TSTP Solution File: KRS215+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS215+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 17:45:13 EDT 2022
% Result : Theorem 0.85s 0.80s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS215+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 09:57:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.85/0.80 % SZS status Theorem
% 0.85/0.80 % SZS output start Proof
% 0.85/0.80 tff(status_type, type, (
% 0.85/0.80 status: ( $i * $i * $i ) > $o)).
% 0.85/0.80 tff(csa_type, type, (
% 0.85/0.80 csa: $i)).
% 0.85/0.80 tff(nevera_type, type, (
% 0.85/0.80 nevera: ( $i * $i ) > $o)).
% 0.85/0.80 tff(tptp_fun_C_24_type, type, (
% 0.85/0.80 tptp_fun_C_24: ( $i * $i ) > $i)).
% 0.85/0.80 tff(tptp_fun_Ax_25_type, type, (
% 0.85/0.80 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 0.85/0.80 tff(model_type, type, (
% 0.85/0.80 model: ( $i * $i ) > $o)).
% 0.85/0.80 tff(tptp_fun_I1_14_type, type, (
% 0.85/0.80 tptp_fun_I1_14: ( $i * $i ) > $i)).
% 0.85/0.80 tff(not_type, type, (
% 0.85/0.80 not: $i > $i)).
% 0.85/0.80 tff(thm_type, type, (
% 0.85/0.80 thm: $i)).
% 0.85/0.80 tff(tptp_fun_I1_3_type, type, (
% 0.85/0.80 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.85/0.80 tff(nota_type, type, (
% 0.85/0.80 nota: ( $i * $i ) > $o)).
% 0.85/0.80 tff(tptp_fun_C_22_type, type, (
% 0.85/0.80 tptp_fun_C_22: ( $i * $i ) > $i)).
% 0.85/0.80 tff(tptp_fun_Ax_23_type, type, (
% 0.85/0.80 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 0.85/0.80 tff(tptp_fun_F_29_type, type, (
% 0.85/0.80 tptp_fun_F_29: $i)).
% 0.85/0.80 tff(tptp_fun_Ax_43_type, type, (
% 0.85/0.80 tptp_fun_Ax_43: $i)).
% 0.85/0.80 tff(tptp_fun_I2_31_type, type, (
% 0.85/0.80 tptp_fun_I2_31: $i)).
% 0.85/0.80 tff(tptp_fun_I1_30_type, type, (
% 0.85/0.80 tptp_fun_I1_30: $i)).
% 0.85/0.80 tff(tptp_fun_C_33_type, type, (
% 0.85/0.80 tptp_fun_C_33: $i)).
% 0.85/0.80 tff(1,plain,
% 0.85/0.80 (^[I: $i, F: $i] : refl(((~model(I, F)) <=> model(I, not(F))) <=> ((~model(I, F)) <=> model(I, not(F))))),
% 0.85/0.80 inference(bind,[status(th)],[])).
% 0.85/0.80 tff(2,plain,
% 0.85/0.80 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.85/0.80 inference(quant_intro,[status(thm)],[1])).
% 0.85/0.80 tff(3,plain,
% 0.85/0.80 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.85/0.80 inference(rewrite,[status(thm)],[])).
% 0.85/0.80 tff(4,plain,
% 0.85/0.80 (^[I: $i, F: $i] : rewrite((~(model(I, F) <=> model(I, not(F)))) <=> ((~model(I, F)) <=> model(I, not(F))))),
% 0.85/0.80 inference(bind,[status(th)],[])).
% 0.85/0.80 tff(5,plain,
% 0.85/0.80 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.85/0.80 inference(quant_intro,[status(thm)],[4])).
% 0.85/0.80 tff(6,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','completeness')).
% 0.85/0.80 tff(7,plain,
% 0.85/0.80 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.85/0.80 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.85/0.80 tff(8,plain,
% 0.85/0.80 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.85/0.80 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.85/0.80 tff(9,plain,(
% 0.85/0.80 ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.85/0.80 inference(skolemize,[status(sab)],[8])).
% 0.85/0.80 tff(10,plain,
% 0.85/0.80 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 0.85/0.80 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.85/0.80 tff(11,plain,
% 0.85/0.80 ((~![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))),
% 0.85/0.80 inference(quant_inst,[status(thm)],[])).
% 0.85/0.80 tff(12,plain,
% 0.85/0.80 ((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))),
% 0.85/0.80 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.85/0.80 tff(13,plain,
% 0.85/0.80 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))))))),
% 0.85/0.80 inference(bind,[status(th)],[])).
% 0.85/0.80 tff(14,plain,
% 0.85/0.80 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))),
% 0.85/0.80 inference(quant_intro,[status(thm)],[13])).
% 0.85/0.80 tff(15,plain,
% 0.85/0.80 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))))),
% 0.85/0.80 inference(bind,[status(th)],[])).
% 0.85/0.80 tff(16,plain,
% 0.85/0.80 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.85/0.80 inference(quant_intro,[status(thm)],[15])).
% 0.85/0.80 tff(17,plain,
% 0.85/0.80 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))))),
% 0.85/0.80 inference(bind,[status(th)],[])).
% 0.85/0.80 tff(18,plain,
% 0.85/0.80 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.85/0.80 inference(quant_intro,[status(thm)],[17])).
% 0.85/0.80 tff(19,plain,
% 0.85/0.80 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.85/0.80 inference(transitivity,[status(thm)],[18, 16])).
% 0.85/0.80 tff(20,plain,
% 0.85/0.80 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) <=> (status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))), trans(monotonicity(rewrite((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) <=> (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))), (((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))) <=> ((~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))) | (~status(Ax, C, csa))))), rewrite(((~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))) | (~status(Ax, C, csa))) <=> ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))), (((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))) <=> ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))), (((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ((status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))) & ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))), rewrite(((status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))) & ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))), (((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(21,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[20])).
% 0.85/0.81 tff(22,plain,
% 0.85/0.81 (^[Ax: $i, C: $i] : rewrite(((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(23,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[22])).
% 0.85/0.81 tff(24,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa)) <=> ![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 0.85/0.81 inference(rewrite,[status(thm)],[])).
% 0.85/0.81 tff(25,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','csa')).
% 0.85/0.81 tff(26,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.85/0.81 tff(27,plain,(
% 0.85/0.81 ![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 0.85/0.81 inference(skolemize,[status(sab)],[26])).
% 0.85/0.81 tff(28,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.85/0.81 tff(29,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.85/0.81 tff(30,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.85/0.81 tff(31,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[30, 14])).
% 0.85/0.81 tff(32,plain,
% 0.85/0.81 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))))))) | (~(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | (~model(I1, not(tptp_fun_C_24(csa, csa)))))))))),
% 0.85/0.81 inference(quant_inst,[status(thm)],[])).
% 0.85/0.81 tff(33,plain,
% 0.85/0.81 (~((~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))))))) | (~(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | (~model(I1, not(tptp_fun_C_24(csa, csa))))))))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.85/0.81 tff(34,plain,
% 0.85/0.81 (((~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))))))) | (~(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | (~model(I1, not(tptp_fun_C_24(csa, csa)))))))) | ((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))))))),
% 0.85/0.81 inference(tautology,[status(thm)],[])).
% 0.85/0.81 tff(35,plain,
% 0.85/0.81 ((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.85/0.81 tff(36,assumption,(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)), introduced(assumption)).
% 0.85/0.81 tff(37,plain,
% 0.85/0.81 ((~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))))))) | (~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))))),
% 0.85/0.81 inference(tautology,[status(thm)],[])).
% 0.85/0.81 tff(38,plain,
% 0.85/0.81 ((~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))))))) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.85/0.81 tff(39,plain,
% 0.85/0.81 (~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.85/0.81 tff(40,plain,
% 0.85/0.81 (((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))) | model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))),
% 0.85/0.81 inference(tautology,[status(thm)],[])).
% 0.85/0.81 tff(41,plain,
% 0.85/0.81 (model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.85/0.81 tff(42,plain,
% 0.85/0.81 ((~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))),
% 0.85/0.81 inference(tautology,[status(thm)],[])).
% 0.85/0.81 tff(43,plain,
% 0.85/0.81 ((~((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa)))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.85/0.81 tff(44,plain,
% 0.85/0.81 (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[43, 12])).
% 0.85/0.81 tff(45,plain,
% 0.85/0.81 (^[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)))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(46,plain,
% 0.85/0.81 (![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))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[45])).
% 0.85/0.81 tff(47,plain,
% 0.85/0.81 (^[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)))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(48,plain,
% 0.85/0.81 (![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))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[47])).
% 0.85/0.81 tff(49,plain,
% 0.85/0.81 (^[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)))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(50,plain,
% 0.85/0.81 (![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))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[49])).
% 0.85/0.81 tff(51,plain,
% 0.85/0.81 (![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))))))),
% 0.85/0.81 inference(transitivity,[status(thm)],[50, 48])).
% 0.85/0.81 tff(52,plain,
% 0.85/0.81 (^[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))))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(53,plain,
% 0.85/0.81 (![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))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[52])).
% 0.85/0.81 tff(54,plain,
% 0.85/0.81 (![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))),
% 0.85/0.81 inference(rewrite,[status(thm)],[])).
% 0.85/0.81 tff(55,plain,
% 0.85/0.81 (^[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)))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(56,plain,
% 0.85/0.81 (![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))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[55])).
% 0.85/0.81 tff(57,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')).
% 0.85/0.81 tff(58,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.85/0.81 tff(59,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.85/0.81 tff(60,plain,(
% 0.85/0.81 ![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))))),
% 0.85/0.81 inference(skolemize,[status(sab)],[59])).
% 0.85/0.81 tff(61,plain,
% 0.85/0.81 (![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))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.85/0.81 tff(62,plain,
% 0.85/0.81 (![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))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.85/0.81 tff(63,plain,
% 0.85/0.81 (![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))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[62, 46])).
% 0.85/0.81 tff(64,plain,
% 0.85/0.81 ((~![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(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa)))) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm))) | (~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))))))),
% 0.85/0.81 inference(quant_inst,[status(thm)],[])).
% 0.85/0.81 tff(65,plain,
% 0.85/0.81 (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa)))) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm))) | (~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa))))))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.85/0.81 tff(66,plain,
% 0.85/0.81 (((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa)))) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm))) | (~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))))) | ((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa))))),
% 0.85/0.81 inference(tautology,[status(thm)],[])).
% 0.85/0.81 tff(67,plain,
% 0.85/0.81 ((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.85/0.81 tff(68,plain,
% 0.85/0.81 (^[S1: $i, S2: $i] : refl((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(69,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[68])).
% 0.85/0.81 tff(70,plain,
% 0.85/0.81 (^[S1: $i, S2: $i] : rewrite((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(71,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[70])).
% 0.85/0.81 tff(72,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 0.85/0.81 inference(transitivity,[status(thm)],[71, 69])).
% 0.85/0.81 tff(73,plain,
% 0.85/0.81 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) <=> (nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))), trans(monotonicity(rewrite((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) <=> (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))), rewrite(((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(74,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[73])).
% 0.85/0.81 tff(75,plain,
% 0.85/0.81 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))))),
% 0.85/0.81 inference(bind,[status(th)],[])).
% 0.85/0.81 tff(76,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 0.85/0.81 inference(quant_intro,[status(thm)],[75])).
% 0.85/0.81 tff(77,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 0.85/0.81 inference(rewrite,[status(thm)],[])).
% 0.85/0.81 tff(78,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','nota')).
% 0.85/0.81 tff(79,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.85/0.81 tff(80,plain,(
% 0.85/0.81 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 0.85/0.81 inference(skolemize,[status(sab)],[79])).
% 0.85/0.81 tff(81,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.85/0.81 tff(82,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.85/0.81 tff(83,plain,
% 0.85/0.81 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.85/0.81 tff(84,plain,
% 0.85/0.81 ((~![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))) | (~((~(nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm)))) | (~((~nota(csa, thm)) | (~((~status(tptp_fun_Ax_23(thm, csa), tptp_fun_C_22(thm, csa), csa)) | status(tptp_fun_Ax_23(thm, csa), tptp_fun_C_22(thm, csa), thm)))))))),
% 0.85/0.81 inference(quant_inst,[status(thm)],[])).
% 0.85/0.81 tff(85,plain,
% 0.85/0.81 (~((~(nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm)))) | (~((~nota(csa, thm)) | (~((~status(tptp_fun_Ax_23(thm, csa), tptp_fun_C_22(thm, csa), csa)) | status(tptp_fun_Ax_23(thm, csa), tptp_fun_C_22(thm, csa), thm))))))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.85/0.81 tff(86,plain,
% 0.85/0.81 (((~(nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm)))) | (~((~nota(csa, thm)) | (~((~status(tptp_fun_Ax_23(thm, csa), tptp_fun_C_22(thm, csa), csa)) | status(tptp_fun_Ax_23(thm, csa), tptp_fun_C_22(thm, csa), thm)))))) | (nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm)))),
% 0.85/0.81 inference(tautology,[status(thm)],[])).
% 0.85/0.81 tff(87,plain,
% 0.85/0.81 (nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.85/0.81 tff(88,plain,
% 0.85/0.81 ((~nota(csa, thm)) <=> (~nota(csa, thm))),
% 0.85/0.81 inference(rewrite,[status(thm)],[])).
% 0.85/0.81 tff(89,axiom,(~nota(csa, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nota_csa_thm')).
% 0.85/0.81 tff(90,plain,
% 0.85/0.81 (~nota(csa, thm)),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.85/0.81 tff(91,plain,
% 0.85/0.81 ((~(nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm)))) | nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))),
% 0.85/0.81 inference(tautology,[status(thm)],[])).
% 0.85/0.81 tff(92,plain,
% 0.85/0.81 ((~(nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.85/0.81 tff(93,plain,
% 0.85/0.81 (![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[92, 87])).
% 0.85/0.81 tff(94,plain,
% 0.85/0.81 (((~![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm))),
% 0.85/0.81 inference(rewrite,[status(thm)],[])).
% 0.85/0.81 tff(95,plain,
% 0.85/0.81 ((~![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm))),
% 0.85/0.81 inference(quant_inst,[status(thm)],[])).
% 0.85/0.81 tff(96,plain,
% 0.85/0.81 ((~![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)),
% 0.85/0.81 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.85/0.81 tff(97,plain,
% 0.85/0.81 (status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)),
% 0.85/0.81 inference(unit_resolution,[status(thm)],[96, 93, 36])).
% 0.85/0.81 tff(98,plain,
% 0.85/0.81 ((~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa))))) | (~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))),
% 0.85/0.81 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(99,plain,
% 0.85/0.82 ((~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa))))) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.85/0.82 tff(100,plain,
% 0.85/0.82 (![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[99, 67])).
% 0.85/0.82 tff(101,plain,
% 0.85/0.82 (((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa))))) | model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(102,plain,
% 0.85/0.82 (model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[101, 39])).
% 0.85/0.82 tff(103,plain,
% 0.85/0.82 (((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa)))) <=> ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa)))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(104,plain,
% 0.85/0.82 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa)))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(105,plain,
% 0.85/0.82 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.85/0.82 tff(106,plain,
% 0.85/0.82 ($false),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[105, 102, 100, 44])).
% 0.85/0.82 tff(107,plain,(~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)), inference(lemma,lemma(discharge,[]))).
% 0.85/0.82 tff(108,plain,
% 0.85/0.82 (^[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))))))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(109,plain,
% 0.85/0.82 (![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)))))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[108])).
% 0.85/0.82 tff(110,plain,
% 0.85/0.82 (^[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)))))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(111,plain,
% 0.85/0.82 (![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))))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[110])).
% 0.85/0.82 tff(112,plain,
% 0.85/0.82 (^[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)))))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(113,plain,
% 0.85/0.82 (![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))))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[112])).
% 0.85/0.82 tff(114,plain,
% 0.85/0.82 (![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))))))),
% 0.85/0.82 inference(transitivity,[status(thm)],[113, 111])).
% 0.85/0.82 tff(115,plain,
% 0.85/0.82 (^[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))))))))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(116,plain,
% 0.85/0.82 (![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))))))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[115])).
% 0.85/0.82 tff(117,plain,
% 0.85/0.82 (![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))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(118,plain,
% 0.85/0.82 (^[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)))),
% 0.85/0.82 inference(bind,[status(th)],[])).
% 0.85/0.82 tff(119,plain,
% 0.85/0.82 (![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))),
% 0.85/0.82 inference(quant_intro,[status(thm)],[118])).
% 0.85/0.82 tff(120,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')).
% 0.85/0.82 tff(121,plain,
% 0.85/0.82 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.85/0.82 tff(122,plain,
% 0.85/0.82 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.85/0.82 tff(123,plain,(
% 0.85/0.82 ![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))))),
% 0.85/0.82 inference(skolemize,[status(sab)],[122])).
% 0.85/0.82 tff(124,plain,
% 0.85/0.82 (![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))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.85/0.82 tff(125,plain,
% 0.85/0.82 (![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))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[124, 114])).
% 0.85/0.82 tff(126,plain,
% 0.85/0.82 (![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)))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[125, 109])).
% 0.85/0.82 tff(127,plain,
% 0.85/0.82 (((~![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(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))))) <=> ((~![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(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(128,plain,
% 0.85/0.82 ((~((~((~((~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)))) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | (~status(Ax, C, csa))))))) <=> (~((~(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(129,plain,
% 0.85/0.82 (((~![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(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)))) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | (~status(Ax, C, csa)))))))) <=> ((~![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(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))))))),
% 0.85/0.82 inference(monotonicity,[status(thm)],[128])).
% 0.85/0.82 tff(130,plain,
% 0.85/0.82 (((~![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(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)))) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | (~status(Ax, C, csa)))))))) <=> ((~![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(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))))))),
% 0.85/0.82 inference(transitivity,[status(thm)],[129, 127])).
% 0.85/0.82 tff(131,plain,
% 0.85/0.82 ((~![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(csa, csa), tptp_fun_C_24(csa, csa), csa)) | (~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)))) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | (~status(Ax, C, csa)))))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(132,plain,
% 0.85/0.82 ((~![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(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.85/0.82 tff(133,plain,
% 0.85/0.82 (~((~(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[132, 126])).
% 0.85/0.82 tff(134,plain,
% 0.85/0.82 (((~(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))) | (status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(135,plain,
% 0.85/0.82 (status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa)),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.85/0.82 tff(136,plain,
% 0.85/0.82 ((~(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa)),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(137,plain,
% 0.85/0.82 (status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa)),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.85/0.82 tff(138,plain,
% 0.85/0.82 (nevera(csa, csa)),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[137, 107])).
% 0.85/0.82 tff(139,plain,
% 0.85/0.82 (((~(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa) | nevera(csa, csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))) | ((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(140,plain,
% 0.85/0.82 ((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[139, 133])).
% 0.85/0.82 tff(141,plain,
% 0.85/0.82 ((~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))) | (~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(142,plain,
% 0.85/0.82 ((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.85/0.82 tff(143,plain,
% 0.85/0.82 (![Ax: $i, C: $i] : (~status(Ax, C, csa))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[142, 138])).
% 0.85/0.82 tff(144,assumption,(~((~model(I2!31, F!29)) <=> model(I2!31, not(F!29)))), introduced(assumption)).
% 0.85/0.82 tff(145,plain,
% 0.85/0.82 ((~![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))) | ((~model(I2!31, F!29)) <=> model(I2!31, not(F!29)))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(146,plain,
% 0.85/0.82 ($false),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[145, 10, 144])).
% 0.85/0.82 tff(147,plain,((~model(I2!31, F!29)) <=> model(I2!31, not(F!29))), inference(lemma,lemma(discharge,[]))).
% 0.85/0.82 tff(148,plain,
% 0.85/0.82 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(149,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 0.85/0.82 tff(150,plain,
% 0.85/0.82 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 0.85/0.82 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.85/0.82 tff(151,plain,
% 0.85/0.82 (~model(I2!31, F!29)),
% 0.85/0.82 inference(and_elim,[status(thm)],[150])).
% 0.85/0.82 tff(152,plain,
% 0.85/0.82 ((~((~model(I2!31, F!29)) <=> model(I2!31, not(F!29)))) | model(I2!31, F!29) | model(I2!31, not(F!29))),
% 0.85/0.82 inference(tautology,[status(thm)],[])).
% 0.85/0.82 tff(153,plain,
% 0.85/0.82 ((~((~model(I2!31, F!29)) <=> model(I2!31, not(F!29)))) | model(I2!31, not(F!29))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.85/0.82 tff(154,plain,
% 0.85/0.82 (model(I2!31, not(F!29))),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[153, 147])).
% 0.85/0.82 tff(155,assumption,(status(not(C!33), C!33, csa)), introduced(assumption)).
% 0.85/0.82 tff(156,plain,
% 0.85/0.82 ((~![Ax: $i, C: $i] : (~status(Ax, C, csa))) | (~status(not(C!33), C!33, csa))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(157,plain,
% 0.85/0.82 ($false),
% 0.85/0.82 inference(unit_resolution,[status(thm)],[156, 143, 155])).
% 0.85/0.82 tff(158,plain,(~status(not(C!33), C!33, csa)), inference(lemma,lemma(discharge,[]))).
% 0.85/0.82 tff(159,plain,
% 0.85/0.82 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(not(C!33), C!33, csa)) | model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33)))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(not(C!33), C!33, csa)) | model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33)))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33))))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(160,plain,
% 0.85/0.82 ((~((~((~status(not(C!33), C!33, csa)) | (~((~model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33))) | (~model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33))))))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, not(C!33)))))))) <=> (~((~((~status(not(C!33), C!33, csa)) | model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33)))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33)))))))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(161,plain,
% 0.85/0.82 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(not(C!33), C!33, csa)) | (~((~model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33))) | (~model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33))))))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, not(C!33))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(not(C!33), C!33, csa)) | model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33)))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33))))))))),
% 0.85/0.82 inference(monotonicity,[status(thm)],[160])).
% 0.85/0.82 tff(162,plain,
% 0.85/0.82 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(not(C!33), C!33, csa)) | (~((~model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33))) | (~model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33))))))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, not(C!33))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(not(C!33), C!33, csa)) | model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33)))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33))))))))),
% 0.85/0.82 inference(transitivity,[status(thm)],[161, 159])).
% 0.85/0.82 tff(163,plain,
% 0.85/0.82 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(not(C!33), C!33, csa)) | (~((~model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33))) | (~model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33))))))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, not(C!33))))))))),
% 0.85/0.82 inference(quant_inst,[status(thm)],[])).
% 0.85/0.82 tff(164,plain,
% 0.85/0.82 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(not(C!33), C!33, csa)) | model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33)))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33)))))))),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.93/0.82 tff(165,plain,
% 0.93/0.82 (~((~((~status(not(C!33), C!33, csa)) | model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33)))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33))))))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[164, 31])).
% 0.93/0.82 tff(166,plain,
% 0.93/0.82 (((~((~status(not(C!33), C!33, csa)) | model(tptp_fun_I1_14(C!33, not(C!33)), not(C!33)))) | (~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33)))))) | (status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33))))),
% 0.93/0.82 inference(tautology,[status(thm)],[])).
% 0.93/0.82 tff(167,plain,
% 0.93/0.82 (status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33)))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.93/0.82 tff(168,plain,
% 0.93/0.82 ((~(status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33))))) | status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33)))),
% 0.93/0.82 inference(tautology,[status(thm)],[])).
% 0.93/0.82 tff(169,plain,
% 0.93/0.82 (status(not(C!33), C!33, csa) | ![I1: $i] : (~model(I1, not(C!33)))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.93/0.82 tff(170,plain,
% 0.93/0.82 (![I1: $i] : (~model(I1, not(C!33)))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[169, 158])).
% 0.93/0.82 tff(171,plain,
% 0.93/0.82 ((~![I1: $i] : (~model(I1, not(C!33)))) | (~model(I2!31, not(C!33)))),
% 0.93/0.82 inference(quant_inst,[status(thm)],[])).
% 0.93/0.82 tff(172,plain,
% 0.93/0.82 (~model(I2!31, not(C!33))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.93/0.82 tff(173,plain,
% 0.93/0.82 (^[I: $i, F: $i] : refl((model(I, F) <=> (~model(I, not(F)))) <=> (model(I, F) <=> (~model(I, not(F)))))),
% 0.93/0.82 inference(bind,[status(th)],[])).
% 0.93/0.82 tff(174,plain,
% 0.93/0.82 (![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F)))) <=> ![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F))))),
% 0.93/0.82 inference(quant_intro,[status(thm)],[173])).
% 0.93/0.82 tff(175,plain,
% 0.93/0.82 (![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F)))) <=> ![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F))))),
% 0.93/0.82 inference(rewrite,[status(thm)],[])).
% 0.93/0.82 tff(176,axiom,(![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F))))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','not')).
% 0.93/0.82 tff(177,plain,
% 0.93/0.82 (![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F))))),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.93/0.82 tff(178,plain,(
% 0.93/0.82 ![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F))))),
% 0.93/0.82 inference(skolemize,[status(sab)],[177])).
% 0.93/0.82 tff(179,plain,
% 0.93/0.82 (![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F))))),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.93/0.82 tff(180,plain,
% 0.93/0.82 ((~![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F))))) | (model(I2!31, C!33) <=> (~model(I2!31, not(C!33))))),
% 0.93/0.82 inference(quant_inst,[status(thm)],[])).
% 0.93/0.82 tff(181,plain,
% 0.93/0.82 (model(I2!31, C!33) <=> (~model(I2!31, not(C!33)))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.93/0.82 tff(182,plain,
% 0.93/0.82 ((~(model(I2!31, C!33) <=> (~model(I2!31, not(C!33))))) | model(I2!31, C!33) | model(I2!31, not(C!33))),
% 0.93/0.82 inference(tautology,[status(thm)],[])).
% 0.93/0.82 tff(183,plain,
% 0.93/0.82 (model(I2!31, C!33) | model(I2!31, not(C!33))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.93/0.82 tff(184,plain,
% 0.93/0.82 (model(I2!31, C!33)),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[183, 172])).
% 0.93/0.82 tff(185,assumption,(~((~model(tptp_fun_I1_3(Ax!43, C!33), Ax!43)) <=> model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43)))), introduced(assumption)).
% 0.93/0.82 tff(186,plain,
% 0.93/0.82 ((~![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))) | ((~model(tptp_fun_I1_3(Ax!43, C!33), Ax!43)) <=> model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43)))),
% 0.93/0.82 inference(quant_inst,[status(thm)],[])).
% 0.93/0.82 tff(187,plain,
% 0.93/0.82 ($false),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[186, 10, 185])).
% 0.93/0.82 tff(188,plain,((~model(tptp_fun_I1_3(Ax!43, C!33), Ax!43)) <=> model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43))), inference(lemma,lemma(discharge,[]))).
% 0.93/0.83 tff(189,assumption,(~status(C!33, Ax!43, thm)), introduced(assumption)).
% 0.93/0.83 tff(190,plain,
% 0.93/0.83 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(C!33, Ax!43, csa)) | (~((~model(tptp_fun_I1_14(Ax!43, C!33), C!33)) | (~model(tptp_fun_I1_14(Ax!43, C!33), not(Ax!43))))))) | (~(status(C!33, Ax!43, csa) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))))))),
% 0.93/0.83 inference(quant_inst,[status(thm)],[])).
% 0.93/0.83 tff(191,plain,
% 0.93/0.83 (~((~((~status(C!33, Ax!43, csa)) | (~((~model(tptp_fun_I1_14(Ax!43, C!33), C!33)) | (~model(tptp_fun_I1_14(Ax!43, C!33), not(Ax!43))))))) | (~(status(C!33, Ax!43, csa) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43)))))))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[190, 31])).
% 0.93/0.83 tff(192,plain,
% 0.93/0.83 (((~((~status(C!33, Ax!43, csa)) | (~((~model(tptp_fun_I1_14(Ax!43, C!33), C!33)) | (~model(tptp_fun_I1_14(Ax!43, C!33), not(Ax!43))))))) | (~(status(C!33, Ax!43, csa) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))))) | (status(C!33, Ax!43, csa) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43)))))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(193,plain,
% 0.93/0.83 (status(C!33, Ax!43, csa) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.93/0.83 tff(194,plain,
% 0.93/0.83 (((~![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))) | ((~status(C!33, Ax!43, csa)) | status(C!33, Ax!43, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))) | (~status(C!33, Ax!43, csa)) | status(C!33, Ax!43, thm))),
% 0.93/0.83 inference(rewrite,[status(thm)],[])).
% 0.93/0.83 tff(195,plain,
% 0.93/0.83 ((~![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))) | ((~status(C!33, Ax!43, csa)) | status(C!33, Ax!43, thm))),
% 0.93/0.83 inference(quant_inst,[status(thm)],[])).
% 0.93/0.83 tff(196,plain,
% 0.93/0.83 ((~![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))) | (~status(C!33, Ax!43, csa)) | status(C!33, Ax!43, thm)),
% 0.93/0.83 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.93/0.83 tff(197,plain,
% 0.93/0.83 (~status(C!33, Ax!43, csa)),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[196, 93, 189])).
% 0.93/0.83 tff(198,plain,
% 0.93/0.83 ((~(status(C!33, Ax!43, csa) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43)))))) | status(C!33, Ax!43, csa) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(199,plain,
% 0.93/0.83 ((~(status(C!33, Ax!43, csa) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43)))))) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.93/0.83 tff(200,plain,
% 0.93/0.83 (![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[199, 193])).
% 0.93/0.83 tff(201,assumption,(model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43))), introduced(assumption)).
% 0.93/0.83 tff(202,plain,
% 0.93/0.83 ((~![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(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm))) | (~((~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))))))),
% 0.93/0.83 inference(quant_inst,[status(thm)],[])).
% 0.93/0.83 tff(203,plain,
% 0.93/0.83 (~((~((~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm))) | (~((~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43)))))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[202, 63])).
% 0.93/0.83 tff(204,plain,
% 0.93/0.83 (((~((~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm))) | (~((~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))))) | ((~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(205,plain,
% 0.93/0.83 ((~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm)),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.93/0.83 tff(206,plain,
% 0.93/0.83 ((~((~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm))) | (~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm)),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(207,plain,
% 0.93/0.83 ((~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm)),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.93/0.83 tff(208,plain,
% 0.93/0.83 (~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[207, 189])).
% 0.93/0.83 tff(209,plain,
% 0.93/0.83 (((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43)) | model(tptp_fun_I1_3(Ax!43, C!33), C!33)),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(210,plain,
% 0.93/0.83 (model(tptp_fun_I1_3(Ax!43, C!33), C!33)),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.93/0.83 tff(211,plain,
% 0.93/0.83 (((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))) | ((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | (~model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43))))) <=> ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))) | (~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | (~model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43))))),
% 0.93/0.83 inference(rewrite,[status(thm)],[])).
% 0.93/0.83 tff(212,plain,
% 0.93/0.83 ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))) | ((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | (~model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43))))),
% 0.93/0.83 inference(quant_inst,[status(thm)],[])).
% 0.93/0.83 tff(213,plain,
% 0.93/0.83 ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, not(Ax!43))))) | (~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | (~model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43)))),
% 0.93/0.83 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.93/0.83 tff(214,plain,
% 0.93/0.83 ($false),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[213, 210, 201, 200])).
% 0.93/0.83 tff(215,plain,(status(C!33, Ax!43, thm) | (~model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43)))), inference(lemma,lemma(discharge,[]))).
% 0.93/0.83 tff(216,plain,
% 0.93/0.83 (~model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[215, 189])).
% 0.93/0.83 tff(217,plain,
% 0.93/0.83 (((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43)) | (~model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(218,plain,
% 0.93/0.83 (~model(tptp_fun_I1_3(Ax!43, C!33), Ax!43)),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[217, 208])).
% 0.93/0.83 tff(219,plain,
% 0.93/0.83 ((~((~model(tptp_fun_I1_3(Ax!43, C!33), Ax!43)) <=> model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43)))) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43) | model(tptp_fun_I1_3(Ax!43, C!33), not(Ax!43))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(220,plain,
% 0.93/0.83 ($false),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[219, 218, 216, 188])).
% 0.93/0.83 tff(221,plain,(status(C!33, Ax!43, thm)), inference(lemma,lemma(discharge,[]))).
% 0.93/0.83 tff(222,plain,
% 0.93/0.83 (((~((~((~model(tptp_fun_I1_3(Ax!43, C!33), C!33)) | model(tptp_fun_I1_3(Ax!43, C!33), Ax!43))) | status(C!33, Ax!43, thm))) | (~((~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))))) | ((~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43)))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(223,plain,
% 0.93/0.83 ((~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[222, 203])).
% 0.93/0.83 tff(224,plain,
% 0.93/0.83 ((~((~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43)))) | (~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(225,plain,
% 0.93/0.83 ((~status(C!33, Ax!43, thm)) | ![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.93/0.83 tff(226,plain,
% 0.93/0.83 (![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[225, 221])).
% 0.93/0.83 tff(227,plain,
% 0.93/0.83 (((~![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))) | ((~model(I2!31, C!33)) | model(I2!31, Ax!43))) <=> ((~![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))) | (~model(I2!31, C!33)) | model(I2!31, Ax!43))),
% 0.93/0.83 inference(rewrite,[status(thm)],[])).
% 0.93/0.83 tff(228,plain,
% 0.93/0.83 ((~![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))) | ((~model(I2!31, C!33)) | model(I2!31, Ax!43))),
% 0.93/0.83 inference(quant_inst,[status(thm)],[])).
% 0.93/0.83 tff(229,plain,
% 0.93/0.83 ((~![I1: $i] : ((~model(I1, C!33)) | model(I1, Ax!43))) | (~model(I2!31, C!33)) | model(I2!31, Ax!43)),
% 0.93/0.83 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.93/0.83 tff(230,plain,
% 0.93/0.83 ((~model(I2!31, C!33)) | model(I2!31, Ax!43)),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[229, 226])).
% 0.93/0.83 tff(231,plain,
% 0.93/0.83 (model(I2!31, Ax!43)),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[230, 184])).
% 0.93/0.83 tff(232,assumption,(![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))), introduced(assumption)).
% 0.93/0.83 tff(233,plain,
% 0.93/0.83 (((~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))) | ((~model(I2!31, Ax!43)) | (~model(I2!31, not(F!29))))) <=> ((~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))) | (~model(I2!31, Ax!43)) | (~model(I2!31, not(F!29))))),
% 0.93/0.83 inference(rewrite,[status(thm)],[])).
% 0.93/0.83 tff(234,plain,
% 0.93/0.83 ((~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))) | ((~model(I2!31, Ax!43)) | (~model(I2!31, not(F!29))))),
% 0.93/0.83 inference(quant_inst,[status(thm)],[])).
% 0.93/0.83 tff(235,plain,
% 0.93/0.83 ((~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))) | (~model(I2!31, Ax!43)) | (~model(I2!31, not(F!29)))),
% 0.93/0.83 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.93/0.83 tff(236,plain,
% 0.93/0.83 ($false),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[235, 232, 231, 154])).
% 0.93/0.83 tff(237,plain,(~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))), inference(lemma,lemma(discharge,[]))).
% 0.93/0.83 tff(238,plain,
% 0.93/0.83 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(Ax!43, F!29, csa)) | (~((~model(tptp_fun_I1_14(F!29, Ax!43), Ax!43)) | (~model(tptp_fun_I1_14(F!29, Ax!43), not(F!29))))))) | (~(status(Ax!43, F!29, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))))))),
% 0.93/0.83 inference(quant_inst,[status(thm)],[])).
% 0.93/0.83 tff(239,plain,
% 0.93/0.83 (~((~((~status(Ax!43, F!29, csa)) | (~((~model(tptp_fun_I1_14(F!29, Ax!43), Ax!43)) | (~model(tptp_fun_I1_14(F!29, Ax!43), not(F!29))))))) | (~(status(Ax!43, F!29, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29)))))))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[238, 31])).
% 0.93/0.83 tff(240,plain,
% 0.93/0.83 (((~((~status(Ax!43, F!29, csa)) | (~((~model(tptp_fun_I1_14(F!29, Ax!43), Ax!43)) | (~model(tptp_fun_I1_14(F!29, Ax!43), not(F!29))))))) | (~(status(Ax!43, F!29, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))))) | (status(Ax!43, F!29, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29)))))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(241,plain,
% 0.93/0.83 (status(Ax!43, F!29, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.93/0.83 tff(242,plain,
% 0.93/0.83 ((~(status(Ax!43, F!29, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29)))))) | status(Ax!43, F!29, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))),
% 0.93/0.83 inference(tautology,[status(thm)],[])).
% 0.93/0.83 tff(243,plain,
% 0.93/0.83 (status(Ax!43, F!29, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(F!29))))),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.93/0.83 tff(244,plain,
% 0.93/0.83 (status(Ax!43, F!29, csa)),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[243, 237])).
% 0.93/0.83 tff(245,plain,
% 0.93/0.83 ((~![Ax: $i, C: $i] : (~status(Ax, C, csa))) | (~status(Ax!43, F!29, csa))),
% 0.93/0.83 inference(quant_inst,[status(thm)],[])).
% 0.93/0.83 tff(246,plain,
% 0.93/0.83 ($false),
% 0.93/0.83 inference(unit_resolution,[status(thm)],[245, 244, 143])).
% 0.93/0.83 % SZS output end Proof
%------------------------------------------------------------------------------