TSTP Solution File: NUN087+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN087+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 : Sun Sep 18 13:27:58 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN087+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 16:28:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(r4_type, type, (
% 0.13/0.41 r4: ( $i * $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_Y24_0_type, type, (
% 0.13/0.41 tptp_fun_Y24_0: $i)).
% 0.13/0.41 tff(tptp_fun_Y8_14_type, type, (
% 0.13/0.41 tptp_fun_Y8_14: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y17_15_type, type, (
% 0.13/0.41 tptp_fun_Y17_15: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y18_16_type, type, (
% 0.13/0.41 tptp_fun_Y18_16: $i > $i)).
% 0.13/0.41 tff(r1_type, type, (
% 0.13/0.41 r1: $i > $o)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[X5: $i] : rewrite((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))) <=> (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~r1(tptp_fun_Y18_16(X5))) | (~(tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))) <=> ![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~r1(tptp_fun_Y18_16(X5))) | (~(tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (^[X5: $i] : rewrite(((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))) <=> (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (![X5: $i] : ((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))) <=> ![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(6,axiom,(![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_5a')).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.41 tff(8,plain,(
% 0.13/0.41 ![X5: $i] : ((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[7])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~r1(tptp_fun_Y18_16(X5))) | (~(tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~r1(tptp_fun_Y18_16(X5))) | (~(tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))))) | (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))) | (tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y8_14(Y24!0)),
% 0.21/0.41 inference(symmetry,[status(thm)],[14])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))) | r1(tptp_fun_Y18_16(Y24!0))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (r1(tptp_fun_Y18_16(Y24!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[16, 12])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ((r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y18_16(Y24!0)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (^[X19: $i] : trans(monotonicity(rewrite((r1(X19) & (X19 = Y24!0)) <=> (~((~r1(X19)) | (~(X19 = Y24!0))))), rewrite(((~r1(X19)) & (~(X19 = Y24!0))) <=> (~(r1(X19) | (X19 = Y24!0)))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))), rewrite(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (^[Y24: $i] : quant_intro(proof_bind(^[X19: $i] : rewrite((((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))))), (![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.41 tff(27,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.41 tff(30,plain,(
% 0.21/0.41 $oeq(![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))), ![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))))),
% 0.21/0.41 inference(transitivity,[status(sab)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[35, 32, 19])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0))) | (tptp_fun_Y18_16(Y24!0) = Y24!0)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (tptp_fun_Y18_16(Y24!0) = Y24!0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (Y24!0 = tptp_fun_Y18_16(Y24!0)),
% 0.21/0.41 inference(symmetry,[status(thm)],[38])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (Y24!0 = tptp_fun_Y8_14(Y24!0)),
% 0.21/0.41 inference(transitivity,[status(thm)],[39, 15])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))) | r1(tptp_fun_Y17_15(Y24!0))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (r1(tptp_fun_Y17_15(Y24!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[41, 12])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y17_15(Y24!0)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[47, 32, 44])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0))) | (tptp_fun_Y17_15(Y24!0) = Y24!0)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (tptp_fun_Y17_15(Y24!0) = Y24!0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (Y24!0 = tptp_fun_Y17_15(Y24!0)),
% 0.21/0.41 inference(symmetry,[status(thm)],[50])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (r4(Y24!0, Y24!0, Y24!0) <=> r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[51, 40])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0)) <=> r4(Y24!0, Y24!0, Y24!0)),
% 0.21/0.41 inference(symmetry,[status(thm)],[52])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))) | r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[54, 12])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (r4(Y24!0, Y24!0, Y24!0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 53])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 ((~$true) <=> $false),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 ((r1(Y24!0) | $true) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((Y24!0 = Y24!0) <=> $true),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.21/0.41 inference(transitivity,[status(thm)],[62, 60])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[64, 59])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[68, 59])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.21/0.41 inference(transitivity,[status(thm)],[70, 67])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[71])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.21/0.41 inference(transitivity,[status(thm)],[72, 66])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[73, 65])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.21/0.41 inference(transitivity,[status(thm)],[74, 58])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.21/0.41 inference(transitivity,[status(thm)],[76, 57])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (r1(Y24!0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[79, 32])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (^[Y1: $i, Y3: $i, Y2: $i] : rewrite((((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (![Y1: $i, Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (^[Y1: $i, Y3: $i, Y2: $i] : refl((((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3)))) <=> (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (![Y1: $i, Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y1: $i, Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (![Y1: $i] : ![Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y1: $i, Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(pull_quant,[status(thm)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (^[Y1: $i] : pull_quant((![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y1: $i] : ![Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y1: $i, Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[87, 85])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y1: $i, Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[88, 84])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (^[Y1: $i] : rewrite((![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))) <=> (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))) <=> ![Y1: $i, Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (^[Y1: $i] : rewrite((![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))) | ![Y3: $i] : (~(r1(Y3) & (Y1 = Y3)))) <=> (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (![Y1: $i] : (![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))) | ![Y3: $i] : (~(r1(Y3) & (Y1 = Y3)))) <=> ![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 ((~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))) <=> (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(96,axiom,(~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zerotimeszeroeqzero')).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[97, 95])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[100, 95])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[101, 95])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (^[Y1: $i] : nnf_neg(nnf_neg(proof_bind(^[Y2: $i] : refl($oeq((~(r1(Y2) & r4(Y2, Y2, Y1))), (~(r1(Y2) & r4(Y2, Y2, Y1)))))), $oeq((~?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1))), ![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))))), nnf_neg(proof_bind(^[Y3: $i] : refl($oeq((~(r1(Y3) & (Y1 = Y3))), (~(r1(Y3) & (Y1 = Y3)))))), $oeq((~?[Y3: $i] : (r1(Y3) & (Y1 = Y3))), ![Y3: $i] : (~(r1(Y3) & (Y1 = Y3))))), $oeq((~(?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))), (![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))) | ![Y3: $i] : (~(r1(Y3) & (Y1 = Y3))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(105,plain,(
% 0.21/0.42 ![Y1: $i] : (![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))) | ![Y3: $i] : (~(r1(Y3) & (Y1 = Y3))))),
% 0.21/0.42 inference(nnf-neg,[status(sab)],[103, 104])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[105, 94])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (![Y1: $i, Y3: $i, Y2: $i] : (((~r1(Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y3)) | (~(Y1 = Y3))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[106, 92])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[107, 82])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (((~![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))) | ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))) | (~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r1(Y24!0)) | $false) <=> ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r1(Y24!0)) | $false)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[111, 110])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (((~![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))) | ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))) | ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (((~![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))) | ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))) | (~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[113, 109])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 ((~![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))) | ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r1(Y24!0)) | (~(Y24!0 = Y24!0)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 ((~![Y1: $i, Y3: $i, Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y3)) | (~(Y1 = Y3)))) | (~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[116, 108, 80, 56])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------