%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN645-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:39:45 AM UTC 2025
% Result : Unsatisfiable 0.78s 1.01s
% Output : Proof 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN645-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.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 12:39:07 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.78/1.01 % SZS status Unsatisfiable
% 0.78/1.01 % SZS output start Proof
% 0.78/1.01 tff(p25_type, type, (
% 0.78/1.01 p25: ( $i * $i ) > $o)).
% 0.78/1.01 tff(f13_type, type, (
% 0.78/1.01 f13: $i > $i)).
% 0.78/1.01 tff(f14_type, type, (
% 0.78/1.01 f14: ( $i * $i ) > $i)).
% 0.78/1.01 tff(f21_type, type, (
% 0.78/1.01 f21: ( $i * $i * $i * $i * $i ) > $i)).
% 0.78/1.01 tff(c28_type, type, (
% 0.78/1.01 c28: $i)).
% 0.78/1.01 tff(c31_type, type, (
% 0.78/1.01 c31: $i)).
% 0.78/1.01 tff(c30_type, type, (
% 0.78/1.01 c30: $i)).
% 0.78/1.01 tff(c27_type, type, (
% 0.78/1.01 c27: $i)).
% 0.78/1.01 tff(c29_type, type, (
% 0.78/1.01 c29: $i)).
% 0.78/1.01 tff(f16_type, type, (
% 0.78/1.01 f16: ( $i * $i * $i ) > $i)).
% 0.78/1.01 tff(c32_type, type, (
% 0.78/1.01 c32: $i)).
% 0.78/1.01 tff(f10_type, type, (
% 0.78/1.01 f10: ( $i * $i ) > $i)).
% 0.78/1.01 tff(f11_type, type, (
% 0.78/1.01 f11: ( $i * $i ) > $i)).
% 0.78/1.01 tff(p23_type, type, (
% 0.78/1.01 p23: ( $i * $i ) > $o)).
% 0.78/1.01 tff(f8_type, type, (
% 0.78/1.01 f8: $i > $i)).
% 0.78/1.01 tff(p12_type, type, (
% 0.78/1.01 p12: ( $i * $i ) > $o)).
% 0.78/1.01 tff(p24_type, type, (
% 0.78/1.01 p24: $i > $o)).
% 0.78/1.01 tff(f17_type, type, (
% 0.78/1.01 f17: ( $i * $i ) > $i)).
% 0.78/1.01 tff(p22_type, type, (
% 0.78/1.01 p22: ( $i * $i ) > $o)).
% 0.78/1.01 tff(f3_type, type, (
% 0.78/1.01 f3: $i > $i)).
% 0.78/1.01 tff(f4_type, type, (
% 0.78/1.01 f4: $i > $i)).
% 0.78/1.01 tff(f5_type, type, (
% 0.78/1.01 f5: $i > $i)).
% 0.78/1.01 tff(c26_type, type, (
% 0.78/1.01 c26: $i)).
% 0.78/1.01 tff(1,plain,
% 0.78/1.01 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : refl(((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(2,plain,
% 0.78/1.01 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[1])).
% 0.78/1.01 tff(3,plain,
% 0.78/1.01 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(4,plain,
% 0.78/1.01 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : trans(monotonicity(trans(monotonicity(rewrite(((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) <=> (p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))), ((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) <=> ((p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p22(f3(f4(f5(c26))), X5))))), rewrite(((p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p22(f3(f4(f5(c26))), X5))) <=> ((~p22(f3(f4(f5(c26))), X5)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))), ((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) <=> ((~p22(f3(f4(f5(c26))), X5)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))))), (((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> (((~p22(f3(f4(f5(c26))), X5)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))))), rewrite((((~p22(f3(f4(f5(c26))), X5)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))), (((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(5,plain,
% 0.78/1.01 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[4])).
% 0.78/1.01 tff(6,axiom,(![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_41')).
% 0.78/1.01 tff(7,plain,
% 0.78/1.01 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.78/1.01 tff(8,plain,
% 0.78/1.01 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.78/1.01 tff(9,plain,(
% 0.78/1.01 ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))),
% 0.78/1.02 inference(skolemize,[status(sab)],[8])).
% 0.78/1.02 tff(10,plain,
% 0.78/1.02 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.78/1.02 tff(11,plain,
% 0.78/1.02 ((~p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31)))) <=> (~p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(12,axiom,(~p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f17_is_not_p24_32')).
% 0.78/1.02 tff(13,plain,
% 0.78/1.02 (~p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31)))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.78/1.02 tff(14,plain,
% 0.78/1.02 ((~p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31))) <=> (~p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(15,axiom,(~p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p12_22')).
% 0.78/1.02 tff(16,plain,
% 0.78/1.02 (~p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.78/1.02 tff(17,plain,
% 0.78/1.02 (p23(c28, f8(f10(c29, f11(c27, c30)))) <=> p23(c28, f8(f10(c29, f11(c27, c30))))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(18,axiom,(p23(c28, f8(f10(c29, f11(c27, c30))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p23_9')).
% 0.78/1.02 tff(19,plain,
% 0.78/1.02 (p23(c28, f8(f10(c29, f11(c27, c30))))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.78/1.02 tff(20,plain,
% 0.78/1.02 (p22(f3(f4(f5(c26))), c27) <=> p22(f3(f4(f5(c26))), c27)),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(21,axiom,(p22(f3(f4(f5(c26))), c27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p22_7')).
% 0.78/1.02 tff(22,plain,
% 0.78/1.02 (p22(f3(f4(f5(c26))), c27)),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.78/1.02 tff(23,plain,
% 0.78/1.02 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))) | (p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30)))))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30)))))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(24,plain,
% 0.78/1.02 (((~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30)))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31))) <=> (p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30)))))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(25,plain,
% 0.78/1.02 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30)))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))) | (p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30))))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[24])).
% 0.78/1.02 tff(26,plain,
% 0.78/1.02 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30)))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30)))))),
% 0.78/1.02 inference(transitivity,[status(thm)],[25, 23])).
% 0.78/1.02 tff(27,plain,
% 0.78/1.02 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30)))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(28,plain,
% 0.78/1.02 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p23(f21(X4, X5, X6, X7, X3), f8(f10(X4, f11(X5, X6)))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30))))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.78/1.02 tff(29,plain,
% 0.78/1.02 (p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30))))),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[28, 22, 19, 16, 13, 10])).
% 0.78/1.02 tff(30,plain,
% 0.78/1.02 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : refl(((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3)))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3)))))),
% 0.78/1.02 inference(bind,[status(th)],[])).
% 0.78/1.02 tff(31,plain,
% 0.78/1.02 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3)))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))),
% 0.78/1.02 inference(quant_intro,[status(thm)],[30])).
% 0.78/1.02 tff(32,plain,
% 0.78/1.02 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3)))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(33,plain,
% 0.78/1.02 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : trans(monotonicity(rewrite((p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))) | (~p22(f3(f4(f5(c26))), X5))) <=> ((~p22(f3(f4(f5(c26))), X5)) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))), (((p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> (((~p22(f3(f4(f5(c26))), X5)) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3)))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))))), rewrite((((~p22(f3(f4(f5(c26))), X5)) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3)))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))), (((p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))))),
% 0.78/1.02 inference(bind,[status(th)],[])).
% 0.78/1.02 tff(34,plain,
% 0.78/1.02 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))),
% 0.78/1.02 inference(quant_intro,[status(thm)],[33])).
% 0.78/1.02 tff(35,axiom,(![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p25_37')).
% 0.78/1.02 tff(36,plain,
% 0.78/1.02 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.78/1.02 tff(37,plain,
% 0.78/1.02 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.78/1.02 tff(38,plain,(
% 0.78/1.02 ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))),
% 0.78/1.02 inference(skolemize,[status(sab)],[37])).
% 0.78/1.02 tff(39,plain,
% 0.78/1.02 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.78/1.02 tff(40,plain,
% 0.78/1.02 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30))))) | p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30))))) | p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(41,plain,
% 0.78/1.02 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30))))) | p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(42,plain,
% 0.78/1.02 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p25(f13(f14(X7, f16(f10(X4, f11(X5, X6)), c32, X7))), f13(f14(X7, X3))))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(f21(c29, c27, c30, c31, c28), f8(f10(c29, f11(c27, c30))))) | p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.78/1.02 tff(43,plain,
% 0.78/1.02 (p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[42, 22, 39, 29])).
% 0.78/1.02 tff(44,assumption,(~p12(c31, c31)), introduced(assumption)).
% 0.78/1.02 tff(45,plain,
% 0.78/1.02 (^[X0: $i] : refl(p12(X0, X0) <=> p12(X0, X0))),
% 0.78/1.02 inference(bind,[status(th)],[])).
% 0.78/1.02 tff(46,plain,
% 0.78/1.02 (![X0: $i] : p12(X0, X0) <=> ![X0: $i] : p12(X0, X0)),
% 0.78/1.02 inference(quant_intro,[status(thm)],[45])).
% 0.78/1.02 tff(47,plain,
% 0.78/1.02 (![X0: $i] : p12(X0, X0) <=> ![X0: $i] : p12(X0, X0)),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(48,axiom,(![X0: $i] : p12(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_1')).
% 0.78/1.02 tff(49,plain,
% 0.78/1.02 (![X0: $i] : p12(X0, X0)),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.78/1.02 tff(50,plain,(
% 0.78/1.02 ![X0: $i] : p12(X0, X0)),
% 0.78/1.02 inference(skolemize,[status(sab)],[49])).
% 0.78/1.02 tff(51,plain,
% 0.78/1.02 (![X0: $i] : p12(X0, X0)),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.78/1.02 tff(52,plain,
% 0.78/1.02 ((~![X0: $i] : p12(X0, X0)) | p12(c31, c31)),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(53,plain,
% 0.78/1.02 ($false),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[52, 51, 44])).
% 0.78/1.02 tff(54,plain,(p12(c31, c31)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.02 tff(55,assumption,(~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))), introduced(assumption)).
% 0.78/1.02 tff(56,plain,
% 0.78/1.02 ((~![X0: $i] : p12(X0, X0)) | p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(57,plain,
% 0.78/1.02 ($false),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[56, 51, 55])).
% 0.78/1.02 tff(58,plain,(p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))), inference(lemma,lemma(discharge,[]))).
% 0.78/1.02 tff(59,plain,
% 0.78/1.02 (^[X12: $i, X11: $i, X13: $i, X10: $i] : refl(((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13))) <=> ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13))))),
% 0.78/1.02 inference(bind,[status(th)],[])).
% 0.78/1.02 tff(60,plain,
% 0.78/1.02 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13))) <=> ![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))),
% 0.78/1.02 inference(quant_intro,[status(thm)],[59])).
% 0.78/1.02 tff(61,plain,
% 0.78/1.02 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13))) <=> ![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(62,plain,
% 0.78/1.02 (^[X12: $i, X11: $i, X13: $i, X10: $i] : trans(monotonicity(rewrite((p12(f14(X10, X11), f14(X12, X13)) | (~p12(X10, X12))) <=> ((~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))), (((p12(f14(X10, X11), f14(X12, X13)) | (~p12(X10, X12))) | (~p12(X11, X13))) <=> (((~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13))) | (~p12(X11, X13))))), rewrite((((~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13))) | (~p12(X11, X13))) <=> ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))), (((p12(f14(X10, X11), f14(X12, X13)) | (~p12(X10, X12))) | (~p12(X11, X13))) <=> ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))))),
% 0.86/1.02 inference(bind,[status(th)],[])).
% 0.86/1.02 tff(63,plain,
% 0.86/1.02 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((p12(f14(X10, X11), f14(X12, X13)) | (~p12(X10, X12))) | (~p12(X11, X13))) <=> ![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))),
% 0.86/1.02 inference(quant_intro,[status(thm)],[62])).
% 0.86/1.02 tff(64,axiom,(![X12: $i, X11: $i, X13: $i, X10: $i] : ((p12(f14(X10, X11), f14(X12, X13)) | (~p12(X10, X12))) | (~p12(X11, X13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_26')).
% 0.86/1.02 tff(65,plain,
% 0.86/1.02 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.86/1.02 tff(66,plain,
% 0.86/1.02 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.86/1.02 tff(67,plain,(
% 0.86/1.02 ![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))),
% 0.86/1.02 inference(skolemize,[status(sab)],[66])).
% 0.86/1.02 tff(68,plain,
% 0.86/1.02 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.86/1.02 tff(69,plain,
% 0.86/1.02 (((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))) | ((~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))) | (~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))))) <=> ((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))) | (~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))) | (~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(70,plain,
% 0.86/1.02 (((~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))) | (~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28)))) <=> ((~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))) | (~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(71,plain,
% 0.86/1.02 (((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))) | ((~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))) | (~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))))) <=> ((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))) | ((~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))) | (~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28)))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[70])).
% 0.86/1.02 tff(72,plain,
% 0.86/1.02 (((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))) | ((~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))) | (~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))))) <=> ((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))) | (~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))) | (~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[71, 69])).
% 0.86/1.03 tff(73,plain,
% 0.86/1.03 ((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))) | ((~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28))) | (~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(74,plain,
% 0.86/1.03 ((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p12(X11, X13)) | (~p12(X10, X12)) | p12(f14(X10, X11), f14(X12, X13)))) | (~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))) | (~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.86/1.03 tff(75,plain,
% 0.86/1.03 ((~p12(c31, c31)) | p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28))) | (~p12(f21(c29, c27, c30, c31, c28), f21(c29, c27, c30, c31, c28)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[74, 68])).
% 0.86/1.03 tff(76,plain,
% 0.86/1.03 (p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[75, 58, 54])).
% 0.86/1.03 tff(77,plain,
% 0.86/1.03 (^[X9: $i, X8: $i] : refl(((~p12(X8, X9)) | p12(f13(X8), f13(X9))) <=> ((~p12(X8, X9)) | p12(f13(X8), f13(X9))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(78,plain,
% 0.86/1.03 (![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9))) <=> ![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[77])).
% 0.86/1.03 tff(79,plain,
% 0.86/1.03 (![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9))) <=> ![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(80,plain,
% 0.86/1.03 (^[X9: $i, X8: $i] : rewrite((p12(f13(X8), f13(X9)) | (~p12(X8, X9))) <=> ((~p12(X8, X9)) | p12(f13(X8), f13(X9))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(81,plain,
% 0.86/1.03 (![X9: $i, X8: $i] : (p12(f13(X8), f13(X9)) | (~p12(X8, X9))) <=> ![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[80])).
% 0.86/1.03 tff(82,axiom,(![X9: $i, X8: $i] : (p12(f13(X8), f13(X9)) | (~p12(X8, X9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_11')).
% 0.86/1.03 tff(83,plain,
% 0.86/1.03 (![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.86/1.03 tff(84,plain,
% 0.86/1.03 (![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.86/1.03 tff(85,plain,(
% 0.86/1.03 ![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))),
% 0.86/1.03 inference(skolemize,[status(sab)],[84])).
% 0.86/1.03 tff(86,plain,
% 0.86/1.03 (![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.86/1.03 tff(87,plain,
% 0.86/1.03 (((~![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))) | ((~p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28)))) | p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))) <=> ((~![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))) | (~p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28)))) | p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(88,plain,
% 0.86/1.03 ((~![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))) | ((~p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28)))) | p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(89,plain,
% 0.86/1.03 ((~![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))) | (~p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28)))) | p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.86/1.03 tff(90,plain,
% 0.86/1.03 ((~p12(f14(c31, f21(c29, c27, c30, c31, c28)), f14(c31, f21(c29, c27, c30, c31, c28)))) | p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.86/1.03 tff(91,plain,
% 0.86/1.03 (p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[90, 76])).
% 0.86/1.03 tff(92,assumption,(~p12(f14(c31, c28), f14(c31, c28))), introduced(assumption)).
% 0.86/1.03 tff(93,plain,
% 0.86/1.03 ((~![X0: $i] : p12(X0, X0)) | p12(f14(c31, c28), f14(c31, c28))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(94,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[93, 51, 92])).
% 0.86/1.03 tff(95,plain,(p12(f14(c31, c28), f14(c31, c28))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(96,plain,
% 0.86/1.03 (((~![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))) | ((~p12(f14(c31, c28), f14(c31, c28))) | p12(f13(f14(c31, c28)), f13(f14(c31, c28))))) <=> ((~![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))) | (~p12(f14(c31, c28), f14(c31, c28))) | p12(f13(f14(c31, c28)), f13(f14(c31, c28))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(97,plain,
% 0.86/1.03 ((~![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))) | ((~p12(f14(c31, c28), f14(c31, c28))) | p12(f13(f14(c31, c28)), f13(f14(c31, c28))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(98,plain,
% 0.86/1.03 ((~![X9: $i, X8: $i] : ((~p12(X8, X9)) | p12(f13(X8), f13(X9)))) | (~p12(f14(c31, c28), f14(c31, c28))) | p12(f13(f14(c31, c28)), f13(f14(c31, c28)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.86/1.03 tff(99,plain,
% 0.86/1.03 ((~p12(f14(c31, c28), f14(c31, c28))) | p12(f13(f14(c31, c28)), f13(f14(c31, c28)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[98, 86])).
% 0.86/1.03 tff(100,plain,
% 0.86/1.03 (p12(f13(f14(c31, c28)), f13(f14(c31, c28)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.86/1.03 tff(101,plain,
% 0.86/1.03 (p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31)))) <=> p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(102,axiom,(p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_33')).
% 0.86/1.03 tff(103,plain,
% 0.86/1.03 (p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.86/1.03 tff(104,plain,
% 0.86/1.03 (^[X0: $i, X2: $i, X1: $i] : refl((p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1))) <=> (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(105,plain,
% 0.86/1.03 (![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[104])).
% 0.86/1.03 tff(106,plain,
% 0.86/1.03 (![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(107,plain,
% 0.86/1.03 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p12(X1, X2) | (~p12(X0, X1))) <=> (p12(X1, X2) | (~p12(X0, X1)))), (((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2))) <=> ((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2))))), rewrite(((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2))) <=> (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))), (((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2))) <=> (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(108,plain,
% 0.86/1.03 (![X0: $i, X2: $i, X1: $i] : ((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[107])).
% 0.86/1.03 tff(109,axiom,(![X0: $i, X2: $i, X1: $i] : ((p12(X1, X2) | (~p12(X0, X1))) | (~p12(X0, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_16')).
% 0.86/1.03 tff(110,plain,
% 0.86/1.03 (![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.86/1.03 tff(111,plain,
% 0.86/1.03 (![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.86/1.03 tff(112,plain,(
% 0.86/1.03 ![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))),
% 0.86/1.03 inference(skolemize,[status(sab)],[111])).
% 0.86/1.03 tff(113,plain,
% 0.86/1.03 (![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.86/1.03 tff(114,plain,
% 0.86/1.03 (((~![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))) | (p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))) | p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28)))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(115,plain,
% 0.86/1.03 ((p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28)))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31)))))) <=> (p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28)))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(116,plain,
% 0.86/1.03 (((~![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))) | (p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28)))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))) | (p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[115])).
% 0.86/1.03 tff(117,plain,
% 0.86/1.03 (((~![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))) | (p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28)))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))) | p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28)))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[116, 114])).
% 0.86/1.03 tff(118,plain,
% 0.86/1.03 ((~![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))) | (p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28)))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(119,plain,
% 0.86/1.03 ((~![X0: $i, X2: $i, X1: $i] : (p12(X1, X2) | (~p12(X0, X2)) | (~p12(X0, X1)))) | p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))))) | (~p12(f13(f14(c31, c28)), f13(f14(c31, c28))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.86/1.03 tff(120,plain,
% 0.86/1.03 (p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[119, 113, 103, 100])).
% 0.86/1.03 tff(121,plain,
% 0.86/1.03 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : refl(((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(122,plain,
% 0.86/1.03 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[121])).
% 0.86/1.03 tff(123,plain,
% 0.86/1.03 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(124,plain,
% 0.86/1.03 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) <=> (p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))), (((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) <=> ((p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p22(f3(f4(f5(c26))), X5))))), rewrite(((p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p22(f3(f4(f5(c26))), X5))) <=> ((~p22(f3(f4(f5(c26))), X5)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))), (((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) <=> ((~p22(f3(f4(f5(c26))), X5)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))))), ((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> (((~p22(f3(f4(f5(c26))), X5)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))))), rewrite((((~p22(f3(f4(f5(c26))), X5)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)))), ((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))))), (((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))) <=> (((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))))), rewrite((((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7))) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))), (((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))) <=> ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(125,plain,
% 0.86/1.03 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3)))))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[124])).
% 0.86/1.03 tff(126,axiom,(![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((((p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7)))) | (~p22(f3(f4(f5(c26))), X5))) | (~p23(X3, f8(f10(X4, f11(X5, X6)))))) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_42')).
% 0.86/1.03 tff(127,plain,
% 0.86/1.03 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.86/1.03 tff(128,plain,
% 0.86/1.03 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.86/1.03 tff(129,plain,(
% 0.86/1.03 ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))),
% 0.86/1.03 inference(skolemize,[status(sab)],[128])).
% 0.86/1.03 tff(130,plain,
% 0.86/1.03 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.86/1.04 tff(131,plain,
% 0.86/1.04 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))) | (p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(132,plain,
% 0.86/1.04 (((~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))) <=> (p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(133,plain,
% 0.86/1.04 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))) | (p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[132])).
% 0.86/1.04 tff(134,plain,
% 0.86/1.04 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[133, 131])).
% 0.86/1.04 tff(135,plain,
% 0.86/1.04 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(136,plain,
% 0.86/1.04 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i] : ((~p22(f3(f4(f5(c26))), X5)) | (~p23(X3, f8(f10(X4, f11(X5, X6))))) | p24(f17(f10(X4, f11(X5, X6)), f16(f10(X4, f11(X5, X6)), c32, X7))) | p12(X3, f16(f10(X4, f11(X5, X6)), c32, X7)) | (~p25(f13(f14(X7, X3)), f13(f14(X7, f21(X4, X5, X6, X7, X3))))))) | p12(c28, f16(f10(c29, f11(c27, c30)), c32, c31)) | p24(f17(f10(c29, f11(c27, c30)), f16(f10(c29, f11(c27, c30)), c32, c31))) | (~p22(f3(f4(f5(c26))), c27)) | (~p23(c28, f8(f10(c29, f11(c27, c30))))) | (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.86/1.04 tff(137,plain,
% 0.86/1.04 (~p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[136, 22, 19, 16, 13, 130])).
% 0.86/1.04 tff(138,plain,
% 0.86/1.04 (^[X67: $i, X68: $i, X66: $i, X69: $i] : refl(((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67)) <=> ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67)))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(139,plain,
% 0.86/1.04 (![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67)) <=> ![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[138])).
% 0.86/1.04 tff(140,plain,
% 0.86/1.04 (![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67)) <=> ![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(141,plain,
% 0.86/1.04 (^[X67: $i, X68: $i, X66: $i, X69: $i] : trans(monotonicity(trans(monotonicity(rewrite((p25(X66, X67) | (~p12(X69, X67))) <=> ((~p12(X69, X67)) | p25(X66, X67))), (((p25(X66, X67) | (~p12(X69, X67))) | (~p25(X68, X69))) <=> (((~p12(X69, X67)) | p25(X66, X67)) | (~p25(X68, X69))))), rewrite((((~p12(X69, X67)) | p25(X66, X67)) | (~p25(X68, X69))) <=> ((~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))), (((p25(X66, X67) | (~p12(X69, X67))) | (~p25(X68, X69))) <=> ((~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67)))), ((((p25(X66, X67) | (~p12(X69, X67))) | (~p25(X68, X69))) | (~p12(X68, X66))) <=> (((~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67)) | (~p12(X68, X66))))), rewrite((((~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67)) | (~p12(X68, X66))) <=> ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))), ((((p25(X66, X67) | (~p12(X69, X67))) | (~p25(X68, X69))) | (~p12(X68, X66))) <=> ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(142,plain,
% 0.86/1.04 (![X67: $i, X68: $i, X66: $i, X69: $i] : (((p25(X66, X67) | (~p12(X69, X67))) | (~p25(X68, X69))) | (~p12(X68, X66))) <=> ![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[141])).
% 0.86/1.04 tff(143,axiom,(![X67: $i, X68: $i, X66: $i, X69: $i] : (((p25(X66, X67) | (~p12(X69, X67))) | (~p25(X68, X69))) | (~p12(X68, X66)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p25_23')).
% 0.86/1.04 tff(144,plain,
% 0.86/1.04 (![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.86/1.04 tff(145,plain,
% 0.86/1.04 (![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.86/1.04 tff(146,plain,(
% 0.86/1.04 ![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))),
% 0.86/1.04 inference(skolemize,[status(sab)],[145])).
% 0.86/1.04 tff(147,plain,
% 0.86/1.04 (![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.86/1.04 tff(148,plain,
% 0.86/1.04 (((~![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))) | (p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))) <=> ((~![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))) | p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(149,plain,
% 0.86/1.04 (((~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) <=> (p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(150,plain,
% 0.86/1.04 (((~![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))) | ((~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))) <=> ((~![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))) | (p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[149])).
% 0.86/1.04 tff(151,plain,
% 0.86/1.04 (((~![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))) | ((~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))) <=> ((~![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))) | p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[150, 148])).
% 0.86/1.05 tff(152,plain,
% 0.86/1.05 ((~![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))) | ((~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(153,plain,
% 0.86/1.05 ((~![X67: $i, X68: $i, X66: $i, X69: $i] : ((~p12(X68, X66)) | (~p25(X68, X69)) | (~p12(X69, X67)) | p25(X66, X67))) | p25(f13(f14(c31, c28)), f13(f14(c31, f21(c29, c27, c30, c31, c28)))) | (~p12(f13(f14(c31, f21(c29, c27, c30, c31, c28))), f13(f14(c31, f21(c29, c27, c30, c31, c28))))) | (~p12(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, c28)))) | (~p25(f13(f14(c31, f16(f10(c29, f11(c27, c30)), c32, c31))), f13(f14(c31, f21(c29, c27, c30, c31, c28)))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.86/1.05 tff(154,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[153, 147, 137, 120, 91, 43])).
% 0.86/1.05 % SZS output end Proof
% 0.86/1.05 % E exiting
%------------------------------------------------------------------------------