%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS215+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 Jun 21 05:13:35 AM UTC 2025
% Result : Theorem 1.00s 1.18s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS215+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:12:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.00/1.18 % SZS status Theorem
% 1.00/1.18 % SZS output start Proof
% 1.00/1.18 tff(model_type, type, (
% 1.00/1.18 model: ( $i * $i ) > $o)).
% 1.00/1.18 tff(not_type, type, (
% 1.00/1.18 not: $i > $i)).
% 1.00/1.18 tff(tptp_fun_C_42_type, type, (
% 1.00/1.18 tptp_fun_C_42: $i)).
% 1.00/1.18 tff(tptp_fun_I1_44_type, type, (
% 1.00/1.18 tptp_fun_I1_44: $i)).
% 1.00/1.18 tff(tptp_fun_Ax_34_type, type, (
% 1.00/1.18 tptp_fun_Ax_34: $i)).
% 1.00/1.18 tff(status_type, type, (
% 1.00/1.18 status: ( $i * $i * $i ) > $o)).
% 1.00/1.18 tff(csa_type, type, (
% 1.00/1.18 csa: $i)).
% 1.00/1.18 tff(nevera_type, type, (
% 1.00/1.18 nevera: ( $i * $i ) > $o)).
% 1.00/1.18 tff(tptp_fun_C_24_type, type, (
% 1.00/1.18 tptp_fun_C_24: ( $i * $i ) > $i)).
% 1.00/1.18 tff(tptp_fun_Ax_25_type, type, (
% 1.00/1.18 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 1.00/1.18 tff(tptp_fun_I1_14_type, type, (
% 1.00/1.18 tptp_fun_I1_14: ( $i * $i ) > $i)).
% 1.00/1.18 tff(thm_type, type, (
% 1.00/1.18 thm: $i)).
% 1.00/1.18 tff(tptp_fun_I1_3_type, type, (
% 1.00/1.18 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 1.00/1.18 tff(nota_type, type, (
% 1.00/1.18 nota: ( $i * $i ) > $o)).
% 1.00/1.18 tff(tptp_fun_C_22_type, type, (
% 1.00/1.18 tptp_fun_C_22: ( $i * $i ) > $i)).
% 1.00/1.18 tff(tptp_fun_Ax_23_type, type, (
% 1.00/1.18 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 1.00/1.18 tff(tptp_fun_Ax_43_type, type, (
% 1.00/1.18 tptp_fun_Ax_43: $i)).
% 1.00/1.18 tff(tptp_fun_I2_45_type, type, (
% 1.00/1.18 tptp_fun_I2_45: $i)).
% 1.00/1.18 tff(1,assumption,(status(Ax!34, C!42, csa)), introduced(assumption)).
% 1.00/1.18 tff(2,plain,
% 1.00/1.18 (^[I: $i, F: $i] : refl((~(model(I, F) <=> model(I, not(F)))) <=> (~(model(I, F) <=> model(I, not(F)))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(3,plain,
% 1.00/1.18 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[2])).
% 1.00/1.18 tff(4,plain,
% 1.00/1.18 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(5,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','completeness')).
% 1.00/1.18 tff(6,plain,
% 1.00/1.18 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.00/1.18 tff(7,plain,(
% 1.00/1.18 ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 1.00/1.18 inference(skolemize,[status(sab)],[6])).
% 1.00/1.18 tff(8,plain,
% 1.00/1.18 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.00/1.18 tff(9,plain,
% 1.00/1.18 ((~![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)))))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(10,plain,
% 1.00/1.18 (~(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))))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[9, 8])).
% 1.00/1.18 tff(11,plain,
% 1.00/1.18 (^[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)))))))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(12,plain,
% 1.00/1.18 (![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))))))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[11])).
% 1.00/1.18 tff(13,plain,
% 1.00/1.18 (^[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))))))))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(14,plain,
% 1.00/1.18 (![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)))))))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[13])).
% 1.00/1.18 tff(15,plain,
% 1.00/1.18 (^[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))))))))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(16,plain,
% 1.00/1.18 (![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)))))))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[15])).
% 1.00/1.18 tff(17,plain,
% 1.00/1.18 (![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)))))))))),
% 1.00/1.18 inference(transitivity,[status(thm)],[16, 14])).
% 1.00/1.18 tff(18,plain,
% 1.00/1.18 (^[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)))))))))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(19,plain,
% 1.00/1.18 (![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)))))))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[18])).
% 1.00/1.18 tff(20,plain,
% 1.00/1.18 (^[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)))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(21,plain,
% 1.00/1.18 (![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))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[20])).
% 1.00/1.18 tff(22,plain,
% 1.00/1.18 (![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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(23,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','csa')).
% 1.00/1.18 tff(24,plain,
% 1.00/1.18 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.00/1.18 tff(25,plain,(
% 1.00/1.18 ![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))))),
% 1.00/1.18 inference(skolemize,[status(sab)],[24])).
% 1.00/1.18 tff(26,plain,
% 1.00/1.18 (![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))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.00/1.18 tff(27,plain,
% 1.00/1.18 (![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)))))))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[26, 19])).
% 1.00/1.18 tff(28,plain,
% 1.00/1.18 (![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)))))))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[27, 17])).
% 1.00/1.18 tff(29,plain,
% 1.00/1.18 (![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))))))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[28, 12])).
% 1.00/1.18 tff(30,plain,
% 1.00/1.18 ((~![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)))))))))),
% 1.00/1.18 inference(quant_inst,[status(thm)],[])).
% 1.00/1.18 tff(31,plain,
% 1.00/1.18 (~((~((~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))))))))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.00/1.18 tff(32,plain,
% 1.00/1.18 (((~((~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)))))))),
% 1.00/1.18 inference(tautology,[status(thm)],[])).
% 1.00/1.18 tff(33,plain,
% 1.00/1.18 ((~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))))))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.00/1.18 tff(34,assumption,(status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)), introduced(assumption)).
% 1.00/1.18 tff(35,plain,
% 1.00/1.18 ((~((~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))))))),
% 1.00/1.18 inference(tautology,[status(thm)],[])).
% 1.00/1.18 tff(36,plain,
% 1.00/1.18 ((~((~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))))))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[35, 34])).
% 1.00/1.18 tff(37,plain,
% 1.00/1.18 (~((~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)))))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[36, 33])).
% 1.00/1.18 tff(38,plain,
% 1.00/1.18 (((~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)))),
% 1.00/1.18 inference(tautology,[status(thm)],[])).
% 1.00/1.18 tff(39,plain,
% 1.00/1.18 (model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), not(tptp_fun_C_24(csa, csa)))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[38, 37])).
% 1.00/1.18 tff(40,plain,
% 1.00/1.18 ((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))))),
% 1.00/1.18 inference(tautology,[status(thm)],[])).
% 1.00/1.18 tff(41,plain,
% 1.00/1.18 ((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)))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[40, 39])).
% 1.00/1.18 tff(42,plain,
% 1.00/1.18 (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))),
% 1.00/1.18 inference(unit_resolution,[status(thm)],[41, 10])).
% 1.00/1.18 tff(43,plain,
% 1.00/1.18 (^[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)))))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(44,plain,
% 1.00/1.18 (![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))))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[43])).
% 1.00/1.18 tff(45,plain,
% 1.00/1.18 (^[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)))))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(46,plain,
% 1.00/1.18 (![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))))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[45])).
% 1.00/1.18 tff(47,plain,
% 1.00/1.18 (^[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)))))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(48,plain,
% 1.00/1.18 (![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))))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[47])).
% 1.00/1.18 tff(49,plain,
% 1.00/1.18 (![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))))))),
% 1.00/1.18 inference(transitivity,[status(thm)],[48, 46])).
% 1.00/1.18 tff(50,plain,
% 1.00/1.18 (^[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))))))))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(51,plain,
% 1.00/1.18 (![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))))))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[50])).
% 1.00/1.18 tff(52,plain,
% 1.00/1.18 (![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))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(53,plain,
% 1.00/1.18 (^[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)))),
% 1.00/1.18 inference(bind,[status(th)],[])).
% 1.00/1.18 tff(54,plain,
% 1.00/1.18 (![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))),
% 1.00/1.18 inference(quant_intro,[status(thm)],[53])).
% 1.00/1.18 tff(55,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','thm')).
% 1.00/1.18 tff(56,plain,
% 1.00/1.18 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.00/1.18 tff(57,plain,
% 1.00/1.18 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.00/1.18 tff(58,plain,(
% 1.00/1.18 ![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))))),
% 1.00/1.18 inference(skolemize,[status(sab)],[57])).
% 1.00/1.18 tff(59,plain,
% 1.00/1.18 (![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))))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[58, 51])).
% 1.00/1.18 tff(60,plain,
% 1.00/1.18 (![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))))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[59, 49])).
% 1.00/1.18 tff(61,plain,
% 1.00/1.18 (![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))))))),
% 1.00/1.18 inference(modus_ponens,[status(thm)],[60, 44])).
% 1.00/1.18 tff(62,plain,
% 1.00/1.18 (((~![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))))))) | (~((~((~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))))) | (~((~((~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)))))) <=> ((~![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))))))) | (~((~((~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))))) | (~((~((~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))))))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(63,plain,
% 1.00/1.18 ((~((~((~((~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))))) | (~((~((~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)))))),
% 1.00/1.18 inference(rewrite,[status(thm)],[])).
% 1.00/1.18 tff(64,plain,
% 1.00/1.18 (((~![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)))))))) <=> ((~![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))))))) | (~((~((~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))))) | (~((~((~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))))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[63])).
% 1.00/1.19 tff(65,plain,
% 1.00/1.19 (((~![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)))))))) <=> ((~![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))))))) | (~((~((~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))))) | (~((~((~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))))))),
% 1.00/1.19 inference(transitivity,[status(thm)],[64, 62])).
% 1.00/1.19 tff(66,plain,
% 1.00/1.19 ((~![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)))))))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(67,plain,
% 1.00/1.19 ((~![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))))))) | (~((~((~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))))) | (~((~((~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)))))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.00/1.19 tff(68,plain,
% 1.00/1.19 (~((~((~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))))) | (~((~((~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))))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[67, 61])).
% 1.00/1.19 tff(69,plain,
% 1.00/1.19 (((~((~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))))) | (~((~((~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))))),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(70,plain,
% 1.00/1.19 ((~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)))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[69, 68])).
% 1.00/1.19 tff(71,plain,
% 1.00/1.19 (^[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))))))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(72,plain,
% 1.00/1.19 (![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)))))))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[71])).
% 1.00/1.19 tff(73,plain,
% 1.00/1.19 (^[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))))))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(74,plain,
% 1.00/1.19 (![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)))))))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[73])).
% 1.00/1.19 tff(75,plain,
% 1.00/1.19 (![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)))))))),
% 1.00/1.19 inference(transitivity,[status(thm)],[74, 72])).
% 1.00/1.19 tff(76,plain,
% 1.00/1.19 (^[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)))))))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(77,plain,
% 1.00/1.19 (![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)))))))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[76])).
% 1.00/1.19 tff(78,plain,
% 1.00/1.19 (^[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)))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(79,plain,
% 1.00/1.19 (![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))))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[78])).
% 1.00/1.19 tff(80,plain,
% 1.00/1.19 (![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(81,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nota')).
% 1.00/1.19 tff(82,plain,
% 1.00/1.19 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.00/1.19 tff(83,plain,(
% 1.00/1.19 ![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))))),
% 1.00/1.19 inference(skolemize,[status(sab)],[82])).
% 1.00/1.19 tff(84,plain,
% 1.00/1.19 (![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))))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.00/1.19 tff(85,plain,
% 1.00/1.19 (![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)))))))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[84, 77])).
% 1.00/1.19 tff(86,plain,
% 1.00/1.19 (![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)))))))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[85, 75])).
% 1.00/1.19 tff(87,plain,
% 1.00/1.19 ((~![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)))))))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(88,plain,
% 1.00/1.19 (~((~(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))))))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.00/1.19 tff(89,plain,
% 1.00/1.19 (((~(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)))),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(90,plain,
% 1.00/1.19 (nota(csa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[89, 88])).
% 1.00/1.19 tff(91,plain,
% 1.00/1.19 ((~nota(csa, thm)) <=> (~nota(csa, thm))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(92,axiom,(~nota(csa, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nota_csa_thm')).
% 1.00/1.19 tff(93,plain,
% 1.00/1.19 (~nota(csa, thm)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.00/1.19 tff(94,plain,
% 1.00/1.19 ((~(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))),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(95,plain,
% 1.00/1.19 ((~(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))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.00/1.19 tff(96,plain,
% 1.00/1.19 (![Ax: $i, C: $i] : ((~status(Ax, C, csa)) | status(Ax, C, thm))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[95, 90])).
% 1.00/1.19 tff(97,plain,
% 1.00/1.19 (((~![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(98,plain,
% 1.00/1.19 ((~![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))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(99,plain,
% 1.00/1.19 ((~![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)),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.00/1.19 tff(100,plain,
% 1.00/1.19 (status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), thm)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[99, 96, 34])).
% 1.00/1.19 tff(101,plain,
% 1.00/1.19 ((~((~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)))),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(102,plain,
% 1.00/1.19 ((~((~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)))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[101, 100])).
% 1.00/1.19 tff(103,plain,
% 1.00/1.19 (![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[102, 70])).
% 1.00/1.19 tff(104,plain,
% 1.00/1.19 (((~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))),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(105,plain,
% 1.00/1.19 (model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[104, 37])).
% 1.00/1.19 tff(106,plain,
% 1.00/1.19 (((~![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)))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(107,plain,
% 1.00/1.19 ((~![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)))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(108,plain,
% 1.00/1.19 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(csa, csa))) | model(I1, tptp_fun_C_24(csa, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_Ax_25(csa, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(csa, csa), tptp_fun_Ax_25(csa, csa)), tptp_fun_C_24(csa, csa))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.00/1.19 tff(109,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[108, 105, 103, 42])).
% 1.00/1.19 tff(110,plain,(~status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(111,plain,
% 1.00/1.19 (^[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))))))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(112,plain,
% 1.00/1.19 (![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)))))))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[111])).
% 1.00/1.19 tff(113,plain,
% 1.00/1.19 (^[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)))))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(114,plain,
% 1.00/1.19 (![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))))))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[113])).
% 1.00/1.19 tff(115,plain,
% 1.00/1.19 (^[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)))))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(116,plain,
% 1.00/1.19 (![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))))))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[115])).
% 1.00/1.19 tff(117,plain,
% 1.00/1.19 (![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))))))),
% 1.00/1.19 inference(transitivity,[status(thm)],[116, 114])).
% 1.00/1.19 tff(118,plain,
% 1.00/1.19 (^[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))))))))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(119,plain,
% 1.00/1.19 (![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))))))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[118])).
% 1.00/1.19 tff(120,plain,
% 1.00/1.19 (![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))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(121,plain,
% 1.00/1.19 (^[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)))),
% 1.00/1.19 inference(bind,[status(th)],[])).
% 1.00/1.19 tff(122,plain,
% 1.00/1.19 (![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))),
% 1.00/1.19 inference(quant_intro,[status(thm)],[121])).
% 1.00/1.19 tff(123,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nevera')).
% 1.00/1.19 tff(124,plain,
% 1.00/1.19 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.00/1.19 tff(125,plain,
% 1.00/1.19 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[124, 120])).
% 1.00/1.19 tff(126,plain,(
% 1.00/1.19 ![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))))),
% 1.00/1.19 inference(skolemize,[status(sab)],[125])).
% 1.00/1.19 tff(127,plain,
% 1.00/1.19 (![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))))))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[126, 119])).
% 1.00/1.19 tff(128,plain,
% 1.00/1.19 (![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))))))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[127, 117])).
% 1.00/1.19 tff(129,plain,
% 1.00/1.19 (![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)))))))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[128, 112])).
% 1.00/1.19 tff(130,plain,
% 1.00/1.19 (((~![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)))))))) | (~((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, 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)))))))) | (~((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))))))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(131,plain,
% 1.00/1.19 ((~((~((~((~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))))))) <=> (~((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))))),
% 1.00/1.19 inference(rewrite,[status(thm)],[])).
% 1.00/1.19 tff(132,plain,
% 1.00/1.19 (((~![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)))))))) | (~((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))))))),
% 1.00/1.19 inference(monotonicity,[status(thm)],[131])).
% 1.00/1.19 tff(133,plain,
% 1.00/1.19 (((~![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)))))))) | (~((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))))))),
% 1.00/1.19 inference(transitivity,[status(thm)],[132, 130])).
% 1.00/1.19 tff(134,plain,
% 1.00/1.19 ((~![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)))))))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(135,plain,
% 1.00/1.19 ((~![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)))))))) | (~((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))))),
% 1.00/1.19 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.00/1.19 tff(136,plain,
% 1.00/1.19 (~((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[135, 129])).
% 1.00/1.19 tff(137,plain,
% 1.00/1.19 (((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))) | (nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(138,plain,
% 1.00/1.19 (nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[137, 136])).
% 1.00/1.19 tff(139,plain,
% 1.00/1.19 ((~(nevera(csa, csa) | 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)),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(140,plain,
% 1.00/1.19 (nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.00/1.19 tff(141,plain,
% 1.00/1.19 (nevera(csa, csa)),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[140, 110])).
% 1.00/1.19 tff(142,plain,
% 1.00/1.19 (((~(nevera(csa, csa) | status(tptp_fun_Ax_25(csa, csa), tptp_fun_C_24(csa, csa), csa))) | (~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))))) | ((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(143,plain,
% 1.00/1.19 ((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[142, 136])).
% 1.00/1.19 tff(144,plain,
% 1.00/1.19 ((~((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa)))) | (~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))),
% 1.00/1.19 inference(tautology,[status(thm)],[])).
% 1.00/1.19 tff(145,plain,
% 1.00/1.19 ((~nevera(csa, csa)) | ![Ax: $i, C: $i] : (~status(Ax, C, csa))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[144, 143])).
% 1.00/1.19 tff(146,plain,
% 1.00/1.19 (![Ax: $i, C: $i] : (~status(Ax, C, csa))),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[145, 141])).
% 1.00/1.19 tff(147,plain,
% 1.00/1.19 ((~![Ax: $i, C: $i] : (~status(Ax, C, csa))) | (~status(Ax!34, C!42, csa))),
% 1.00/1.19 inference(quant_inst,[status(thm)],[])).
% 1.00/1.19 tff(148,plain,
% 1.00/1.19 ($false),
% 1.00/1.19 inference(unit_resolution,[status(thm)],[147, 146, 1])).
% 1.00/1.19 tff(149,plain,(~status(Ax!34, C!42, csa)), inference(lemma,lemma(discharge,[]))).
% 1.00/1.19 tff(150,plain,
% 1.00/1.19 ((~![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!34, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, Ax!34), Ax!34)) | (~model(tptp_fun_I1_14(C!42, Ax!34), not(C!42))))))) | (~(status(Ax!34, C!42, csa) | ![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))))))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(151,plain,
% 1.00/1.20 (~((~((~status(Ax!34, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, Ax!34), Ax!34)) | (~model(tptp_fun_I1_14(C!42, Ax!34), not(C!42))))))) | (~(status(Ax!34, C!42, csa) | ![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42)))))))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[150, 29])).
% 1.00/1.20 tff(152,plain,
% 1.00/1.20 (((~((~status(Ax!34, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, Ax!34), Ax!34)) | (~model(tptp_fun_I1_14(C!42, Ax!34), not(C!42))))))) | (~(status(Ax!34, C!42, csa) | ![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))))) | (status(Ax!34, C!42, csa) | ![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42)))))),
% 1.00/1.20 inference(tautology,[status(thm)],[])).
% 1.00/1.20 tff(153,plain,
% 1.00/1.20 (status(Ax!34, C!42, csa) | ![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[152, 151])).
% 1.00/1.20 tff(154,plain,
% 1.00/1.20 ((~(status(Ax!34, C!42, csa) | ![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42)))))) | status(Ax!34, C!42, csa) | ![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))),
% 1.00/1.20 inference(tautology,[status(thm)],[])).
% 1.00/1.20 tff(155,plain,
% 1.00/1.20 (status(Ax!34, C!42, csa) | ![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[154, 153])).
% 1.00/1.20 tff(156,plain,
% 1.00/1.20 (![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[155, 149])).
% 1.00/1.20 tff(157,plain,
% 1.00/1.20 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I1!44, Ax!34) <=> model(I1!44, not(Ax!34))))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(158,plain,
% 1.00/1.20 (~(model(I1!44, Ax!34) <=> model(I1!44, not(Ax!34)))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[157, 8])).
% 1.00/1.20 tff(159,assumption,(![Ax: $i, C: $i] : (~status(Ax, C, csa))), introduced(assumption)).
% 1.00/1.20 tff(160,assumption,(status(Ax!43, Ax!34, csa)), introduced(assumption)).
% 1.00/1.20 tff(161,plain,
% 1.00/1.20 ((~![Ax: $i, C: $i] : (~status(Ax, C, csa))) | (~status(Ax!43, Ax!34, csa))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(162,plain,
% 1.00/1.20 ($false),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[161, 160, 159])).
% 1.00/1.20 tff(163,plain,((~status(Ax!43, Ax!34, csa)) | (~![Ax: $i, C: $i] : (~status(Ax, C, csa)))), inference(lemma,lemma(discharge,[]))).
% 1.00/1.20 tff(164,plain,
% 1.00/1.20 (~status(Ax!43, Ax!34, csa)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[163, 146])).
% 1.00/1.20 tff(165,plain,
% 1.00/1.20 ((~![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, Ax!34, csa)) | (~((~model(tptp_fun_I1_14(Ax!34, Ax!43), Ax!43)) | (~model(tptp_fun_I1_14(Ax!34, Ax!43), not(Ax!34))))))) | (~(status(Ax!43, Ax!34, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))))))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(166,plain,
% 1.00/1.20 (~((~((~status(Ax!43, Ax!34, csa)) | (~((~model(tptp_fun_I1_14(Ax!34, Ax!43), Ax!43)) | (~model(tptp_fun_I1_14(Ax!34, Ax!43), not(Ax!34))))))) | (~(status(Ax!43, Ax!34, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34)))))))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[165, 29])).
% 1.00/1.20 tff(167,plain,
% 1.00/1.20 (((~((~status(Ax!43, Ax!34, csa)) | (~((~model(tptp_fun_I1_14(Ax!34, Ax!43), Ax!43)) | (~model(tptp_fun_I1_14(Ax!34, Ax!43), not(Ax!34))))))) | (~(status(Ax!43, Ax!34, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))))) | (status(Ax!43, Ax!34, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34)))))),
% 1.00/1.20 inference(tautology,[status(thm)],[])).
% 1.00/1.20 tff(168,plain,
% 1.00/1.20 (status(Ax!43, Ax!34, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[167, 166])).
% 1.00/1.20 tff(169,plain,
% 1.00/1.20 ((~(status(Ax!43, Ax!34, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34)))))) | status(Ax!43, Ax!34, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))),
% 1.00/1.20 inference(tautology,[status(thm)],[])).
% 1.00/1.20 tff(170,plain,
% 1.00/1.20 (status(Ax!43, Ax!34, csa) | ![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[169, 168])).
% 1.00/1.20 tff(171,plain,
% 1.00/1.20 (![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[170, 164])).
% 1.00/1.20 tff(172,plain,
% 1.00/1.20 (?[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))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(173,plain,
% 1.00/1.20 (^[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)))),
% 1.00/1.20 inference(bind,[status(th)],[])).
% 1.00/1.20 tff(174,plain,
% 1.00/1.20 (?[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))),
% 1.00/1.20 inference(quant_intro,[status(thm)],[173])).
% 1.00/1.20 tff(175,axiom,(?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','non_thm_spt')).
% 1.00/1.20 tff(176,plain,
% 1.00/1.20 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.00/1.20 tff(177,plain,
% 1.00/1.20 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.00/1.20 tff(178,plain,
% 1.00/1.20 (model(I1!44, Ax!43)),
% 1.00/1.20 inference(and_elim,[status(thm)],[177])).
% 1.00/1.20 tff(179,plain,
% 1.00/1.20 (((~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))) | ((~model(I1!44, Ax!43)) | (~model(I1!44, not(Ax!34))))) <=> ((~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))) | (~model(I1!44, Ax!43)) | (~model(I1!44, not(Ax!34))))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(180,plain,
% 1.00/1.20 ((~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))) | ((~model(I1!44, Ax!43)) | (~model(I1!44, not(Ax!34))))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(181,plain,
% 1.00/1.20 ((~![I1: $i] : ((~model(I1, Ax!43)) | (~model(I1, not(Ax!34))))) | (~model(I1!44, Ax!43)) | (~model(I1!44, not(Ax!34)))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.00/1.20 tff(182,plain,
% 1.00/1.20 (~model(I1!44, not(Ax!34))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[181, 178, 171])).
% 1.00/1.20 tff(183,plain,
% 1.00/1.20 ((model(I1!44, Ax!34) <=> model(I1!44, not(Ax!34))) | model(I1!44, Ax!34) | model(I1!44, not(Ax!34))),
% 1.00/1.20 inference(tautology,[status(thm)],[])).
% 1.00/1.20 tff(184,plain,
% 1.00/1.20 ((model(I1!44, Ax!34) <=> model(I1!44, not(Ax!34))) | model(I1!44, Ax!34)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[183, 182])).
% 1.00/1.20 tff(185,plain,
% 1.00/1.20 (model(I1!44, Ax!34)),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[184, 158])).
% 1.00/1.20 tff(186,plain,
% 1.00/1.20 (((~![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))) | ((~model(I1!44, Ax!34)) | (~model(I1!44, not(C!42))))) <=> ((~![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))) | (~model(I1!44, Ax!34)) | (~model(I1!44, not(C!42))))),
% 1.00/1.20 inference(rewrite,[status(thm)],[])).
% 1.00/1.20 tff(187,plain,
% 1.00/1.20 ((~![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))) | ((~model(I1!44, Ax!34)) | (~model(I1!44, not(C!42))))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(188,plain,
% 1.00/1.20 ((~![I1: $i] : ((~model(I1, Ax!34)) | (~model(I1, not(C!42))))) | (~model(I1!44, Ax!34)) | (~model(I1!44, not(C!42)))),
% 1.00/1.20 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.00/1.20 tff(189,plain,
% 1.00/1.20 (~model(I1!44, not(C!42))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[188, 185, 156])).
% 1.00/1.20 tff(190,plain,
% 1.00/1.20 (~model(I1!44, C!42)),
% 1.00/1.20 inference(and_elim,[status(thm)],[177])).
% 1.00/1.20 tff(191,plain,
% 1.00/1.20 ((model(I1!44, C!42) <=> model(I1!44, not(C!42))) | model(I1!44, C!42) | model(I1!44, not(C!42))),
% 1.00/1.20 inference(tautology,[status(thm)],[])).
% 1.00/1.20 tff(192,plain,
% 1.00/1.20 (model(I1!44, C!42) <=> model(I1!44, not(C!42))),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[191, 190, 189])).
% 1.00/1.20 tff(193,plain,
% 1.00/1.20 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I1!44, C!42) <=> model(I1!44, not(C!42))))),
% 1.00/1.20 inference(quant_inst,[status(thm)],[])).
% 1.00/1.20 tff(194,plain,
% 1.00/1.20 ($false),
% 1.00/1.20 inference(unit_resolution,[status(thm)],[193, 8, 192])).
% 1.00/1.20 % SZS output end Proof
% 1.00/1.20 % E exiting
%------------------------------------------------------------------------------