TSTP Solution File: NUN069+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN069+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:27:53 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN069+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 16:04:33 EDT 2022
% 0.12/0.33 % 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(r2_type, type, (
% 0.19/0.39 r2: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y15_6_type, type, (
% 0.19/0.39 tptp_fun_Y15_6: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y24_0_type, type, (
% 0.19/0.39 tptp_fun_Y24_0: $i)).
% 0.19/0.39 tff(r3_type, type, (
% 0.19/0.39 r3: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y7_7_type, type, (
% 0.19/0.39 tptp_fun_Y7_7: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y4_4_type, type, (
% 0.19/0.39 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y5_5_type, type, (
% 0.19/0.39 tptp_fun_Y5_5: ( $i * $i ) > $i)).
% 0.19/0.39 tff(r1_type, type, (
% 0.19/0.39 r1: $i > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[X1: $i, X8: $i] : rewrite((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1))) <=> (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1))) <=> ![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[X1: $i, X8: $i] : trans(monotonicity(rewrite(((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) <=> (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)))), ((((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))) <=> ((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))), rewrite(((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))) <=> (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))), ((((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))) <=> (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![X1: $i, X8: $i] : (((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))) <=> ![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(6,axiom,(![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1a')).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.40 tff(8,plain,(
% 0.19/0.40 ![X1: $i, X8: $i] : (((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[7])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))) | (~(tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))) | (~(tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))) | (~(tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.40 tff(22,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.40 tff(25,plain,(
% 0.19/0.40 $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)))))),
% 0.19/0.40 inference(transitivity,[status(sab)],[24])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (((~![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~$true) <=> $false),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ((r1(Y24!0) | $true) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((Y24!0 = Y24!0) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.19/0.40 inference(transitivity,[status(thm)],[33, 31])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[35, 30])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[39, 30])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.19/0.40 inference(transitivity,[status(thm)],[41, 38])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.19/0.40 inference(transitivity,[status(thm)],[43, 37])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[44, 36])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.19/0.40 inference(transitivity,[status(thm)],[45, 29])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (((~![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))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~![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))),
% 0.19/0.40 inference(transitivity,[status(thm)],[47, 28])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~![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))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (r1(Y24!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[50, 27])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (^[Y1: $i, Y2: $i] : refl(((~r1(Y2)) | (~r2(Y2, Y1))) <=> ((~r1(Y2)) | (~r2(Y2, Y1))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1))) <=> ![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (^[Y1: $i, Y2: $i] : trans(monotonicity(rewrite((r1(Y2) & r2(Y2, Y1)) <=> (~((~r1(Y2)) | (~r2(Y2, Y1))))), ((~(r1(Y2) & r2(Y2, Y1))) <=> (~(~((~r1(Y2)) | (~r2(Y2, Y1))))))), rewrite((~(~((~r1(Y2)) | (~r2(Y2, Y1))))) <=> ((~r1(Y2)) | (~r2(Y2, Y1)))), ((~(r1(Y2) & r2(Y2, Y1))) <=> ((~r1(Y2)) | (~r2(Y2, Y1)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![Y1: $i, Y2: $i] : (~(r1(Y2) & r2(Y2, Y1))) <=> ![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))) <=> (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~?[Y1: $i] : ((Y1 = Y1) & ?[Y2: $i] : (r1(Y2) & r2(Y2, Y1)))) <=> (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(58,axiom,(~?[Y1: $i] : ((Y1 = Y1) & ?[Y2: $i] : (r1(Y2) & r2(Y2, Y1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','oneeqone')).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 56])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (^[Y1: $i, Y2: $i] : refl($oeq((~(r1(Y2) & r2(Y2, Y1))), (~(r1(Y2) & r2(Y2, Y1)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(67,plain,(
% 0.19/0.40 ![Y1: $i, Y2: $i] : (~(r1(Y2) & r2(Y2, Y1)))),
% 0.19/0.40 inference(nnf-neg,[status(sab)],[65, 66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 55])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 53])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (((~![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((~![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 69, 51, 14])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------