%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS263+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 Jun 21 05:13:39 AM UTC 2025
% Result : Theorem 9.86s 10.04s
% Output : Proof 9.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS263+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.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 19:21:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 9.86/10.04 % SZS status Theorem
% 9.86/10.04 % SZS output start Proof
% 9.86/10.04 tff(model_type, type, (
% 9.86/10.04 model: ( $i * $i ) > $o)).
% 9.86/10.04 tff(tptp_fun_F_28_type, type, (
% 9.86/10.04 tptp_fun_F_28: $i)).
% 9.86/10.04 tff(tptp_fun_C_42_type, type, (
% 9.86/10.04 tptp_fun_C_42: $i)).
% 9.86/10.04 tff(tptp_fun_I1_0_type, type, (
% 9.86/10.04 tptp_fun_I1_0: $i > $i)).
% 9.86/10.04 tff(status_type, type, (
% 9.86/10.04 status: ( $i * $i * $i ) > $o)).
% 9.86/10.04 tff(sap_type, type, (
% 9.86/10.04 sap: $i)).
% 9.86/10.04 tff(tptp_fun_I2_1_type, type, (
% 9.86/10.04 tptp_fun_I2_1: $i > $i)).
% 9.86/10.04 tff(wtc_type, type, (
% 9.86/10.04 wtc: $i)).
% 9.86/10.04 tff(tptp_fun_I3_11_type, type, (
% 9.86/10.04 tptp_fun_I3_11: $i > $i)).
% 9.86/10.04 tff(tptp_fun_I2_8_type, type, (
% 9.86/10.04 tptp_fun_I2_8: $i > $i)).
% 9.86/10.04 tff(tptp_fun_I2_45_type, type, (
% 9.86/10.04 tptp_fun_I2_45: $i)).
% 9.86/10.04 tff(tptp_fun_I1_44_type, type, (
% 9.86/10.04 tptp_fun_I1_44: $i)).
% 9.86/10.04 tff(tptp_fun_Ax_43_type, type, (
% 9.86/10.04 tptp_fun_Ax_43: $i)).
% 9.86/10.04 tff(nevera_type, type, (
% 9.86/10.04 nevera: ( $i * $i ) > $o)).
% 9.86/10.04 tff(tptp_fun_C_24_type, type, (
% 9.86/10.04 tptp_fun_C_24: ( $i * $i ) > $i)).
% 9.86/10.04 tff(tptp_fun_Ax_25_type, type, (
% 9.86/10.04 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 9.86/10.04 tff(thm_type, type, (
% 9.86/10.04 thm: $i)).
% 9.86/10.04 tff(nota_type, type, (
% 9.86/10.04 nota: ( $i * $i ) > $o)).
% 9.86/10.04 tff(tptp_fun_C_22_type, type, (
% 9.86/10.04 tptp_fun_C_22: ( $i * $i ) > $i)).
% 9.86/10.04 tff(tptp_fun_Ax_23_type, type, (
% 9.86/10.04 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 9.86/10.04 tff(tptp_fun_I1_3_type, type, (
% 9.86/10.04 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 9.86/10.04 tff(mighta_type, type, (
% 9.86/10.04 mighta: ( $i * $i ) > $o)).
% 9.86/10.04 tff(tptp_fun_C_18_type, type, (
% 9.86/10.04 tptp_fun_C_18: ( $i * $i ) > $i)).
% 9.86/10.04 tff(tptp_fun_Ax_19_type, type, (
% 9.86/10.04 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 9.86/10.04 tff(tptp_fun_I4_41_type, type, (
% 9.86/10.04 tptp_fun_I4_41: $i)).
% 9.86/10.04 tff(1,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax)))))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(2,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[1])).
% 9.86/10.04 tff(3,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(4,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[3])).
% 9.86/10.04 tff(5,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(6,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[5])).
% 9.86/10.04 tff(7,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 9.86/10.04 inference(transitivity,[status(thm)],[6, 4])).
% 9.86/10.04 tff(8,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite(((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) <=> ((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))), rewrite((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))) <=> (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))), ((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))), rewrite((((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))), ((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(9,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[8])).
% 9.86/10.04 tff(10,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap)))) <=> (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(11,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap)))) <=> ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[10])).
% 9.86/10.04 tff(12,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 9.86/10.04 inference(rewrite,[status(thm)],[])).
% 9.86/10.04 tff(13,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : rewrite(((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(14,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[13])).
% 9.86/10.04 tff(15,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','sap')).
% 9.86/10.04 tff(16,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[15, 14])).
% 9.86/10.04 tff(17,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[16, 12])).
% 9.86/10.04 tff(18,plain,(
% 9.86/10.04 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap))))),
% 9.86/10.04 inference(skolemize,[status(sab)],[17])).
% 9.86/10.04 tff(19,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[18, 11])).
% 9.86/10.04 tff(20,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[19, 9])).
% 9.86/10.04 tff(21,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[20, 7])).
% 9.86/10.04 tff(22,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[21, 2])).
% 9.86/10.04 tff(23,plain,
% 9.86/10.04 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~(model(tptp_fun_I2_1(F!28), F!28) | ![I1: $i] : (~model(I1, C!42)) | (~status(C!42, F!28, sap)))) | (~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~(model(tptp_fun_I2_1(F!28), F!28) | ![I1: $i] : (~model(I1, C!42)) | (~status(C!42, F!28, sap)))) | (~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))))))),
% 9.86/10.04 inference(rewrite,[status(thm)],[])).
% 9.86/10.04 tff(24,plain,
% 9.86/10.04 ((~((~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))) | (~(model(tptp_fun_I2_1(F!28), F!28) | (~status(C!42, F!28, sap)) | ![I1: $i] : (~model(I1, C!42)))))) <=> (~((~(model(tptp_fun_I2_1(F!28), F!28) | ![I1: $i] : (~model(I1, C!42)) | (~status(C!42, F!28, sap)))) | (~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap)))))),
% 9.86/10.04 inference(rewrite,[status(thm)],[])).
% 9.86/10.04 tff(25,plain,
% 9.86/10.04 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))) | (~(model(tptp_fun_I2_1(F!28), F!28) | (~status(C!42, F!28, sap)) | ![I1: $i] : (~model(I1, C!42))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~(model(tptp_fun_I2_1(F!28), F!28) | ![I1: $i] : (~model(I1, C!42)) | (~status(C!42, F!28, sap)))) | (~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))))))),
% 9.86/10.04 inference(monotonicity,[status(thm)],[24])).
% 9.86/10.04 tff(26,plain,
% 9.86/10.04 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))) | (~(model(tptp_fun_I2_1(F!28), F!28) | (~status(C!42, F!28, sap)) | ![I1: $i] : (~model(I1, C!42))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~(model(tptp_fun_I2_1(F!28), F!28) | ![I1: $i] : (~model(I1, C!42)) | (~status(C!42, F!28, sap)))) | (~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))))))),
% 9.86/10.04 inference(transitivity,[status(thm)],[25, 23])).
% 9.86/10.04 tff(27,plain,
% 9.86/10.04 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))) | (~(model(tptp_fun_I2_1(F!28), F!28) | (~status(C!42, F!28, sap)) | ![I1: $i] : (~model(I1, C!42))))))),
% 9.86/10.04 inference(quant_inst,[status(thm)],[])).
% 9.86/10.04 tff(28,plain,
% 9.86/10.04 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~(model(tptp_fun_I2_1(F!28), F!28) | ![I1: $i] : (~model(I1, C!42)) | (~status(C!42, F!28, sap)))) | (~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap)))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[27, 26])).
% 9.86/10.04 tff(29,plain,
% 9.86/10.04 (~((~(model(tptp_fun_I2_1(F!28), F!28) | ![I1: $i] : (~model(I1, C!42)) | (~status(C!42, F!28, sap)))) | (~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))))),
% 9.86/10.04 inference(unit_resolution,[status(thm)],[28, 22])).
% 9.86/10.04 tff(30,plain,
% 9.86/10.04 (((~(model(tptp_fun_I2_1(F!28), F!28) | ![I1: $i] : (~model(I1, C!42)) | (~status(C!42, F!28, sap)))) | (~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap)))) | ((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))),
% 9.86/10.04 inference(tautology,[status(thm)],[])).
% 9.86/10.04 tff(31,plain,
% 9.86/10.04 ((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap)),
% 9.86/10.04 inference(unit_resolution,[status(thm)],[30, 29])).
% 9.86/10.04 tff(32,assumption,(status(C!42, F!28, sap)), introduced(assumption)).
% 9.86/10.04 tff(33,assumption,((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28))))))), introduced(assumption)).
% 9.86/10.04 tff(34,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C)))))))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(35,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[34])).
% 9.86/10.04 tff(36,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(37,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[36])).
% 9.86/10.04 tff(38,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(39,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[38])).
% 9.86/10.04 tff(40,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 9.86/10.04 inference(transitivity,[status(thm)],[39, 37])).
% 9.86/10.04 tff(41,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) <=> (status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) <=> (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))) <=> ((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, wtc))))), rewrite(((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, wtc))) <=> ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))) <=> ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))), (((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))), rewrite(((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))), (((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(42,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[41])).
% 9.86/10.04 tff(43,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(44,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[43])).
% 9.86/10.04 tff(45,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 9.86/10.04 inference(rewrite,[status(thm)],[])).
% 9.86/10.04 tff(46,plain,
% 9.86/10.04 (^[Ax: $i, C: $i] : rewrite((((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)))),
% 9.86/10.04 inference(bind,[status(th)],[])).
% 9.86/10.04 tff(47,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 9.86/10.04 inference(quant_intro,[status(thm)],[46])).
% 9.86/10.04 tff(48,axiom,(![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','wtc')).
% 9.86/10.04 tff(49,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[48, 47])).
% 9.86/10.04 tff(50,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[49, 45])).
% 9.86/10.04 tff(51,plain,(
% 9.86/10.04 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 9.86/10.04 inference(skolemize,[status(sab)],[50])).
% 9.86/10.04 tff(52,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[51, 44])).
% 9.86/10.04 tff(53,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[52, 42])).
% 9.86/10.04 tff(54,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[53, 40])).
% 9.86/10.04 tff(55,plain,
% 9.86/10.04 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))),
% 9.86/10.04 inference(modus_ponens,[status(thm)],[54, 35])).
% 9.86/10.04 tff(56,plain,
% 9.86/10.04 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28)))))))))),
% 9.86/10.05 inference(rewrite,[status(thm)],[])).
% 9.86/10.05 tff(57,plain,
% 9.86/10.05 ((~((~(status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!28, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, F!28)))))))) <=> (~((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28))))))))),
% 9.86/10.05 inference(rewrite,[status(thm)],[])).
% 9.86/10.05 tff(58,plain,
% 9.86/10.05 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!28, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28)))))))))),
% 9.86/10.05 inference(monotonicity,[status(thm)],[57])).
% 9.86/10.05 tff(59,plain,
% 9.86/10.05 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!28, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28)))))))))),
% 9.86/10.05 inference(transitivity,[status(thm)],[58, 56])).
% 9.86/10.05 tff(60,plain,
% 9.86/10.05 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!28, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, F!28))))))))),
% 9.86/10.05 inference(quant_inst,[status(thm)],[])).
% 9.86/10.05 tff(61,plain,
% 9.86/10.05 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28))))))))),
% 9.86/10.05 inference(modus_ponens,[status(thm)],[60, 59])).
% 9.86/10.05 tff(62,plain,
% 9.86/10.05 ($false),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[61, 55, 33])).
% 9.86/10.05 tff(63,plain,(~((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28)))))))), inference(lemma,lemma(discharge,[]))).
% 9.86/10.05 tff(64,plain,
% 9.86/10.05 (((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | (~((~status(C!42, F!28, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!28))))))) | (![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))),
% 9.86/10.05 inference(tautology,[status(thm)],[])).
% 9.86/10.05 tff(65,plain,
% 9.86/10.05 (![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28))),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[64, 63])).
% 9.86/10.05 tff(66,assumption,(~model(tptp_fun_I3_11(F!28), F!28)), introduced(assumption)).
% 9.86/10.05 tff(67,plain,
% 9.86/10.05 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 9.86/10.05 inference(bind,[status(th)],[])).
% 9.86/10.05 tff(68,plain,
% 9.86/10.05 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 9.86/10.05 inference(quant_intro,[status(thm)],[67])).
% 9.86/10.05 tff(69,plain,
% 9.86/10.05 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 9.86/10.05 inference(rewrite,[status(thm)],[])).
% 9.86/10.05 tff(70,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','tautology')).
% 9.86/10.05 tff(71,plain,
% 9.86/10.05 (?[F: $i] : ![I: $i] : model(I, F)),
% 9.86/10.05 inference(modus_ponens,[status(thm)],[70, 69])).
% 9.86/10.05 tff(72,plain,(
% 9.86/10.05 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 9.86/10.05 inference(transitivity,[status(sab)],[71])).
% 9.86/10.05 tff(73,plain,
% 9.86/10.05 (![I: $i] : model(I, F!28)),
% 9.86/10.05 inference(modus_ponens,[status(thm)],[72, 68])).
% 9.86/10.05 tff(74,plain,
% 9.86/10.05 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I3_11(F!28), F!28)),
% 9.86/10.05 inference(quant_inst,[status(thm)],[])).
% 9.86/10.05 tff(75,plain,
% 9.86/10.05 ($false),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[74, 73, 66])).
% 9.86/10.05 tff(76,plain,(model(tptp_fun_I3_11(F!28), F!28)), inference(lemma,lemma(discharge,[]))).
% 9.86/10.05 tff(77,assumption,(![I1: $i] : (~model(I1, C!42))), introduced(assumption)).
% 9.86/10.05 tff(78,plain,
% 9.86/10.05 (?[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))),
% 9.86/10.05 inference(rewrite,[status(thm)],[])).
% 9.86/10.05 tff(79,plain,
% 9.86/10.05 (^[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)))),
% 9.86/10.05 inference(bind,[status(th)],[])).
% 9.86/10.05 tff(80,plain,
% 9.86/10.05 (?[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))),
% 9.86/10.05 inference(quant_intro,[status(thm)],[79])).
% 9.86/10.05 tff(81,axiom,(?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','non_thm_spt')).
% 9.86/10.05 tff(82,plain,
% 9.86/10.05 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 9.86/10.05 inference(modus_ponens,[status(thm)],[81, 80])).
% 9.86/10.05 tff(83,plain,
% 9.86/10.05 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 9.86/10.05 inference(modus_ponens,[status(thm)],[82, 78])).
% 9.86/10.05 tff(84,plain,
% 9.86/10.05 (model(I2!45, C!42)),
% 9.86/10.05 inference(and_elim,[status(thm)],[83])).
% 9.86/10.05 tff(85,plain,
% 9.86/10.05 ((~![I1: $i] : (~model(I1, C!42))) | (~model(I2!45, C!42))),
% 9.86/10.05 inference(quant_inst,[status(thm)],[])).
% 9.86/10.05 tff(86,plain,
% 9.86/10.05 ($false),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[85, 84, 77])).
% 9.86/10.05 tff(87,plain,(~![I1: $i] : (~model(I1, C!42))), inference(lemma,lemma(discharge,[]))).
% 9.86/10.05 tff(88,assumption,(![I2: $i] : model(I2, C!42)), introduced(assumption)).
% 9.86/10.05 tff(89,plain,
% 9.86/10.05 (~model(I1!44, C!42)),
% 9.86/10.05 inference(and_elim,[status(thm)],[83])).
% 9.86/10.05 tff(90,plain,
% 9.86/10.05 ((~![I2: $i] : model(I2, C!42)) | model(I1!44, C!42)),
% 9.86/10.05 inference(quant_inst,[status(thm)],[])).
% 9.86/10.05 tff(91,plain,
% 9.86/10.05 ($false),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[90, 89, 88])).
% 9.86/10.05 tff(92,plain,(~![I2: $i] : model(I2, C!42)), inference(lemma,lemma(discharge,[]))).
% 9.86/10.05 tff(93,plain,
% 9.86/10.05 ((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | ![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28))),
% 9.86/10.05 inference(tautology,[status(thm)],[])).
% 9.86/10.05 tff(94,plain,
% 9.86/10.05 ((~(![I2: $i] : model(I2, C!42) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, wtc) | (~model(tptp_fun_I3_11(F!28), F!28)))) | status(C!42, F!28, wtc)),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[93, 92, 87, 76])).
% 9.86/10.05 tff(95,plain,
% 9.86/10.05 (status(C!42, F!28, wtc)),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[94, 65])).
% 9.86/10.05 tff(96,assumption,(status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)), introduced(assumption)).
% 9.86/10.05 tff(97,plain,
% 9.86/10.05 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)))))))))),
% 9.86/10.05 inference(rewrite,[status(thm)],[])).
% 9.86/10.05 tff(98,plain,
% 9.86/10.05 ((~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))))))))) <=> (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))))))))),
% 9.86/10.05 inference(rewrite,[status(thm)],[])).
% 9.86/10.05 tff(99,plain,
% 9.86/10.05 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)))))))))),
% 9.86/10.05 inference(monotonicity,[status(thm)],[98])).
% 9.86/10.05 tff(100,plain,
% 9.86/10.05 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)))))))))),
% 9.86/10.05 inference(transitivity,[status(thm)],[99, 97])).
% 9.86/10.05 tff(101,plain,
% 9.86/10.05 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~(model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | (~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc)))))))))),
% 9.86/10.05 inference(quant_inst,[status(thm)],[])).
% 9.86/10.05 tff(102,plain,
% 9.86/10.05 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))))))))),
% 9.86/10.05 inference(modus_ponens,[status(thm)],[101, 100])).
% 9.86/10.05 tff(103,plain,
% 9.86/10.05 (~((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)))))))),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[102, 55])).
% 9.86/10.05 tff(104,plain,
% 9.86/10.05 (((~(status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc) | ![I2: $i] : model(I2, tptp_fun_Ax_23(thm, wtc)) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wtc))) | (~model(tptp_fun_I3_11(tptp_fun_C_22(thm, wtc)), tptp_fun_C_22(thm, wtc))))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))))))) | ((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)))))),
% 9.86/10.05 inference(tautology,[status(thm)],[])).
% 9.86/10.05 tff(105,plain,
% 9.86/10.05 ((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))))),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[104, 103])).
% 9.86/10.05 tff(106,assumption,(~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))), introduced(assumption)).
% 9.86/10.05 tff(107,plain,
% 9.86/10.05 (((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)),
% 9.86/10.05 inference(tautology,[status(thm)],[])).
% 9.86/10.05 tff(108,plain,
% 9.86/10.05 (status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[107, 106])).
% 9.86/10.05 tff(109,plain,
% 9.86/10.05 ((~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)))))) | (~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))))),
% 9.86/10.05 inference(tautology,[status(thm)],[])).
% 9.86/10.05 tff(110,plain,
% 9.86/10.05 ((~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)))))) | (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))))),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[109, 108])).
% 9.86/10.05 tff(111,plain,
% 9.86/10.05 (~((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc)))),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[110, 105])).
% 9.86/10.05 tff(112,plain,
% 9.86/10.05 (((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I2_8(tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | ![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))),
% 9.86/10.05 inference(tautology,[status(thm)],[])).
% 9.86/10.05 tff(113,plain,
% 9.86/10.05 (![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))),
% 9.86/10.05 inference(unit_resolution,[status(thm)],[112, 111])).
% 9.86/10.05 tff(114,plain,
% 9.86/10.05 (^[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)))))))),
% 9.86/10.05 inference(bind,[status(th)],[])).
% 9.86/10.05 tff(115,plain,
% 9.86/10.05 (![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))))))),
% 9.86/10.05 inference(quant_intro,[status(thm)],[114])).
% 9.86/10.05 tff(116,plain,
% 9.86/10.05 (^[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)))))))),
% 9.86/10.05 inference(bind,[status(th)],[])).
% 9.86/10.05 tff(117,plain,
% 9.86/10.05 (![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))))))),
% 9.86/10.05 inference(quant_intro,[status(thm)],[116])).
% 9.86/10.05 tff(118,plain,
% 9.86/10.05 (^[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)))))))),
% 9.86/10.05 inference(bind,[status(th)],[])).
% 9.86/10.05 tff(119,plain,
% 9.86/10.05 (![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))))))),
% 9.86/10.05 inference(quant_intro,[status(thm)],[118])).
% 9.86/10.05 tff(120,plain,
% 9.86/10.05 (![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))))))),
% 9.86/10.05 inference(transitivity,[status(thm)],[119, 117])).
% 9.86/10.05 tff(121,plain,
% 9.86/10.05 (^[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))))))))),
% 9.86/10.05 inference(bind,[status(th)],[])).
% 9.86/10.05 tff(122,plain,
% 9.86/10.05 (![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))))))),
% 9.86/10.05 inference(quant_intro,[status(thm)],[121])).
% 9.86/10.05 tff(123,plain,
% 9.86/10.05 (![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))),
% 9.86/10.05 inference(rewrite,[status(thm)],[])).
% 9.86/10.05 tff(124,plain,
% 9.86/10.05 (^[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)))),
% 9.86/10.05 inference(bind,[status(th)],[])).
% 9.86/10.05 tff(125,plain,
% 9.86/10.05 (![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))),
% 9.86/10.05 inference(quant_intro,[status(thm)],[124])).
% 9.86/10.05 tff(126,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')).
% 9.86/10.05 tff(127,plain,
% 9.86/10.05 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 9.86/10.05 inference(modus_ponens,[status(thm)],[126, 125])).
% 9.86/10.05 tff(128,plain,
% 9.86/10.05 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[127, 123])).
% 9.86/10.06 tff(129,plain,(
% 9.86/10.06 ![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))))),
% 9.86/10.06 inference(skolemize,[status(sab)],[128])).
% 9.86/10.06 tff(130,plain,
% 9.86/10.06 (![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))))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[129, 122])).
% 9.86/10.06 tff(131,plain,
% 9.86/10.06 (![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))))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[130, 120])).
% 9.86/10.06 tff(132,plain,
% 9.86/10.06 (![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))))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[131, 115])).
% 9.86/10.06 tff(133,plain,
% 9.86/10.06 (((~![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_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), 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_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))))))),
% 9.86/10.06 inference(rewrite,[status(thm)],[])).
% 9.86/10.06 tff(134,plain,
% 9.86/10.06 ((~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))))) <=> (~((~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))))),
% 9.86/10.06 inference(rewrite,[status(thm)],[])).
% 9.86/10.06 tff(135,plain,
% 9.86/10.06 (((~![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_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc)))))))) <=> ((~![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_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))))))),
% 9.86/10.06 inference(monotonicity,[status(thm)],[134])).
% 9.86/10.06 tff(136,plain,
% 9.86/10.06 (((~![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_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc)))))))) <=> ((~![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_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))))))),
% 9.86/10.06 inference(transitivity,[status(thm)],[135, 133])).
% 9.86/10.06 tff(137,plain,
% 9.86/10.06 ((~![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_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc)))))))),
% 9.86/10.06 inference(quant_inst,[status(thm)],[])).
% 9.86/10.06 tff(138,plain,
% 9.86/10.06 ((~![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_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[137, 136])).
% 9.86/10.06 tff(139,plain,
% 9.86/10.06 (~((~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[138, 132])).
% 9.86/10.06 tff(140,plain,
% 9.86/10.06 (((~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wtc))) | model(I1, tptp_fun_C_22(thm, wtc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))) | ((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))),
% 9.86/10.06 inference(tautology,[status(thm)],[])).
% 9.86/10.06 tff(141,plain,
% 9.86/10.06 ((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[140, 139])).
% 9.86/10.06 tff(142,plain,
% 9.86/10.06 (((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)) | (~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))),
% 9.86/10.06 inference(tautology,[status(thm)],[])).
% 9.86/10.06 tff(143,plain,
% 9.86/10.06 (~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[142, 106])).
% 9.86/10.06 tff(144,plain,
% 9.86/10.06 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)),
% 9.86/10.06 inference(tautology,[status(thm)],[])).
% 9.86/10.06 tff(145,plain,
% 9.86/10.06 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc))))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[144, 143])).
% 9.86/10.06 tff(146,plain,
% 9.86/10.06 (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[145, 141])).
% 9.86/10.06 tff(147,plain,
% 9.86/10.06 (((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_Ax_23(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc))) | (~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc)))),
% 9.86/10.06 inference(tautology,[status(thm)],[])).
% 9.86/10.06 tff(148,plain,
% 9.86/10.06 (~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[147, 146])).
% 9.86/10.06 tff(149,plain,
% 9.86/10.06 ((~![I3: $i] : model(I3, tptp_fun_C_22(thm, wtc))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wtc), tptp_fun_Ax_23(thm, wtc)), tptp_fun_C_22(thm, wtc))),
% 9.86/10.06 inference(quant_inst,[status(thm)],[])).
% 9.86/10.06 tff(150,plain,
% 9.86/10.06 ($false),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[149, 148, 113])).
% 9.86/10.06 tff(151,plain,((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)), inference(lemma,lemma(discharge,[]))).
% 9.86/10.06 tff(152,plain,
% 9.86/10.06 (^[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))))))))),
% 9.86/10.06 inference(bind,[status(th)],[])).
% 9.86/10.06 tff(153,plain,
% 9.86/10.06 (![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)))))))),
% 9.86/10.06 inference(quant_intro,[status(thm)],[152])).
% 9.86/10.06 tff(154,plain,
% 9.86/10.06 (^[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))))))))),
% 9.86/10.06 inference(bind,[status(th)],[])).
% 9.86/10.06 tff(155,plain,
% 9.86/10.06 (![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)))))))),
% 9.86/10.06 inference(quant_intro,[status(thm)],[154])).
% 9.86/10.06 tff(156,plain,
% 9.86/10.06 (![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)))))))),
% 9.86/10.06 inference(transitivity,[status(thm)],[155, 153])).
% 9.86/10.06 tff(157,plain,
% 9.86/10.06 (^[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)))))))))),
% 9.86/10.06 inference(bind,[status(th)],[])).
% 9.86/10.06 tff(158,plain,
% 9.86/10.06 (![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)))))))),
% 9.86/10.06 inference(quant_intro,[status(thm)],[157])).
% 9.86/10.06 tff(159,plain,
% 9.86/10.06 (^[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)))))),
% 9.86/10.06 inference(bind,[status(th)],[])).
% 9.86/10.06 tff(160,plain,
% 9.86/10.06 (![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))))),
% 9.86/10.06 inference(quant_intro,[status(thm)],[159])).
% 9.86/10.06 tff(161,plain,
% 9.86/10.06 (![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))),
% 9.86/10.06 inference(rewrite,[status(thm)],[])).
% 9.86/10.06 tff(162,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')).
% 9.86/10.06 tff(163,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[162, 161])).
% 9.86/10.06 tff(164,plain,(
% 9.86/10.06 ![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))))),
% 9.86/10.06 inference(skolemize,[status(sab)],[163])).
% 9.86/10.06 tff(165,plain,
% 9.86/10.06 (![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))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[164, 160])).
% 9.86/10.06 tff(166,plain,
% 9.86/10.06 (![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)))))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[165, 158])).
% 9.86/10.06 tff(167,plain,
% 9.86/10.06 (![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)))))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[166, 156])).
% 9.86/10.06 tff(168,plain,
% 9.86/10.06 ((~![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(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm)))) | (~((~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))))))),
% 9.86/10.06 inference(quant_inst,[status(thm)],[])).
% 9.86/10.06 tff(169,plain,
% 9.86/10.06 (~((~(nota(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm)))) | (~((~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))))))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[168, 167])).
% 9.86/10.06 tff(170,plain,
% 9.86/10.06 (((~(nota(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm)))) | (~((~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))))) | ((~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))))),
% 9.86/10.06 inference(tautology,[status(thm)],[])).
% 9.86/10.06 tff(171,plain,
% 9.86/10.06 ((~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[170, 169])).
% 9.86/10.06 tff(172,plain,
% 9.86/10.06 ((~((~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm))))) | (~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))),
% 9.86/10.06 inference(tautology,[status(thm)],[])).
% 9.86/10.06 tff(173,plain,
% 9.86/10.06 ((~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[172, 171])).
% 9.86/10.06 tff(174,plain,
% 9.86/10.06 (~nota(wtc, thm)),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[173, 151])).
% 9.86/10.06 tff(175,plain,
% 9.86/10.06 (((~(nota(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm)))) | (~((~nota(wtc, thm)) | (~((~status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), wtc)) | status(tptp_fun_Ax_23(thm, wtc), tptp_fun_C_22(thm, wtc), thm)))))) | (nota(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm)))),
% 9.86/10.06 inference(tautology,[status(thm)],[])).
% 9.86/10.06 tff(176,plain,
% 9.86/10.06 (nota(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[175, 169])).
% 9.86/10.06 tff(177,plain,
% 9.86/10.06 ((~(nota(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm)))) | nota(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm))),
% 9.86/10.06 inference(tautology,[status(thm)],[])).
% 9.86/10.06 tff(178,plain,
% 9.86/10.06 (nota(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[177, 176])).
% 9.86/10.06 tff(179,plain,
% 9.86/10.06 (![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm))),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[178, 174])).
% 9.86/10.06 tff(180,plain,
% 9.86/10.06 (((~![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm))),
% 9.86/10.06 inference(rewrite,[status(thm)],[])).
% 9.86/10.06 tff(181,plain,
% 9.86/10.06 ((~![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm))),
% 9.86/10.06 inference(quant_inst,[status(thm)],[])).
% 9.86/10.06 tff(182,plain,
% 9.86/10.06 ((~![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm)),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[181, 180])).
% 9.86/10.06 tff(183,plain,
% 9.86/10.06 (status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm)),
% 9.86/10.06 inference(unit_resolution,[status(thm)],[182, 179, 96])).
% 9.86/10.06 tff(184,plain,
% 9.86/10.06 (^[S1: $i, S2: $i] : refl((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 9.86/10.06 inference(bind,[status(th)],[])).
% 9.86/10.06 tff(185,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 9.86/10.06 inference(quant_intro,[status(thm)],[184])).
% 9.86/10.06 tff(186,plain,
% 9.86/10.06 (^[S1: $i, S2: $i] : rewrite((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 9.86/10.06 inference(bind,[status(th)],[])).
% 9.86/10.06 tff(187,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 9.86/10.06 inference(quant_intro,[status(thm)],[186])).
% 9.86/10.06 tff(188,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 9.86/10.06 inference(transitivity,[status(thm)],[187, 185])).
% 9.86/10.06 tff(189,plain,
% 9.86/10.06 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) <=> (mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))), trans(monotonicity(rewrite((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) <=> (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))), rewrite(((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))))),
% 9.86/10.06 inference(bind,[status(th)],[])).
% 9.86/10.06 tff(190,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 9.86/10.06 inference(quant_intro,[status(thm)],[189])).
% 9.86/10.06 tff(191,plain,
% 9.86/10.06 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))))),
% 9.86/10.06 inference(bind,[status(th)],[])).
% 9.86/10.06 tff(192,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 9.86/10.06 inference(quant_intro,[status(thm)],[191])).
% 9.86/10.06 tff(193,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 9.86/10.06 inference(rewrite,[status(thm)],[])).
% 9.86/10.06 tff(194,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','mighta')).
% 9.86/10.06 tff(195,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[194, 193])).
% 9.86/10.06 tff(196,plain,(
% 9.86/10.06 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 9.86/10.06 inference(skolemize,[status(sab)],[195])).
% 9.86/10.06 tff(197,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[196, 192])).
% 9.86/10.06 tff(198,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[197, 190])).
% 9.86/10.06 tff(199,plain,
% 9.86/10.06 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 9.86/10.06 inference(modus_ponens,[status(thm)],[198, 188])).
% 9.86/10.06 tff(200,plain,
% 9.86/10.06 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)))))))))),
% 9.86/10.07 inference(rewrite,[status(thm)],[])).
% 9.86/10.07 tff(201,plain,
% 9.86/10.07 ((~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)))))))) <=> (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc))))))))),
% 9.86/10.07 inference(rewrite,[status(thm)],[])).
% 9.86/10.07 tff(202,plain,
% 9.86/10.07 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)))))))))),
% 9.86/10.07 inference(monotonicity,[status(thm)],[201])).
% 9.86/10.07 tff(203,plain,
% 9.86/10.07 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)))))))))),
% 9.86/10.07 inference(transitivity,[status(thm)],[202, 200])).
% 9.86/10.07 tff(204,plain,
% 9.86/10.07 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm))))))))),
% 9.86/10.07 inference(quant_inst,[status(thm)],[])).
% 9.86/10.07 tff(205,plain,
% 9.86/10.07 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc))))))))),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[204, 203])).
% 9.86/10.07 tff(206,plain,
% 9.86/10.07 (~((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc)))))))),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[205, 199])).
% 9.86/10.07 tff(207,plain,
% 9.86/10.07 (((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | (~((~mighta(wtc, thm)) | (~((~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), thm)) | (~status(tptp_fun_Ax_19(thm, wtc), tptp_fun_C_18(thm, wtc), wtc))))))) | (mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))),
% 9.86/10.07 inference(tautology,[status(thm)],[])).
% 9.86/10.07 tff(208,plain,
% 9.86/10.07 (mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[207, 206])).
% 9.86/10.07 tff(209,plain,
% 9.86/10.07 ((~mighta(wtc, thm)) <=> (~mighta(wtc, thm))),
% 9.86/10.07 inference(rewrite,[status(thm)],[])).
% 9.86/10.07 tff(210,axiom,(~mighta(wtc, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mighta_wtc_thm')).
% 9.86/10.07 tff(211,plain,
% 9.86/10.07 (~mighta(wtc, thm)),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[210, 209])).
% 9.86/10.07 tff(212,plain,
% 9.86/10.07 ((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))),
% 9.86/10.07 inference(tautology,[status(thm)],[])).
% 9.86/10.07 tff(213,plain,
% 9.86/10.07 ((~(mighta(wtc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[212, 211])).
% 9.86/10.07 tff(214,plain,
% 9.86/10.07 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[213, 208])).
% 9.86/10.07 tff(215,plain,
% 9.86/10.07 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | ((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)))),
% 9.86/10.07 inference(rewrite,[status(thm)],[])).
% 9.86/10.07 tff(216,plain,
% 9.86/10.07 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | ((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)))),
% 9.86/10.07 inference(quant_inst,[status(thm)],[])).
% 9.86/10.07 tff(217,plain,
% 9.86/10.07 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wtc)))) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), thm)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc))),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[216, 215])).
% 9.86/10.07 tff(218,plain,
% 9.86/10.07 ($false),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[217, 214, 96, 183])).
% 9.86/10.07 tff(219,plain,(~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)), inference(lemma,lemma(discharge,[]))).
% 9.86/10.07 tff(220,plain,
% 9.86/10.07 (((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap))) | status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)),
% 9.86/10.07 inference(tautology,[status(thm)],[])).
% 9.86/10.07 tff(221,plain,
% 9.86/10.07 ((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap))),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[220, 219])).
% 9.86/10.07 tff(222,plain,
% 9.86/10.07 (^[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))))))))),
% 9.86/10.07 inference(bind,[status(th)],[])).
% 9.86/10.07 tff(223,plain,
% 9.86/10.07 (![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)))))))),
% 9.86/10.07 inference(quant_intro,[status(thm)],[222])).
% 9.86/10.07 tff(224,plain,
% 9.86/10.07 (^[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)))))))),
% 9.86/10.07 inference(bind,[status(th)],[])).
% 9.86/10.07 tff(225,plain,
% 9.86/10.07 (![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))))))),
% 9.86/10.07 inference(quant_intro,[status(thm)],[224])).
% 9.86/10.07 tff(226,plain,
% 9.86/10.07 (^[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)))))))),
% 9.86/10.07 inference(bind,[status(th)],[])).
% 9.86/10.07 tff(227,plain,
% 9.86/10.07 (![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))))))),
% 9.86/10.07 inference(quant_intro,[status(thm)],[226])).
% 9.86/10.07 tff(228,plain,
% 9.86/10.07 (![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))))))),
% 9.86/10.07 inference(transitivity,[status(thm)],[227, 225])).
% 9.86/10.07 tff(229,plain,
% 9.86/10.07 (^[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))))))))),
% 9.86/10.07 inference(bind,[status(th)],[])).
% 9.86/10.07 tff(230,plain,
% 9.86/10.07 (![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))))))),
% 9.86/10.07 inference(quant_intro,[status(thm)],[229])).
% 9.86/10.07 tff(231,plain,
% 9.86/10.07 (![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))),
% 9.86/10.07 inference(rewrite,[status(thm)],[])).
% 9.86/10.07 tff(232,plain,
% 9.86/10.07 (^[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)))),
% 9.86/10.07 inference(bind,[status(th)],[])).
% 9.86/10.07 tff(233,plain,
% 9.86/10.07 (![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))),
% 9.86/10.07 inference(quant_intro,[status(thm)],[232])).
% 9.86/10.07 tff(234,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')).
% 9.86/10.07 tff(235,plain,
% 9.86/10.07 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[234, 233])).
% 9.86/10.07 tff(236,plain,
% 9.86/10.07 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[235, 231])).
% 9.86/10.07 tff(237,plain,(
% 9.86/10.07 ![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))))),
% 9.86/10.07 inference(skolemize,[status(sab)],[236])).
% 9.86/10.07 tff(238,plain,
% 9.86/10.07 (![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))))))),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[237, 230])).
% 9.86/10.07 tff(239,plain,
% 9.86/10.07 (![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))))))),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[238, 228])).
% 9.86/10.07 tff(240,plain,
% 9.86/10.07 (![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)))))))),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[239, 223])).
% 9.86/10.07 tff(241,plain,
% 9.86/10.07 (((~![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(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc)))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))))))),
% 9.86/10.07 inference(rewrite,[status(thm)],[])).
% 9.86/10.07 tff(242,plain,
% 9.86/10.07 ((~((~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))) | (~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | (~status(Ax, C, sap))))))) <=> (~((~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc)))))),
% 9.86/10.07 inference(rewrite,[status(thm)],[])).
% 9.86/10.07 tff(243,plain,
% 9.86/10.07 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))) | (~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | (~status(Ax, C, sap)))))))) <=> ((~![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(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))))))),
% 9.86/10.07 inference(monotonicity,[status(thm)],[242])).
% 9.86/10.07 tff(244,plain,
% 9.86/10.07 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))) | (~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | (~status(Ax, C, sap)))))))) <=> ((~![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(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))))))),
% 9.86/10.07 inference(transitivity,[status(thm)],[243, 241])).
% 9.86/10.07 tff(245,plain,
% 9.86/10.07 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))) | (~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, wtc)) | (~status(Ax, C, sap)))))))),
% 9.86/10.07 inference(quant_inst,[status(thm)],[])).
% 9.86/10.07 tff(246,plain,
% 9.86/10.07 ((~![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(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc)))))),
% 9.86/10.07 inference(modus_ponens,[status(thm)],[245, 244])).
% 9.86/10.07 tff(247,plain,
% 9.86/10.07 (~((~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))))),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[246, 240])).
% 9.86/10.07 tff(248,plain,
% 9.86/10.07 (((~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc)))) | ((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))),
% 9.86/10.07 inference(tautology,[status(thm)],[])).
% 9.86/10.07 tff(249,plain,
% 9.86/10.07 ((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc)),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[248, 247])).
% 9.86/10.07 tff(250,plain,
% 9.86/10.07 ((~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc))) | (~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc)),
% 9.86/10.07 inference(tautology,[status(thm)],[])).
% 9.86/10.07 tff(251,plain,
% 9.86/10.07 ((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc)),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[250, 249])).
% 9.86/10.07 tff(252,plain,
% 9.86/10.07 (nevera(sap, wtc)),
% 9.86/10.07 inference(unit_resolution,[status(thm)],[251, 221])).
% 9.86/10.07 tff(253,plain,
% 9.86/10.07 (((~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~((~((~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), wtc)) | (~status(tptp_fun_Ax_25(wtc, sap), tptp_fun_C_24(wtc, sap), sap)))) | nevera(sap, wtc)))) | ((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))),
% 9.86/10.08 inference(tautology,[status(thm)],[])).
% 9.86/10.08 tff(254,plain,
% 9.86/10.08 ((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc)))),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[253, 247])).
% 9.86/10.08 tff(255,plain,
% 9.86/10.08 ((~((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc))))) | (~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc)))),
% 9.86/10.08 inference(tautology,[status(thm)],[])).
% 9.86/10.08 tff(256,plain,
% 9.86/10.08 ((~nevera(sap, wtc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc)))),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[255, 254])).
% 9.86/10.08 tff(257,plain,
% 9.86/10.08 (![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc)))),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[256, 252])).
% 9.86/10.08 tff(258,plain,
% 9.86/10.08 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc)))) | ((~status(C!42, F!28, sap)) | (~status(C!42, F!28, wtc)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc)))) | (~status(C!42, F!28, sap)) | (~status(C!42, F!28, wtc)))),
% 9.86/10.08 inference(rewrite,[status(thm)],[])).
% 9.86/10.08 tff(259,plain,
% 9.86/10.08 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc)))) | ((~status(C!42, F!28, sap)) | (~status(C!42, F!28, wtc)))),
% 9.86/10.08 inference(quant_inst,[status(thm)],[])).
% 9.86/10.08 tff(260,plain,
% 9.86/10.08 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, wtc)))) | (~status(C!42, F!28, sap)) | (~status(C!42, F!28, wtc))),
% 9.86/10.08 inference(modus_ponens,[status(thm)],[259, 258])).
% 9.86/10.08 tff(261,plain,
% 9.86/10.08 ($false),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[260, 257, 95, 32])).
% 9.86/10.08 tff(262,plain,(~status(C!42, F!28, sap)), inference(lemma,lemma(discharge,[]))).
% 9.86/10.08 tff(263,plain,
% 9.86/10.08 ((~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap)),
% 9.86/10.08 inference(tautology,[status(thm)],[])).
% 9.86/10.08 tff(264,plain,
% 9.86/10.08 ((~((~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))) | status(C!42, F!28, sap))) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28)))))),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[263, 262])).
% 9.86/10.08 tff(265,plain,
% 9.86/10.08 (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28))))),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[264, 31])).
% 9.86/10.08 tff(266,plain,
% 9.86/10.08 (((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : (~model(I2, F!28)))) | ![I2: $i] : (~model(I2, F!28))),
% 9.86/10.08 inference(tautology,[status(thm)],[])).
% 9.86/10.08 tff(267,plain,
% 9.86/10.08 (![I2: $i] : (~model(I2, F!28))),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[266, 265])).
% 9.86/10.08 tff(268,plain,
% 9.86/10.08 ((~![I: $i] : model(I, F!28)) | model(I4!41, F!28)),
% 9.86/10.08 inference(quant_inst,[status(thm)],[])).
% 9.86/10.08 tff(269,plain,
% 9.86/10.08 (model(I4!41, F!28)),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[268, 73])).
% 9.86/10.08 tff(270,plain,
% 9.86/10.08 ((~![I2: $i] : (~model(I2, F!28))) | (~model(I4!41, F!28))),
% 9.86/10.08 inference(quant_inst,[status(thm)],[])).
% 9.86/10.08 tff(271,plain,
% 9.86/10.08 ($false),
% 9.86/10.08 inference(unit_resolution,[status(thm)],[270, 269, 267])).
% 9.86/10.08 % SZS output end Proof
% 9.86/10.08 % E exiting
%------------------------------------------------------------------------------