16) | c1_1(a259)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[721, 718])).
% 0.55/0.73 tff(723,plain,
% 0.55/0.73 ((~hskp16) | c1_1(a259)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[722, 718])).
% 0.55/0.73 tff(724,plain,
% 0.55/0.73 ((~hskp16) | c1_1(a259)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[723, 718])).
% 0.55/0.73 tff(725,plain,
% 0.55/0.73 (c1_1(a259)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[724, 705])).
% 0.55/0.73 tff(726,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a259) | c3_1(a259) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a259) | c3_1(a259) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | (~c1_1(a259)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(727,plain,
% 0.55/0.73 (((~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a259) | c3_1(a259) | (~c1_1(a259)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239))) <=> (c2_1(a259) | c3_1(a259) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | (~c1_1(a259)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(728,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a259) | c3_1(a259) | (~c1_1(a259)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a259) | c3_1(a259) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | (~c1_1(a259))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[727])).
% 0.55/0.74 tff(729,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a259) | c3_1(a259) | (~c1_1(a259)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a259) | c3_1(a259) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | (~c1_1(a259)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[728, 726])).
% 0.55/0.74 tff(730,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a259) | c3_1(a259) | (~c1_1(a259)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(731,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a259) | c3_1(a259) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c3_1(a239)) | (~c1_1(a259))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.55/0.74 tff(732,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[731, 142, 580, 581, 725, 623, 717, 711, 44, 43, 622, 612])).
% 0.55/0.74 tff(733,plain,(c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | (~c3_1(a239)) | c1_1(a239) | c2_1(a239) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(734,plain,
% 0.55/0.74 (c3_1(a237)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[733, 611, 581, 580, 44, 43, 45])).
% 0.55/0.74 tff(735,plain,
% 0.55/0.74 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(736,plain,
% 0.55/0.74 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[735])).
% 0.55/0.74 tff(737,plain,
% 0.55/0.74 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(738,plain,
% 0.55/0.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp3))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(739,plain,
% 0.55/0.74 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[738])).
% 0.55/0.74 tff(740,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.55/0.74 tff(741,plain,
% 0.55/0.74 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.55/0.74 tff(742,plain,
% 0.55/0.74 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[741, 737])).
% 0.55/0.74 tff(743,plain,(
% 0.55/0.74 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.74 inference(skolemize,[status(sab)],[742])).
% 0.55/0.74 tff(744,plain,
% 0.55/0.74 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[743, 736])).
% 0.55/0.74 tff(745,plain,
% 0.55/0.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)) | c0_1(a239))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(746,plain,
% 0.55/0.74 ((hskp3 | (~ndr1_0) | (~c0_1(a237)) | (~c3_1(a237)) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | c0_1(a239)) <=> (hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)) | c0_1(a239))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(747,plain,
% 0.55/0.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c0_1(a237)) | (~c3_1(a237)) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)) | c0_1(a239)))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[746])).
% 0.55/0.74 tff(748,plain,
% 0.55/0.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c0_1(a237)) | (~c3_1(a237)) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)) | c0_1(a239))),
% 0.55/0.74 inference(transitivity,[status(thm)],[747, 745])).
% 0.55/0.74 tff(749,plain,
% 0.55/0.74 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c0_1(a237)) | (~c3_1(a237)) | (~c1_1(a237)) | c2_1(a239) | c1_1(a239) | c0_1(a239))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(750,plain,
% 0.55/0.74 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)) | c0_1(a239)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.55/0.74 tff(751,plain,
% 0.55/0.74 (c1_1(a239) | (~c3_1(a237)) | c0_1(a239)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[750, 142, 45, 582, 580, 43, 744])).
% 0.55/0.74 tff(752,plain,
% 0.55/0.74 (c0_1(a239)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[751, 734, 44])).
% 0.55/0.74 tff(753,plain,
% 0.55/0.74 (hskp12 | (~c0_1(a239))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[671, 142, 45, 611, 44, 251])).
% 0.55/0.74 tff(754,plain,
% 0.55/0.74 (hskp12),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[753, 752])).
% 0.55/0.74 tff(755,plain,
% 0.55/0.74 (~c3_1(a252)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[263, 754])).
% 0.55/0.74 tff(756,plain,
% 0.55/0.74 (~c1_1(a252)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[269, 754])).
% 0.55/0.74 tff(757,plain,
% 0.55/0.74 (c0_1(a252)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[277, 754])).
% 0.55/0.74 tff(758,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a252) | c3_1(a252) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a252)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(759,plain,
% 0.55/0.74 (((~ndr1_0) | c2_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c3_1(a252) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a252)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(760,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a252) | c3_1(a252) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a252))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[759])).
% 0.55/0.74 tff(761,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a252)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[760, 758])).
% 0.55/0.74 tff(762,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(763,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a252) | c3_1(a252) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a252))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.55/0.74 tff(764,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[763, 142, 757, 611, 756, 755, 44, 43, 235, 752])).
% 0.55/0.74 tff(765,plain,(c1_1(a239) | c2_1(a239) | hskp3 | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a237))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(766,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[765, 579, 571, 44, 43, 45, 563])).
% 0.55/0.74 tff(767,plain,(hskp3 | c1_1(a239) | c2_1(a239) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(768,plain,
% 0.55/0.74 (hskp3),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[767, 204, 43, 44])).
% 0.55/0.74 tff(769,plain,
% 0.55/0.74 (((~hskp3) | (~c3_1(a238))) <=> ((~hskp3) | (~c3_1(a238)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(770,plain,
% 0.55/0.74 (((~c3_1(a238)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a238)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(771,axiom,((~c3_1(a238)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.55/0.74 tff(772,plain,
% 0.55/0.74 ((~hskp3) | (~c3_1(a238))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[771, 770])).
% 0.55/0.74 tff(773,plain,
% 0.55/0.74 ((~hskp3) | (~c3_1(a238))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[772, 769])).
% 0.55/0.74 tff(774,plain,
% 0.55/0.74 (~c3_1(a238)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[773, 768])).
% 0.55/0.74 tff(775,plain,
% 0.55/0.74 (((~hskp3) | (~c2_1(a238))) <=> ((~hskp3) | (~c2_1(a238)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(776,plain,
% 0.55/0.74 (((~c2_1(a238)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a238)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(777,axiom,((~c2_1(a238)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.55/0.74 tff(778,plain,
% 0.55/0.74 ((~hskp3) | (~c2_1(a238))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.55/0.74 tff(779,plain,
% 0.55/0.74 ((~hskp3) | (~c2_1(a238))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[778, 775])).
% 0.55/0.74 tff(780,plain,
% 0.55/0.74 (~c2_1(a238)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[779, 768])).
% 0.55/0.74 tff(781,assumption,(hskp28), introduced(assumption)).
% 0.55/0.74 tff(782,plain,
% 0.55/0.74 (c0_1(a237)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[570, 781])).
% 0.55/0.74 tff(783,plain,
% 0.55/0.74 (c1_1(a237)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[578, 781])).
% 0.55/0.74 tff(784,plain,
% 0.55/0.74 (c2_1(a237)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[562, 781])).
% 0.55/0.74 tff(785,plain,
% 0.55/0.74 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(786,plain,
% 0.55/0.74 ((hskp4 | (~ndr1_0) | (~c0_1(a237)) | (~c3_1(a237)) | (~c1_1(a237))) <=> (hskp4 | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(787,plain,
% 0.55/0.74 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a237)) | (~c3_1(a237)) | (~c1_1(a237)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[786])).
% 0.55/0.74 tff(788,plain,
% 0.55/0.74 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a237)) | (~c3_1(a237)) | (~c1_1(a237)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[787, 785])).
% 0.55/0.74 tff(789,plain,
% 0.55/0.74 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a237)) | (~c3_1(a237)) | (~c1_1(a237)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(790,plain,
% 0.55/0.74 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c3_1(a237))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.55/0.74 tff(791,plain,
% 0.55/0.74 (hskp4 | (~c3_1(a237))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[790, 142, 582, 580, 10])).
% 0.55/0.74 tff(792,plain,
% 0.55/0.74 (~c3_1(a237)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[791, 204])).
% 0.55/0.74 tff(793,assumption,(~c3_1(a238)), introduced(assumption)).
% 0.55/0.74 tff(794,assumption,(~c2_1(a238)), introduced(assumption)).
% 0.55/0.74 tff(795,plain,
% 0.55/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)) | c1_1(a238))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)) | c1_1(a238))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(796,plain,
% 0.55/0.74 ((hskp4 | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a238) | c1_1(a238) | c3_1(a238)) <=> (hskp4 | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)) | c1_1(a238))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(797,plain,
% 0.55/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a238) | c1_1(a238) | c3_1(a238))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)) | c1_1(a238)))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[796])).
% 0.55/0.74 tff(798,plain,
% 0.55/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a238) | c1_1(a238) | c3_1(a238))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)) | c1_1(a238))),
% 0.55/0.74 inference(transitivity,[status(thm)],[797, 795])).
% 0.55/0.74 tff(799,plain,
% 0.55/0.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a238) | c1_1(a238) | c3_1(a238))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(800,plain,
% 0.55/0.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | (~c0_1(a237)) | (~c2_1(a237)) | c1_1(a238)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.55/0.74 tff(801,plain,
% 0.55/0.74 (hskp4 | c1_1(a238)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[800, 142, 582, 580, 581, 794, 793, 601])).
% 0.55/0.74 tff(802,plain,
% 0.55/0.74 (c1_1(a238)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[801, 204])).
% 0.55/0.74 tff(803,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a239) | c2_1(a239) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a238)) | (~c3_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a239) | c2_1(a239) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a238)) | (~c3_1(a239)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(804,plain,
% 0.55/0.74 (((~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239))) <=> (c1_1(a239) | c2_1(a239) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a238)) | (~c3_1(a239)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(805,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a239) | c2_1(a239) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a238)) | (~c3_1(a239))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[804])).
% 0.55/0.74 tff(806,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a239) | c2_1(a239) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a238)) | (~c3_1(a239)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[805, 803])).
% 0.55/0.74 tff(807,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c1_1(a237)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(808,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a239) | c2_1(a239) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a238)) | (~c3_1(a239))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.55/0.74 tff(809,plain,
% 0.55/0.74 (c1_1(a239) | c3_1(a237) | (~c1_1(a238)) | (~c3_1(a239))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[808, 142, 580, 581, 43, 794, 793, 622])).
% 0.55/0.74 tff(810,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[809, 802, 792, 44, 611])).
% 0.55/0.74 tff(811,plain,(hskp4 | c1_1(a239) | (~c1_1(a237)) | (~c2_1(a237)) | c2_1(a239) | c2_1(a238) | c3_1(a238) | (~c0_1(a237))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(812,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[811, 784, 783, 44, 204, 43, 774, 780, 782])).
% 0.55/0.74 tff(813,plain,((~hskp28) | c1_1(a239) | hskp4 | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(814,plain,
% 0.55/0.74 (~hskp28),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[813, 204, 44, 43])).
% 0.55/0.74 tff(815,plain,
% 0.55/0.74 (hskp10),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[554, 814, 43, 204, 44])).
% 0.55/0.74 tff(816,plain,
% 0.55/0.74 (~c2_1(a249)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[240, 815])).
% 0.55/0.74 tff(817,plain,
% 0.55/0.74 (((~hskp3) | c0_1(a238)) <=> ((~hskp3) | c0_1(a238))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(818,axiom,((~hskp3) | c0_1(a238)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.55/0.74 tff(819,plain,
% 0.55/0.74 ((~hskp3) | c0_1(a238)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.55/0.74 tff(820,plain,
% 0.55/0.74 ((~hskp3) | c0_1(a238)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[819, 817])).
% 0.55/0.74 tff(821,plain,
% 0.55/0.74 ((~hskp3) | c0_1(a238)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[820, 817])).
% 0.55/0.74 tff(822,plain,
% 0.55/0.74 ((~hskp3) | c0_1(a238)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[821, 817])).
% 0.55/0.74 tff(823,plain,
% 0.55/0.74 ((~hskp3) | c0_1(a238)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[822, 817])).
% 0.55/0.74 tff(824,plain,
% 0.55/0.74 (c0_1(a238)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[823, 768])).
% 0.55/0.74 tff(825,plain,
% 0.55/0.74 (c3_1(a249)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[212, 815])).
% 0.55/0.74 tff(826,plain,
% 0.55/0.74 (c0_1(a249)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[220, 815])).
% 0.55/0.74 tff(827,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(828,plain,
% 0.55/0.74 (((~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a249) | (~c1_1(a249)) | (~c3_1(a249)) | c2_1(a238) | c3_1(a238) | (~c0_1(a238))) <=> (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(829,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a249) | (~c1_1(a249)) | (~c3_1(a249)) | c2_1(a238) | c3_1(a238) | (~c0_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[828])).
% 0.55/0.74 tff(830,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a249) | (~c1_1(a249)) | (~c3_1(a249)) | c2_1(a238) | c3_1(a238) | (~c0_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[829, 827])).
% 0.55/0.74 tff(831,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a249) | (~c1_1(a249)) | (~c3_1(a249)) | c2_1(a238) | c3_1(a238) | (~c0_1(a238)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(832,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.55/0.74 tff(833,plain,
% 0.55/0.74 (~c1_1(a249)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[832, 142, 826, 825, 824, 816, 780, 774, 20])).
% 0.55/0.74 tff(834,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | c1_1(a238) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | c1_1(a238) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(835,plain,
% 0.55/0.74 (((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a238) | c1_1(a238) | c3_1(a238)) <=> (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | c1_1(a238) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(836,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a238) | c1_1(a238) | c3_1(a238))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | c1_1(a238) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[835])).
% 0.55/0.74 tff(837,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a238) | c1_1(a238) | c3_1(a238))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | c1_1(a238) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.74 inference(transitivity,[status(thm)],[836, 834])).
% 0.55/0.74 tff(838,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a238) | c1_1(a238) | c3_1(a238))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(839,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | c1_1(a238) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[838, 837])).
% 0.55/0.74 tff(840,plain,
% 0.55/0.74 (c1_1(a238)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[839, 142, 826, 825, 816, 780, 774, 528, 833])).
% 0.55/0.74 tff(841,plain,
% 0.55/0.74 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(842,plain,
% 0.55/0.74 ((hskp18 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249))) <=> (hskp18 | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(843,plain,
% 0.55/0.74 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[842])).
% 0.55/0.75 tff(844,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.75 inference(transitivity,[status(thm)],[843, 841])).
% 0.55/0.75 tff(845,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(846,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.55/0.75 tff(847,plain,
% 0.55/0.75 (hskp18),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[846, 142, 826, 825, 816, 56, 833])).
% 0.55/0.75 tff(848,plain,
% 0.55/0.75 (c2_1(a265)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[295, 847])).
% 0.55/0.75 tff(849,plain,
% 0.55/0.75 (c1_1(a265)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[303, 847])).
% 0.55/0.75 tff(850,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(851,plain,
% 0.55/0.75 (((~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249))) <=> (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(852,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[851])).
% 0.55/0.75 tff(853,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[852, 850])).
% 0.55/0.75 tff(854,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(855,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.55/0.75 tff(856,plain,
% 0.55/0.75 (c3_1(a265)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[855, 142, 849, 848, 825, 816, 780, 774, 622, 840, 833])).
% 0.55/0.75 tff(857,plain,
% 0.55/0.75 (~c0_1(a265)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[192, 847])).
% 0.55/0.75 tff(858,plain,
% 0.55/0.75 (hskp11),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[310, 142, 849, 848, 857, 66, 856])).
% 0.55/0.75 tff(859,plain,
% 0.55/0.75 (~c3_1(a251)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[326, 858])).
% 0.55/0.75 tff(860,plain,
% 0.55/0.75 (c2_1(a251)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[334, 858])).
% 0.55/0.75 tff(861,plain,
% 0.55/0.75 (c0_1(a251)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[341, 142, 814, 204, 860, 859, 203])).
% 0.55/0.75 tff(862,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(863,plain,
% 0.55/0.75 ((hskp4 | (~ndr1_0) | (~c2_1(a265)) | (~c3_1(a265)) | (~c1_1(a265)) | c2_1(a239) | c1_1(a239) | c0_1(a239)) <=> (hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(864,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a265)) | (~c3_1(a265)) | (~c1_1(a265)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[863])).
% 0.55/0.75 tff(865,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a265)) | (~c3_1(a265)) | (~c1_1(a265)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[864, 862])).
% 0.55/0.75 tff(866,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a265)) | (~c3_1(a265)) | (~c1_1(a265)) | c2_1(a239) | c1_1(a239) | c0_1(a239))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(867,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a265)) | (~c3_1(a265)) | (~c2_1(a265))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.55/0.75 tff(868,plain,
% 0.55/0.75 (c0_1(a239)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[867, 142, 204, 849, 848, 44, 43, 466, 856])).
% 0.55/0.75 tff(869,plain,
% 0.55/0.75 (~c1_1(a251)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[367, 858])).
% 0.55/0.75 tff(870,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a239) | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a239) | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(871,plain,
% 0.55/0.75 (((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a239) | c1_1(a239) | c3_1(a239)) <=> (c3_1(a239) | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(872,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a239) | c1_1(a239) | c3_1(a239))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a239) | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[871])).
% 0.55/0.75 tff(873,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a239) | c1_1(a239) | c3_1(a239))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a239) | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.55/0.75 inference(transitivity,[status(thm)],[872, 870])).
% 0.55/0.75 tff(874,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a239) | c1_1(a239) | c3_1(a239))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(875,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a239) | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.55/0.75 tff(876,plain,
% 0.55/0.75 (c3_1(a239)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[875, 142, 826, 825, 816, 44, 43, 528, 833])).
% 0.55/0.75 tff(877,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a251) | c3_1(a251) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a251)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(878,plain,
% 0.55/0.75 (((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251))) <=> (c1_1(a251) | c3_1(a251) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a251)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(879,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a251) | c3_1(a251) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a251))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[878])).
% 0.55/0.75 tff(880,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a251)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[879, 877])).
% 0.55/0.75 tff(881,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a239) | (~c0_1(a239)) | (~c3_1(a239)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(882,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c2_1(a249) | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)) | (~c0_1(a249)) | (~c3_1(a249)) | (~c0_1(a251))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.55/0.75 tff(883,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[882, 142, 826, 825, 876, 869, 859, 816, 44, 235, 868, 861])).
% 0.55/0.75 tff(884,plain,(hskp4 | c1_1(a239) | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(885,plain,
% 0.55/0.75 (hskp4),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[884, 44, 43])).
% 0.55/0.75 tff(886,plain,
% 0.55/0.75 (c3_1(a239)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[590, 885])).
% 0.55/0.75 tff(887,assumption,(~c0_1(a265)), introduced(assumption)).
% 0.55/0.75 tff(888,assumption,(c2_1(a265)), introduced(assumption)).
% 0.55/0.75 tff(889,assumption,(c1_1(a265)), introduced(assumption)).
% 0.55/0.75 tff(890,plain,
% 0.55/0.75 (hskp11 | (~c3_1(a265))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[310, 142, 889, 888, 887, 66])).
% 0.55/0.75 tff(891,plain,
% 0.55/0.75 (~c3_1(a265)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[890, 32])).
% 0.55/0.75 tff(892,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(893,plain,
% 0.55/0.75 ((hskp11 | (~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239))) <=> (hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(894,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[893])).
% 0.55/0.75 tff(895,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[894, 892])).
% 0.55/0.75 tff(896,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(897,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.55/0.75 tff(898,plain,
% 0.55/0.75 (hskp11 | c1_1(a239) | (~c3_1(a239)) | c3_1(a265)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[897, 142, 889, 888, 43, 633])).
% 0.55/0.75 tff(899,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[898, 891, 32, 44, 623])).
% 0.55/0.75 tff(900,plain,(hskp11 | c1_1(a239) | (~c3_1(a239)) | (~c1_1(a265)) | (~c2_1(a265)) | c2_1(a239) | c0_1(a265)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(901,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[900, 296, 304, 44, 886, 32, 43, 193])).
% 0.55/0.75 tff(902,plain,(hskp11 | c1_1(a239) | c2_1(a239) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(903,plain,
% 0.55/0.75 (hskp11),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[902, 31, 43, 44])).
% 0.55/0.75 tff(904,plain,
% 0.55/0.75 (~c1_1(a251)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[367, 903])).
% 0.55/0.75 tff(905,plain,
% 0.55/0.75 (c2_1(a251)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[334, 903])).
% 0.55/0.75 tff(906,plain,
% 0.55/0.75 (c0_1(a251)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[662, 142, 31, 905, 904, 30])).
% 0.55/0.75 tff(907,plain,
% 0.55/0.75 (~c3_1(a251)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[326, 903])).
% 0.55/0.75 tff(908,plain,
% 0.55/0.75 (hskp5 | (~c0_1(a251))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[374, 142, 905, 904, 907, 362])).
% 0.55/0.75 tff(909,plain,
% 0.55/0.75 (hskp5),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[908, 906])).
% 0.55/0.75 tff(910,plain,
% 0.55/0.75 (~c0_1(a241)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[154, 909])).
% 0.55/0.75 tff(911,plain,
% 0.55/0.75 (c2_1(a241)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[170, 909])).
% 0.55/0.75 tff(912,plain,
% 0.55/0.75 (c1_1(a241)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[184, 142, 31, 911, 910, 30])).
% 0.55/0.75 tff(913,plain,
% 0.55/0.75 (~c0_1(a239)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[653, 142, 886, 904, 907, 44, 43, 235, 906])).
% 0.55/0.75 tff(914,plain,
% 0.55/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(915,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[914])).
% 0.55/0.75 tff(916,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(917,plain,
% 0.55/0.75 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(918,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[917])).
% 0.55/0.75 tff(919,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 0.55/0.75 tff(920,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.55/0.75 tff(921,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[920, 916])).
% 0.55/0.75 tff(922,plain,(
% 0.55/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.75 inference(skolemize,[status(sab)],[921])).
% 0.55/0.75 tff(923,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[922, 915])).
% 0.55/0.75 tff(924,plain,
% 0.55/0.75 (c3_1(a241)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[162, 909])).
% 0.55/0.75 tff(925,plain,
% 0.55/0.75 (hskp20 | (~c1_1(a241))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[385, 142, 905, 911, 907, 910, 352, 906])).
% 0.55/0.75 tff(926,plain,
% 0.55/0.75 (hskp20),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[925, 912])).
% 0.55/0.75 tff(927,plain,
% 0.55/0.75 (c1_1(a271)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[396, 926])).
% 0.55/0.75 tff(928,plain,
% 0.55/0.75 (c0_1(a271)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[404, 926])).
% 0.55/0.75 tff(929,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a241) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a241)) | (~c3_1(a241)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a241) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a241)) | (~c3_1(a241)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(930,plain,
% 0.55/0.75 (((~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)) | c0_1(a241) | (~c1_1(a241)) | (~c3_1(a241)) | c2_1(a239) | c1_1(a239) | c0_1(a239)) <=> (c0_1(a241) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a241)) | (~c3_1(a241)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(931,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)) | c0_1(a241) | (~c1_1(a241)) | (~c3_1(a241)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a241) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a241)) | (~c3_1(a241)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[930])).
% 0.55/0.75 tff(932,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)) | c0_1(a241) | (~c1_1(a241)) | (~c3_1(a241)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a241) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a241)) | (~c3_1(a241)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[931, 929])).
% 0.55/0.75 tff(933,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)) | c0_1(a241) | (~c1_1(a241)) | (~c3_1(a241)) | c2_1(a239) | c1_1(a239) | c0_1(a239))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(934,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a241) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c1_1(a241)) | (~c3_1(a241)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.55/0.75 tff(935,plain,
% 0.55/0.75 (~c3_1(a271)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[934, 142, 928, 927, 924, 910, 44, 43, 923, 913, 912])).
% 0.55/0.75 tff(936,plain,
% 0.55/0.75 (~c2_1(a271)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[424, 926])).
% 0.55/0.75 tff(937,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[544, 142, 31, 927, 886, 936, 44, 43, 538, 935])).
% 0.55/0.75 tff(938,plain,(hskp10 | c1_1(a239) | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(939,plain,
% 0.55/0.75 (hskp10),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[938, 44, 43])).
% 0.55/0.75 tff(940,plain,
% 0.55/0.75 (~c2_1(a249)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[240, 939])).
% 0.55/0.75 tff(941,plain,
% 0.55/0.75 (c3_1(a249)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[212, 939])).
% 0.55/0.75 tff(942,plain,
% 0.55/0.75 (c0_1(a249)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[220, 939])).
% 0.55/0.75 tff(943,plain,
% 0.55/0.75 (hskp18 | c1_1(a249)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[846, 142, 942, 941, 940, 56])).
% 0.55/0.75 tff(944,plain,
% 0.55/0.75 (c1_1(a249)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[943, 46])).
% 0.55/0.75 tff(945,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(946,plain,
% 0.55/0.75 ((hskp18 | (~ndr1_0) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)) | c2_1(a239) | c1_1(a239) | (~c0_1(a239))) <=> (hskp18 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(947,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)) | c2_1(a239) | c1_1(a239) | (~c0_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[946])).
% 0.55/0.75 tff(948,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)) | c2_1(a239) | c1_1(a239) | (~c0_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[947, 945])).
% 0.55/0.75 tff(949,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a239) | c1_1(a239) | (~c3_1(a239)) | c2_1(a239) | c1_1(a239) | (~c0_1(a239)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(950,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.55/0.75 tff(951,plain,
% 0.55/0.75 (hskp18 | c1_1(a239) | (~c3_1(a239)) | (~c0_1(a239))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[950, 142, 43, 56])).
% 0.55/0.75 tff(952,plain,
% 0.55/0.75 (~c0_1(a239)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[951, 46, 44, 886])).
% 0.55/0.75 tff(953,plain,
% 0.55/0.75 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(954,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[953])).
% 0.55/0.75 tff(955,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(956,plain,
% 0.55/0.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(957,plain,
% 0.55/0.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[956])).
% 0.55/0.75 tff(958,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.55/0.75 tff(959,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.55/0.75 tff(960,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[959, 955])).
% 0.55/0.75 tff(961,plain,(
% 0.55/0.75 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.76 inference(skolemize,[status(sab)],[960])).
% 0.55/0.76 tff(962,plain,
% 0.55/0.76 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[961, 954])).
% 0.55/0.76 tff(963,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c1_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(964,plain,
% 0.55/0.76 ((hskp2 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c1_1(a249)) | c2_1(a239) | c1_1(a239) | c0_1(a239)) <=> (hskp2 | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(965,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c1_1(a249)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c1_1(a249))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[964])).
% 0.55/0.76 tff(966,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c1_1(a249)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(transitivity,[status(thm)],[965, 963])).
% 0.55/0.76 tff(967,plain,
% 0.55/0.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c1_1(a249)) | c2_1(a239) | c1_1(a239) | c0_1(a239))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(968,plain,
% 0.55/0.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c2_1(a249) | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c1_1(a249))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.55/0.76 tff(969,plain,
% 0.55/0.76 (hskp2 | c0_1(a239) | (~c1_1(a249))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[968, 142, 942, 940, 44, 43, 962])).
% 0.55/0.76 tff(970,plain,
% 0.55/0.76 (hskp2),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[969, 952, 944])).
% 0.55/0.76 tff(971,plain,
% 0.55/0.76 (((~hskp2) | (~c0_1(a236))) <=> ((~hskp2) | (~c0_1(a236)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(972,plain,
% 0.55/0.76 (((~c0_1(a236)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a236)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(973,axiom,((~c0_1(a236)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.55/0.76 tff(974,plain,
% 0.55/0.76 ((~hskp2) | (~c0_1(a236))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[973, 972])).
% 0.55/0.76 tff(975,plain,
% 0.55/0.76 ((~hskp2) | (~c0_1(a236))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[974, 971])).
% 0.55/0.76 tff(976,plain,
% 0.55/0.76 (~c0_1(a236)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[975, 970])).
% 0.55/0.76 tff(977,plain,
% 0.55/0.76 (((~hskp2) | c3_1(a236)) <=> ((~hskp2) | c3_1(a236))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(978,axiom,((~hskp2) | c3_1(a236)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.55/0.76 tff(979,plain,
% 0.55/0.76 ((~hskp2) | c3_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[978, 977])).
% 0.55/0.76 tff(980,plain,
% 0.55/0.76 ((~hskp2) | c3_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[979, 977])).
% 0.55/0.76 tff(981,plain,
% 0.55/0.76 ((~hskp2) | c3_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[980, 977])).
% 0.55/0.76 tff(982,plain,
% 0.55/0.76 ((~hskp2) | c3_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[981, 977])).
% 0.55/0.76 tff(983,plain,
% 0.55/0.76 ((~hskp2) | c3_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[982, 977])).
% 0.55/0.76 tff(984,plain,
% 0.55/0.76 (c3_1(a236)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[983, 970])).
% 0.55/0.76 tff(985,plain,
% 0.55/0.76 (((~hskp2) | c1_1(a236)) <=> ((~hskp2) | c1_1(a236))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(986,axiom,((~hskp2) | c1_1(a236)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.55/0.76 tff(987,plain,
% 0.55/0.76 ((~hskp2) | c1_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.55/0.76 tff(988,plain,
% 0.55/0.76 ((~hskp2) | c1_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[987, 985])).
% 0.55/0.76 tff(989,plain,
% 0.55/0.76 ((~hskp2) | c1_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[988, 985])).
% 0.55/0.76 tff(990,plain,
% 0.55/0.76 ((~hskp2) | c1_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[989, 985])).
% 0.55/0.76 tff(991,plain,
% 0.55/0.76 ((~hskp2) | c1_1(a236)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[990, 985])).
% 0.55/0.76 tff(992,plain,
% 0.55/0.76 (c1_1(a236)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[991, 970])).
% 0.55/0.76 tff(993,plain,
% 0.55/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a239) | c2_1(a239) | c0_1(a236) | (~ndr1_0) | (~c1_1(a236)) | (~c3_1(a236)) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a239) | c2_1(a239) | c0_1(a236) | (~ndr1_0) | (~c1_1(a236)) | (~c3_1(a236)) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(994,plain,
% 0.55/0.76 (((~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c0_1(a236) | (~c1_1(a236)) | (~c3_1(a236)) | c2_1(a239) | c1_1(a239) | c0_1(a239)) <=> (c1_1(a239) | c2_1(a239) | c0_1(a236) | (~ndr1_0) | (~c1_1(a236)) | (~c3_1(a236)) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(995,plain,
% 0.55/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c0_1(a236) | (~c1_1(a236)) | (~c3_1(a236)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a239) | c2_1(a239) | c0_1(a236) | (~ndr1_0) | (~c1_1(a236)) | (~c3_1(a236)) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[994])).
% 0.55/0.76 tff(996,plain,
% 0.55/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c0_1(a236) | (~c1_1(a236)) | (~c3_1(a236)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a239) | c2_1(a239) | c0_1(a236) | (~ndr1_0) | (~c1_1(a236)) | (~c3_1(a236)) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(transitivity,[status(thm)],[995, 993])).
% 0.55/0.76 tff(997,plain,
% 0.55/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c0_1(a236) | (~c1_1(a236)) | (~c3_1(a236)) | c2_1(a239) | c1_1(a239) | c0_1(a239))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(998,plain,
% 0.55/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a239) | c2_1(a239) | c0_1(a236) | (~ndr1_0) | (~c1_1(a236)) | (~c3_1(a236)) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.55/0.76 tff(999,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[998, 142, 942, 941, 992, 984, 44, 43, 976, 923, 952, 944])).
% 0.55/0.76 tff(1000,plain,(hskp18 | c1_1(a239) | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.76 tff(1001,plain,
% 0.55/0.76 (hskp18),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1000, 44, 43])).
% 0.55/0.76 tff(1002,assumption,(hskp18), introduced(assumption)).
% 0.55/0.76 tff(1003,plain,
% 0.55/0.76 (~c0_1(a265)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[192, 1002])).
% 0.55/0.76 tff(1004,plain,
% 0.55/0.76 (c1_1(a265)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[303, 1002])).
% 0.55/0.76 tff(1005,plain,
% 0.55/0.76 (c2_1(a265)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[295, 1002])).
% 0.55/0.76 tff(1006,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[900, 1005, 1004, 44, 886, 32, 43, 1003])).
% 0.55/0.76 tff(1007,plain,((~hskp18) | c1_1(a239) | hskp11 | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.76 tff(1008,plain,
% 0.55/0.76 (hskp11),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1007, 1001, 44, 43])).
% 0.55/0.76 tff(1009,plain,
% 0.55/0.76 (c2_1(a251)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[334, 1008])).
% 0.55/0.76 tff(1010,plain,
% 0.55/0.76 (~c3_1(a251)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[326, 1008])).
% 0.55/0.76 tff(1011,plain,
% 0.55/0.76 (~c1_1(a251)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[367, 1008])).
% 0.55/0.76 tff(1012,plain,
% 0.55/0.76 (~c0_1(a239)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[686, 45, 44, 886, 1011, 1010, 43, 1009])).
% 0.55/0.76 tff(1013,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1014,plain,
% 0.55/0.76 ((hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a239) | c1_1(a239) | c0_1(a239)) <=> (hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1015,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1014])).
% 0.55/0.76 tff(1016,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a239) | c1_1(a239) | c0_1(a239))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)))),
% 0.55/0.76 inference(transitivity,[status(thm)],[1015, 1013])).
% 0.55/0.76 tff(1017,plain,
% 0.55/0.76 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249)) | c2_1(a239) | c1_1(a239) | c0_1(a239))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1018,plain,
% 0.55/0.76 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a239) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | (~c1_1(a249))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 0.55/0.76 tff(1019,plain,
% 0.55/0.76 (hskp3 | c0_1(a239) | (~c1_1(a249))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1018, 142, 942, 941, 44, 43, 744])).
% 0.55/0.76 tff(1020,plain,
% 0.55/0.76 (~c1_1(a249)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1019, 1012, 45])).
% 0.55/0.76 tff(1021,plain,
% 0.60/0.76 (hskp12 | hskp3 | c1_1(a249)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[257, 142, 942, 941, 251])).
% 0.60/0.76 tff(1022,plain,
% 0.60/0.76 (hskp12),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1021, 1020, 45])).
% 0.60/0.76 tff(1023,plain,
% 0.60/0.76 (~c3_1(a252)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[263, 1022])).
% 0.60/0.76 tff(1024,plain,
% 0.60/0.76 (~c1_1(a252)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[269, 1022])).
% 0.60/0.76 tff(1025,plain,
% 0.60/0.76 (c0_1(a252)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[277, 1022])).
% 0.60/0.76 tff(1026,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[284, 142, 1025, 942, 941, 1024, 1023, 940, 235, 1020])).
% 0.60/0.76 tff(1027,plain,(hskp3 | c1_1(a239) | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(1028,plain,
% 0.60/0.76 (hskp3),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1027, 44, 43])).
% 0.60/0.76 tff(1029,plain,
% 0.60/0.76 (~c3_1(a238)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[773, 1028])).
% 0.60/0.76 tff(1030,plain,
% 0.60/0.76 (~c2_1(a238)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[779, 1028])).
% 0.60/0.76 tff(1031,plain,
% 0.60/0.76 (c0_1(a238)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[823, 1028])).
% 0.60/0.76 tff(1032,plain,
% 0.60/0.76 (~c1_1(a249)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[832, 142, 942, 941, 1031, 940, 1030, 1029, 20])).
% 0.60/0.76 tff(1033,plain,
% 0.60/0.76 (c1_1(a238)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[839, 142, 942, 941, 940, 1030, 1029, 528, 1032])).
% 0.60/0.76 tff(1034,plain,
% 0.60/0.76 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(1035,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1034])).
% 0.60/0.76 tff(1036,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1037,plain,
% 0.60/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(1038,plain,
% 0.60/0.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1037])).
% 0.60/0.76 tff(1039,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.60/0.76 tff(1040,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 0.60/0.76 tff(1041,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1040, 1036])).
% 0.60/0.76 tff(1042,plain,(
% 0.60/0.76 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.76 inference(skolemize,[status(sab)],[1041])).
% 0.60/0.76 tff(1043,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1042, 1035])).
% 0.60/0.76 tff(1044,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp20 | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1045,plain,
% 0.60/0.76 ((hskp20 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238))) <=> (hskp20 | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1046,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c0_1(a249)) | (~c3_1(a249))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1045])).
% 0.60/0.76 tff(1047,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp20 | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c0_1(a249)) | (~c3_1(a249)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1046, 1044])).
% 0.60/0.76 tff(1048,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a238) | c3_1(a238) | (~c1_1(a238)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1049,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp20 | c2_1(a249) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c1_1(a238)) | (~c0_1(a249)) | (~c3_1(a249))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.60/0.76 tff(1050,plain,
% 0.60/0.76 (hskp20 | (~c1_1(a238))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1049, 142, 942, 941, 940, 1030, 1029, 1043])).
% 0.60/0.76 tff(1051,plain,
% 0.60/0.76 (hskp20),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1050, 1033])).
% 0.60/0.76 tff(1052,plain,
% 0.60/0.76 (~c2_1(a271)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[424, 1051])).
% 0.60/0.76 tff(1053,plain,
% 0.60/0.76 (c1_1(a271)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[396, 1051])).
% 0.60/0.76 tff(1054,plain,
% 0.60/0.76 (c0_1(a271)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[404, 1051])).
% 0.60/0.76 tff(1055,plain,
% 0.60/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a271) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a271) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1056,plain,
% 0.60/0.76 (((~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)) | c2_1(a271) | (~c1_1(a271)) | (~c3_1(a271)) | c2_1(a238) | c3_1(a238) | (~c0_1(a238))) <=> (c2_1(a271) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1057,plain,
% 0.60/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)) | c2_1(a271) | (~c1_1(a271)) | (~c3_1(a271)) | c2_1(a238) | c3_1(a238) | (~c0_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a271) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1056])).
% 0.60/0.76 tff(1058,plain,
% 0.60/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)) | c2_1(a271) | (~c1_1(a271)) | (~c3_1(a271)) | c2_1(a238) | c3_1(a238) | (~c0_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a271) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1057, 1055])).
% 0.60/0.76 tff(1059,plain,
% 0.60/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271)) | c2_1(a271) | (~c1_1(a271)) | (~c3_1(a271)) | c2_1(a238) | c3_1(a238) | (~c0_1(a238)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1060,plain,
% 0.60/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a271) | c2_1(a238) | c3_1(a238) | (~ndr1_0) | (~c0_1(a238)) | (~c0_1(a271)) | (~c3_1(a271)) | (~c1_1(a271))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.60/0.76 tff(1061,plain,
% 0.60/0.76 (~c3_1(a271)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1060, 142, 1054, 1053, 1031, 1052, 1030, 1029, 20])).
% 0.60/0.76 tff(1062,plain,
% 0.60/0.76 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(1063,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1062])).
% 0.60/0.76 tff(1064,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1065,plain,
% 0.60/0.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp25) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp25))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(1066,plain,
% 0.60/0.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1065])).
% 0.60/0.76 tff(1067,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.60/0.76 tff(1068,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 0.60/0.76 tff(1069,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1068, 1064])).
% 0.60/0.76 tff(1070,plain,(
% 0.60/0.76 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.60/0.76 inference(skolemize,[status(sab)],[1069])).
% 0.60/0.76 tff(1071,plain,
% 0.60/0.76 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1070, 1063])).
% 0.60/0.76 tff(1072,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a251)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1073,plain,
% 0.60/0.76 ((hskp25 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251))) <=> (hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a251)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1074,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a251))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[1073])).
% 0.60/0.76 tff(1075,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a251)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[1074, 1072])).
% 0.60/0.76 tff(1076,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(1077,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a251))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.60/0.76 tff(1078,plain,
% 0.60/0.76 (hskp25),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1077, 142, 1009, 942, 941, 1011, 1010, 1071, 1032])).
% 0.60/0.76 tff(1079,plain,
% 0.60/0.76 (((~hskp25) | (~c3_1(a294))) <=> ((~hskp25) | (~c3_1(a294)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1080,plain,
% 0.60/0.76 (((~c3_1(a294)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a294)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1081,axiom,((~c3_1(a294)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.60/0.76 tff(1082,plain,
% 0.60/0.76 ((~hskp25) | (~c3_1(a294))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 0.60/0.76 tff(1083,plain,
% 0.60/0.76 ((~hskp25) | (~c3_1(a294))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1082, 1079])).
% 0.60/0.76 tff(1084,plain,
% 0.60/0.76 (~c3_1(a294)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[1083, 1078])).
% 0.60/0.76 tff(1085,plain,
% 0.60/0.76 (((~hskp25) | c2_1(a294)) <=> ((~hskp25) | c2_1(a294))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(1086,axiom,((~hskp25) | c2_1(a294)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.60/0.76 tff(1087,plain,
% 0.60/0.76 ((~hskp25) | c2_1(a294)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.60/0.76 tff(1088,plain,
% 0.60/0.76 ((~hskp25) | c2_1(a294)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[1087, 1085])).
% 0.60/0.77 tff(1089,plain,
% 0.60/0.77 ((~hskp25) | c2_1(a294)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1088, 1085])).
% 0.60/0.77 tff(1090,plain,
% 0.60/0.77 ((~hskp25) | c2_1(a294)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1089, 1085])).
% 0.60/0.77 tff(1091,plain,
% 0.60/0.77 ((~hskp25) | c2_1(a294)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1090, 1085])).
% 0.60/0.77 tff(1092,plain,
% 0.60/0.77 (c2_1(a294)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1091, 1078])).
% 0.60/0.77 tff(1093,plain,
% 0.60/0.77 (((~hskp25) | c1_1(a294)) <=> ((~hskp25) | c1_1(a294))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1094,axiom,((~hskp25) | c1_1(a294)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.60/0.77 tff(1095,plain,
% 0.60/0.77 ((~hskp25) | c1_1(a294)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 0.60/0.77 tff(1096,plain,
% 0.60/0.77 ((~hskp25) | c1_1(a294)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1095, 1093])).
% 0.60/0.77 tff(1097,plain,
% 0.60/0.77 ((~hskp25) | c1_1(a294)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1096, 1093])).
% 0.60/0.77 tff(1098,plain,
% 0.60/0.77 ((~hskp25) | c1_1(a294)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1097, 1093])).
% 0.60/0.77 tff(1099,plain,
% 0.60/0.77 ((~hskp25) | c1_1(a294)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1098, 1093])).
% 0.60/0.77 tff(1100,plain,
% 0.60/0.77 (c1_1(a294)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1099, 1078])).
% 0.60/0.77 tff(1101,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a294) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a271) | (~c1_1(a271)) | (~c2_1(a294)) | (~c1_1(a294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a294) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a271) | (~c1_1(a271)) | (~c2_1(a294)) | (~c1_1(a294)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1102,plain,
% 0.60/0.77 (((~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c1_1(a294)) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249))) <=> (c3_1(a294) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a271) | (~c1_1(a271)) | (~c2_1(a294)) | (~c1_1(a294)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1103,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c1_1(a294)) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a294) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a271) | (~c1_1(a271)) | (~c2_1(a294)) | (~c1_1(a294))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1102])).
% 0.60/0.77 tff(1104,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c1_1(a294)) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a294) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a271) | (~c1_1(a271)) | (~c2_1(a294)) | (~c1_1(a294)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1103, 1101])).
% 0.60/0.77 tff(1105,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c1_1(a294)) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1106,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a294) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a271) | (~c1_1(a271)) | (~c2_1(a294)) | (~c1_1(a294))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 0.60/0.77 tff(1107,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1106, 142, 1100, 1092, 1053, 941, 1084, 1052, 940, 622, 1032, 1061])).
% 0.60/0.77 tff(1108,plain,(c1_1(a239) | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1109,plain,
% 0.60/0.77 (c1_1(a239)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1108, 43])).
% 0.60/0.77 tff(1110,plain,
% 0.60/0.77 (((~hskp4) | (~c1_1(a239))) <=> ((~hskp4) | (~c1_1(a239)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1111,plain,
% 0.60/0.77 (((~c1_1(a239)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a239)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1112,axiom,((~c1_1(a239)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.60/0.77 tff(1113,plain,
% 0.60/0.77 ((~hskp4) | (~c1_1(a239))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 0.60/0.77 tff(1114,plain,
% 0.60/0.77 ((~hskp4) | (~c1_1(a239))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1113, 1110])).
% 0.60/0.77 tff(1115,plain,
% 0.60/0.77 (~hskp4),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1114, 1109])).
% 0.60/0.77 tff(1116,plain,
% 0.60/0.77 (((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | c3_1(a239) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0))) <=> ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp31 | hskp4 | c3_1(a239) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1117,plain,
% 0.60/0.77 ((hskp31 | hskp4 | (~ndr1_0) | c2_1(a239) | c3_1(a239) | (~c1_1(a239))) <=> (hskp31 | hskp4 | c3_1(a239) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1118,plain,
% 0.60/0.77 (((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | (~ndr1_0) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)))) <=> ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | c3_1(a239) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0)))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1117])).
% 0.60/0.77 tff(1119,plain,
% 0.60/0.77 (((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | (~ndr1_0) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)))) <=> ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp31 | hskp4 | c3_1(a239) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1118, 1116])).
% 0.60/0.77 tff(1120,plain,
% 0.60/0.77 ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp31 | hskp4 | (~ndr1_0) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1121,plain,
% 0.60/0.77 ((~![U: $i] : (hskp31 | hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp31 | hskp4 | c3_1(a239) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 0.60/0.77 tff(1122,plain,
% 0.60/0.77 (hskp31 | hskp4 | c3_1(a239) | (~c1_1(a239))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1121, 142, 43, 419])).
% 0.60/0.77 tff(1123,plain,
% 0.60/0.77 (hskp31),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1122, 583, 1115, 1109])).
% 0.60/0.77 tff(1124,plain,
% 0.60/0.77 (c3_1(a246)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[440, 1123])).
% 0.60/0.77 tff(1125,plain,
% 0.60/0.77 (c0_1(a246)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[448, 1123])).
% 0.60/0.77 tff(1126,plain,
% 0.60/0.77 (~c1_1(a246)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[455, 142, 1115, 1125, 1124, 10])).
% 0.60/0.77 tff(1127,assumption,(~c1_1(a246)), introduced(assumption)).
% 0.60/0.77 tff(1128,assumption,(c3_1(a246)), introduced(assumption)).
% 0.60/0.77 tff(1129,assumption,(c0_1(a246)), introduced(assumption)).
% 0.60/0.77 tff(1130,plain,
% 0.60/0.77 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp10 | hskp5 | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1131,plain,
% 0.60/0.77 ((hskp10 | hskp5 | (~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246))) <=> (hskp10 | hskp5 | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1132,plain,
% 0.60/0.77 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1131])).
% 0.60/0.77 tff(1133,plain,
% 0.60/0.77 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp10 | hskp5 | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1132, 1130])).
% 0.60/0.77 tff(1134,plain,
% 0.60/0.77 ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1135,plain,
% 0.60/0.77 ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp10 | hskp5 | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 0.60/0.77 tff(1136,plain,
% 0.60/0.77 (hskp10 | hskp5),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1135, 142, 1129, 1128, 76, 1127])).
% 0.60/0.77 tff(1137,plain,
% 0.60/0.77 (hskp5),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1136, 31])).
% 0.60/0.77 tff(1138,plain,
% 0.60/0.77 (~c0_1(a241)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[154, 1137])).
% 0.60/0.77 tff(1139,plain,
% 0.60/0.77 (c3_1(a241)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[162, 1137])).
% 0.60/0.77 tff(1140,plain,
% 0.60/0.77 (c2_1(a241)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[170, 1137])).
% 0.60/0.77 tff(1141,plain,
% 0.60/0.77 (~c1_1(a241)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[177, 142, 32, 1140, 1139, 1138, 66])).
% 0.60/0.77 tff(1142,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[184, 142, 31, 1140, 1138, 30, 1141])).
% 0.60/0.77 tff(1143,plain,(hskp10 | hskp11 | (~c0_1(a246)) | (~c3_1(a246)) | c1_1(a246)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1144,plain,
% 0.60/0.77 (hskp10),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1143, 32, 1125, 1124, 1126])).
% 0.60/0.77 tff(1145,plain,
% 0.60/0.77 (hskp3),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[286, 1144, 1115])).
% 0.60/0.77 tff(1146,plain,
% 0.60/0.77 (~c3_1(a238)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[773, 1145])).
% 0.60/0.77 tff(1147,plain,
% 0.60/0.77 (~c2_1(a238)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[779, 1145])).
% 0.60/0.77 tff(1148,plain,
% 0.60/0.77 (~c2_1(a249)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[240, 1144])).
% 0.60/0.77 tff(1149,plain,
% 0.60/0.77 (c0_1(a238)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[823, 1145])).
% 0.60/0.77 tff(1150,plain,
% 0.60/0.77 (c3_1(a249)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[212, 1144])).
% 0.60/0.77 tff(1151,plain,
% 0.60/0.77 (c0_1(a249)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[220, 1144])).
% 0.60/0.77 tff(1152,plain,
% 0.60/0.77 (~c1_1(a249)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[832, 142, 1151, 1150, 1149, 1148, 1147, 1146, 20])).
% 0.60/0.77 tff(1153,plain,
% 0.60/0.77 (hskp18),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[846, 142, 1151, 1150, 1148, 56, 1152])).
% 0.60/0.77 tff(1154,plain,
% 0.60/0.77 (~c0_1(a265)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[192, 1153])).
% 0.60/0.77 tff(1155,plain,
% 0.60/0.77 (c2_1(a265)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[295, 1153])).
% 0.60/0.77 tff(1156,plain,
% 0.60/0.77 (c1_1(a265)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[303, 1153])).
% 0.60/0.77 tff(1157,plain,
% 0.60/0.77 (~c3_1(a265)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[310, 142, 32, 1156, 1155, 1154, 66])).
% 0.60/0.77 tff(1158,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | c3_1(a239) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a239) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1159,plain,
% 0.60/0.77 ((hskp20 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a239) | c3_1(a239) | (~c1_1(a239))) <=> (hskp20 | c3_1(a239) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1160,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | c3_1(a239) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1159])).
% 0.60/0.77 tff(1161,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a239) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1160, 1158])).
% 0.60/0.77 tff(1162,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1163,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a239) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.60/0.77 tff(1164,plain,
% 0.60/0.77 (hskp20),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1163, 142, 1151, 1150, 583, 1148, 1109, 43, 1043])).
% 0.60/0.77 tff(1165,plain,
% 0.60/0.77 (c1_1(a271)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[396, 1164])).
% 0.60/0.77 tff(1166,plain,
% 0.60/0.77 (c0_1(a271)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[404, 1164])).
% 0.60/0.77 tff(1167,plain,
% 0.60/0.77 (~c3_1(a271)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[408, 142, 1115, 1166, 1165, 10])).
% 0.60/0.77 tff(1168,plain,
% 0.60/0.77 (~c2_1(a271)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[424, 1164])).
% 0.60/0.77 tff(1169,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)) | c3_1(a271) | (~c1_1(a271)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)) | c3_1(a271) | (~c1_1(a271)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1170,plain,
% 0.60/0.77 (((~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249))) <=> (c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)) | c3_1(a271) | (~c1_1(a271)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1171,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)) | c3_1(a271) | (~c1_1(a271))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1170])).
% 0.60/0.77 tff(1172,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)) | c3_1(a271) | (~c1_1(a271)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1171, 1169])).
% 0.60/0.77 tff(1173,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a265)) | c3_1(a265) | (~c1_1(a265)) | c2_1(a271) | c3_1(a271) | (~c1_1(a271)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1174,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a271) | c2_1(a249) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | c3_1(a265) | (~c1_1(a265)) | (~c2_1(a265)) | c3_1(a271) | (~c1_1(a271))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.60/0.77 tff(1175,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1174, 142, 1165, 1156, 1155, 1150, 1168, 1148, 622, 1152, 1167, 1157])).
% 0.60/0.77 tff(1176,plain,(hskp11 | c3_1(a239) | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(1177,plain,
% 0.60/0.77 (hskp11),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1176, 583, 43])).
% 0.60/0.77 tff(1178,plain,
% 0.60/0.77 (c2_1(a251)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[334, 1177])).
% 0.60/0.77 tff(1179,plain,
% 0.60/0.77 (((~hskp31) | c2_1(a246)) <=> ((~hskp31) | c2_1(a246))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1180,axiom,((~hskp31) | c2_1(a246)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.60/0.77 tff(1181,plain,
% 0.60/0.77 ((~hskp31) | c2_1(a246)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.60/0.77 tff(1182,plain,
% 0.60/0.77 ((~hskp31) | c2_1(a246)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1181, 1179])).
% 0.60/0.77 tff(1183,plain,
% 0.60/0.77 ((~hskp31) | c2_1(a246)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1182, 1179])).
% 0.60/0.77 tff(1184,plain,
% 0.60/0.77 ((~hskp31) | c2_1(a246)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1183, 1179])).
% 0.60/0.77 tff(1185,plain,
% 0.60/0.77 ((~hskp31) | c2_1(a246)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1184, 1179])).
% 0.60/0.77 tff(1186,plain,
% 0.60/0.77 (c2_1(a246)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1185, 1123])).
% 0.60/0.77 tff(1187,plain,
% 0.60/0.77 (~c3_1(a251)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[326, 1177])).
% 0.60/0.77 tff(1188,plain,
% 0.60/0.77 (~c1_1(a251)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[367, 1177])).
% 0.60/0.77 tff(1189,plain,
% 0.60/0.77 (c0_1(a251)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[663, 31])).
% 0.60/0.77 tff(1190,plain,
% 0.60/0.77 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(1191,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1190])).
% 0.60/0.77 tff(1192,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1193,plain,
% 0.60/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(1194,plain,
% 0.60/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1193])).
% 0.60/0.77 tff(1195,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.60/0.77 tff(1196,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 0.60/0.77 tff(1197,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1196, 1192])).
% 0.60/0.77 tff(1198,plain,(
% 0.60/0.77 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[1197])).
% 0.60/0.77 tff(1199,plain,
% 0.60/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1198, 1191])).
% 0.60/0.77 tff(1200,plain,
% 0.60/0.77 (c1_1(a241)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[184, 142, 31, 1140, 1138, 30])).
% 0.60/0.77 tff(1201,plain,
% 0.60/0.77 (hskp20 | (~c1_1(a241))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[385, 142, 656, 1140, 646, 1138, 352, 1189])).
% 0.60/0.77 tff(1202,plain,
% 0.60/0.77 (hskp20),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1201, 1200])).
% 0.60/0.77 tff(1203,plain,
% 0.60/0.77 (~c2_1(a271)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[424, 1202])).
% 0.60/0.77 tff(1204,plain,
% 0.60/0.77 (c1_1(a271)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[396, 1202])).
% 0.60/0.77 tff(1205,plain,
% 0.60/0.77 (c0_1(a271)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[404, 1202])).
% 0.60/0.77 tff(1206,assumption,(c2_1(a246)), introduced(assumption)).
% 0.60/0.77 tff(1207,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c2_1(a271) | (~ndr1_0) | (~c2_1(a246)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a271)) | (~c1_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c2_1(a271) | (~ndr1_0) | (~c2_1(a246)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a271)) | (~c1_1(a271)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1208,plain,
% 0.60/0.77 ((hskp7 | (~ndr1_0) | c2_1(a271) | (~c0_1(a271)) | (~c1_1(a271)) | c1_1(a246) | (~c3_1(a246)) | (~c2_1(a246))) <=> (hskp7 | c2_1(a271) | (~ndr1_0) | (~c2_1(a246)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a271)) | (~c1_1(a271)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1209,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a271) | (~c0_1(a271)) | (~c1_1(a271)) | c1_1(a246) | (~c3_1(a246)) | (~c2_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c2_1(a271) | (~ndr1_0) | (~c2_1(a246)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a271)) | (~c1_1(a271))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[1208])).
% 0.60/0.77 tff(1210,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a271) | (~c0_1(a271)) | (~c1_1(a271)) | c1_1(a246) | (~c3_1(a246)) | (~c2_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c2_1(a271) | (~ndr1_0) | (~c2_1(a246)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a271)) | (~c1_1(a271)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[1209, 1207])).
% 0.60/0.77 tff(1211,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a271) | (~c0_1(a271)) | (~c1_1(a271)) | c1_1(a246) | (~c3_1(a246)) | (~c2_1(a246)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(1212,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c2_1(a271) | (~ndr1_0) | (~c2_1(a246)) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a271)) | (~c1_1(a271))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 0.60/0.77 tff(1213,plain,
% 0.60/0.77 (hskp7),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1212, 142, 1206, 1128, 1205, 1204, 1203, 1199, 1127])).
% 0.60/0.77 tff(1214,plain,
% 0.60/0.77 (((~hskp7) | (~c2_1(a244))) <=> ((~hskp7) | (~c2_1(a244)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1215,plain,
% 0.60/0.77 (((~c2_1(a244)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a244)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1216,axiom,((~c2_1(a244)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.60/0.77 tff(1217,plain,
% 0.60/0.77 ((~hskp7) | (~c2_1(a244))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 0.60/0.77 tff(1218,plain,
% 0.60/0.77 ((~hskp7) | (~c2_1(a244))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1217, 1214])).
% 0.60/0.77 tff(1219,plain,
% 0.60/0.77 (~c2_1(a244)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[1218, 1213])).
% 0.60/0.77 tff(1220,plain,
% 0.60/0.77 (((~hskp7) | (~c1_1(a244))) <=> ((~hskp7) | (~c1_1(a244)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1221,plain,
% 0.60/0.77 (((~c1_1(a244)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a244)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(1222,axiom,((~c1_1(a244)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.60/0.77 tff(1223,plain,
% 0.60/0.77 ((~hskp7) | (~c1_1(a244))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 0.60/0.77 tff(1224,plain,
% 0.60/0.77 ((~hskp7) | (~c1_1(a244))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1223, 1220])).
% 0.60/0.78 tff(1225,plain,
% 0.60/0.78 (~c1_1(a244)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1224, 1213])).
% 0.60/0.78 tff(1226,plain,
% 0.60/0.78 (((~hskp7) | c0_1(a244)) <=> ((~hskp7) | c0_1(a244))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1227,axiom,((~hskp7) | c0_1(a244)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.60/0.78 tff(1228,plain,
% 0.60/0.78 ((~hskp7) | c0_1(a244)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.60/0.78 tff(1229,plain,
% 0.60/0.78 ((~hskp7) | c0_1(a244)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1228, 1226])).
% 0.60/0.78 tff(1230,plain,
% 0.60/0.78 ((~hskp7) | c0_1(a244)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1229, 1226])).
% 0.60/0.78 tff(1231,plain,
% 0.60/0.78 ((~hskp7) | c0_1(a244)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1230, 1226])).
% 0.60/0.78 tff(1232,plain,
% 0.60/0.78 ((~hskp7) | c0_1(a244)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1231, 1226])).
% 0.60/0.78 tff(1233,plain,
% 0.60/0.78 (c0_1(a244)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1232, 1213])).
% 0.60/0.78 tff(1234,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a251) | c3_1(a251) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a244)) | (~c3_1(a244)) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a244)) | (~c3_1(a244)) | (~c0_1(a251)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1235,plain,
% 0.60/0.78 (((~ndr1_0) | c2_1(a244) | (~c0_1(a244)) | (~c3_1(a244)) | c1_1(a244) | (~c0_1(a244)) | (~c3_1(a244)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251))) <=> (c1_1(a251) | c3_1(a251) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a244)) | (~c3_1(a244)) | (~c0_1(a251)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1236,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a244) | (~c0_1(a244)) | (~c3_1(a244)) | c1_1(a244) | (~c0_1(a244)) | (~c3_1(a244)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a251) | c3_1(a251) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a244)) | (~c3_1(a244)) | (~c0_1(a251))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1235])).
% 0.60/0.78 tff(1237,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a244) | (~c0_1(a244)) | (~c3_1(a244)) | c1_1(a244) | (~c0_1(a244)) | (~c3_1(a244)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a244)) | (~c3_1(a244)) | (~c0_1(a251)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1236, 1234])).
% 0.60/0.78 tff(1238,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a244) | (~c0_1(a244)) | (~c3_1(a244)) | c1_1(a244) | (~c0_1(a244)) | (~c3_1(a244)) | c1_1(a251) | c3_1(a251) | (~c0_1(a251)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1239,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a251) | c3_1(a251) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c0_1(a244)) | (~c3_1(a244)) | (~c0_1(a251))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 0.60/0.78 tff(1240,plain,
% 0.60/0.78 (~c3_1(a244)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1239, 142, 1233, 647, 646, 1225, 1219, 235, 1189])).
% 0.60/0.78 tff(1241,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c0_1(a244)) | c3_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c0_1(a244)) | c3_1(a244))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1242,plain,
% 0.60/0.78 (((~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c2_1(a244) | c1_1(a244) | (~c0_1(a244)) | c2_1(a244) | c1_1(a244) | c3_1(a244)) <=> (c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c0_1(a244)) | c3_1(a244))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1243,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c2_1(a244) | c1_1(a244) | (~c0_1(a244)) | c2_1(a244) | c1_1(a244) | c3_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c0_1(a244)) | c3_1(a244)))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1242])).
% 0.60/0.78 tff(1244,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c2_1(a244) | c1_1(a244) | (~c0_1(a244)) | c2_1(a244) | c1_1(a244) | c3_1(a244))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c0_1(a244)) | c3_1(a244))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1243, 1241])).
% 0.60/0.78 tff(1245,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c2_1(a244) | c1_1(a244) | (~c0_1(a244)) | c2_1(a244) | c1_1(a244) | c3_1(a244))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1246,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a244) | c2_1(a244) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c0_1(a244)) | c3_1(a244)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.60/0.78 tff(1247,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1246, 142, 1129, 1128, 1233, 1225, 1219, 528, 1127, 1240])).
% 0.60/0.78 tff(1248,plain,(hskp10 | (~c0_1(a246)) | (~c3_1(a246)) | c1_1(a246) | c1_1(a251) | c3_1(a251) | (~c2_1(a246)) | (~c2_1(a251))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1249,plain,
% 0.60/0.78 (hskp10),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1248, 1125, 1124, 1126, 1188, 1187, 1186, 1178])).
% 0.60/0.78 tff(1250,plain,
% 0.60/0.78 (hskp3),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[286, 1249, 1115])).
% 0.60/0.78 tff(1251,plain,
% 0.60/0.78 (~c3_1(a238)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[773, 1250])).
% 0.60/0.78 tff(1252,plain,
% 0.60/0.78 (~c2_1(a238)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[779, 1250])).
% 0.60/0.78 tff(1253,plain,
% 0.60/0.78 (~c2_1(a249)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[240, 1249])).
% 0.60/0.78 tff(1254,plain,
% 0.60/0.78 (c0_1(a238)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[823, 1250])).
% 0.60/0.78 tff(1255,plain,
% 0.60/0.78 (c3_1(a249)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[212, 1249])).
% 0.60/0.78 tff(1256,plain,
% 0.60/0.78 (c0_1(a249)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[220, 1249])).
% 0.60/0.78 tff(1257,plain,
% 0.60/0.78 (~c1_1(a249)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[832, 142, 1256, 1255, 1254, 1253, 1252, 1251, 20])).
% 0.60/0.78 tff(1258,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c2_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c2_1(a251)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1259,plain,
% 0.60/0.78 ((hskp25 | (~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251))) <=> (hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c2_1(a251)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1260,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | (~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c2_1(a251))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1259])).
% 0.60/0.78 tff(1261,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | (~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c2_1(a251)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1260, 1258])).
% 0.60/0.78 tff(1262,plain,
% 0.60/0.78 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp25 | (~ndr1_0) | c1_1(a246) | (~c0_1(a246)) | (~c3_1(a246)) | c1_1(a251) | c3_1(a251) | (~c2_1(a251)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1263,plain,
% 0.60/0.78 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp25 | c1_1(a251) | c3_1(a251) | (~ndr1_0) | (~c3_1(a246)) | c1_1(a246) | (~c0_1(a246)) | (~c2_1(a251))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.60/0.78 tff(1264,plain,
% 0.60/0.78 (hskp25),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1263, 142, 1125, 1124, 1178, 1188, 1187, 1071, 1126])).
% 0.60/0.78 tff(1265,plain,
% 0.60/0.78 (~c3_1(a294)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1083, 1264])).
% 0.60/0.78 tff(1266,plain,
% 0.60/0.78 (c2_1(a294)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1091, 1264])).
% 0.60/0.78 tff(1267,plain,
% 0.60/0.78 (c1_1(a294)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1099, 1264])).
% 0.60/0.78 tff(1268,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a239) | c3_1(a294) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a294)) | (~c1_1(a294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a239) | c3_1(a294) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a294)) | (~c1_1(a294)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1269,plain,
% 0.60/0.78 (((~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c1_1(a294)) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249))) <=> (c3_1(a239) | c3_1(a294) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a294)) | (~c1_1(a294)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1270,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c1_1(a294)) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a239) | c3_1(a294) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a294)) | (~c1_1(a294))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1269])).
% 0.60/0.78 tff(1271,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c1_1(a294)) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a239) | c3_1(a294) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a294)) | (~c1_1(a294)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1270, 1268])).
% 0.60/0.78 tff(1272,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c1_1(a294)) | c2_1(a239) | c3_1(a239) | (~c1_1(a239)) | c2_1(a249) | c1_1(a249) | (~c3_1(a249)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1273,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a239) | c3_1(a294) | c2_1(a249) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a249)) | c1_1(a249) | (~c2_1(a294)) | (~c1_1(a294))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.60/0.78 tff(1274,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1273, 142, 1267, 1266, 1255, 583, 1265, 1253, 1109, 43, 622, 1257])).
% 0.60/0.78 tff(1275,plain,(c3_1(a239) | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1276,plain,
% 0.60/0.78 (c3_1(a239)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1275, 43])).
% 0.60/0.78 tff(1277,plain,
% 0.60/0.78 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~c1_1(a239)) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~c1_1(a239)) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1278,plain,
% 0.60/0.78 ((hskp4 | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a239)) | (~c1_1(a239))) <=> (hskp4 | (~c1_1(a239)) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1279,plain,
% 0.60/0.78 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a239)) | (~c1_1(a239)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~c1_1(a239)) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1278])).
% 0.60/0.78 tff(1280,plain,
% 0.60/0.78 (((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a239)) | (~c1_1(a239)))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~c1_1(a239)) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1279, 1277])).
% 0.60/0.78 tff(1281,plain,
% 0.60/0.78 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp4 | (~ndr1_0) | (~c0_1(a239)) | (~c3_1(a239)) | (~c1_1(a239)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1282,plain,
% 0.60/0.78 ((~![U: $i] : (hskp4 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp4 | (~c1_1(a239)) | (~ndr1_0) | (~c3_1(a239)) | (~c0_1(a239))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.60/0.78 tff(1283,plain,
% 0.60/0.78 ((~c3_1(a239)) | (~c0_1(a239))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1282, 142, 1115, 1109, 10])).
% 0.60/0.78 tff(1284,plain,
% 0.60/0.78 (~c0_1(a239)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1283, 1276])).
% 0.60/0.78 tff(1285,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a265) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | c3_1(a265) | (~c1_1(a265)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a265) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | c3_1(a265) | (~c1_1(a265)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1286,plain,
% 0.60/0.78 (((~ndr1_0) | c2_1(a239) | (~c3_1(a239)) | (~c1_1(a239)) | c0_1(a265) | c3_1(a265) | (~c1_1(a265)) | c2_1(a239) | c0_1(a239) | (~c1_1(a239))) <=> (c0_1(a265) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | c3_1(a265) | (~c1_1(a265)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1287,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c3_1(a239)) | (~c1_1(a239)) | c0_1(a265) | c3_1(a265) | (~c1_1(a265)) | c2_1(a239) | c0_1(a239) | (~c1_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a265) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | c3_1(a265) | (~c1_1(a265))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1286])).
% 0.60/0.78 tff(1288,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c3_1(a239)) | (~c1_1(a239)) | c0_1(a265) | c3_1(a265) | (~c1_1(a265)) | c2_1(a239) | c0_1(a239) | (~c1_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a265) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | c3_1(a265) | (~c1_1(a265)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1287, 1285])).
% 0.60/0.78 tff(1289,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c3_1(a239)) | (~c1_1(a239)) | c0_1(a265) | c3_1(a265) | (~c1_1(a265)) | c2_1(a239) | c0_1(a239) | (~c1_1(a239)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1290,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a265) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | c3_1(a265) | (~c1_1(a265))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 0.60/0.78 tff(1291,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1290, 142, 304, 1276, 193, 1109, 43, 42, 1284, 311])).
% 0.60/0.78 tff(1292,plain,(hskp11 | c2_1(a239) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1293,plain,
% 0.60/0.78 (hskp11),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1292, 31, 43])).
% 0.60/0.78 tff(1294,plain,
% 0.60/0.78 (~c1_1(a251)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[367, 1293])).
% 0.60/0.78 tff(1295,plain,
% 0.60/0.78 (c2_1(a251)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[334, 1293])).
% 0.60/0.78 tff(1296,plain,
% 0.60/0.78 (c0_1(a251)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[662, 142, 31, 1295, 1294, 30])).
% 0.60/0.78 tff(1297,plain,
% 0.60/0.78 (~c3_1(a251)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[326, 1293])).
% 0.60/0.78 tff(1298,plain,
% 0.60/0.78 (hskp5 | (~c0_1(a251))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[374, 142, 1295, 1294, 1297, 362])).
% 0.60/0.78 tff(1299,plain,
% 0.60/0.78 (hskp5),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1298, 1296])).
% 0.60/0.78 tff(1300,plain,
% 0.60/0.78 (~c0_1(a241)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[154, 1299])).
% 0.60/0.78 tff(1301,plain,
% 0.60/0.78 (c2_1(a241)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[170, 1299])).
% 0.60/0.78 tff(1302,plain,
% 0.60/0.78 (c1_1(a241)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[184, 142, 31, 1301, 1300, 30])).
% 0.60/0.78 tff(1303,plain,
% 0.60/0.78 (hskp20 | (~c1_1(a241))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[385, 142, 1295, 1301, 1297, 1300, 352, 1296])).
% 0.60/0.78 tff(1304,plain,
% 0.60/0.78 (hskp20),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1303, 1302])).
% 0.60/0.78 tff(1305,plain,
% 0.60/0.78 (c1_1(a271)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[396, 1304])).
% 0.60/0.78 tff(1306,plain,
% 0.60/0.78 (c0_1(a271)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[404, 1304])).
% 0.60/0.78 tff(1307,plain,
% 0.60/0.78 (~c3_1(a271)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[408, 142, 1115, 1306, 1305, 10])).
% 0.60/0.78 tff(1308,plain,
% 0.60/0.78 (~c2_1(a271)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[424, 1304])).
% 0.60/0.78 tff(1309,plain,
% 0.60/0.78 (hskp31),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[431, 142, 1115, 1305, 1308, 419, 1307])).
% 0.60/0.78 tff(1310,plain,
% 0.60/0.78 (c0_1(a246)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[448, 1309])).
% 0.60/0.78 tff(1311,plain,
% 0.60/0.78 (c2_1(a246)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1185, 1309])).
% 0.60/0.78 tff(1312,plain,
% 0.60/0.78 (c3_1(a246)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[440, 1309])).
% 0.60/0.78 tff(1313,plain,
% 0.60/0.78 (c1_1(a246)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1248, 1312, 31, 1295, 1294, 1297, 1311, 1310])).
% 0.60/0.78 tff(1314,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[455, 142, 1115, 1310, 1312, 10, 1313])).
% 0.60/0.78 tff(1315,plain,(hskp10 | c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1316,plain,
% 0.60/0.78 (hskp10),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1315, 43])).
% 0.60/0.78 tff(1317,plain,
% 0.60/0.78 (hskp3),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[286, 1316, 1115])).
% 0.60/0.78 tff(1318,plain,
% 0.60/0.78 (~c3_1(a238)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[773, 1317])).
% 0.60/0.78 tff(1319,plain,
% 0.60/0.78 (~c2_1(a238)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[779, 1317])).
% 0.60/0.78 tff(1320,plain,
% 0.60/0.78 (~c2_1(a249)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[240, 1316])).
% 0.60/0.78 tff(1321,plain,
% 0.60/0.78 (c0_1(a238)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[823, 1317])).
% 0.60/0.78 tff(1322,plain,
% 0.60/0.78 (c3_1(a249)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[212, 1316])).
% 0.60/0.78 tff(1323,plain,
% 0.60/0.78 (c0_1(a249)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[220, 1316])).
% 0.60/0.78 tff(1324,plain,
% 0.60/0.78 (~c1_1(a249)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[832, 142, 1323, 1322, 1321, 1320, 1319, 1318, 20])).
% 0.60/0.78 tff(1325,plain,
% 0.60/0.78 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(1326,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[1325])).
% 0.60/0.78 tff(1327,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1328,plain,
% 0.60/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(1329,plain,
% 0.60/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[1328])).
% 0.60/0.78 tff(1330,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.60/0.78 tff(1331,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 0.60/0.78 tff(1332,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1331, 1327])).
% 0.60/0.78 tff(1333,plain,(
% 0.60/0.78 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[1332])).
% 0.60/0.78 tff(1334,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1333, 1326])).
% 0.60/0.78 tff(1335,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1336,plain,
% 0.60/0.78 ((hskp15 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a239) | c0_1(a239) | (~c1_1(a239))) <=> (hskp15 | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1337,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a239) | c0_1(a239) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1336])).
% 0.60/0.78 tff(1338,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a239) | c0_1(a239) | (~c1_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1337, 1335])).
% 0.60/0.79 tff(1339,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a239) | c0_1(a239) | (~c1_1(a239)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1340,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | c0_1(a239) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 0.60/0.79 tff(1341,plain,
% 0.60/0.79 (hskp15),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1340, 142, 1323, 1322, 1109, 43, 1334, 1284, 1324])).
% 0.60/0.79 tff(1342,plain,
% 0.60/0.79 (((~hskp15) | (~c3_1(a258))) <=> ((~hskp15) | (~c3_1(a258)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1343,plain,
% 0.60/0.79 (((~c3_1(a258)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a258)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1344,axiom,((~c3_1(a258)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.60/0.79 tff(1345,plain,
% 0.60/0.79 ((~hskp15) | (~c3_1(a258))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 0.60/0.79 tff(1346,plain,
% 0.60/0.79 ((~hskp15) | (~c3_1(a258))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1345, 1342])).
% 0.60/0.79 tff(1347,plain,
% 0.60/0.79 (~c3_1(a258)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1346, 1341])).
% 0.60/0.79 tff(1348,plain,
% 0.60/0.79 (((~hskp15) | (~c2_1(a258))) <=> ((~hskp15) | (~c2_1(a258)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1349,plain,
% 0.60/0.79 (((~c2_1(a258)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a258)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1350,axiom,((~c2_1(a258)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.60/0.79 tff(1351,plain,
% 0.60/0.79 ((~hskp15) | (~c2_1(a258))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.60/0.79 tff(1352,plain,
% 0.60/0.79 ((~hskp15) | (~c2_1(a258))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1351, 1348])).
% 0.60/0.79 tff(1353,plain,
% 0.60/0.79 (~c2_1(a258)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1352, 1341])).
% 0.60/0.79 tff(1354,plain,
% 0.60/0.79 (((~hskp15) | (~c0_1(a258))) <=> ((~hskp15) | (~c0_1(a258)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1355,plain,
% 0.60/0.79 (((~c0_1(a258)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a258)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1356,axiom,((~c0_1(a258)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.60/0.79 tff(1357,plain,
% 0.60/0.79 ((~hskp15) | (~c0_1(a258))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 0.60/0.79 tff(1358,plain,
% 0.60/0.79 ((~hskp15) | (~c0_1(a258))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1357, 1354])).
% 0.60/0.79 tff(1359,plain,
% 0.60/0.79 (~c0_1(a258)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1358, 1341])).
% 0.60/0.79 tff(1360,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a258) | c2_1(a258) | c3_1(a258) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c1_1(a258)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a258) | c2_1(a258) | c3_1(a258) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c1_1(a258)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1361,plain,
% 0.60/0.79 (((~ndr1_0) | c2_1(a239) | (~c3_1(a239)) | (~c1_1(a239)) | c0_1(a258) | c3_1(a258) | (~c1_1(a258)) | c2_1(a258) | c0_1(a258) | (~c1_1(a258))) <=> (c0_1(a258) | c2_1(a258) | c3_1(a258) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c1_1(a258)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1362,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c3_1(a239)) | (~c1_1(a239)) | c0_1(a258) | c3_1(a258) | (~c1_1(a258)) | c2_1(a258) | c0_1(a258) | (~c1_1(a258)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a258) | c2_1(a258) | c3_1(a258) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c1_1(a258))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1361])).
% 0.60/0.79 tff(1363,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c3_1(a239)) | (~c1_1(a239)) | c0_1(a258) | c3_1(a258) | (~c1_1(a258)) | c2_1(a258) | c0_1(a258) | (~c1_1(a258)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a258) | c2_1(a258) | c3_1(a258) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c1_1(a258)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1362, 1360])).
% 0.60/0.79 tff(1364,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a239) | (~c3_1(a239)) | (~c1_1(a239)) | c0_1(a258) | c3_1(a258) | (~c1_1(a258)) | c2_1(a258) | c0_1(a258) | (~c1_1(a258)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1365,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a258) | c2_1(a258) | c3_1(a258) | (~c1_1(a239)) | c2_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c1_1(a258))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 0.60/0.79 tff(1366,plain,
% 0.60/0.79 (~c1_1(a258)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1365, 142, 1276, 1359, 1353, 1347, 1109, 43, 42])).
% 0.60/0.79 tff(1367,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a258) | c3_1(a258) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | c1_1(a258))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a258) | c3_1(a258) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | c1_1(a258))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1368,plain,
% 0.60/0.79 (((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a258) | c1_1(a258) | c3_1(a258)) <=> (c2_1(a258) | c3_1(a258) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | c1_1(a258))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1369,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a258) | c1_1(a258) | c3_1(a258))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a258) | c3_1(a258) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | c1_1(a258)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1368])).
% 0.60/0.79 tff(1370,plain,
% 0.60/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a258) | c1_1(a258) | c3_1(a258))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a258) | c3_1(a258) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | c1_1(a258))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1369, 1367])).
% 0.60/0.79 tff(1371,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a249) | (~c0_1(a249)) | (~c3_1(a249)) | c2_1(a249) | c1_1(a249) | (~c0_1(a249)) | c2_1(a258) | c1_1(a258) | c3_1(a258))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1372,plain,
% 0.60/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a258) | c3_1(a258) | c2_1(a249) | (~ndr1_0) | (~c0_1(a249)) | (~c3_1(a249)) | c1_1(a249) | c1_1(a258)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 0.60/0.79 tff(1373,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1372, 142, 1323, 1322, 1353, 1347, 1320, 528, 1324, 1366])).
% 0.60/0.79 tff(1374,plain,(c2_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1375,plain,
% 0.60/0.79 (((~hskp4) | (~c2_1(a239))) <=> ((~hskp4) | (~c2_1(a239)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1376,plain,
% 0.60/0.79 (((~c2_1(a239)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a239)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1377,axiom,((~c2_1(a239)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.60/0.79 tff(1378,plain,
% 0.60/0.79 ((~hskp4) | (~c2_1(a239))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 0.60/0.79 tff(1379,plain,
% 0.60/0.79 ((~hskp4) | (~c2_1(a239))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1378, 1375])).
% 0.60/0.79 tff(1380,plain,
% 0.60/0.79 (~hskp4),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1379, 1374])).
% 0.60/0.79 tff(1381,plain,
% 0.60/0.79 (hskp11 | hskp28 | hskp10),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[319, 1380])).
% 0.60/0.79 tff(1382,plain,
% 0.60/0.79 (hskp28),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1381, 32, 31])).
% 0.60/0.79 tff(1383,plain,
% 0.60/0.79 (c1_1(a237)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[578, 1382])).
% 0.60/0.79 tff(1384,plain,
% 0.60/0.79 (c0_1(a237)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[570, 1382])).
% 0.60/0.79 tff(1385,plain,
% 0.60/0.79 (~c3_1(a237)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[790, 142, 1380, 1384, 1383, 10])).
% 0.60/0.79 tff(1386,plain,
% 0.60/0.79 (c2_1(a237)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[562, 1382])).
% 0.60/0.79 tff(1387,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | c0_1(a265) | (~ndr1_0) | (~c0_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a265)) | (~c2_1(a265)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp20 | c0_1(a265) | (~ndr1_0) | (~c0_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1388,plain,
% 0.60/0.79 ((hskp20 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c0_1(a237)) | c0_1(a265) | (~c1_1(a265)) | (~c2_1(a265))) <=> (hskp20 | c0_1(a265) | (~ndr1_0) | (~c0_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1389,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c0_1(a237)) | c0_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | c0_1(a265) | (~ndr1_0) | (~c0_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a265)) | (~c2_1(a265))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1388])).
% 0.60/0.79 tff(1390,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c0_1(a237)) | c0_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp20 | c0_1(a265) | (~ndr1_0) | (~c0_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1389, 1387])).
% 0.60/0.79 tff(1391,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a237)) | c3_1(a237) | (~c0_1(a237)) | c0_1(a265) | (~c1_1(a265)) | (~c2_1(a265)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1392,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp20 | c0_1(a265) | (~ndr1_0) | (~c0_1(a237)) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a265)) | (~c2_1(a265))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.60/0.79 tff(1393,plain,
% 0.60/0.79 (hskp20),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1392, 142, 1384, 1386, 304, 296, 193, 352, 1385])).
% 0.60/0.79 tff(1394,plain,
% 0.60/0.79 (c1_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[396, 1393])).
% 0.60/0.79 tff(1395,plain,
% 0.60/0.79 (c0_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[404, 1393])).
% 0.60/0.79 tff(1396,plain,
% 0.60/0.79 (~c3_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[408, 142, 1380, 1395, 1394, 10])).
% 0.60/0.79 tff(1397,plain,
% 0.60/0.79 (~c2_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[424, 1393])).
% 0.60/0.79 tff(1398,plain,
% 0.60/0.79 (hskp31),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[431, 142, 1380, 1394, 1397, 419, 1396])).
% 0.60/0.79 tff(1399,plain,
% 0.60/0.79 (c3_1(a246)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[440, 1398])).
% 0.60/0.79 tff(1400,plain,
% 0.60/0.79 (c0_1(a246)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[448, 1398])).
% 0.60/0.79 tff(1401,plain,
% 0.60/0.79 (c1_1(a246)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1143, 1400, 31, 1399, 32])).
% 0.60/0.79 tff(1402,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[455, 142, 1380, 1400, 1399, 10, 1401])).
% 0.60/0.79 tff(1403,plain,(hskp11 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1404,plain,
% 0.60/0.79 (hskp11),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1403, 31])).
% 0.60/0.79 tff(1405,plain,
% 0.60/0.79 (~c1_1(a251)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[367, 1404])).
% 0.60/0.79 tff(1406,plain,
% 0.60/0.79 (c2_1(a251)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[334, 1404])).
% 0.60/0.79 tff(1407,plain,
% 0.60/0.79 (c0_1(a251)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[662, 142, 31, 1406, 1405, 30])).
% 0.60/0.79 tff(1408,plain,
% 0.60/0.79 (~c3_1(a251)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[326, 1404])).
% 0.60/0.79 tff(1409,plain,
% 0.60/0.79 (hskp5 | (~c0_1(a251))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[374, 142, 1406, 1405, 1408, 362])).
% 0.60/0.79 tff(1410,plain,
% 0.60/0.79 (hskp5),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1409, 1407])).
% 0.60/0.79 tff(1411,plain,
% 0.60/0.79 (~c0_1(a241)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[154, 1410])).
% 0.60/0.79 tff(1412,plain,
% 0.60/0.79 (c2_1(a241)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[170, 1410])).
% 0.60/0.79 tff(1413,plain,
% 0.60/0.79 (c1_1(a241)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[184, 142, 31, 1412, 1411, 30])).
% 0.60/0.79 tff(1414,plain,
% 0.60/0.79 (hskp20 | (~c1_1(a241))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[385, 142, 1406, 1412, 1408, 1411, 352, 1407])).
% 0.60/0.79 tff(1415,plain,
% 0.60/0.79 (hskp20),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1414, 1413])).
% 0.60/0.79 tff(1416,plain,
% 0.60/0.79 (c1_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[396, 1415])).
% 0.60/0.79 tff(1417,plain,
% 0.60/0.79 (c0_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[404, 1415])).
% 0.60/0.79 tff(1418,plain,
% 0.60/0.79 (~c3_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[408, 142, 1380, 1417, 1416, 10])).
% 0.60/0.79 tff(1419,plain,
% 0.60/0.79 (~c2_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[424, 1415])).
% 0.60/0.79 tff(1420,plain,
% 0.60/0.79 (hskp31),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[431, 142, 1380, 1416, 1419, 419, 1418])).
% 0.60/0.79 tff(1421,plain,
% 0.60/0.79 (c0_1(a246)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[448, 1420])).
% 0.60/0.79 tff(1422,plain,
% 0.60/0.79 (c2_1(a246)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1185, 1420])).
% 0.60/0.79 tff(1423,plain,
% 0.60/0.79 (c3_1(a246)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[440, 1420])).
% 0.60/0.79 tff(1424,plain,
% 0.60/0.79 (c1_1(a246)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1248, 1423, 31, 1406, 1405, 1408, 1422, 1421])).
% 0.60/0.79 tff(1425,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[455, 142, 1380, 1421, 1423, 10, 1424])).
% 0.60/0.79 tff(1426,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1427,plain,
% 0.60/0.79 ((~hskp10) | hskp3),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[286, 1380])).
% 0.60/0.79 tff(1428,plain,
% 0.60/0.79 (hskp3),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1427, 1426])).
% 0.60/0.79 tff(1429,plain,
% 0.60/0.79 (~c3_1(a238)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[773, 1428])).
% 0.60/0.79 tff(1430,plain,
% 0.60/0.79 (~c2_1(a238)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[779, 1428])).
% 0.60/0.79 tff(1431,plain,
% 0.60/0.79 (~c2_1(a249)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[240, 1426])).
% 0.60/0.79 tff(1432,plain,
% 0.60/0.79 (c0_1(a238)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[823, 1428])).
% 0.60/0.79 tff(1433,plain,
% 0.60/0.79 (c3_1(a249)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[212, 1426])).
% 0.60/0.79 tff(1434,plain,
% 0.60/0.79 (c0_1(a249)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[220, 1426])).
% 0.60/0.79 tff(1435,plain,
% 0.60/0.79 (~c1_1(a249)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[832, 142, 1434, 1433, 1432, 1431, 1430, 1429, 20])).
% 0.60/0.79 tff(1436,plain,
% 0.60/0.79 (c1_1(a238)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[839, 142, 1434, 1433, 1431, 1430, 1429, 528, 1435])).
% 0.60/0.79 tff(1437,plain,
% 0.60/0.79 (hskp20 | (~c1_1(a238))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1049, 142, 1434, 1433, 1431, 1430, 1429, 1043])).
% 0.60/0.79 tff(1438,plain,
% 0.60/0.79 (hskp20),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1437, 1436])).
% 0.60/0.79 tff(1439,plain,
% 0.60/0.79 (c1_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[396, 1438])).
% 0.60/0.79 tff(1440,plain,
% 0.60/0.79 (c0_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[404, 1438])).
% 0.60/0.79 tff(1441,plain,
% 0.60/0.79 (~c3_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[408, 142, 1380, 1440, 1439, 10])).
% 0.60/0.79 tff(1442,plain,
% 0.60/0.79 (~c2_1(a271)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[424, 1438])).
% 0.60/0.79 tff(1443,plain,
% 0.60/0.79 (hskp18),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[846, 142, 1434, 1433, 1431, 56, 1435])).
% 0.60/0.79 tff(1444,plain,
% 0.60/0.79 (c2_1(a265)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[295, 1443])).
% 0.60/0.79 tff(1445,plain,
% 0.60/0.79 (c1_1(a265)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[303, 1443])).
% 0.60/0.79 tff(1446,plain,
% 0.60/0.79 (c3_1(a265)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[855, 142, 1445, 1444, 1433, 1431, 1430, 1429, 622, 1436, 1435])).
% 0.60/0.79 tff(1447,plain,
% 0.60/0.79 (~c0_1(a265)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[192, 1443])).
% 0.60/0.79 tff(1448,plain,
% 0.60/0.79 (hskp11),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[310, 142, 1445, 1444, 1447, 66, 1446])).
% 0.60/0.79 tff(1449,plain,
% 0.60/0.79 (~c3_1(a251)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[326, 1448])).
% 0.60/0.79 tff(1450,plain,
% 0.60/0.79 (~c1_1(a251)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[367, 1448])).
% 0.60/0.79 tff(1451,plain,
% 0.60/0.79 (c2_1(a251)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[334, 1448])).
% 0.60/0.79 tff(1452,plain,
% 0.60/0.79 (hskp25),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1077, 142, 1451, 1434, 1433, 1450, 1449, 1071, 1435])).
% 0.60/0.79 tff(1453,plain,
% 0.60/0.79 (~c3_1(a294)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1083, 1452])).
% 0.60/0.79 tff(1454,plain,
% 0.60/0.79 (c2_1(a294)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1091, 1452])).
% 0.60/0.79 tff(1455,plain,
% 0.60/0.79 (c1_1(a294)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1099, 1452])).
% 0.60/0.79 tff(1456,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1106, 142, 1455, 1454, 1439, 1433, 1453, 1442, 1431, 622, 1435, 1441])).
% 0.60/0.79 % SZS output end Proof
% 0.60/0.80 % E exiting
%------------------------------------------------------------------------------