%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS255+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:38 AM UTC 2025
% Result : Theorem 0.55s 0.74s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS255+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:17:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.55/0.74 % SZS status Theorem
% 0.55/0.74 % SZS output start Proof
% 0.55/0.74 tff(model_type, type, (
% 0.55/0.74 model: ( $i * $i ) > $o)).
% 0.55/0.74 tff(tptp_fun_F_29_type, type, (
% 0.55/0.74 tptp_fun_F_29: $i)).
% 0.55/0.74 tff(tptp_fun_I1_0_type, type, (
% 0.55/0.74 tptp_fun_I1_0: $i > $i)).
% 0.55/0.74 tff(status_type, type, (
% 0.55/0.74 status: ( $i * $i * $i ) > $o)).
% 0.55/0.74 tff(sap_type, type, (
% 0.55/0.74 sap: $i)).
% 0.55/0.74 tff(tptp_fun_I2_1_type, type, (
% 0.55/0.74 tptp_fun_I2_1: $i > $i)).
% 0.55/0.74 tff(thm_type, type, (
% 0.55/0.74 thm: $i)).
% 0.55/0.74 tff(tptp_fun_I1_3_type, type, (
% 0.55/0.74 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.55/0.74 tff(mighta_type, type, (
% 0.55/0.74 mighta: ( $i * $i ) > $o)).
% 0.55/0.74 tff(tptp_fun_C_18_type, type, (
% 0.55/0.74 tptp_fun_C_18: ( $i * $i ) > $i)).
% 0.55/0.74 tff(tptp_fun_Ax_19_type, type, (
% 0.55/0.74 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 0.55/0.74 tff(tptp_fun_I1_30_type, type, (
% 0.55/0.74 tptp_fun_I1_30: $i)).
% 0.55/0.74 tff(tptp_fun_I2_31_type, type, (
% 0.55/0.74 tptp_fun_I2_31: $i)).
% 0.55/0.74 tff(1,plain,
% 0.55/0.74 (^[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)))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(2,plain,
% 0.55/0.74 (![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))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[1])).
% 0.55/0.74 tff(3,plain,
% 0.55/0.74 (^[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)))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(4,plain,
% 0.55/0.74 (![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))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[3])).
% 0.55/0.74 tff(5,plain,
% 0.55/0.74 (^[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)))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(6,plain,
% 0.55/0.74 (![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))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[5])).
% 0.55/0.74 tff(7,plain,
% 0.55/0.74 (![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))))))),
% 0.55/0.74 inference(transitivity,[status(thm)],[6, 4])).
% 0.55/0.74 tff(8,plain,
% 0.55/0.74 (^[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))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(9,plain,
% 0.55/0.74 (![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))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[8])).
% 0.55/0.74 tff(10,plain,
% 0.55/0.74 (^[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)))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(11,plain,
% 0.55/0.74 (![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))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[10])).
% 0.55/0.74 tff(12,plain,
% 0.55/0.74 (![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))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(13,plain,
% 0.55/0.74 (^[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)))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(14,plain,
% 0.55/0.74 (![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))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[13])).
% 0.55/0.74 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')).
% 0.55/0.74 tff(16,plain,
% 0.55/0.74 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.55/0.74 tff(17,plain,
% 0.55/0.74 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.55/0.74 tff(18,plain,(
% 0.55/0.74 ![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))))),
% 0.55/0.74 inference(skolemize,[status(sab)],[17])).
% 0.55/0.74 tff(19,plain,
% 0.55/0.74 (![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))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.55/0.74 tff(20,plain,
% 0.55/0.74 (![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))))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.55/0.74 tff(21,plain,
% 0.55/0.74 (![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))))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.55/0.74 tff(22,plain,
% 0.55/0.74 (![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))))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.55/0.74 tff(23,plain,
% 0.55/0.74 (((~![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))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)))) | (~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, 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))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)))) | (~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(24,plain,
% 0.55/0.74 ((~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)) | ![I1: $i] : (~model(I1, F!29)))))) <=> (~((~(![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)))) | (~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap)))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(25,plain,
% 0.55/0.74 (((~![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(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)) | ![I1: $i] : (~model(I1, F!29))))))) <=> ((~![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))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)))) | (~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[24])).
% 0.55/0.74 tff(26,plain,
% 0.55/0.74 (((~![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(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)) | ![I1: $i] : (~model(I1, F!29))))))) <=> ((~![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))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)))) | (~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[25, 23])).
% 0.55/0.75 tff(27,plain,
% 0.55/0.75 ((~![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(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~(model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)) | ![I1: $i] : (~model(I1, F!29))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(28,plain,
% 0.55/0.75 ((~![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))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)))) | (~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap)))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.55/0.75 tff(29,plain,
% 0.55/0.75 (~((~(![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)))) | (~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.55/0.75 tff(30,plain,
% 0.55/0.75 (((~(![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(F!29), F!29) | (~status(F!29, F!29, sap)))) | (~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap)))) | ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))),
% 0.55/0.75 inference(tautology,[status(thm)],[])).
% 0.55/0.75 tff(31,plain,
% 0.55/0.75 ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.55/0.75 tff(32,plain,
% 0.55/0.75 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C)))))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(33,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[32])).
% 0.55/0.75 tff(34,plain,
% 0.55/0.75 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(35,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[34])).
% 0.55/0.75 tff(36,plain,
% 0.55/0.75 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(37,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[36])).
% 0.55/0.75 tff(38,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[37, 35])).
% 0.55/0.75 tff(39,plain,
% 0.55/0.75 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))), rewrite((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(40,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[39])).
% 0.55/0.75 tff(41,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(42,plain,
% 0.55/0.75 (^[Ax: $i, C: $i] : rewrite((![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(43,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[42])).
% 0.55/0.75 tff(44,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','thm')).
% 0.55/0.75 tff(45,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.55/0.75 tff(46,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.55/0.75 tff(47,plain,(
% 0.55/0.75 ![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))),
% 0.55/0.75 inference(skolemize,[status(sab)],[46])).
% 0.55/0.75 tff(48,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.55/0.75 tff(49,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.55/0.75 tff(50,plain,
% 0.55/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[49, 33])).
% 0.55/0.75 tff(51,plain,
% 0.55/0.75 (((~![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(F!29, F!29, 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(F!29, F!29, thm))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(52,plain,
% 0.55/0.75 ((~(~status(F!29, F!29, thm))) <=> status(F!29, F!29, thm)),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(53,plain,
% 0.55/0.75 (((~status(F!29, F!29, thm)) | $false) <=> (~status(F!29, F!29, thm))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(54,plain,
% 0.55/0.75 ((~$true) <=> $false),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(55,plain,
% 0.55/0.75 (((~status(F!29, F!29, thm)) | $true) <=> $true),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(56,plain,
% 0.55/0.75 (![I1: $i] : $true <=> $true),
% 0.55/0.75 inference(elim_unused_vars,[status(thm)],[])).
% 0.55/0.75 tff(57,plain,
% 0.55/0.75 (![I1: $i] : $true <=> ![I1: $i] : $true),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(58,plain,
% 0.55/0.75 (![I1: $i] : $true <=> $true),
% 0.55/0.75 inference(transitivity,[status(thm)],[57, 56])).
% 0.55/0.75 tff(59,plain,
% 0.55/0.75 (^[I1: $i] : rewrite(((~model(I1, F!29)) | model(I1, F!29)) <=> $true)),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(60,plain,
% 0.55/0.75 (![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)) <=> ![I1: $i] : $true),
% 0.55/0.75 inference(quant_intro,[status(thm)],[59])).
% 0.55/0.75 tff(61,plain,
% 0.55/0.75 (![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)) <=> $true),
% 0.55/0.75 inference(transitivity,[status(thm)],[60, 58])).
% 0.55/0.75 tff(62,plain,
% 0.55/0.75 (((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))) <=> ((~status(F!29, F!29, thm)) | $true)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[61])).
% 0.55/0.75 tff(63,plain,
% 0.55/0.75 (((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))) <=> $true),
% 0.55/0.75 inference(transitivity,[status(thm)],[62, 55])).
% 0.55/0.75 tff(64,plain,
% 0.55/0.75 ((~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)))) <=> (~$true)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[63])).
% 0.55/0.75 tff(65,plain,
% 0.55/0.75 ((~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)))) <=> $false),
% 0.55/0.75 inference(transitivity,[status(thm)],[64, 54])).
% 0.55/0.75 tff(66,plain,
% 0.55/0.75 ((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) <=> (~status(F!29, F!29, thm))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(67,plain,
% 0.55/0.75 (((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))) <=> ((~status(F!29, F!29, thm)) | $false)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[66, 65])).
% 0.55/0.75 tff(68,plain,
% 0.55/0.75 (((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))) <=> (~status(F!29, F!29, thm))),
% 0.55/0.75 inference(transitivity,[status(thm)],[67, 53])).
% 0.55/0.75 tff(69,plain,
% 0.55/0.75 ((~((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)))))) <=> (~(~status(F!29, F!29, thm)))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[68])).
% 0.55/0.75 tff(70,plain,
% 0.55/0.75 ((~((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29)))))) <=> status(F!29, F!29, thm)),
% 0.55/0.75 inference(transitivity,[status(thm)],[69, 52])).
% 0.55/0.75 tff(71,plain,
% 0.55/0.75 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))))) <=> ((~![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(F!29, F!29, thm))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[70])).
% 0.55/0.75 tff(72,plain,
% 0.55/0.75 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))))) <=> ((~![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(F!29, F!29, thm))),
% 0.55/0.75 inference(transitivity,[status(thm)],[71, 51])).
% 0.55/0.75 tff(73,plain,
% 0.55/0.75 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!29, F!29), F!29)) | model(tptp_fun_I1_3(F!29, F!29), F!29))) | status(F!29, F!29, thm))) | (~((~status(F!29, F!29, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, F!29))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(74,plain,
% 0.55/0.75 ((~![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(F!29, F!29, thm)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.55/0.75 tff(75,plain,
% 0.55/0.75 (status(F!29, F!29, thm)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[74, 50])).
% 0.55/0.75 tff(76,plain,
% 0.55/0.75 (^[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)))))))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(77,plain,
% 0.55/0.75 (![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))))))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[76])).
% 0.55/0.75 tff(78,plain,
% 0.55/0.75 (^[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)))))))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(79,plain,
% 0.55/0.75 (![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))))))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[78])).
% 0.55/0.75 tff(80,plain,
% 0.55/0.75 (![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))))))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[79, 77])).
% 0.55/0.75 tff(81,plain,
% 0.55/0.75 (^[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))))))))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(82,plain,
% 0.55/0.75 (![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))))))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[81])).
% 0.55/0.75 tff(83,plain,
% 0.55/0.75 (^[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)))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(84,plain,
% 0.55/0.75 (![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))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[83])).
% 0.55/0.75 tff(85,plain,
% 0.55/0.75 (![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))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(86,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')).
% 0.55/0.75 tff(87,plain,
% 0.55/0.75 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.55/0.75 tff(88,plain,(
% 0.55/0.75 ![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))))),
% 0.55/0.75 inference(skolemize,[status(sab)],[87])).
% 0.55/0.75 tff(89,plain,
% 0.55/0.75 (![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))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.55/0.75 tff(90,plain,
% 0.55/0.75 (![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))))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.55/0.75 tff(91,plain,
% 0.55/0.75 (![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))))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.55/0.75 tff(92,plain,
% 0.55/0.75 (((~![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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), 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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm)))))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(93,plain,
% 0.55/0.75 ((~((~(mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sap))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm)))))))) <=> (~((~(mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm))))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(94,plain,
% 0.55/0.75 (((~![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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sap))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), 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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm)))))))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[93])).
% 0.55/0.76 tff(95,plain,
% 0.55/0.76 (((~![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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sap))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), 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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm)))))))))),
% 0.55/0.76 inference(transitivity,[status(thm)],[94, 92])).
% 0.55/0.76 tff(96,plain,
% 0.55/0.76 ((~![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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sap))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm))))))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(97,plain,
% 0.55/0.76 ((~![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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm))))))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.55/0.76 tff(98,plain,
% 0.55/0.76 (~((~(mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm)))))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[97, 91])).
% 0.55/0.76 tff(99,plain,
% 0.55/0.76 (((~(mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | (~((~mighta(sap, thm)) | (~((~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), sap)) | (~status(tptp_fun_Ax_19(thm, sap), tptp_fun_C_18(thm, sap), thm))))))) | (mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(100,plain,
% 0.55/0.76 (mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.55/0.76 tff(101,plain,
% 0.55/0.76 ((~mighta(sap, thm)) <=> (~mighta(sap, thm))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(102,axiom,(~mighta(sap, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mighta_sap_thm')).
% 0.55/0.76 tff(103,plain,
% 0.55/0.76 (~mighta(sap, thm)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.55/0.76 tff(104,plain,
% 0.55/0.76 ((~(mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm)))),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(105,plain,
% 0.55/0.76 ((~(mighta(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.55/0.76 tff(106,plain,
% 0.55/0.76 (![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[105, 100])).
% 0.55/0.76 tff(107,plain,
% 0.55/0.76 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm)))) | ((~status(F!29, F!29, sap)) | (~status(F!29, F!29, thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm)))) | (~status(F!29, F!29, sap)) | (~status(F!29, F!29, thm)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(108,plain,
% 0.55/0.76 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm)))) | ((~status(F!29, F!29, sap)) | (~status(F!29, F!29, thm)))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(109,plain,
% 0.55/0.76 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, thm)))) | (~status(F!29, F!29, sap)) | (~status(F!29, F!29, thm))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.55/0.76 tff(110,plain,
% 0.55/0.76 (~status(F!29, F!29, sap)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[109, 106, 75])).
% 0.55/0.76 tff(111,plain,
% 0.55/0.76 ((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap)),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(112,plain,
% 0.55/0.76 ((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))) | status(F!29, F!29, sap))) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29)))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.55/0.76 tff(113,plain,
% 0.55/0.76 (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[112, 31])).
% 0.55/0.76 tff(114,plain,
% 0.55/0.76 (((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, F!29)))) | ![I2: $i] : (~model(I2, F!29))),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(115,plain,
% 0.55/0.76 (![I2: $i] : (~model(I2, F!29))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.55/0.76 tff(116,plain,
% 0.55/0.76 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(117,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 0.55/0.76 tff(118,plain,
% 0.55/0.76 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.55/0.76 tff(119,plain,
% 0.55/0.76 (model(I1!30, F!29)),
% 0.55/0.76 inference(and_elim,[status(thm)],[118])).
% 0.55/0.76 tff(120,plain,
% 0.55/0.76 ((~![I2: $i] : (~model(I2, F!29))) | (~model(I1!30, F!29))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(121,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[120, 119, 115])).
% 0.55/0.76 % SZS output end Proof
% 0.55/0.76 % E exiting
%------------------------------------------------------------------------------