TSTP Solution File: NUN059+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 13:27:49 EDT 2022
% Result : Theorem 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.36 % Computer : n014.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri Sep 2 16:12:31 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.16/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.36 Usage: tptp [options] [-file:]file
% 0.16/0.36 -h, -? prints this message.
% 0.16/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.36 -m, -model generate model.
% 0.16/0.36 -p, -proof generate proof.
% 0.16/0.36 -c, -core generate unsat core of named formulas.
% 0.16/0.36 -st, -statistics display statistics.
% 0.16/0.36 -t:timeout set timeout (in second).
% 0.16/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.36 -<param>:<value> configuration parameter and value.
% 0.16/0.36 -o:<output-file> file to place output in.
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(r4_type, type, (
% 0.23/0.42 r4: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_Y24_0_type, type, (
% 0.23/0.42 tptp_fun_Y24_0: $i)).
% 0.23/0.42 tff(tptp_fun_Y8_14_type, type, (
% 0.23/0.42 tptp_fun_Y8_14: $i > $i)).
% 0.23/0.42 tff(tptp_fun_Y17_15_type, type, (
% 0.23/0.42 tptp_fun_Y17_15: $i > $i)).
% 0.23/0.42 tff(tptp_fun_Y18_16_type, type, (
% 0.23/0.42 tptp_fun_Y18_16: $i > $i)).
% 0.23/0.42 tff(r1_type, type, (
% 0.23/0.42 r1: $i > $o)).
% 0.23/0.42 tff(r3_type, type, (
% 0.23/0.42 r3: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_Y9_12_type, type, (
% 0.23/0.42 tptp_fun_Y9_12: $i > $i)).
% 0.23/0.42 tff(tptp_fun_Y16_13_type, type, (
% 0.23/0.42 tptp_fun_Y16_13: $i > $i)).
% 0.23/0.42 tff(1,plain,
% 0.23/0.42 (^[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))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(2,plain,
% 0.23/0.42 (![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)))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.42 tff(3,plain,
% 0.23/0.42 (^[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))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(4,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(6,axiom,(![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_5a')).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.23/0.42 tff(8,plain,(
% 0.23/0.42 ![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))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[7])).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.23/0.42 tff(10,plain,
% 0.23/0.42 (![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)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 ((~![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)))))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 (~((~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))))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (((~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))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(14,plain,
% 0.23/0.42 (tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.23/0.42 tff(15,plain,
% 0.23/0.42 (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y8_14(Y24!0)),
% 0.23/0.42 inference(symmetry,[status(thm)],[14])).
% 0.23/0.42 tff(16,plain,
% 0.23/0.42 (((~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))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 (r1(tptp_fun_Y18_16(Y24!0))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[16, 12])).
% 0.23/0.42 tff(18,plain,
% 0.23/0.42 ((r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y18_16(Y24!0)))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(19,plain,
% 0.23/0.42 (r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.23/0.42 tff(22,plain,
% 0.23/0.42 (^[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))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(23,plain,
% 0.23/0.42 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.23/0.42 tff(24,plain,
% 0.23/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(25,plain,
% 0.23/0.42 (^[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))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.23/0.42 tff(27,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.23/0.42 tff(30,plain,(
% 0.23/0.42 $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)))))),
% 0.23/0.42 inference(transitivity,[status(sab)],[29])).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.23/0.42 tff(33,plain,
% 0.23/0.42 (((~![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))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(34,plain,
% 0.23/0.42 ((~![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))))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 ((~![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.42 tff(36,plain,
% 0.23/0.42 (~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[35, 32, 19])).
% 0.23/0.42 tff(37,plain,
% 0.23/0.42 (((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0))) | (tptp_fun_Y18_16(Y24!0) = Y24!0)),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(38,plain,
% 0.23/0.42 (tptp_fun_Y18_16(Y24!0) = Y24!0),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.23/0.42 tff(39,plain,
% 0.23/0.42 (Y24!0 = tptp_fun_Y18_16(Y24!0)),
% 0.23/0.42 inference(symmetry,[status(thm)],[38])).
% 0.23/0.42 tff(40,plain,
% 0.23/0.42 (Y24!0 = tptp_fun_Y8_14(Y24!0)),
% 0.23/0.42 inference(transitivity,[status(thm)],[39, 15])).
% 0.23/0.42 tff(41,plain,
% 0.23/0.42 (((~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))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(42,plain,
% 0.23/0.42 (r1(tptp_fun_Y17_15(Y24!0))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[41, 12])).
% 0.23/0.42 tff(43,plain,
% 0.23/0.42 ((r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y17_15(Y24!0)))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(44,plain,
% 0.23/0.42 (r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.23/0.42 tff(45,plain,
% 0.23/0.42 (((~![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))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(46,plain,
% 0.23/0.42 ((~![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))))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(47,plain,
% 0.23/0.42 ((~![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)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.23/0.42 tff(48,plain,
% 0.23/0.42 (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[47, 32, 44])).
% 0.23/0.43 tff(49,plain,
% 0.23/0.43 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0))) | (tptp_fun_Y17_15(Y24!0) = Y24!0)),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(50,plain,
% 0.23/0.43 (tptp_fun_Y17_15(Y24!0) = Y24!0),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.23/0.43 tff(51,plain,
% 0.23/0.43 (Y24!0 = tptp_fun_Y17_15(Y24!0)),
% 0.23/0.43 inference(symmetry,[status(thm)],[50])).
% 0.23/0.43 tff(52,plain,
% 0.23/0.43 (r4(Y24!0, Y24!0, Y24!0) <=> r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[51, 40])).
% 0.23/0.43 tff(53,plain,
% 0.23/0.43 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0)) <=> r4(Y24!0, Y24!0, Y24!0)),
% 0.23/0.43 inference(symmetry,[status(thm)],[52])).
% 0.23/0.43 tff(54,plain,
% 0.23/0.43 (((~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))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(55,plain,
% 0.23/0.43 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[54, 12])).
% 0.23/0.43 tff(56,plain,
% 0.23/0.43 (r4(Y24!0, Y24!0, Y24!0)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[55, 53])).
% 0.23/0.43 tff(57,plain,
% 0.23/0.43 (^[X4: $i] : rewrite((r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4)) <=> (~((~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) | (~(tptp_fun_Y9_12(X4) = X4)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(58,plain,
% 0.23/0.43 (![X4: $i] : (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4)) <=> ![X4: $i] : (~((~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) | (~(tptp_fun_Y9_12(X4) = X4))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[57])).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 (^[X4: $i] : rewrite(((r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) & (tptp_fun_Y9_12(X4) = X4)) <=> (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4)))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(60,plain,
% 0.23/0.43 (![X4: $i] : ((r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) & (tptp_fun_Y9_12(X4) = X4)) <=> ![X4: $i] : (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[59])).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(62,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.23/0.43 tff(63,plain,
% 0.23/0.43 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.23/0.43 tff(64,plain,(
% 0.23/0.43 ![X4: $i] : ((r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) & (tptp_fun_Y9_12(X4) = X4))),
% 0.23/0.43 inference(skolemize,[status(sab)],[63])).
% 0.23/0.43 tff(65,plain,
% 0.23/0.43 (![X4: $i] : (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.23/0.43 tff(66,plain,
% 0.23/0.43 (![X4: $i] : (~((~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) | (~(tptp_fun_Y9_12(X4) = X4))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.23/0.43 tff(67,plain,
% 0.23/0.43 ((~![X4: $i] : (~((~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) | (~(tptp_fun_Y9_12(X4) = X4))))) | (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(68,plain,
% 0.23/0.43 (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.23/0.43 tff(69,plain,
% 0.23/0.43 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0))) | (tptp_fun_Y9_12(Y24!0) = Y24!0)),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(70,plain,
% 0.23/0.43 (tptp_fun_Y9_12(Y24!0) = Y24!0),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.23/0.43 tff(71,plain,
% 0.23/0.43 (Y24!0 = tptp_fun_Y9_12(Y24!0)),
% 0.23/0.43 inference(symmetry,[status(thm)],[70])).
% 0.23/0.43 tff(72,plain,
% 0.23/0.43 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0))) | r1(tptp_fun_Y16_13(Y24!0))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(73,plain,
% 0.23/0.43 (r1(tptp_fun_Y16_13(Y24!0))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[72, 68])).
% 0.23/0.43 tff(74,plain,
% 0.23/0.43 ((r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_13(Y24!0)))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(75,plain,
% 0.23/0.43 (r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.23/0.43 tff(76,plain,
% 0.23/0.43 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(77,plain,
% 0.23/0.43 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(78,plain,
% 0.23/0.43 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.43 tff(79,plain,
% 0.23/0.43 (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[78, 32, 75])).
% 0.23/0.43 tff(80,plain,
% 0.23/0.43 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0))) | (tptp_fun_Y16_13(Y24!0) = Y24!0)),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(81,plain,
% 0.23/0.43 (tptp_fun_Y16_13(Y24!0) = Y24!0),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.23/0.43 tff(82,plain,
% 0.23/0.43 (Y24!0 = tptp_fun_Y16_13(Y24!0)),
% 0.23/0.43 inference(symmetry,[status(thm)],[81])).
% 0.23/0.43 tff(83,plain,
% 0.23/0.43 (r3(Y24!0, Y24!0, Y24!0) <=> r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[82, 71])).
% 0.23/0.43 tff(84,plain,
% 0.23/0.43 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0)) <=> r3(Y24!0, Y24!0, Y24!0)),
% 0.23/0.43 inference(symmetry,[status(thm)],[83])).
% 0.23/0.43 tff(85,plain,
% 0.23/0.43 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0))) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(86,plain,
% 0.23/0.43 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[85, 68])).
% 0.23/0.43 tff(87,plain,
% 0.23/0.43 (r3(Y24!0, Y24!0, Y24!0)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[86, 84])).
% 0.23/0.43 tff(88,plain,
% 0.23/0.43 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : trans(monotonicity(rewrite(((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) <=> ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)))), trans(monotonicity(rewrite(((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))) <=> ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))), (((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), rewrite(((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ((~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))), (((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ((~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))), ((((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), rewrite((((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))), ((((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(89,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[88])).
% 0.23/0.43 tff(90,plain,
% 0.23/0.43 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : refl((((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(91,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[90])).
% 0.23/0.43 tff(92,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ![Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(pull_quant,[status(thm)],[])).
% 0.23/0.43 tff(93,plain,
% 0.23/0.43 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y6: $i] : pull_quant(((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ![Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), (![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ![Y6: $i] : ![Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), pull_quant(![Y6: $i] : ![Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ![Y6: $i, Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))), (![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ![Y6: $i, Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), ((![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i, Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))))), pull_quant((![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i, Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), ((![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(94,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ![Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[93])).
% 0.23/0.43 tff(95,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[94, 92])).
% 0.23/0.43 tff(96,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[95, 91])).
% 0.23/0.43 tff(97,plain,
% 0.23/0.43 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : rewrite((![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(98,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[97])).
% 0.23/0.43 tff(99,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[98, 96])).
% 0.23/0.43 tff(100,plain,
% 0.23/0.43 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : rewrite((![Y5: $i] : (~(r4(Y2, Y2, Y5) & (Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))) <=> (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(101,plain,
% 0.23/0.43 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : (~(r4(Y2, Y2, Y5) & (Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[100])).
% 0.23/0.43 tff(102,plain,
% 0.23/0.43 ((~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))) <=> (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(103,axiom,(~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fermattothepoweroftwo')).
% 0.23/0.43 tff(104,plain,
% 0.23/0.43 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.23/0.43 tff(105,plain,
% 0.23/0.43 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[104, 102])).
% 0.23/0.44 tff(106,plain,
% 0.23/0.44 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[105, 102])).
% 0.23/0.44 tff(107,plain,
% 0.23/0.44 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.23/0.44 tff(108,plain,
% 0.23/0.44 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[107, 102])).
% 0.23/0.44 tff(109,plain,
% 0.23/0.44 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[108, 102])).
% 0.23/0.44 tff(110,plain,
% 0.23/0.44 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.23/0.44 tff(111,plain,
% 0.23/0.44 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : nnf_neg(nnf_neg(proof_bind(^[Y5: $i] : refl($oeq((~(r4(Y2, Y2, Y5) & (Y4 = Y5))), (~(r4(Y2, Y2, Y5) & (Y4 = Y5)))))), $oeq((~?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5))), ![Y5: $i] : (~(r4(Y2, Y2, Y5) & (Y4 = Y5))))), nnf_neg(proof_bind(^[Y6: $i] : nnf_neg(refl($oeq((~r4(Y3, Y3, Y6)), (~r4(Y3, Y3, Y6)))), nnf_neg(proof_bind(^[Y7: $i] : refl($oeq((~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))), (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))), $oeq((~?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))), ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))), $oeq((~(r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))), ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))))), $oeq((~?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))), ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))), $oeq((~(?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))), (![Y5: $i] : (~(r4(Y2, Y2, Y5) & (Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(112,plain,(
% 0.23/0.44 ![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : (~(r4(Y2, Y2, Y5) & (Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))),
% 0.23/0.44 inference(nnf-neg,[status(sab)],[110, 111])).
% 0.23/0.44 tff(113,plain,
% 0.23/0.44 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (![Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[112, 101])).
% 0.23/0.44 tff(114,plain,
% 0.23/0.44 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : (((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5))) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[113, 99])).
% 0.23/0.44 tff(115,plain,
% 0.23/0.44 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[114, 89])).
% 0.23/0.44 tff(116,plain,
% 0.23/0.44 (((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) | ((~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(117,plain,
% 0.23/0.44 (((~r4(Y24!0, Y24!0, Y24!0)) | $false | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0))) <=> ((~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(118,plain,
% 0.23/0.44 ((~$true) <=> $false),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(119,plain,
% 0.23/0.44 ((Y24!0 = Y24!0) <=> $true),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(120,plain,
% 0.23/0.44 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.23/0.44 inference(monotonicity,[status(thm)],[119])).
% 0.23/0.44 tff(121,plain,
% 0.23/0.44 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.23/0.44 inference(transitivity,[status(thm)],[120, 118])).
% 0.23/0.44 tff(122,plain,
% 0.23/0.44 (((~r4(Y24!0, Y24!0, Y24!0)) | (~(Y24!0 = Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0))) <=> ((~r4(Y24!0, Y24!0, Y24!0)) | $false | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0)))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[121])).
% 0.23/0.44 tff(123,plain,
% 0.23/0.44 (((~r4(Y24!0, Y24!0, Y24!0)) | (~(Y24!0 = Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0))) <=> ((~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.23/0.44 inference(transitivity,[status(thm)],[122, 117])).
% 0.23/0.44 tff(124,plain,
% 0.23/0.44 (((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) | ((~r4(Y24!0, Y24!0, Y24!0)) | (~(Y24!0 = Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) | ((~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[123])).
% 0.23/0.44 tff(125,plain,
% 0.23/0.44 (((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) | ((~r4(Y24!0, Y24!0, Y24!0)) | (~(Y24!0 = Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.23/0.44 inference(transitivity,[status(thm)],[124, 116])).
% 0.23/0.44 tff(126,plain,
% 0.23/0.44 ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) | ((~r4(Y24!0, Y24!0, Y24!0)) | (~(Y24!0 = Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(127,plain,
% 0.23/0.44 ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i, Y5: $i] : ((~r4(Y2, Y2, Y5)) | (~(Y4 = Y5)) | (~r4(Y3, Y3, Y6)) | (~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.23/0.44 tff(128,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[127, 115, 87, 56])).
% 0.23/0.44 % SZS output end Proof
%------------------------------------------------------------------------------