%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN600-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:39:39 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN600-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:38:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(p18_type, type, (
% 0.12/0.38 p18: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f15_type, type, (
% 0.12/0.38 f15: $i > $i)).
% 0.12/0.38 tff(f16_type, type, (
% 0.12/0.38 f16: $i > $i)).
% 0.12/0.38 tff(c21_type, type, (
% 0.12/0.38 c21: $i)).
% 0.12/0.38 tff(f9_type, type, (
% 0.12/0.38 f9: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f10_type, type, (
% 0.12/0.38 f10: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f11_type, type, (
% 0.12/0.38 f11: $i > $i)).
% 0.12/0.38 tff(f12_type, type, (
% 0.12/0.38 f12: $i > $i)).
% 0.12/0.38 tff(c20_type, type, (
% 0.12/0.38 c20: $i)).
% 0.12/0.38 tff(f13_type, type, (
% 0.12/0.38 f13: $i > $i)).
% 0.12/0.38 tff(f14_type, type, (
% 0.12/0.38 f14: $i > $i)).
% 0.12/0.38 tff(f4_type, type, (
% 0.12/0.38 f4: $i > $i)).
% 0.12/0.38 tff(f6_type, type, (
% 0.12/0.38 f6: $i > $i)).
% 0.12/0.38 tff(c22_type, type, (
% 0.12/0.38 c22: $i)).
% 0.12/0.38 tff(p7_type, type, (
% 0.12/0.38 p7: ( $i * $i ) > $o)).
% 0.12/0.38 tff(p19_type, type, (
% 0.12/0.38 p19: $i > $o)).
% 0.12/0.38 tff(p17_type, type, (
% 0.12/0.38 p17: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f8_type, type, (
% 0.12/0.38 f8: ( $i * $i ) > $i)).
% 0.12/0.38 tff(p3_type, type, (
% 0.12/0.38 p3: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,assumption,(~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[X32: $i] : refl(p7(X32, X32) <=> p7(X32, X32))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X32: $i] : p7(X32, X32) <=> ![X32: $i] : p7(X32, X32)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X32: $i] : p7(X32, X32) <=> ![X32: $i] : p7(X32, X32)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,axiom,(![X32: $i] : p7(X32, X32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_4')).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![X32: $i] : p7(X32, X32)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,plain,(
% 0.12/0.38 ![X32: $i] : p7(X32, X32)),
% 0.12/0.38 inference(skolemize,[status(sab)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X32: $i] : p7(X32, X32)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 ((~![X32: $i] : p7(X32, X32)) | p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.38 tff(11,plain,(p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(12,assumption,(~p7(f16(c22), f16(c21))), introduced(assumption)).
% 0.12/0.38 tff(13,assumption,(~p7(f16(c21), f16(c21))), introduced(assumption)).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((~![X32: $i] : p7(X32, X32)) | p7(f16(c21), f16(c21))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 8, 13])).
% 0.12/0.38 tff(16,plain,(p7(f16(c21), f16(c21))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[X32: $i, X34: $i, X33: $i] : refl((p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33))) <=> (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33))) <=> ![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33))) <=> ![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (^[X32: $i, X34: $i, X33: $i] : trans(monotonicity(rewrite((p7(X33, X34) | (~p7(X32, X33))) <=> (p7(X33, X34) | (~p7(X32, X33)))), (((p7(X33, X34) | (~p7(X32, X33))) | (~p7(X32, X34))) <=> ((p7(X33, X34) | (~p7(X32, X33))) | (~p7(X32, X34))))), rewrite(((p7(X33, X34) | (~p7(X32, X33))) | (~p7(X32, X34))) <=> (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))), (((p7(X33, X34) | (~p7(X32, X33))) | (~p7(X32, X34))) <=> (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![X32: $i, X34: $i, X33: $i] : ((p7(X33, X34) | (~p7(X32, X33))) | (~p7(X32, X34))) <=> ![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.38 tff(22,axiom,(![X32: $i, X34: $i, X33: $i] : ((p7(X33, X34) | (~p7(X32, X33))) | (~p7(X32, X34)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_19')).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.12/0.38 tff(25,plain,(
% 0.12/0.38 ![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (p7(f16(c21), f16(c22)) <=> p7(f16(c21), f16(c22))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,axiom,(p7(f16(c21), f16(c22))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_7')).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (p7(f16(c21), f16(c22))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (((~![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))) | ((~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))) | p7(f16(c22), f16(c21)))) <=> ((~![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))) | (~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))) | p7(f16(c22), f16(c21)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((p7(f16(c22), f16(c21)) | (~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22)))) <=> ((~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))) | p7(f16(c22), f16(c21)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (((~![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))) | (p7(f16(c22), f16(c21)) | (~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))))) <=> ((~![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))) | ((~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))) | p7(f16(c22), f16(c21))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (((~![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))) | (p7(f16(c22), f16(c21)) | (~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))))) <=> ((~![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))) | (~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))) | p7(f16(c22), f16(c21)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[32, 30])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))) | (p7(f16(c22), f16(c21)) | (~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~![X32: $i, X34: $i, X33: $i] : (p7(X33, X34) | (~p7(X32, X34)) | (~p7(X32, X33)))) | (~p7(f16(c21), f16(c21))) | (~p7(f16(c21), f16(c22))) | p7(f16(c22), f16(c21))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[35, 29, 26, 16, 12])).
% 0.12/0.38 tff(37,plain,(p7(f16(c22), f16(c21))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (^[X42: $i, X41: $i] : refl(((~p7(X41, X42)) | p7(f15(X41), f15(X42))) <=> ((~p7(X41, X42)) | p7(f15(X41), f15(X42))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42))) <=> ![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42))) <=> ![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (^[X42: $i, X41: $i] : rewrite((p7(f15(X41), f15(X42)) | (~p7(X41, X42))) <=> ((~p7(X41, X42)) | p7(f15(X41), f15(X42))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![X42: $i, X41: $i] : (p7(f15(X41), f15(X42)) | (~p7(X41, X42))) <=> ![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.38 tff(43,axiom,(![X42: $i, X41: $i] : (p7(f15(X41), f15(X42)) | (~p7(X41, X42)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_17')).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.12/0.38 tff(46,plain,(
% 0.12/0.38 ![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[45])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (((~![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))) | ((~p7(f16(c22), f16(c21))) | p7(f15(f16(c22)), f15(f16(c21))))) <=> ((~![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))) | (~p7(f16(c22), f16(c21))) | p7(f15(f16(c22)), f15(f16(c21))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))) | ((~p7(f16(c22), f16(c21))) | p7(f15(f16(c22)), f15(f16(c21))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((~![X42: $i, X41: $i] : ((~p7(X41, X42)) | p7(f15(X41), f15(X42)))) | (~p7(f16(c22), f16(c21))) | p7(f15(f16(c22)), f15(f16(c21)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ((~p7(f16(c22), f16(c21))) | p7(f15(f16(c22)), f15(f16(c21)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (p7(f15(f16(c22)), f15(f16(c21)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[51, 37])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (^[X4: $i] : refl(((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4)))) <=> ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4)))) <=> ![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4)))) <=> ![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (^[X4: $i] : rewrite((p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))) | (~p19(X4))) <=> ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (![X4: $i] : (p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))) | (~p19(X4))) <=> ![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.12/0.39 tff(58,axiom,(![X4: $i] : (p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))) | (~p19(X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p18_27')).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.12/0.39 tff(61,plain,(
% 0.12/0.39 ![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[60])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (p19(c22) <=> p19(c22)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(64,axiom,(p19(c22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c22_is_p19_2')).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (p19(c22)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (((~![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))) | ((~p19(c22)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22))))) <=> ((~![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))) | (~p19(c22)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 ((~![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))) | ((~p19(c22)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~![X4: $i] : ((~p19(X4)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X4))))) | (~p19(c22)) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[68, 65, 62])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (^[X6: $i, X7: $i, X5: $i, X8: $i] : refl(((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6)) <=> ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6)) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6)) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (^[X6: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p18(X5, X6) | (~p7(X7, X5))) <=> ((~p7(X7, X5)) | p18(X5, X6))), (((p18(X5, X6) | (~p7(X7, X5))) | (~p7(X8, X6))) <=> (((~p7(X7, X5)) | p18(X5, X6)) | (~p7(X8, X6))))), rewrite((((~p7(X7, X5)) | p18(X5, X6)) | (~p7(X8, X6))) <=> ((~p7(X7, X5)) | (~p7(X8, X6)) | p18(X5, X6))), (((p18(X5, X6) | (~p7(X7, X5))) | (~p7(X8, X6))) <=> ((~p7(X7, X5)) | (~p7(X8, X6)) | p18(X5, X6)))), ((((p18(X5, X6) | (~p7(X7, X5))) | (~p7(X8, X6))) | (~p18(X7, X8))) <=> (((~p7(X7, X5)) | (~p7(X8, X6)) | p18(X5, X6)) | (~p18(X7, X8))))), rewrite((((~p7(X7, X5)) | (~p7(X8, X6)) | p18(X5, X6)) | (~p18(X7, X8))) <=> ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))), ((((p18(X5, X6) | (~p7(X7, X5))) | (~p7(X8, X6))) | (~p18(X7, X8))) <=> ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![X6: $i, X7: $i, X5: $i, X8: $i] : (((p18(X5, X6) | (~p7(X7, X5))) | (~p7(X8, X6))) | (~p18(X7, X8))) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.12/0.39 tff(75,axiom,(![X6: $i, X7: $i, X5: $i, X8: $i] : (((p18(X5, X6) | (~p7(X7, X5))) | (~p7(X8, X6))) | (~p18(X7, X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p18_23')).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.12/0.39 tff(78,plain,(
% 0.12/0.39 ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))),
% 0.12/0.39 inference(skolemize,[status(sab)],[77])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))) | (p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) <=> (p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))) | ((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))) | (p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[81])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))) | ((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[82, 80])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))) | ((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22)))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p7(X7, X5)) | (~p18(X7, X8)) | (~p7(X8, X6)) | p18(X5, X6))) | p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c22))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[85, 79, 69, 52, 11])).
% 0.12/0.40 tff(87,assumption,(~p3(f12(c20), f12(c20))), introduced(assumption)).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (^[X16: $i] : refl(p3(X16, X16) <=> p3(X16, X16))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (![X16: $i] : p3(X16, X16) <=> ![X16: $i] : p3(X16, X16)),
% 0.12/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (![X16: $i] : p3(X16, X16) <=> ![X16: $i] : p3(X16, X16)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(91,axiom,(![X16: $i] : p3(X16, X16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_6')).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (![X16: $i] : p3(X16, X16)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.12/0.40 tff(93,plain,(
% 0.12/0.40 ![X16: $i] : p3(X16, X16)),
% 0.12/0.40 inference(skolemize,[status(sab)],[92])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 (![X16: $i] : p3(X16, X16)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 ((~![X16: $i] : p3(X16, X16)) | p3(f12(c20), f12(c20))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[95, 94, 87])).
% 0.12/0.40 tff(97,plain,(p3(f12(c20), f12(c20))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 (^[X23: $i, X24: $i] : refl(((~p3(X23, X24)) | p3(f14(X23), f14(X24))) <=> ((~p3(X23, X24)) | p3(f14(X23), f14(X24))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24))) <=> ![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24))) <=> ![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (^[X23: $i, X24: $i] : rewrite((p3(f14(X23), f14(X24)) | (~p3(X23, X24))) <=> ((~p3(X23, X24)) | p3(f14(X23), f14(X24))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : (p3(f14(X23), f14(X24)) | (~p3(X23, X24))) <=> ![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.12/0.40 tff(103,axiom,(![X23: $i, X24: $i] : (p3(f14(X23), f14(X24)) | (~p3(X23, X24)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_14')).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.12/0.40 tff(106,plain,(
% 0.12/0.40 ![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[105])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (((~![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))) | ((~p3(f12(c20), f12(c20))) | p3(f14(f12(c20)), f14(f12(c20))))) <=> ((~![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))) | (~p3(f12(c20), f12(c20))) | p3(f14(f12(c20)), f14(f12(c20))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(109,plain,
% 0.12/0.40 ((~![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))) | ((~p3(f12(c20), f12(c20))) | p3(f14(f12(c20)), f14(f12(c20))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 ((~![X23: $i, X24: $i] : ((~p3(X23, X24)) | p3(f14(X23), f14(X24)))) | (~p3(f12(c20), f12(c20))) | p3(f14(f12(c20)), f14(f12(c20)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.12/0.40 tff(111,plain,
% 0.12/0.40 ((~p3(f12(c20), f12(c20))) | p3(f14(f12(c20)), f14(f12(c20)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.12/0.40 tff(112,plain,
% 0.12/0.40 (p3(f14(f12(c20)), f14(f12(c20)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[111, 97])).
% 0.12/0.40 tff(113,plain,
% 0.12/0.40 (^[X20: $i, X19: $i] : refl(((~p3(X19, X20)) | p3(f11(X19), f11(X20))) <=> ((~p3(X19, X20)) | p3(f11(X19), f11(X20))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(114,plain,
% 0.12/0.40 (![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20))) <=> ![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[113])).
% 0.12/0.40 tff(115,plain,
% 0.12/0.40 (![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20))) <=> ![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(116,plain,
% 0.12/0.40 (^[X20: $i, X19: $i] : rewrite((p3(f11(X19), f11(X20)) | (~p3(X19, X20))) <=> ((~p3(X19, X20)) | p3(f11(X19), f11(X20))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 (![X20: $i, X19: $i] : (p3(f11(X19), f11(X20)) | (~p3(X19, X20))) <=> ![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[116])).
% 0.12/0.40 tff(118,axiom,(![X20: $i, X19: $i] : (p3(f11(X19), f11(X20)) | (~p3(X19, X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_12')).
% 0.12/0.40 tff(119,plain,
% 0.12/0.40 (![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 (![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.12/0.40 tff(121,plain,(
% 0.12/0.40 ![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[120])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 (![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 (((~![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))) | ((~p3(f14(f12(c20)), f14(f12(c20)))) | p3(f11(f14(f12(c20))), f11(f14(f12(c20)))))) <=> ((~![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))) | (~p3(f14(f12(c20)), f14(f12(c20)))) | p3(f11(f14(f12(c20))), f11(f14(f12(c20)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 ((~![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))) | ((~p3(f14(f12(c20)), f14(f12(c20)))) | p3(f11(f14(f12(c20))), f11(f14(f12(c20)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 ((~![X20: $i, X19: $i] : ((~p3(X19, X20)) | p3(f11(X19), f11(X20)))) | (~p3(f14(f12(c20)), f14(f12(c20)))) | p3(f11(f14(f12(c20))), f11(f14(f12(c20))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.12/0.40 tff(126,plain,
% 0.12/0.40 ((~p3(f14(f12(c20)), f14(f12(c20)))) | p3(f11(f14(f12(c20))), f11(f14(f12(c20))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 (p3(f11(f14(f12(c20))), f11(f14(f12(c20))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[126, 112])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 (^[X39: $i, X40: $i] : refl(((~p3(X39, X40)) | p7(f13(X39), f13(X40))) <=> ((~p3(X39, X40)) | p7(f13(X39), f13(X40))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(129,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40))) <=> ![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.12/0.40 tff(130,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40))) <=> ![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 (^[X39: $i, X40: $i] : rewrite((p7(f13(X39), f13(X40)) | (~p3(X39, X40))) <=> ((~p3(X39, X40)) | p7(f13(X39), f13(X40))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(132,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : (p7(f13(X39), f13(X40)) | (~p3(X39, X40))) <=> ![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[131])).
% 0.12/0.40 tff(133,axiom,(![X39: $i, X40: $i] : (p7(f13(X39), f13(X40)) | (~p3(X39, X40)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_16')).
% 0.12/0.40 tff(134,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.12/0.40 tff(135,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.12/0.40 tff(136,plain,(
% 0.12/0.40 ![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[135])).
% 0.12/0.40 tff(137,plain,
% 0.12/0.40 (![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.12/0.40 tff(138,plain,
% 0.12/0.40 (((~![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))) | ((~p3(f11(f14(f12(c20))), f11(f14(f12(c20))))) | p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20))))))) <=> ((~![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))) | (~p3(f11(f14(f12(c20))), f11(f14(f12(c20))))) | p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(139,plain,
% 0.12/0.40 ((~![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))) | ((~p3(f11(f14(f12(c20))), f11(f14(f12(c20))))) | p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(140,plain,
% 0.12/0.40 ((~![X39: $i, X40: $i] : ((~p3(X39, X40)) | p7(f13(X39), f13(X40)))) | (~p3(f11(f14(f12(c20))), f11(f14(f12(c20))))) | p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.12/0.40 tff(141,plain,
% 0.12/0.40 (p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[140, 137, 127])).
% 0.12/0.40 tff(142,plain,
% 0.12/0.40 (^[X47: $i, X45: $i, X46: $i, X48: $i] : refl(((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48))) <=> ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(143,plain,
% 0.12/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48))) <=> ![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[142])).
% 0.12/0.40 tff(144,plain,
% 0.12/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48))) <=> ![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(145,plain,
% 0.12/0.40 (^[X47: $i, X45: $i, X46: $i, X48: $i] : trans(monotonicity(rewrite((p7(f8(X45, X46), f8(X47, X48)) | (~p7(X45, X47))) <=> ((~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))), (((p7(f8(X45, X46), f8(X47, X48)) | (~p7(X45, X47))) | (~p7(X46, X48))) <=> (((~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48))) | (~p7(X46, X48))))), rewrite((((~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48))) | (~p7(X46, X48))) <=> ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))), (((p7(f8(X45, X46), f8(X47, X48)) | (~p7(X45, X47))) | (~p7(X46, X48))) <=> ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(146,plain,
% 0.12/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((p7(f8(X45, X46), f8(X47, X48)) | (~p7(X45, X47))) | (~p7(X46, X48))) <=> ![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[145])).
% 0.12/0.40 tff(147,axiom,(![X47: $i, X45: $i, X46: $i, X48: $i] : ((p7(f8(X45, X46), f8(X47, X48)) | (~p7(X45, X47))) | (~p7(X46, X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_26')).
% 0.12/0.40 tff(148,plain,
% 0.12/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.12/0.40 tff(149,plain,
% 0.12/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.12/0.40 tff(150,plain,(
% 0.12/0.40 ![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[149])).
% 0.12/0.40 tff(151,plain,
% 0.12/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.12/0.40 tff(152,plain,
% 0.12/0.40 (((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))) | ((~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))) | (~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(153,plain,
% 0.12/0.40 (((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) <=> ((~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(154,plain,
% 0.12/0.40 (((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))) | ((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))) | ((~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[153])).
% 0.12/0.41 tff(155,plain,
% 0.12/0.41 (((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))) | ((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))) | (~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[154, 152])).
% 0.12/0.41 tff(156,plain,
% 0.12/0.41 ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))) | ((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(157,plain,
% 0.12/0.41 ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p7(X46, X48)) | (~p7(X45, X47)) | p7(f8(X45, X46), f8(X47, X48)))) | (~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 ((~p7(f13(f11(f14(f12(c20)))), f13(f11(f14(f12(c20)))))) | (~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[157, 151])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 ((~p7(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[158, 141])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 (p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[159, 11])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 (^[X4: $i] : refl(((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) <=> ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(162,plain,
% 0.19/0.41 (![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) <=> ![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[161])).
% 0.19/0.41 tff(163,plain,
% 0.19/0.41 (![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) <=> ![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(164,plain,
% 0.19/0.41 (^[X4: $i] : rewrite((p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p19(X4))) <=> ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(165,plain,
% 0.19/0.41 (![X4: $i] : (p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p19(X4))) <=> ![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[164])).
% 0.19/0.41 tff(166,axiom,(![X4: $i] : (p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p19(X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p17_28')).
% 0.19/0.41 tff(167,plain,
% 0.19/0.41 (![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.41 tff(168,plain,
% 0.19/0.41 (![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.19/0.41 tff(169,plain,(
% 0.19/0.41 ![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[168])).
% 0.19/0.41 tff(170,plain,
% 0.19/0.41 (![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.19/0.41 tff(171,plain,
% 0.19/0.41 (((~![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) | ((~p19(c22)) | p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ((~![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) | (~p19(c22)) | p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(172,plain,
% 0.19/0.41 ((~![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) | ((~p19(c22)) | p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(173,plain,
% 0.19/0.41 ((~![X4: $i] : ((~p19(X4)) | p17(f15(f16(X4)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(X4))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) | (~p19(c22)) | p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.41 tff(174,plain,
% 0.19/0.41 (p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[173, 65, 170])).
% 0.19/0.41 tff(175,plain,
% 0.19/0.41 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1)) <=> ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(176,plain,
% 0.19/0.41 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1)) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[175])).
% 0.19/0.41 tff(177,plain,
% 0.19/0.41 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1)) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(178,plain,
% 0.19/0.42 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((p17(X0, X1) | (~p7(X2, X0))) <=> ((~p7(X2, X0)) | p17(X0, X1))), (((p17(X0, X1) | (~p7(X2, X0))) | (~p7(X3, X1))) <=> (((~p7(X2, X0)) | p17(X0, X1)) | (~p7(X3, X1))))), rewrite((((~p7(X2, X0)) | p17(X0, X1)) | (~p7(X3, X1))) <=> ((~p7(X3, X1)) | (~p7(X2, X0)) | p17(X0, X1))), (((p17(X0, X1) | (~p7(X2, X0))) | (~p7(X3, X1))) <=> ((~p7(X3, X1)) | (~p7(X2, X0)) | p17(X0, X1)))), ((((p17(X0, X1) | (~p7(X2, X0))) | (~p7(X3, X1))) | (~p17(X2, X3))) <=> (((~p7(X3, X1)) | (~p7(X2, X0)) | p17(X0, X1)) | (~p17(X2, X3))))), rewrite((((~p7(X3, X1)) | (~p7(X2, X0)) | p17(X0, X1)) | (~p17(X2, X3))) <=> ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))), ((((p17(X0, X1) | (~p7(X2, X0))) | (~p7(X3, X1))) | (~p17(X2, X3))) <=> ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(179,plain,
% 0.19/0.42 (![X0: $i, X3: $i, X2: $i, X1: $i] : (((p17(X0, X1) | (~p7(X2, X0))) | (~p7(X3, X1))) | (~p17(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.42 tff(180,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : (((p17(X0, X1) | (~p7(X2, X0))) | (~p7(X3, X1))) | (~p17(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p17_22')).
% 0.19/0.42 tff(181,plain,
% 0.19/0.42 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.42 tff(182,plain,
% 0.19/0.42 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.19/0.42 tff(183,plain,(
% 0.19/0.42 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))),
% 0.19/0.42 inference(skolemize,[status(sab)],[182])).
% 0.19/0.42 tff(184,plain,
% 0.19/0.42 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.19/0.42 tff(185,plain,
% 0.19/0.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))) | (p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))) | p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(186,plain,
% 0.19/0.42 (((~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) <=> (p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(187,plain,
% 0.19/0.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))) | ((~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))) | (p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[186])).
% 0.19/0.42 tff(188,plain,
% 0.19/0.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))) | ((~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))) | p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[187, 185])).
% 0.19/0.42 tff(189,plain,
% 0.19/0.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))) | ((~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(190,plain,
% 0.19/0.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~p7(X3, X1)) | (~p17(X2, X3)) | (~p7(X2, X0)) | p17(X0, X1))) | p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))) | (~p7(f15(f16(c22)), f15(f16(c21)))) | (~p7(f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p17(f15(f16(c22)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.42 tff(191,plain,
% 0.19/0.42 (p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[190, 184, 174, 52, 160])).
% 0.19/0.42 tff(192,plain,
% 0.19/0.42 (![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28)) <=> ![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(193,plain,
% 0.19/0.42 (^[X27: $i, X28: $i] : refl(((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28)) <=> ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 (![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28)) <=> ![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28)) <=> ![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (^[X27: $i, X28: $i] : trans(monotonicity(trans(monotonicity(rewrite((p3(f4(f6(X27)), X28) | (~p19(X27))) <=> ((~p19(X27)) | p3(f4(f6(X27)), X28))), (((p3(f4(f6(X27)), X28) | (~p19(X27))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27))))) <=> (((~p19(X27)) | p3(f4(f6(X27)), X28)) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27))))))), rewrite((((~p19(X27)) | p3(f4(f6(X27)), X28)) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27))))) <=> ((~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))), (((p3(f4(f6(X27)), X28) | (~p19(X27))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27))))) <=> ((~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28)))), ((((p3(f4(f6(X27)), X28) | (~p19(X27))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27))))) | (~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> (((~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28)) | (~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))))), rewrite((((~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28)) | (~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))), ((((p3(f4(f6(X27)), X28) | (~p19(X27))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27))))) | (~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 (![X27: $i, X28: $i] : (((p3(f4(f6(X27)), X28) | (~p19(X27))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27))))) | (~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))))))) <=> ![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[196])).
% 0.19/0.43 tff(198,axiom,(![X27: $i, X28: $i] : (((p3(f4(f6(X27)), X28) | (~p19(X27))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27))))) | (~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_29')).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.19/0.43 tff(201,plain,(
% 0.19/0.43 ![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.43 inference(skolemize,[status(sab)],[200])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 (![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 (![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[202, 192])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 ((~p3(f4(f6(c21)), f4(f6(c22)))) <=> (~p3(f4(f6(c21)), f4(f6(c22))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(205,axiom,(~p3(f4(f6(c21)), f4(f6(c22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p3_8')).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (~p3(f4(f6(c21)), f4(f6(c22)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.19/0.43 tff(207,plain,
% 0.19/0.43 (p19(c21) <=> p19(c21)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(208,axiom,(p19(c21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c21_is_p19_1')).
% 0.19/0.43 tff(209,plain,
% 0.19/0.43 (p19(c21)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.19/0.43 tff(210,plain,
% 0.19/0.43 (((~![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))) | (p3(f4(f6(c21)), f4(f6(c22))) | (~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21)))) <=> ((~![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))) | p3(f4(f6(c21)), f4(f6(c22))) | (~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 (((~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21)) | p3(f4(f6(c21)), f4(f6(c22)))) <=> (p3(f4(f6(c21)), f4(f6(c22))) | (~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(212,plain,
% 0.19/0.43 (((~![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))) | ((~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21)) | p3(f4(f6(c21)), f4(f6(c22))))) <=> ((~![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))) | (p3(f4(f6(c21)), f4(f6(c22))) | (~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[211])).
% 0.19/0.44 tff(213,plain,
% 0.19/0.44 (((~![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))) | ((~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21)) | p3(f4(f6(c21)), f4(f6(c22))))) <=> ((~![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))) | p3(f4(f6(c21)), f4(f6(c22))) | (~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[212, 210])).
% 0.19/0.44 tff(214,plain,
% 0.19/0.44 ((~![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))) | ((~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21)) | p3(f4(f6(c21)), f4(f6(c22))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(215,plain,
% 0.19/0.44 ((~![X27: $i, X28: $i] : ((~p17(f15(f16(X27)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), X28), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(X27)))) | (~p19(X27)) | p3(f4(f6(X27)), X28))) | p3(f4(f6(c21)), f4(f6(c22))) | (~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21)))) | (~p19(c21))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.19/0.44 tff(216,plain,
% 0.19/0.44 ((~p17(f15(f16(c21)), f8(f13(f11(f14(f12(c20)))), f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20))))))))))))) | (~p18(f9(f10(f13(f11(f14(f12(c20)))), f4(f6(c22))), f10(f13(f11(f14(f12(c20)))), f11(f12(f12(f12(f12(f12(f12(f12(c20)))))))))), f15(f16(c21))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[215, 209, 206, 203])).
% 0.19/0.44 tff(217,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[216, 191, 86])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------