%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN616-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:39:41 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SYN616-1 : TPTP v9.0.0. Released v2.5.0.
% 0.05/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:40:46 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(p2_type, type, (
% 0.21/0.38 p2: ( $i * $i ) > $o)).
% 0.21/0.38 tff(f6_type, type, (
% 0.21/0.38 f6: $i > $i)).
% 0.21/0.38 tff(c21_type, type, (
% 0.21/0.38 c21: $i)).
% 0.21/0.38 tff(f3_type, type, (
% 0.21/0.38 f3: $i > $i)).
% 0.21/0.38 tff(f5_type, type, (
% 0.21/0.38 f5: $i > $i)).
% 0.21/0.38 tff(c20_type, type, (
% 0.21/0.38 c20: $i)).
% 0.21/0.38 tff(f7_type, type, (
% 0.21/0.38 f7: ( $i * $i ) > $i)).
% 0.21/0.38 tff(f12_type, type, (
% 0.21/0.38 f12: ( $i * $i ) > $i)).
% 0.21/0.38 tff(c28_type, type, (
% 0.21/0.38 c28: $i)).
% 0.21/0.38 tff(f8_type, type, (
% 0.21/0.38 f8: ( $i * $i ) > $i)).
% 0.21/0.38 tff(c22_type, type, (
% 0.21/0.38 c22: $i)).
% 0.21/0.38 tff(c25_type, type, (
% 0.21/0.38 c25: $i)).
% 0.21/0.38 tff(f11_type, type, (
% 0.21/0.38 f11: ( $i * $i * $i ) > $i)).
% 0.21/0.38 tff(c24_type, type, (
% 0.21/0.38 c24: $i)).
% 0.21/0.38 tff(c23_type, type, (
% 0.21/0.38 c23: $i)).
% 0.21/0.38 tff(p14_type, type, (
% 0.21/0.38 p14: ( $i * $i * $i ) > $o)).
% 0.21/0.38 tff(1,assumption,(~p2(f5(c20), f5(c20))), introduced(assumption)).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (^[X31: $i] : refl(p2(X31, X31) <=> p2(X31, X31))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (![X31: $i] : p2(X31, X31) <=> ![X31: $i] : p2(X31, X31)),
% 0.21/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (![X31: $i] : p2(X31, X31) <=> ![X31: $i] : p2(X31, X31)),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(5,axiom,(![X31: $i] : p2(X31, X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (![X31: $i] : p2(X31, X31)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.38 tff(7,plain,(
% 0.21/0.38 ![X31: $i] : p2(X31, X31)),
% 0.21/0.38 inference(skolemize,[status(sab)],[6])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (![X31: $i] : p2(X31, X31)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 ((~![X31: $i] : p2(X31, X31)) | p2(f5(c20), f5(c20))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.38 tff(11,plain,(p2(f5(c20), f5(c20))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (^[X45: $i, X44: $i] : refl(((~p2(X44, X45)) | p2(f3(X44), f3(X45))) <=> ((~p2(X44, X45)) | p2(f3(X44), f3(X45))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45))) <=> ![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45))) <=> ![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (^[X45: $i, X44: $i] : rewrite((p2(f3(X44), f3(X45)) | (~p2(X44, X45))) <=> ((~p2(X44, X45)) | p2(f3(X44), f3(X45))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (![X45: $i, X44: $i] : (p2(f3(X44), f3(X45)) | (~p2(X44, X45))) <=> ![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.38 tff(17,axiom,(![X45: $i, X44: $i] : (p2(f3(X44), f3(X45)) | (~p2(X44, X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_12')).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.38 tff(20,plain,(
% 0.21/0.38 ![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[19])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 (![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (((~![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))) | ((~p2(f5(c20), f5(c20))) | p2(f3(f5(c20)), f3(f5(c20))))) <=> ((~![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))) | (~p2(f5(c20), f5(c20))) | p2(f3(f5(c20)), f3(f5(c20))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 ((~![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))) | ((~p2(f5(c20), f5(c20))) | p2(f3(f5(c20)), f3(f5(c20))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 ((~![X45: $i, X44: $i] : ((~p2(X44, X45)) | p2(f3(X44), f3(X45)))) | (~p2(f5(c20), f5(c20))) | p2(f3(f5(c20)), f3(f5(c20)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 ((~p2(f5(c20), f5(c20))) | p2(f3(f5(c20)), f3(f5(c20)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (p2(f3(f5(c20)), f3(f5(c20)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.21/0.39 tff(27,assumption,(~p2(c22, c22)), introduced(assumption)).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~![X31: $i] : p2(X31, X31)) | p2(c22, c22)),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[28, 8, 27])).
% 0.21/0.39 tff(30,plain,(p2(c22, c22)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20)))) <=> p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(32,axiom,(p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_19')).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (^[X31: $i, X32: $i, X33: $i] : refl(((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (^[X31: $i, X32: $i, X33: $i] : trans(monotonicity(rewrite((p2(X32, X33) | (~p2(X31, X32))) <=> ((~p2(X31, X32)) | p2(X32, X33))), (((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> (((~p2(X31, X32)) | p2(X32, X33)) | (~p2(X31, X33))))), rewrite((((~p2(X31, X32)) | p2(X32, X33)) | (~p2(X31, X33))) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))), (((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (![X31: $i, X32: $i, X33: $i] : ((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.39 tff(39,axiom,(![X31: $i, X32: $i, X33: $i] : ((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_17')).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.39 tff(42,plain,(
% 0.21/0.39 ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.21/0.39 inference(skolemize,[status(sab)],[41])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) <=> ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[46, 44])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[49, 43, 33])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 (^[X43: $i, X42: $i, X41: $i, X40: $i] : refl(((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) <=> ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 (^[X43: $i, X42: $i, X41: $i, X40: $i] : trans(monotonicity(rewrite((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) <=> ((~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))), (((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) | (~p2(X41, X43))) <=> (((~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) | (~p2(X41, X43))))), rewrite((((~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) | (~p2(X41, X43))) <=> ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))), (((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) | (~p2(X41, X43))) <=> ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) | (~p2(X41, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.39 tff(56,axiom,(![X43: $i, X42: $i, X41: $i, X40: $i] : ((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) | (~p2(X41, X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_27')).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.21/0.39 tff(59,plain,(
% 0.21/0.39 ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[58])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 (p2(c25, c28) <=> p2(c25, c28)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(62,axiom,(p2(c25, c28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_7')).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (p2(c25, c28)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))) | ((~p2(c25, c28)) | (~p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))) | (~p2(c25, c28)) | (~p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))) | ((~p2(c25, c28)) | (~p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))) | (~p2(c25, c28)) | (~p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 (p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[66, 63, 60, 50])).
% 0.21/0.39 tff(68,plain,
% 0.21/0.39 (^[X53: $i, X55: $i, X52: $i, X54: $i] : refl(((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55))) <=> ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.39 tff(70,plain,
% 0.21/0.39 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(71,plain,
% 0.21/0.39 (^[X53: $i, X55: $i, X52: $i, X54: $i] : trans(monotonicity(rewrite((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) <=> ((~p2(X53, X55)) | p2(f7(X52, X53), f7(X54, X55)))), (((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) | (~p2(X52, X54))) <=> (((~p2(X53, X55)) | p2(f7(X52, X53), f7(X54, X55))) | (~p2(X52, X54))))), rewrite((((~p2(X53, X55)) | p2(f7(X52, X53), f7(X54, X55))) | (~p2(X52, X54))) <=> ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))), (((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) | (~p2(X52, X54))) <=> ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) | (~p2(X52, X54))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.39 tff(73,axiom,(![X53: $i, X55: $i, X52: $i, X54: $i] : ((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) | (~p2(X52, X54)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_28')).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.40 tff(76,plain,(
% 0.21/0.40 ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[75])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | ((~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (((~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) <=> ((~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | ((~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | ((~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | ((~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | ((~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 ((~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[83, 77, 67])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[84, 30])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (^[X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : refl(((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9)) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 (^[X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p14(X7, X8, X9) | (~p2(X12, X9))) <=> ((~p2(X12, X9)) | p14(X7, X8, X9))), (((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) <=> (((~p2(X12, X9)) | p14(X7, X8, X9)) | (~p2(X11, X8))))), rewrite((((~p2(X12, X9)) | p14(X7, X8, X9)) | (~p2(X11, X8))) <=> ((~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9))), (((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) <=> ((~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)))), ((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) <=> (((~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)) | (~p2(X10, X7))))), rewrite((((~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)) | (~p2(X10, X7))) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9))), ((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)))), (((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) | (~p14(X10, X11, X12))) <=> (((~p2(X10, X7)) | (~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)) | (~p14(X10, X11, X12))))), rewrite((((~p2(X10, X7)) | (~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)) | (~p14(X10, X11, X12))) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))), (((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) | (~p14(X10, X11, X12))) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) | (~p14(X10, X11, X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.40 tff(91,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) | (~p14(X10, X11, X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p14_31')).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.40 tff(94,plain,(
% 0.21/0.40 ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.21/0.40 inference(skolemize,[status(sab)],[93])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 ((~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21))) <=> (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(97,axiom,(~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p14_30')).
% 0.21/0.40 tff(98,plain,
% 0.21/0.40 (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21)) <=> p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(100,axiom,(p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p14_29')).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 (((~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))) | (~p2(f6(c21), f6(c21))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21))) <=> (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(104,plain,
% 0.21/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | ((~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))) | (~p2(f6(c21), f6(c21))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | ((~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))) | (~p2(f6(c21), f6(c21))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[104, 102])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | ((~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))) | (~p2(f6(c21), f6(c21))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 ((~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[107, 101, 98, 95])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (~p2(f6(c21), f6(c21))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[108, 85, 26])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 ((~![X31: $i] : p2(X31, X31)) | p2(f6(c21), f6(c21))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[110, 8, 109])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------