TSTP Solution File: KRS263+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS263+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:45:21 EDT 2022
% Result : Theorem 1.04s 0.93s
% Output : Proof 1.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KRS263+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Sep 1 09:37:37 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.21/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.36 Usage: tptp [options] [-file:]file
% 0.21/0.36 -h, -? prints this message.
% 0.21/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.36 -m, -model generate model.
% 0.21/0.36 -p, -proof generate proof.
% 0.21/0.36 -c, -core generate unsat core of named formulas.
% 0.21/0.36 -st, -statistics display statistics.
% 0.21/0.36 -t:timeout set timeout (in second).
% 0.21/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.36 -<param>:<value> configuration parameter and value.
% 0.21/0.36 -o:<output-file> file to place output in.
% 1.04/0.93 % SZS status Theorem
% 1.04/0.93 % SZS output start Proof
% 1.04/0.93 tff(status_type, type, (
% 1.04/0.93 status: ( $i * $i * $i ) > $o)).
% 1.04/0.93 tff(wtc_type, type, (
% 1.04/0.93 wtc: $i)).
% 1.04/0.93 tff(nevera_type, type, (
% 1.04/0.93 nevera: ( $i * $i ) > $o)).
% 1.04/0.93 tff(tptp_fun_C_24_type, type, (
% 1.04/0.93 tptp_fun_C_24: ( $i * $i ) > $i)).
% 1.04/0.93 tff(tptp_fun_Ax_25_type, type, (
% 1.04/0.93 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 1.04/0.93 tff(model_type, type, (
% 1.04/0.93 model: ( $i * $i ) > $o)).
% 1.04/0.93 tff(tptp_fun_I1_3_type, type, (
% 1.04/0.93 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 1.04/0.93 tff(thm_type, type, (
% 1.04/0.93 thm: $i)).
% 1.04/0.93 tff(mighta_type, type, (
% 1.04/0.93 mighta: ( $i * $i ) > $o)).
% 1.04/0.93 tff(tptp_fun_C_18_type, type, (
% 1.04/0.93 tptp_fun_C_18: ( $i * $i ) > $i)).
% 1.04/0.93 tff(tptp_fun_Ax_19_type, type, (
% 1.04/0.93 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 1.04/0.93 tff(tptp_fun_I1_0_type, type, (
% 1.04/0.93 tptp_fun_I1_0: $i > $i)).
% 1.04/0.93 tff(tptp_fun_I2_8_type, type, (
% 1.04/0.93 tptp_fun_I2_8: $i > $i)).
% 1.04/0.93 tff(tptp_fun_I3_11_type, type, (
% 1.04/0.93 tptp_fun_I3_11: $i > $i)).
% 1.04/0.93 tff(tptp_fun_Ax_43_type, type, (
% 1.04/0.93 tptp_fun_Ax_43: $i)).
% 1.04/0.93 tff(tptp_fun_C_42_type, type, (
% 1.04/0.93 tptp_fun_C_42: $i)).
% 1.04/0.93 tff(tptp_fun_I1_44_type, type, (
% 1.04/0.93 tptp_fun_I1_44: $i)).
% 1.04/0.93 tff(tptp_fun_I2_45_type, type, (
% 1.04/0.93 tptp_fun_I2_45: $i)).
% 1.04/0.93 tff(tau_type, type, (
% 1.04/0.93 tau: $i)).
% 1.04/0.93 tff(tptp_fun_I1_10_type, type, (
% 1.04/0.93 tptp_fun_I1_10: ( $i * $i ) > $i)).
% 1.04/0.93 tff(tptp_fun_F_28_type, type, (
% 1.04/0.93 tptp_fun_F_28: $i)).
% 1.04/0.93 tff(1,plain,
% 1.04/0.93 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C)))))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(2,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[1])).
% 1.04/0.93 tff(3,plain,
% 1.04/0.93 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(4,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[3])).
% 1.04/0.93 tff(5,plain,
% 1.04/0.93 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(6,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[5])).
% 1.04/0.93 tff(7,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.04/0.93 inference(transitivity,[status(thm)],[6, 4])).
% 1.04/0.93 tff(8,plain,
% 1.04/0.93 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))), rewrite((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(9,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[8])).
% 1.04/0.93 tff(10,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(11,plain,
% 1.04/0.93 (^[Ax: $i, C: $i] : rewrite((![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(12,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[11])).
% 1.04/0.93 tff(13,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','thm')).
% 1.04/0.93 tff(14,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.04/0.93 tff(15,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.04/0.93 tff(16,plain,(
% 1.04/0.93 ![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))),
% 1.04/0.93 inference(skolemize,[status(sab)],[15])).
% 1.04/0.93 tff(17,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[16, 9])).
% 1.04/0.93 tff(18,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[17, 7])).
% 1.04/0.93 tff(19,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[18, 2])).
% 1.04/0.93 tff(20,plain,
% 1.04/0.93 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm))) | (~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(wtc, wtc))) | model(I1, tptp_fun_C_24(wtc, wtc)))))))),
% 1.04/0.93 inference(quant_inst,[status(thm)],[])).
% 1.04/0.93 tff(21,plain,
% 1.04/0.93 (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm))) | (~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(wtc, wtc))) | model(I1, tptp_fun_C_24(wtc, wtc))))))),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.04/0.93 tff(22,plain,
% 1.04/0.93 (((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm))) | (~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(wtc, wtc))) | model(I1, tptp_fun_C_24(wtc, wtc)))))) | ((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm))),
% 1.04/0.93 inference(tautology,[status(thm)],[])).
% 1.04/0.93 tff(23,plain,
% 1.04/0.93 ((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[22, 21])).
% 1.04/0.93 tff(24,assumption,(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)), introduced(assumption)).
% 1.04/0.93 tff(25,plain,
% 1.04/0.93 (^[S1: $i, S2: $i] : refl((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(26,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[25])).
% 1.04/0.93 tff(27,plain,
% 1.04/0.93 (^[S1: $i, S2: $i] : rewrite((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(28,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[27])).
% 1.04/0.93 tff(29,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.04/0.93 inference(transitivity,[status(thm)],[28, 26])).
% 1.04/0.93 tff(30,plain,
% 1.04/0.93 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) <=> (mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))), trans(monotonicity(rewrite((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) <=> (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))), rewrite(((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(31,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[30])).
% 1.04/0.93 tff(32,plain,
% 1.04/0.93 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))))),
% 1.04/0.93 inference(bind,[status(th)],[])).
% 1.04/0.93 tff(33,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 1.04/0.93 inference(quant_intro,[status(thm)],[32])).
% 1.04/0.93 tff(34,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(35,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','mighta')).
% 1.04/0.93 tff(36,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.04/0.93 tff(37,plain,(
% 1.04/0.93 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 1.04/0.93 inference(skolemize,[status(sab)],[36])).
% 1.04/0.93 tff(38,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[37, 33])).
% 1.04/0.93 tff(39,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[38, 31])).
% 1.04/0.93 tff(40,plain,
% 1.04/0.93 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[39, 29])).
% 1.04/0.93 tff(41,plain,
% 1.04/0.93 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm))))))))),
% 1.04/0.93 inference(quant_inst,[status(thm)],[])).
% 1.04/0.93 tff(42,plain,
% 1.04/0.93 (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)))))))),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[41, 40])).
% 1.04/0.93 tff(43,plain,
% 1.04/0.93 (((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm))))))) | (mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))),
% 1.04/0.93 inference(tautology,[status(thm)],[])).
% 1.04/0.93 tff(44,plain,
% 1.04/0.93 (mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[43, 42])).
% 1.04/0.93 tff(45,plain,
% 1.04/0.93 ((~mighta(wtc, thm)) <=> (~mighta(wtc, thm))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(46,axiom,(~mighta(wtc, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mighta_wtc_thm')).
% 1.04/0.93 tff(47,plain,
% 1.04/0.93 (~mighta(wtc, thm)),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.04/0.93 tff(48,plain,
% 1.04/0.93 ((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))),
% 1.04/0.93 inference(tautology,[status(thm)],[])).
% 1.04/0.93 tff(49,plain,
% 1.04/0.93 ((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[48, 47])).
% 1.04/0.93 tff(50,plain,
% 1.04/0.93 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[49, 44])).
% 1.04/0.93 tff(51,plain,
% 1.04/0.93 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | ((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)))),
% 1.04/0.93 inference(rewrite,[status(thm)],[])).
% 1.04/0.93 tff(52,plain,
% 1.04/0.93 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | ((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)))),
% 1.04/0.93 inference(quant_inst,[status(thm)],[])).
% 1.04/0.93 tff(53,plain,
% 1.04/0.93 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc))),
% 1.04/0.93 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.04/0.93 tff(54,plain,
% 1.04/0.93 (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)),
% 1.04/0.93 inference(unit_resolution,[status(thm)],[53, 50, 24])).
% 1.04/0.93 tff(55,plain,
% 1.04/0.93 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm)),
% 1.04/0.94 inference(tautology,[status(thm)],[])).
% 1.04/0.94 tff(56,plain,
% 1.04/0.94 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc))))),
% 1.04/0.94 inference(unit_resolution,[status(thm)],[55, 54])).
% 1.04/0.94 tff(57,plain,
% 1.04/0.94 (~((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))),
% 1.04/0.94 inference(unit_resolution,[status(thm)],[56, 23])).
% 1.04/0.94 tff(58,plain,
% 1.04/0.94 (((~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc))) | (~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc)))),
% 1.04/0.94 inference(tautology,[status(thm)],[])).
% 1.04/0.94 tff(59,plain,
% 1.04/0.94 (~model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc))),
% 1.04/0.94 inference(unit_resolution,[status(thm)],[58, 57])).
% 1.04/0.94 tff(60,plain,
% 1.04/0.94 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C)))))))))),
% 1.04/0.94 inference(bind,[status(th)],[])).
% 1.04/0.94 tff(61,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))),
% 1.04/0.94 inference(quant_intro,[status(thm)],[60])).
% 1.04/0.94 tff(62,plain,
% 1.04/0.94 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 1.04/0.94 inference(bind,[status(th)],[])).
% 1.04/0.94 tff(63,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 1.04/0.94 inference(quant_intro,[status(thm)],[62])).
% 1.04/0.94 tff(64,plain,
% 1.04/0.94 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 1.04/0.94 inference(bind,[status(th)],[])).
% 1.04/0.94 tff(65,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 1.04/0.94 inference(quant_intro,[status(thm)],[64])).
% 1.04/0.94 tff(66,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 1.04/0.94 inference(transitivity,[status(thm)],[65, 63])).
% 1.04/0.94 tff(67,plain,
% 1.04/0.94 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) <=> (status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) <=> (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))) <=> ((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, wtc))))), rewrite(((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, wtc))) <=> ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))) <=> ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))), (((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))), rewrite(((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))), (((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))))),
% 1.04/0.94 inference(bind,[status(th)],[])).
% 1.04/0.94 tff(68,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 1.04/0.94 inference(quant_intro,[status(thm)],[67])).
% 1.04/0.94 tff(69,plain,
% 1.04/0.94 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~(~model(I2, Ax))) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))))),
% 1.04/0.94 inference(bind,[status(th)],[])).
% 1.04/0.94 tff(70,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~(~model(I2, Ax))) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 1.04/0.94 inference(quant_intro,[status(thm)],[69])).
% 1.04/0.94 tff(71,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 1.04/0.94 inference(rewrite,[status(thm)],[])).
% 1.04/0.94 tff(72,plain,
% 1.04/0.94 (^[Ax: $i, C: $i] : rewrite((((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)))),
% 1.04/0.94 inference(bind,[status(th)],[])).
% 1.04/0.94 tff(73,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 1.04/0.94 inference(quant_intro,[status(thm)],[72])).
% 1.04/0.94 tff(74,axiom,(![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','wtc')).
% 1.04/0.94 tff(75,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.04/0.94 tff(76,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.04/0.94 tff(77,plain,(
% 1.04/0.94 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~(~model(I2, Ax))) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 1.04/0.94 inference(skolemize,[status(sab)],[76])).
% 1.04/0.94 tff(78,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.04/0.94 tff(79,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[78, 68])).
% 1.04/0.94 tff(80,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[79, 66])).
% 1.04/0.94 tff(81,plain,
% 1.04/0.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))),
% 1.04/0.94 inference(modus_ponens,[status(thm)],[80, 61])).
% 1.04/0.94 tff(82,plain,
% 1.04/0.94 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | (~model(tptp_fun_I3_11(tptp_fun_C_24(wtc, wtc)), tptp_fun_C_24(wtc, wtc))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_25(wtc, wtc))) | ![I2: $i] : model(I2, tptp_fun_Ax_25(wtc, wtc)))) | (~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc)))))))))),
% 1.04/0.94 inference(quant_inst,[status(thm)],[])).
% 1.04/0.94 tff(83,plain,
% 1.04/0.94 (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | (~model(tptp_fun_I3_11(tptp_fun_C_24(wtc, wtc)), tptp_fun_C_24(wtc, wtc))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_25(wtc, wtc))) | ![I2: $i] : model(I2, tptp_fun_Ax_25(wtc, wtc)))) | (~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc))))))))),
% 1.04/0.94 inference(unit_resolution,[status(thm)],[82, 81])).
% 1.04/0.94 tff(84,plain,
% 1.04/0.94 (((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | (~model(tptp_fun_I3_11(tptp_fun_C_24(wtc, wtc)), tptp_fun_C_24(wtc, wtc))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_25(wtc, wtc))) | ![I2: $i] : model(I2, tptp_fun_Ax_25(wtc, wtc)))) | (~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc)))))))) | ((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc))))))),
% 1.04/0.94 inference(tautology,[status(thm)],[])).
% 1.04/0.94 tff(85,plain,
% 1.04/0.94 ((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc)))))),
% 1.13/0.94 inference(unit_resolution,[status(thm)],[84, 83])).
% 1.13/0.94 tff(86,plain,
% 1.13/0.94 ((~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc))))))) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc)))))),
% 1.13/0.94 inference(tautology,[status(thm)],[])).
% 1.13/0.94 tff(87,plain,
% 1.13/0.94 ((~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc))))))) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc)))))),
% 1.13/0.94 inference(unit_resolution,[status(thm)],[86, 24])).
% 1.13/0.94 tff(88,plain,
% 1.13/0.94 (~(model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc))))),
% 1.13/0.94 inference(unit_resolution,[status(thm)],[87, 85])).
% 1.13/0.94 tff(89,plain,
% 1.13/0.94 ((model(tptp_fun_I2_8(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_25(wtc, wtc)), tptp_fun_Ax_25(wtc, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc)))) | ![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc))),
% 1.13/0.94 inference(tautology,[status(thm)],[])).
% 1.13/0.94 tff(90,plain,
% 1.13/0.94 (![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc))),
% 1.13/0.94 inference(unit_resolution,[status(thm)],[89, 88])).
% 1.13/0.94 tff(91,plain,
% 1.13/0.94 ((~![I3: $i] : model(I3, tptp_fun_C_24(wtc, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_24(wtc, wtc), tptp_fun_Ax_25(wtc, wtc)), tptp_fun_C_24(wtc, wtc))),
% 1.13/0.94 inference(quant_inst,[status(thm)],[])).
% 1.13/0.94 tff(92,plain,
% 1.13/0.94 ($false),
% 1.13/0.94 inference(unit_resolution,[status(thm)],[91, 90, 59])).
% 1.13/0.94 tff(93,plain,(~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)), inference(lemma,lemma(discharge,[]))).
% 1.13/0.94 tff(94,plain,
% 1.13/0.94 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))))))),
% 1.13/0.94 inference(bind,[status(th)],[])).
% 1.13/0.94 tff(95,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 1.13/0.94 inference(quant_intro,[status(thm)],[94])).
% 1.13/0.94 tff(96,plain,
% 1.13/0.94 (^[S1: $i, S2: $i] : refl((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 1.13/0.94 inference(bind,[status(th)],[])).
% 1.13/0.94 tff(97,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.13/0.94 inference(quant_intro,[status(thm)],[96])).
% 1.13/0.94 tff(98,plain,
% 1.13/0.94 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 1.13/0.94 inference(bind,[status(th)],[])).
% 1.13/0.94 tff(99,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.13/0.94 inference(quant_intro,[status(thm)],[98])).
% 1.13/0.94 tff(100,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.13/0.94 inference(transitivity,[status(thm)],[99, 97])).
% 1.13/0.94 tff(101,plain,
% 1.13/0.94 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))), rewrite((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))))),
% 1.13/0.94 inference(bind,[status(th)],[])).
% 1.13/0.94 tff(102,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.13/0.94 inference(quant_intro,[status(thm)],[101])).
% 1.13/0.94 tff(103,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.13/0.94 inference(rewrite,[status(thm)],[])).
% 1.13/0.94 tff(104,plain,
% 1.13/0.94 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)))),
% 1.13/0.94 inference(bind,[status(th)],[])).
% 1.13/0.94 tff(105,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.13/0.94 inference(quant_intro,[status(thm)],[104])).
% 1.13/0.94 tff(106,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','nevera')).
% 1.13/0.94 tff(107,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.13/0.94 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.13/0.94 tff(108,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.13/0.94 inference(modus_ponens,[status(thm)],[107, 103])).
% 1.13/0.94 tff(109,plain,(
% 1.13/0.94 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))),
% 1.13/0.94 inference(skolemize,[status(sab)],[108])).
% 1.13/0.94 tff(110,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.13/0.94 inference(modus_ponens,[status(thm)],[109, 102])).
% 1.13/0.94 tff(111,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.13/0.94 inference(modus_ponens,[status(thm)],[110, 100])).
% 1.13/0.94 tff(112,plain,
% 1.13/0.94 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 1.13/0.94 inference(modus_ponens,[status(thm)],[111, 95])).
% 1.13/0.94 tff(113,plain,
% 1.13/0.94 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc)))))))),
% 1.13/0.95 inference(rewrite,[status(thm)],[])).
% 1.13/0.95 tff(114,plain,
% 1.13/0.95 ((~((~((~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)))) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | (~status(Ax, C, wtc))))))) <=> (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc))))))),
% 1.13/0.95 inference(rewrite,[status(thm)],[])).
% 1.13/0.95 tff(115,plain,
% 1.13/0.95 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)))) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | (~status(Ax, C, wtc)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc)))))))),
% 1.13/0.95 inference(monotonicity,[status(thm)],[114])).
% 1.13/0.95 tff(116,plain,
% 1.13/0.95 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)))) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | (~status(Ax, C, wtc)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc)))))))),
% 1.13/0.95 inference(transitivity,[status(thm)],[115, 113])).
% 1.13/0.95 tff(117,plain,
% 1.13/0.95 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)) | (~status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc)))) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | (~status(Ax, C, wtc)))))))),
% 1.13/0.95 inference(quant_inst,[status(thm)],[])).
% 1.13/0.95 tff(118,plain,
% 1.13/0.95 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc))))))),
% 1.13/0.95 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.13/0.95 tff(119,plain,
% 1.13/0.95 (~((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc)))))),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[118, 112])).
% 1.13/0.95 tff(120,plain,
% 1.13/0.95 (((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc))))) | (status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))),
% 1.13/0.95 inference(tautology,[status(thm)],[])).
% 1.13/0.95 tff(121,plain,
% 1.13/0.95 (status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc)),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[120, 119])).
% 1.13/0.95 tff(122,plain,
% 1.13/0.95 ((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc)),
% 1.13/0.95 inference(tautology,[status(thm)],[])).
% 1.13/0.95 tff(123,plain,
% 1.13/0.95 (status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc)),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[122, 121])).
% 1.13/0.95 tff(124,plain,
% 1.13/0.95 (nevera(wtc, wtc)),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[123, 93])).
% 1.13/0.95 tff(125,plain,
% 1.13/0.95 (((~(status(tptp_fun_Ax_25(wtc, wtc), tptp_fun_C_24(wtc, wtc), wtc) | nevera(wtc, wtc))) | (~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc))))) | ((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc)))),
% 1.13/0.95 inference(tautology,[status(thm)],[])).
% 1.13/0.95 tff(126,plain,
% 1.13/0.95 ((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc))),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[125, 119])).
% 1.13/0.95 tff(127,plain,
% 1.13/0.95 ((~((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc)))) | (~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc))),
% 1.13/0.95 inference(tautology,[status(thm)],[])).
% 1.13/0.95 tff(128,plain,
% 1.13/0.95 ((~nevera(wtc, wtc)) | ![Ax: $i, C: $i] : (~status(Ax, C, wtc))),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.13/0.95 tff(129,plain,
% 1.13/0.95 (![Ax: $i, C: $i] : (~status(Ax, C, wtc))),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[128, 124])).
% 1.13/0.95 tff(130,assumption,(![I2: $i] : model(I2, C!42)), introduced(assumption)).
% 1.13/0.95 tff(131,plain,
% 1.13/0.95 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C)) <=> ?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 1.13/0.95 inference(rewrite,[status(thm)],[])).
% 1.13/0.95 tff(132,plain,
% 1.13/0.95 (^[I1: $i, Ax: $i, C: $i] : rewrite(((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C)) <=> (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C)))),
% 1.13/0.95 inference(bind,[status(th)],[])).
% 1.13/0.95 tff(133,plain,
% 1.13/0.95 (?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C)) <=> ?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 1.13/0.95 inference(quant_intro,[status(thm)],[132])).
% 1.13/0.95 tff(134,axiom,(?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','non_thm_spt')).
% 1.13/0.95 tff(135,plain,
% 1.13/0.95 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 1.13/0.95 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.13/0.95 tff(136,plain,
% 1.13/0.95 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 1.13/0.95 inference(modus_ponens,[status(thm)],[135, 131])).
% 1.13/0.95 tff(137,plain,
% 1.13/0.95 (~model(I1!44, C!42)),
% 1.13/0.95 inference(and_elim,[status(thm)],[136])).
% 1.13/0.95 tff(138,plain,
% 1.13/0.95 ((~![I2: $i] : model(I2, C!42)) | model(I1!44, C!42)),
% 1.13/0.95 inference(quant_inst,[status(thm)],[])).
% 1.13/0.95 tff(139,plain,
% 1.13/0.95 ($false),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[138, 137, 130])).
% 1.13/0.95 tff(140,plain,(~![I2: $i] : model(I2, C!42)), inference(lemma,lemma(discharge,[]))).
% 1.13/0.95 tff(141,assumption,(~model(tptp_fun_I3_11(Ax!43), Ax!43)), introduced(assumption)).
% 1.13/0.95 tff(142,assumption,(~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)), introduced(assumption)).
% 1.13/0.95 tff(143,assumption,(~model(tptp_fun_I3_11(F!28), F!28)), introduced(assumption)).
% 1.13/0.95 tff(144,plain,
% 1.13/0.95 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 1.13/0.95 inference(bind,[status(th)],[])).
% 1.13/0.95 tff(145,plain,
% 1.13/0.95 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 1.13/0.95 inference(quant_intro,[status(thm)],[144])).
% 1.13/0.95 tff(146,plain,
% 1.13/0.95 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 1.13/0.95 inference(rewrite,[status(thm)],[])).
% 1.13/0.95 tff(147,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','tautology')).
% 1.13/0.95 tff(148,plain,
% 1.13/0.95 (?[F: $i] : ![I: $i] : model(I, F)),
% 1.13/0.95 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.13/0.95 tff(149,plain,(
% 1.13/0.95 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 1.13/0.95 inference(transitivity,[status(sab)],[148])).
% 1.13/0.95 tff(150,plain,
% 1.13/0.95 (![I: $i] : model(I, F!28)),
% 1.13/0.95 inference(modus_ponens,[status(thm)],[149, 145])).
% 1.13/0.95 tff(151,plain,
% 1.13/0.95 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I3_11(F!28), F!28)),
% 1.13/0.95 inference(quant_inst,[status(thm)],[])).
% 1.13/0.95 tff(152,plain,
% 1.13/0.95 ($false),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[151, 150, 143])).
% 1.13/0.95 tff(153,plain,(model(tptp_fun_I3_11(F!28), F!28)), inference(lemma,lemma(discharge,[]))).
% 1.13/0.95 tff(154,plain,
% 1.13/0.95 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(Ax!43, F!28, wtc)) | (~((~model(tptp_fun_I1_0(Ax!43), Ax!43)) | model(tptp_fun_I2_8(Ax!43), Ax!43) | (~![I3: $i] : model(I3, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(Ax!43, F!28, wtc)) | (~((~model(tptp_fun_I1_0(Ax!43), Ax!43)) | model(tptp_fun_I2_8(Ax!43), Ax!43) | (~![I3: $i] : model(I3, F!28)))))))))),
% 1.13/0.95 inference(rewrite,[status(thm)],[])).
% 1.13/0.95 tff(155,plain,
% 1.13/0.95 ((~((~(status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)) | ![I1: $i] : (~model(I1, Ax!43)) | ![I2: $i] : model(I2, Ax!43))) | (~((~status(Ax!43, F!28, wtc)) | (~(model(tptp_fun_I2_8(Ax!43), Ax!43) | (~model(tptp_fun_I1_0(Ax!43), Ax!43)) | (~![I3: $i] : model(I3, F!28)))))))) <=> (~((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(Ax!43, F!28, wtc)) | (~((~model(tptp_fun_I1_0(Ax!43), Ax!43)) | model(tptp_fun_I2_8(Ax!43), Ax!43) | (~![I3: $i] : model(I3, F!28))))))))),
% 1.13/0.95 inference(rewrite,[status(thm)],[])).
% 1.13/0.95 tff(156,plain,
% 1.13/0.95 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)) | ![I1: $i] : (~model(I1, Ax!43)) | ![I2: $i] : model(I2, Ax!43))) | (~((~status(Ax!43, F!28, wtc)) | (~(model(tptp_fun_I2_8(Ax!43), Ax!43) | (~model(tptp_fun_I1_0(Ax!43), Ax!43)) | (~![I3: $i] : model(I3, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(Ax!43, F!28, wtc)) | (~((~model(tptp_fun_I1_0(Ax!43), Ax!43)) | model(tptp_fun_I2_8(Ax!43), Ax!43) | (~![I3: $i] : model(I3, F!28)))))))))),
% 1.13/0.95 inference(monotonicity,[status(thm)],[155])).
% 1.13/0.95 tff(157,plain,
% 1.13/0.95 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)) | ![I1: $i] : (~model(I1, Ax!43)) | ![I2: $i] : model(I2, Ax!43))) | (~((~status(Ax!43, F!28, wtc)) | (~(model(tptp_fun_I2_8(Ax!43), Ax!43) | (~model(tptp_fun_I1_0(Ax!43), Ax!43)) | (~![I3: $i] : model(I3, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(Ax!43, F!28, wtc)) | (~((~model(tptp_fun_I1_0(Ax!43), Ax!43)) | model(tptp_fun_I2_8(Ax!43), Ax!43) | (~![I3: $i] : model(I3, F!28)))))))))),
% 1.13/0.95 inference(transitivity,[status(thm)],[156, 154])).
% 1.13/0.95 tff(158,plain,
% 1.13/0.95 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)) | ![I1: $i] : (~model(I1, Ax!43)) | ![I2: $i] : model(I2, Ax!43))) | (~((~status(Ax!43, F!28, wtc)) | (~(model(tptp_fun_I2_8(Ax!43), Ax!43) | (~model(tptp_fun_I1_0(Ax!43), Ax!43)) | (~![I3: $i] : model(I3, F!28))))))))),
% 1.13/0.95 inference(quant_inst,[status(thm)],[])).
% 1.13/0.95 tff(159,plain,
% 1.13/0.95 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(Ax!43, F!28, wtc)) | (~((~model(tptp_fun_I1_0(Ax!43), Ax!43)) | model(tptp_fun_I2_8(Ax!43), Ax!43) | (~![I3: $i] : model(I3, F!28))))))))),
% 1.13/0.95 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.13/0.95 tff(160,plain,
% 1.13/0.95 (~((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(Ax!43, F!28, wtc)) | (~((~model(tptp_fun_I1_0(Ax!43), Ax!43)) | model(tptp_fun_I2_8(Ax!43), Ax!43) | (~![I3: $i] : model(I3, F!28)))))))),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[159, 81])).
% 1.13/0.95 tff(161,plain,
% 1.13/0.95 (((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(Ax!43, F!28, wtc)) | (~((~model(tptp_fun_I1_0(Ax!43), Ax!43)) | model(tptp_fun_I2_8(Ax!43), Ax!43) | (~![I3: $i] : model(I3, F!28))))))) | (![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))),
% 1.13/0.95 inference(tautology,[status(thm)],[])).
% 1.13/0.95 tff(162,plain,
% 1.13/0.95 (![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28))),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[161, 160])).
% 1.13/0.95 tff(163,assumption,(~model(tptp_fun_I1_3(F!28, Ax!43), F!28)), introduced(assumption)).
% 1.13/0.95 tff(164,plain,
% 1.13/0.95 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28)),
% 1.13/0.95 inference(quant_inst,[status(thm)],[])).
% 1.13/0.95 tff(165,plain,
% 1.13/0.95 ($false),
% 1.13/0.95 inference(unit_resolution,[status(thm)],[164, 150, 163])).
% 1.13/0.95 tff(166,plain,(model(tptp_fun_I1_3(F!28, Ax!43), F!28)), inference(lemma,lemma(discharge,[]))).
% 1.14/0.95 tff(167,plain,
% 1.14/0.95 (((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28)) | (~model(tptp_fun_I1_3(F!28, Ax!43), F!28))),
% 1.14/0.95 inference(tautology,[status(thm)],[])).
% 1.14/0.95 tff(168,plain,
% 1.14/0.95 ((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28)),
% 1.14/0.95 inference(unit_resolution,[status(thm)],[167, 166])).
% 1.14/0.95 tff(169,plain,
% 1.14/0.95 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28))) | status(Ax!43, F!28, thm))) | (~((~status(Ax!43, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!28))))))),
% 1.14/0.95 inference(quant_inst,[status(thm)],[])).
% 1.14/0.95 tff(170,plain,
% 1.14/0.95 (~((~((~((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28))) | status(Ax!43, F!28, thm))) | (~((~status(Ax!43, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!28)))))),
% 1.14/0.95 inference(unit_resolution,[status(thm)],[169, 19])).
% 1.14/0.95 tff(171,plain,
% 1.14/0.95 (((~((~((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28))) | status(Ax!43, F!28, thm))) | (~((~status(Ax!43, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!28))))) | ((~((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28))) | status(Ax!43, F!28, thm))),
% 1.14/0.95 inference(tautology,[status(thm)],[])).
% 1.14/0.95 tff(172,plain,
% 1.14/0.95 ((~((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28))) | status(Ax!43, F!28, thm)),
% 1.14/0.95 inference(unit_resolution,[status(thm)],[171, 170])).
% 1.14/0.95 tff(173,plain,
% 1.14/0.95 ((~((~((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28))) | status(Ax!43, F!28, thm))) | (~((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28))) | status(Ax!43, F!28, thm)),
% 1.14/0.95 inference(tautology,[status(thm)],[])).
% 1.14/0.95 tff(174,plain,
% 1.14/0.95 ((~((~model(tptp_fun_I1_3(F!28, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!28, Ax!43), F!28))) | status(Ax!43, F!28, thm)),
% 1.14/0.95 inference(unit_resolution,[status(thm)],[173, 172])).
% 1.14/0.95 tff(175,plain,
% 1.14/0.95 (status(Ax!43, F!28, thm)),
% 1.14/0.95 inference(unit_resolution,[status(thm)],[174, 168])).
% 1.14/0.95 tff(176,plain,
% 1.14/0.95 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | ((~status(Ax!43, F!28, thm)) | (~status(Ax!43, F!28, wtc)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | (~status(Ax!43, F!28, thm)) | (~status(Ax!43, F!28, wtc)))),
% 1.14/0.95 inference(rewrite,[status(thm)],[])).
% 1.14/0.95 tff(177,plain,
% 1.14/0.95 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | ((~status(Ax!43, F!28, thm)) | (~status(Ax!43, F!28, wtc)))),
% 1.14/0.95 inference(quant_inst,[status(thm)],[])).
% 1.14/0.95 tff(178,plain,
% 1.14/0.95 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | (~status(Ax!43, F!28, thm)) | (~status(Ax!43, F!28, wtc))),
% 1.14/0.95 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.14/0.95 tff(179,plain,
% 1.14/0.95 (~status(Ax!43, F!28, wtc)),
% 1.14/0.95 inference(unit_resolution,[status(thm)],[178, 50, 175])).
% 1.14/0.95 tff(180,assumption,(![I1: $i] : (~model(I1, Ax!43))), introduced(assumption)).
% 1.14/0.95 tff(181,plain,
% 1.14/0.95 (model(I1!44, Ax!43)),
% 1.14/0.95 inference(and_elim,[status(thm)],[136])).
% 1.14/0.95 tff(182,plain,
% 1.14/0.95 ((~![I1: $i] : (~model(I1, Ax!43))) | (~model(I1!44, Ax!43))),
% 1.14/0.95 inference(quant_inst,[status(thm)],[])).
% 1.14/0.95 tff(183,plain,
% 1.14/0.95 ($false),
% 1.14/0.95 inference(unit_resolution,[status(thm)],[182, 181, 180])).
% 1.14/0.95 tff(184,plain,(~![I1: $i] : (~model(I1, Ax!43))), inference(lemma,lemma(discharge,[]))).
% 1.14/0.95 tff(185,plain,
% 1.14/0.95 ((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | ![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28))),
% 1.14/0.95 inference(tautology,[status(thm)],[])).
% 1.14/0.95 tff(186,plain,
% 1.14/0.95 ((~(![I2: $i] : model(I2, Ax!43) | ![I1: $i] : (~model(I1, Ax!43)) | status(Ax!43, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | ![I2: $i] : model(I2, Ax!43) | (~model(tptp_fun_I3_11(F!28), F!28))),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[185, 184, 179])).
% 1.14/0.96 tff(187,plain,
% 1.14/0.96 (![I2: $i] : model(I2, Ax!43) | (~model(tptp_fun_I3_11(F!28), F!28))),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[186, 162])).
% 1.14/0.96 tff(188,plain,
% 1.14/0.96 (![I2: $i] : model(I2, Ax!43)),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[187, 153])).
% 1.14/0.96 tff(189,plain,
% 1.14/0.96 ((~![I2: $i] : model(I2, Ax!43)) | model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)),
% 1.14/0.96 inference(quant_inst,[status(thm)],[])).
% 1.14/0.96 tff(190,plain,
% 1.14/0.96 ($false),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[189, 188, 142])).
% 1.14/0.96 tff(191,plain,(model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)), inference(lemma,lemma(discharge,[]))).
% 1.14/0.96 tff(192,plain,
% 1.14/0.96 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))))),
% 1.14/0.96 inference(bind,[status(th)],[])).
% 1.14/0.96 tff(193,plain,
% 1.14/0.96 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.14/0.96 inference(quant_intro,[status(thm)],[192])).
% 1.14/0.96 tff(194,plain,
% 1.14/0.96 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))))),
% 1.14/0.96 inference(bind,[status(th)],[])).
% 1.14/0.96 tff(195,plain,
% 1.14/0.96 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.14/0.96 inference(quant_intro,[status(thm)],[194])).
% 1.14/0.96 tff(196,plain,
% 1.14/0.96 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.14/0.96 inference(transitivity,[status(thm)],[195, 193])).
% 1.14/0.96 tff(197,plain,
% 1.14/0.96 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C)) <=> (~((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))), ((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) <=> (~(~((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))))), rewrite((~(~((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))) <=> ((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))), ((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) <=> ((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))), (((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) <=> (((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)))), rewrite((((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) <=> (status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))), (((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) <=> (status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))), trans(monotonicity(quant_intro(proof_bind(^[I1: $i] : rewrite((model(I1, Ax) & model(I1, C)) <=> (~((~model(I1, Ax)) | (~model(I1, C)))))), (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))), ((![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau))) <=> (![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))) | (~status(Ax, C, tau))))), rewrite((![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))) | (~status(Ax, C, tau))) <=> ((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))), ((![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau))) <=> ((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))), ((((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) & (![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau)))) <=> ((status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))) & ((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))), rewrite(((status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))) & ((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))) <=> (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))), ((((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) & (![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau)))) <=> (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))))),
% 1.14/0.96 inference(bind,[status(th)],[])).
% 1.14/0.96 tff(198,plain,
% 1.14/0.96 (![Ax: $i, C: $i] : (((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) & (![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.14/0.96 inference(quant_intro,[status(thm)],[197])).
% 1.14/0.96 tff(199,plain,
% 1.14/0.96 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, tau)) <=> ![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, tau))),
% 1.14/0.96 inference(rewrite,[status(thm)],[])).
% 1.14/0.96 tff(200,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, tau))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','tau')).
% 1.14/0.96 tff(201,plain,
% 1.14/0.96 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, tau))),
% 1.14/0.96 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.14/0.96 tff(202,plain,(
% 1.14/0.96 ![Ax: $i, C: $i] : (((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) & (![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau))))),
% 1.14/0.96 inference(skolemize,[status(sab)],[201])).
% 1.14/0.96 tff(203,plain,
% 1.14/0.96 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.14/0.96 inference(modus_ponens,[status(thm)],[202, 198])).
% 1.14/0.96 tff(204,plain,
% 1.14/0.96 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.14/0.96 inference(modus_ponens,[status(thm)],[203, 196])).
% 1.14/0.96 tff(205,plain,
% 1.14/0.96 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43)))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43))))))),
% 1.14/0.96 inference(rewrite,[status(thm)],[])).
% 1.14/0.96 tff(206,plain,
% 1.14/0.96 ((~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : (~((~model(I1, Ax!43)) | (~model(I1, Ax!43)))))))) <=> (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43)))))),
% 1.14/0.96 inference(rewrite,[status(thm)],[])).
% 1.14/0.96 tff(207,plain,
% 1.14/0.96 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : (~((~model(I1, Ax!43)) | (~model(I1, Ax!43))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43))))))),
% 1.14/0.96 inference(monotonicity,[status(thm)],[206])).
% 1.14/0.96 tff(208,plain,
% 1.14/0.96 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : (~((~model(I1, Ax!43)) | (~model(I1, Ax!43))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43))))))),
% 1.14/0.96 inference(transitivity,[status(thm)],[207, 205])).
% 1.14/0.96 tff(209,plain,
% 1.14/0.96 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : (~((~model(I1, Ax!43)) | (~model(I1, Ax!43))))))))),
% 1.14/0.96 inference(quant_inst,[status(thm)],[])).
% 1.14/0.96 tff(210,plain,
% 1.14/0.96 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43)))))),
% 1.14/0.96 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.14/0.96 tff(211,plain,
% 1.14/0.96 (~((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43))))),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[210, 204])).
% 1.14/0.96 tff(212,plain,
% 1.14/0.96 (((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43)))) | (status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))),
% 1.14/0.96 inference(tautology,[status(thm)],[])).
% 1.14/0.96 tff(213,plain,
% 1.14/0.96 (status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43))),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[212, 211])).
% 1.14/0.96 tff(214,plain,
% 1.14/0.96 ((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43))),
% 1.14/0.96 inference(tautology,[status(thm)],[])).
% 1.14/0.96 tff(215,plain,
% 1.14/0.96 (status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43))),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[214, 213])).
% 1.14/0.96 tff(216,plain,
% 1.14/0.96 (status(Ax!43, Ax!43, tau)),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[215, 191])).
% 1.14/0.96 tff(217,plain,
% 1.14/0.96 (((~(status(Ax!43, Ax!43, tau) | (~model(tptp_fun_I1_10(Ax!43, Ax!43), Ax!43)))) | (~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43)))) | ((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43))),
% 1.14/0.96 inference(tautology,[status(thm)],[])).
% 1.14/0.96 tff(218,plain,
% 1.14/0.96 ((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43)),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[217, 211])).
% 1.14/0.96 tff(219,plain,
% 1.14/0.96 ((~((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43))) | (~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43)),
% 1.14/0.96 inference(tautology,[status(thm)],[])).
% 1.14/0.96 tff(220,plain,
% 1.14/0.96 ((~status(Ax!43, Ax!43, tau)) | ![I1: $i] : model(I1, Ax!43)),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[219, 218])).
% 1.14/0.96 tff(221,plain,
% 1.14/0.96 (![I1: $i] : model(I1, Ax!43)),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[220, 216])).
% 1.14/0.96 tff(222,plain,
% 1.14/0.96 ((~![I1: $i] : model(I1, Ax!43)) | model(tptp_fun_I3_11(Ax!43), Ax!43)),
% 1.14/0.96 inference(quant_inst,[status(thm)],[])).
% 1.14/0.96 tff(223,plain,
% 1.14/0.96 ($false),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[222, 221, 141])).
% 1.14/0.96 tff(224,plain,(model(tptp_fun_I3_11(Ax!43), Ax!43)), inference(lemma,lemma(discharge,[]))).
% 1.14/0.96 tff(225,assumption,(![I1: $i] : (~model(I1, C!42))), introduced(assumption)).
% 1.14/0.96 tff(226,plain,
% 1.14/0.96 (model(I2!45, C!42)),
% 1.14/0.96 inference(and_elim,[status(thm)],[136])).
% 1.14/0.96 tff(227,plain,
% 1.14/0.96 ((~![I1: $i] : (~model(I1, C!42))) | (~model(I2!45, C!42))),
% 1.14/0.96 inference(quant_inst,[status(thm)],[])).
% 1.14/0.96 tff(228,plain,
% 1.14/0.96 ($false),
% 1.14/0.96 inference(unit_resolution,[status(thm)],[227, 226, 225])).
% 1.14/0.96 tff(229,plain,(~![I1: $i] : (~model(I1, C!42))), inference(lemma,lemma(discharge,[]))).
% 1.14/0.96 tff(230,plain,
% 1.14/0.96 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, Ax!43))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, Ax!43)))))))))),
% 1.14/0.96 inference(rewrite,[status(thm)],[])).
% 1.14/0.96 tff(231,plain,
% 1.14/0.96 ((~((~(status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, Ax!43)))))))) <=> (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, Ax!43))))))))),
% 1.14/0.96 inference(rewrite,[status(thm)],[])).
% 1.14/0.96 tff(232,plain,
% 1.14/0.96 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, Ax!43))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, Ax!43)))))))))),
% 1.14/0.96 inference(monotonicity,[status(thm)],[231])).
% 1.14/0.96 tff(233,plain,
% 1.14/0.96 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, Ax!43))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, Ax!43)))))))))),
% 1.14/0.96 inference(transitivity,[status(thm)],[232, 230])).
% 1.14/0.96 tff(234,plain,
% 1.14/0.96 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, Ax!43))))))))),
% 1.14/0.96 inference(quant_inst,[status(thm)],[])).
% 1.14/0.96 tff(235,plain,
% 1.14/0.96 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, Ax!43))))))))),
% 1.14/0.97 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.14/0.97 tff(236,plain,
% 1.14/0.97 (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, Ax!43)))))))),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[235, 81])).
% 1.14/0.97 tff(237,plain,
% 1.14/0.97 (((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, Ax!43, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, Ax!43))))))) | (![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))),
% 1.14/0.97 inference(tautology,[status(thm)],[])).
% 1.14/0.97 tff(238,plain,
% 1.14/0.97 (![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42)),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[237, 236])).
% 1.14/0.97 tff(239,plain,
% 1.14/0.97 ((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42))) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42)),
% 1.14/0.97 inference(tautology,[status(thm)],[])).
% 1.14/0.97 tff(240,plain,
% 1.14/0.97 (![I1: $i] : (~model(I1, C!42)) | status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42)),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[239, 238])).
% 1.14/0.97 tff(241,plain,
% 1.14/0.97 (status(C!42, Ax!43, wtc) | (~model(tptp_fun_I3_11(Ax!43), Ax!43)) | ![I2: $i] : model(I2, C!42)),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[240, 229])).
% 1.14/0.97 tff(242,plain,
% 1.14/0.97 (status(C!42, Ax!43, wtc) | ![I2: $i] : model(I2, C!42)),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[241, 224])).
% 1.14/0.97 tff(243,plain,
% 1.14/0.97 (status(C!42, Ax!43, wtc)),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[242, 140])).
% 1.14/0.97 tff(244,plain,
% 1.14/0.97 ((~![Ax: $i, C: $i] : (~status(Ax, C, wtc))) | (~status(C!42, Ax!43, wtc))),
% 1.14/0.97 inference(quant_inst,[status(thm)],[])).
% 1.14/0.97 tff(245,plain,
% 1.14/0.97 ($false),
% 1.14/0.97 inference(unit_resolution,[status(thm)],[244, 243, 129])).
% 1.14/0.97 % SZS output end Proof
%------------------------------------------------------------------------------