%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN650-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:39:46 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
% 0.07/0.12 % Problem : SYN650-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 12:41:05 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(p25_type, type, (
% 0.12/0.38 p25: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f16_type, type, (
% 0.12/0.38 f16: $i > $i)).
% 0.12/0.38 tff(f17_type, type, (
% 0.12/0.38 f17: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f21_type, type, (
% 0.12/0.38 f21: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.38 tff(c33_type, type, (
% 0.12/0.38 c33: $i)).
% 0.12/0.38 tff(c32_type, type, (
% 0.12/0.38 c32: $i)).
% 0.12/0.38 tff(c30_type, type, (
% 0.12/0.38 c30: $i)).
% 0.12/0.38 tff(c27_type, type, (
% 0.12/0.38 c27: $i)).
% 0.12/0.38 tff(c29_type, type, (
% 0.12/0.38 c29: $i)).
% 0.12/0.38 tff(f13_type, type, (
% 0.12/0.38 f13: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f14_type, type, (
% 0.12/0.38 f14: $i > $i)).
% 0.12/0.38 tff(f3_type, type, (
% 0.12/0.38 f3: $i > $i)).
% 0.12/0.38 tff(f4_type, type, (
% 0.12/0.38 f4: $i > $i)).
% 0.12/0.38 tff(f5_type, type, (
% 0.12/0.38 f5: $i > $i)).
% 0.12/0.38 tff(c26_type, type, (
% 0.12/0.38 c26: $i)).
% 0.12/0.38 tff(f15_type, type, (
% 0.12/0.38 f15: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f11_type, type, (
% 0.12/0.38 f11: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f12_type, type, (
% 0.12/0.38 f12: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f9_type, type, (
% 0.12/0.38 f9: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(c31_type, type, (
% 0.12/0.38 c31: $i)).
% 0.12/0.38 tff(p24_type, type, (
% 0.12/0.38 p24: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f20_type, type, (
% 0.12/0.38 f20: $i > $i)).
% 0.12/0.38 tff(p8_type, type, (
% 0.12/0.38 p8: ( $i * $i ) > $o)).
% 0.12/0.38 tff(p23_type, type, (
% 0.12/0.38 p23: $i > $o)).
% 0.12/0.38 tff(f18_type, type, (
% 0.12/0.38 f18: ( $i * $i ) > $i)).
% 0.12/0.38 tff(p22_type, type, (
% 0.12/0.38 p22: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : refl(((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (^[X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) <=> (p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))), (((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) <=> ((p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))))), rewrite(((p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) <=> (p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))), (((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) <=> (p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))))), ((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) <=> ((p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p22(f3(f4(f5(c26))), X32))))), rewrite(((p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p22(f3(f4(f5(c26))), X32))) <=> ((~p22(f3(f4(f5(c26))), X32)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))), ((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) <=> ((~p22(f3(f4(f5(c26))), X32)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))))), (((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> (((~p22(f3(f4(f5(c26))), X32)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))))), rewrite((((~p22(f3(f4(f5(c26))), X32)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))), (((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.39 tff(6,axiom,(![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_44')).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,(
% 0.12/0.39 ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32)))) <=> (~p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(12,axiom,(~p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f18_is_not_p23_34')).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 ((~p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32))) <=> (~p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,axiom,(~p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p8_24')).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (~p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (p24(c33, f20(f11(c29, f12(c27, c30)))) <=> p24(c33, f20(f11(c29, f12(c27, c30))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(18,axiom,(p24(c33, f20(f11(c29, f12(c27, c30))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_10')).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (p24(c33, f20(f11(c29, f12(c27, c30))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (p22(f3(f4(f5(c26))), c27) <=> p22(f3(f4(f5(c26))), c27)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(21,axiom,(p22(f3(f4(f5(c26))), c27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p22_8')).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (p22(f3(f4(f5(c26))), c27)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30)))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)))) <=> ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30)))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30)))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p24(f21(X31, X32, X33, X34, X35), f20(f11(X31, f12(X32, X33)))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30)))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[25, 22, 19, 16, 13, 10])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : refl(((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35)))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35)))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35)))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (^[X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : trans(monotonicity(rewrite((p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))) | (~p22(f3(f4(f5(c26))), X32))) <=> ((~p22(f3(f4(f5(c26))), X32)) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))), (((p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> (((~p22(f3(f4(f5(c26))), X32)) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35)))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))))), rewrite((((~p22(f3(f4(f5(c26))), X32)) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35)))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))), (((p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.39 tff(32,axiom,(![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_40')).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.39 tff(35,plain,(
% 0.19/0.39 ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[34])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30))))) | p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))) <=> ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30))))) | p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30))))) | p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p25(f16(f17(X34, f9(f11(X31, f12(X32, X33)), c31, X34))), f16(f17(X34, X35))))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(f21(c29, c27, c30, c32, c33), f20(f11(c29, f12(c27, c30))))) | p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 22, 36, 26])).
% 0.19/0.40 tff(41,assumption,(~p8(f21(c29, c27, c30, c32, c33), f21(c29, c27, c30, c32, c33))), introduced(assumption)).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (^[X54: $i] : refl(p8(X54, X54) <=> p8(X54, X54))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![X54: $i] : p8(X54, X54) <=> ![X54: $i] : p8(X54, X54)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![X54: $i] : p8(X54, X54) <=> ![X54: $i] : p8(X54, X54)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(45,axiom,(![X54: $i] : p8(X54, X54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_2')).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![X54: $i] : p8(X54, X54)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.40 tff(47,plain,(
% 0.19/0.40 ![X54: $i] : p8(X54, X54)),
% 0.19/0.40 inference(skolemize,[status(sab)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![X54: $i] : p8(X54, X54)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~![X54: $i] : p8(X54, X54)) | p8(f21(c29, c27, c30, c32, c33), f21(c29, c27, c30, c32, c33))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 48, 41])).
% 0.19/0.40 tff(51,plain,(p8(f21(c29, c27, c30, c32, c33), f21(c29, c27, c30, c32, c33))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(52,assumption,(~p8(c32, c32)), introduced(assumption)).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~![X54: $i] : p8(X54, X54)) | p8(c32, c32)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 48, 52])).
% 0.19/0.40 tff(55,plain,(p8(c32, c32)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (^[X72: $i, X70: $i, X69: $i, X71: $i] : refl(((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72))) <=> ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72))) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72))) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (^[X72: $i, X70: $i, X69: $i, X71: $i] : trans(monotonicity(rewrite((p8(f17(X69, X70), f17(X71, X72)) | (~p8(X69, X71))) <=> ((~p8(X69, X71)) | p8(f17(X69, X70), f17(X71, X72)))), (((p8(f17(X69, X70), f17(X71, X72)) | (~p8(X69, X71))) | (~p8(X70, X72))) <=> (((~p8(X69, X71)) | p8(f17(X69, X70), f17(X71, X72))) | (~p8(X70, X72))))), rewrite((((~p8(X69, X71)) | p8(f17(X69, X70), f17(X71, X72))) | (~p8(X70, X72))) <=> ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))), (((p8(f17(X69, X70), f17(X71, X72)) | (~p8(X69, X71))) | (~p8(X70, X72))) <=> ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((p8(f17(X69, X70), f17(X71, X72)) | (~p8(X69, X71))) | (~p8(X70, X72))) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.40 tff(61,axiom,(![X72: $i, X70: $i, X69: $i, X71: $i] : ((p8(f17(X69, X70), f17(X71, X72)) | (~p8(X69, X71))) | (~p8(X70, X72)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_29')).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.40 tff(64,plain,(
% 0.19/0.40 ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[63])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))) | ((~p8(c32, c32)) | (~p8(f21(c29, c27, c30, c32, c33), f21(c29, c27, c30, c32, c33))) | p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33))))) <=> ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))) | (~p8(c32, c32)) | (~p8(f21(c29, c27, c30, c32, c33), f21(c29, c27, c30, c32, c33))) | p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))) | ((~p8(c32, c32)) | (~p8(f21(c29, c27, c30, c32, c33), f21(c29, c27, c30, c32, c33))) | p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))) | (~p8(c32, c32)) | (~p8(f21(c29, c27, c30, c32, c33), f21(c29, c27, c30, c32, c33))) | p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~p8(c32, c32)) | (~p8(f21(c29, c27, c30, c32, c33), f21(c29, c27, c30, c32, c33))) | p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 55, 51])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (^[X67: $i, X68: $i] : refl(((~p8(X67, X68)) | p8(f16(X67), f16(X68))) <=> ((~p8(X67, X68)) | p8(f16(X67), f16(X68))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68))) <=> ![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68))) <=> ![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (^[X67: $i, X68: $i] : rewrite((p8(f16(X67), f16(X68)) | (~p8(X67, X68))) <=> ((~p8(X67, X68)) | p8(f16(X67), f16(X68))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![X67: $i, X68: $i] : (p8(f16(X67), f16(X68)) | (~p8(X67, X68))) <=> ![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.40 tff(76,axiom,(![X67: $i, X68: $i] : (p8(f16(X67), f16(X68)) | (~p8(X67, X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_12')).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.41 tff(79,plain,(
% 0.19/0.41 ![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[78])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (((~![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))) | ((~p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33)))) | p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))) <=> ((~![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))) | (~p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33)))) | p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 ((~![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))) | ((~p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33)))) | p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 ((~![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))) | (~p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33)))) | p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ((~p8(f17(c32, f21(c29, c27, c30, c32, c33)), f17(c32, f21(c29, c27, c30, c32, c33)))) | p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[84, 70])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26)))))) <=> p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(87,axiom,(p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_38')).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (^[X43: $i, X42: $i, X41: $i, X40: $i] : refl(((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41)) <=> ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41)) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41)) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (^[X43: $i, X42: $i, X41: $i, X40: $i] : trans(monotonicity(trans(monotonicity(rewrite((p25(X40, X41) | (~p8(X42, X40))) <=> ((~p8(X42, X40)) | p25(X40, X41))), (((p25(X40, X41) | (~p8(X42, X40))) | (~p8(X43, X41))) <=> (((~p8(X42, X40)) | p25(X40, X41)) | (~p8(X43, X41))))), rewrite((((~p8(X42, X40)) | p25(X40, X41)) | (~p8(X43, X41))) <=> ((~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))), (((p25(X40, X41) | (~p8(X42, X40))) | (~p8(X43, X41))) <=> ((~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41)))), ((((p25(X40, X41) | (~p8(X42, X40))) | (~p8(X43, X41))) | (~p25(X42, X43))) <=> (((~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41)) | (~p25(X42, X43))))), rewrite((((~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41)) | (~p25(X42, X43))) <=> ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))), ((((p25(X40, X41) | (~p8(X42, X40))) | (~p8(X43, X41))) | (~p25(X42, X43))) <=> ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (![X43: $i, X42: $i, X41: $i, X40: $i] : (((p25(X40, X41) | (~p8(X42, X40))) | (~p8(X43, X41))) | (~p25(X42, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.41 tff(94,axiom,(![X43: $i, X42: $i, X41: $i, X40: $i] : (((p25(X40, X41) | (~p8(X42, X40))) | (~p8(X43, X41))) | (~p25(X42, X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_25')).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.41 tff(97,plain,(
% 0.19/0.41 ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))),
% 0.19/0.41 inference(skolemize,[status(sab)],[96])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | ((~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | (~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (((~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) <=> ((~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | ((~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | ((~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | ((~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | (~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | ((~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | (~p8(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p25(f16(f17(c32, f9(f11(c29, f12(c27, c30)), c31, c32))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 98, 88, 85, 40])).
% 0.19/0.42 tff(106,assumption,(~p8(c33, c33)), introduced(assumption)).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((~![X54: $i] : p8(X54, X54)) | p8(c33, c33)),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[107, 48, 106])).
% 0.19/0.42 tff(109,plain,(p8(c33, c33)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))) | ((~p8(c32, c32)) | (~p8(c33, c33)) | p8(f17(c32, c33), f17(c32, c33)))) <=> ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))) | (~p8(c32, c32)) | (~p8(c33, c33)) | p8(f17(c32, c33), f17(c32, c33)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))) | ((~p8(c32, c32)) | (~p8(c33, c33)) | p8(f17(c32, c33), f17(c32, c33)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p8(X69, X71)) | (~p8(X70, X72)) | p8(f17(X69, X70), f17(X71, X72)))) | (~p8(c32, c32)) | (~p8(c33, c33)) | p8(f17(c32, c33), f17(c32, c33))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 ((~p8(c32, c32)) | (~p8(c33, c33)) | p8(f17(c32, c33), f17(c32, c33))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[112, 65])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (p8(f17(c32, c33), f17(c32, c33))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[113, 55, 109])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (((~![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))) | ((~p8(f17(c32, c33), f17(c32, c33))) | p8(f16(f17(c32, c33)), f16(f17(c32, c33))))) <=> ((~![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))) | (~p8(f17(c32, c33), f17(c32, c33))) | p8(f16(f17(c32, c33)), f16(f17(c32, c33))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 ((~![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))) | ((~p8(f17(c32, c33), f17(c32, c33))) | p8(f16(f17(c32, c33)), f16(f17(c32, c33))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 ((~![X67: $i, X68: $i] : ((~p8(X67, X68)) | p8(f16(X67), f16(X68)))) | (~p8(f17(c32, c33), f17(c32, c33))) | p8(f16(f17(c32, c33)), f16(f17(c32, c33)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 ((~p8(f17(c32, c33), f17(c32, c33))) | p8(f16(f17(c32, c33)), f16(f17(c32, c33)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[117, 80])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (p8(f16(f17(c32, c33)), f16(f17(c32, c33)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[118, 114])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (p8(f16(f17(c32, c33)), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26)))))) <=> p8(f16(f17(c32, c33)), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(121,axiom,(p8(f16(f17(c32, c33)), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_35')).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (p8(f16(f17(c32, c33)), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (^[X56: $i, X55: $i, X54: $i] : refl(((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56)) <=> ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56)) <=> ![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56)) <=> ![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (^[X56: $i, X55: $i, X54: $i] : trans(monotonicity(rewrite((p8(X55, X56) | (~p8(X54, X55))) <=> ((~p8(X54, X55)) | p8(X55, X56))), (((p8(X55, X56) | (~p8(X54, X55))) | (~p8(X54, X56))) <=> (((~p8(X54, X55)) | p8(X55, X56)) | (~p8(X54, X56))))), rewrite((((~p8(X54, X55)) | p8(X55, X56)) | (~p8(X54, X56))) <=> ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))), (((p8(X55, X56) | (~p8(X54, X55))) | (~p8(X54, X56))) <=> ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (![X56: $i, X55: $i, X54: $i] : ((p8(X55, X56) | (~p8(X54, X55))) | (~p8(X54, X56))) <=> ![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.42 tff(128,axiom,(![X56: $i, X55: $i, X54: $i] : ((p8(X55, X56) | (~p8(X54, X55))) | (~p8(X54, X56)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_18')).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.19/0.42 tff(131,plain,(
% 0.19/0.42 ![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))),
% 0.19/0.42 inference(skolemize,[status(sab)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (((~![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))) | ((~p8(f16(f17(c32, c33)), f16(f17(c32, c33)))) | (~p8(f16(f17(c32, c33)), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33))))) <=> ((~![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))) | (~p8(f16(f17(c32, c33)), f16(f17(c32, c33)))) | (~p8(f16(f17(c32, c33)), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))) | ((~p8(f16(f17(c32, c33)), f16(f17(c32, c33)))) | (~p8(f16(f17(c32, c33)), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((~![X56: $i, X55: $i, X54: $i] : ((~p8(X54, X56)) | (~p8(X54, X55)) | p8(X55, X56))) | (~p8(f16(f17(c32, c33)), f16(f17(c32, c33)))) | (~p8(f16(f17(c32, c33)), f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))))) | p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 132, 122, 119])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (^[X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : refl(((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[137])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (^[X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) <=> (p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))), (((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) <=> ((p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p22(f3(f4(f5(c26))), X32))))), rewrite(((p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p22(f3(f4(f5(c26))), X32))) <=> ((~p22(f3(f4(f5(c26))), X32)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))), (((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) <=> ((~p22(f3(f4(f5(c26))), X32)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))))), ((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> (((~p22(f3(f4(f5(c26))), X32)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))))), rewrite((((~p22(f3(f4(f5(c26))), X32)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)))), ((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))))), (((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))) <=> (((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))))), rewrite((((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34))) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))), (((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))) <=> ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35)))))) <=> ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.43 tff(142,axiom,(![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((((p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34)))) | (~p22(f3(f4(f5(c26))), X32))) | (~p24(X35, f20(f11(X31, f12(X32, X33)))))) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_45')).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.19/0.43 tff(145,plain,(
% 0.19/0.43 ![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[144])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))) | (p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))) <=> ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (((~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))) <=> (p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))) <=> ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))) | (p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 (((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))) <=> ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[149, 147])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))) | ((~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(152,plain,
% 0.19/0.44 ((~![X31: $i, X32: $i, X35: $i, X34: $i, X33: $i] : ((~p22(f3(f4(f5(c26))), X32)) | (~p24(X35, f20(f11(X31, f12(X32, X33))))) | p23(f18(f11(X31, f12(X32, X33)), f9(f11(X31, f12(X32, X33)), c31, X34))) | p8(X35, f9(f11(X31, f12(X32, X33)), c31, X34)) | (~p25(f16(f17(X34, X35)), f16(f17(X34, f21(X31, X32, X33, X34, X35))))))) | p8(c33, f9(f11(c29, f12(c27, c30)), c31, c32)) | p23(f18(f11(c29, f12(c27, c30)), f9(f11(c29, f12(c27, c30)), c31, c32))) | (~p22(f3(f4(f5(c26))), c27)) | (~p24(c33, f20(f11(c29, f12(c27, c30))))) | (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.44 tff(153,plain,
% 0.19/0.44 (~p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[152, 22, 19, 16, 13, 146])).
% 0.19/0.44 tff(154,plain,
% 0.19/0.44 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | (p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | (~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | (~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(155,plain,
% 0.19/0.44 (((~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) <=> (p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | (~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(156,plain,
% 0.19/0.44 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | ((~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | (p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | (~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.44 tff(157,plain,
% 0.19/0.44 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | ((~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | (~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[156, 154])).
% 0.19/0.44 tff(158,plain,
% 0.19/0.44 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | ((~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p25(X42, X43)) | (~p8(X43, X41)) | (~p8(X42, X40)) | p25(X40, X41))) | p25(f16(f17(c32, c33)), f16(f17(c32, f21(c29, c27, c30, c32, c33)))) | (~p8(f16(f17(c32, f21(c29, c27, c30, c32, c33))), f16(f17(c32, f21(c29, c27, c30, c32, c33))))) | (~p8(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, c33)))) | (~p25(f13(f15(f11(c29, f12(c27, c30)), c32), f14(f3(f4(f5(c26))))), f16(f17(c32, f21(c29, c27, c30, c32, c33)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[159, 98, 153, 85, 136, 105])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------