TSTP Solution File: SYN657-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN657-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 : Thu Sep 29 23:56:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN657-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n023.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 : Mon Sep 5 06:46:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(p6_type, type, (
% 0.19/0.40 p6: ( $i * $i ) > $o)).
% 0.19/0.40 tff(c28_type, type, (
% 0.19/0.40 c28: $i)).
% 0.19/0.40 tff(f21_type, type, (
% 0.19/0.40 f21: $i > $i)).
% 0.19/0.40 tff(f8_type, type, (
% 0.19/0.40 f8: ( $i * $i ) > $i)).
% 0.19/0.40 tff(f9_type, type, (
% 0.19/0.40 f9: ( $i * $i ) > $i)).
% 0.19/0.40 tff(c29_type, type, (
% 0.19/0.40 c29: $i)).
% 0.19/0.40 tff(c27_type, type, (
% 0.19/0.40 c27: $i)).
% 0.19/0.40 tff(f10_type, type, (
% 0.19/0.40 f10: $i > $i)).
% 0.19/0.40 tff(c33_type, type, (
% 0.19/0.40 c33: $i)).
% 0.19/0.40 tff(p24_type, type, (
% 0.19/0.40 p24: ( $i * $i ) > $o)).
% 0.19/0.40 tff(f19_type, type, (
% 0.19/0.40 f19: $i > $i)).
% 0.19/0.40 tff(f20_type, type, (
% 0.19/0.40 f20: ( $i * $i ) > $i)).
% 0.19/0.40 tff(f22_type, type, (
% 0.19/0.40 f22: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(c34_type, type, (
% 0.19/0.40 c34: $i)).
% 0.19/0.40 tff(c31_type, type, (
% 0.19/0.40 c31: $i)).
% 0.19/0.40 tff(p4_type, type, (
% 0.19/0.40 p4: ( $i * $i ) > $o)).
% 0.19/0.40 tff(f5_type, type, (
% 0.19/0.40 f5: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(c36_type, type, (
% 0.19/0.40 c36: $i)).
% 0.19/0.40 tff(p25_type, type, (
% 0.19/0.40 p25: ( $i * $i ) > $o)).
% 0.19/0.40 tff(f18_type, type, (
% 0.19/0.40 f18: $i > $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[X82: $i, X83: $i, X84: $i] : refl(p6(f21(f8(X82, f9(X83, X84))), X83) <=> p6(f21(f8(X82, f9(X83, X84))), X83))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83) <=> ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83) <=> ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,axiom,(![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_15')).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.40 tff(6,plain,(
% 0.19/0.40 ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(skolemize,[status(sab)],[5])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 ((~![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)) | p6(f21(f8(c27, f9(c28, c29))), c28)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (p6(f21(f8(c27, f9(c28, c29))), c28)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,assumption,(~p6(f21(f8(c27, f9(c28, c29))), f10(c33))), introduced(assumption)).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[X25: $i, X27: $i, X26: $i] : refl((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (^[X25: $i, X27: $i, X26: $i] : trans(monotonicity(rewrite((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))))), rewrite(((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))), (((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.40 tff(16,axiom,(![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_49')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.40 tff(19,plain,(
% 0.19/0.40 ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ((~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))) <=> (~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(22,axiom,(~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p4_44')).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[26, 23, 20])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[27, 10])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (^[X25: $i, X27: $i, X26: $i] : refl((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (^[X25: $i, X27: $i, X26: $i] : trans(monotonicity(rewrite((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) <=> (p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> ((p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))))), rewrite(((p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,axiom,(![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_48')).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.41 tff(37,plain,(
% 0.19/0.41 ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[41, 23, 38])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[42, 10])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (^[X20: $i] : refl(((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))) <=> ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (^[X20: $i] : rewrite((p24(f19(f20(c31, c34)), f19(f20(c31, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29)))))) <=> ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![X20: $i] : (p24(f19(f20(c31, c34)), f19(f20(c31, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29)))))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.41 tff(49,axiom,(![X20: $i] : (p24(f19(f20(c31, c34)), f19(f20(c31, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_45')).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.41 tff(52,plain,(
% 0.19/0.41 ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))) | ((~p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))) <=> ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))) | (~p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))) | ((~p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))) | (~p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[56, 53, 43, 28])).
% 0.19/0.42 tff(58,plain,(p6(f21(f8(c27, f9(c28, c29))), f10(c33))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (^[X73: $i, X72: $i, X71: $i] : refl(((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (^[X73: $i, X72: $i, X71: $i] : trans(monotonicity(rewrite((p6(X72, X73) | (~p6(X71, X72))) <=> ((~p6(X71, X72)) | p6(X72, X73))), (((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> (((~p6(X71, X72)) | p6(X72, X73)) | (~p6(X71, X73))))), rewrite((((~p6(X71, X72)) | p6(X72, X73)) | (~p6(X71, X73))) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))), (((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (![X73: $i, X72: $i, X71: $i] : ((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.42 tff(64,axiom,(![X73: $i, X72: $i, X71: $i] : ((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_25')).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.42 tff(67,plain,(
% 0.19/0.42 ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.42 inference(skolemize,[status(sab)],[66])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 ((~p6(c28, f10(c33))) <=> (~p6(c28, f10(c33)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(70,axiom,(~p6(c28, f10(c33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p6_11')).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (~p6(c28, f10(c33))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | ((~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))) <=> ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | (~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | ((~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | (~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 71, 68, 58, 9])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------