%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS268+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 123.70s 123.86s
% Output : Proof 123.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS268+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.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 19:18:24 EDT 2025
% 0.11/0.34 % CPUTime :
% 123.70/123.86 % SZS status Theorem
% 123.70/123.86 % SZS output start Proof
% 123.70/123.86 tff(model_type, type, (
% 123.70/123.86 model: ( $i * $i ) > $o)).
% 123.70/123.86 tff(not_type, type, (
% 123.70/123.86 not: $i > $i)).
% 123.70/123.86 tff(tptp_fun_F_29_type, type, (
% 123.70/123.86 tptp_fun_F_29: $i)).
% 123.70/123.86 tff(status_type, type, (
% 123.70/123.86 status: ( $i * $i * $i ) > $o)).
% 123.70/123.86 tff(wca_type, type, (
% 123.70/123.86 wca: $i)).
% 123.70/123.86 tff(tptp_fun_C_20_type, type, (
% 123.70/123.86 tptp_fun_C_20: ( $i * $i ) > $i)).
% 123.70/123.86 tff(tac_type, type, (
% 123.70/123.86 tac: $i)).
% 123.70/123.86 tff(noc_type, type, (
% 123.70/123.86 noc: $i)).
% 123.70/123.86 tff(tptp_fun_I1_0_type, type, (
% 123.70/123.86 tptp_fun_I1_0: $i > $i)).
% 123.70/123.86 tff(tptp_fun_I3_13_type, type, (
% 123.70/123.86 tptp_fun_I3_13: $i > $i)).
% 123.70/123.86 tff(tptp_fun_I2_1_type, type, (
% 123.70/123.86 tptp_fun_I2_1: $i > $i)).
% 123.70/123.86 tff(thm_type, type, (
% 123.70/123.86 thm: $i)).
% 123.70/123.86 tff(sca_type, type, (
% 123.70/123.86 sca: $i)).
% 123.70/123.86 tff(nota_type, type, (
% 123.70/123.86 nota: ( $i * $i ) > $o)).
% 123.70/123.86 tff(tptp_fun_C_22_type, type, (
% 123.70/123.86 tptp_fun_C_22: ( $i * $i ) > $i)).
% 123.70/123.86 tff(tptp_fun_Ax_23_type, type, (
% 123.70/123.86 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 123.70/123.86 tff(tptp_fun_I1_3_type, type, (
% 123.70/123.86 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 123.70/123.86 tff(tptp_fun_Ax_21_type, type, (
% 123.70/123.86 tptp_fun_Ax_21: ( $i * $i ) > $i)).
% 123.70/123.86 tff(isa_type, type, (
% 123.70/123.86 isa: ( $i * $i ) > $o)).
% 123.70/123.86 tff(tptp_fun_C_18_type, type, (
% 123.70/123.86 tptp_fun_C_18: ( $i * $i ) > $i)).
% 123.70/123.86 tff(tptp_fun_Ax_19_type, type, (
% 123.70/123.86 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 123.70/123.86 tff(mighta_type, type, (
% 123.70/123.86 mighta: ( $i * $i ) > $o)).
% 123.70/123.86 tff(unp_type, type, (
% 123.70/123.86 unp: $i)).
% 123.70/123.86 tff(tptp_fun_F_28_type, type, (
% 123.70/123.86 tptp_fun_F_28: $i)).
% 123.70/123.86 tff(tptp_fun_I2_5_type, type, (
% 123.70/123.86 tptp_fun_I2_5: $i > $i)).
% 123.70/123.86 tff(tptp_fun_I1_30_type, type, (
% 123.70/123.86 tptp_fun_I1_30: $i)).
% 123.70/123.86 tff(tptp_fun_I2_31_type, type, (
% 123.70/123.86 tptp_fun_I2_31: $i)).
% 123.70/123.86 tff(tptp_fun_I2_17_type, type, (
% 123.70/123.86 tptp_fun_I2_17: ( $i * $i ) > $i)).
% 123.70/123.86 tff(tptp_fun_I1_2_type, type, (
% 123.70/123.86 tptp_fun_I1_2: ( $i * $i ) > $i)).
% 123.70/123.86 tff(eqv_type, type, (
% 123.70/123.86 eqv: $i)).
% 123.70/123.86 tff(tptp_fun_I2_4_type, type, (
% 123.70/123.86 tptp_fun_I2_4: ( $i * $i ) > $i)).
% 123.70/123.86 tff(1,plain,
% 123.70/123.86 (^[Ax: $i, C: $i] : rewrite((~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 123.70/123.86 inference(bind,[status(th)],[])).
% 123.70/123.86 tff(2,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.86 inference(quant_intro,[status(thm)],[1])).
% 123.70/123.86 tff(3,plain,
% 123.70/123.86 (^[Ax: $i, C: $i] : refl((~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 123.70/123.86 inference(bind,[status(th)],[])).
% 123.70/123.86 tff(4,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.86 inference(quant_intro,[status(thm)],[3])).
% 123.70/123.86 tff(5,plain,
% 123.70/123.86 (^[Ax: $i, C: $i] : rewrite((~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 123.70/123.86 inference(bind,[status(th)],[])).
% 123.70/123.86 tff(6,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.86 inference(quant_intro,[status(thm)],[5])).
% 123.70/123.86 tff(7,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.86 inference(transitivity,[status(thm)],[6, 4])).
% 123.70/123.86 tff(8,plain,
% 123.70/123.86 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) <=> (![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))), trans(monotonicity(rewrite((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) <=> (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))) <=> ((~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, wca))))), rewrite(((~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, wca))) <=> ((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))) <=> ((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))), (((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))), rewrite(((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))) <=> (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))), (((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))))),
% 123.70/123.86 inference(bind,[status(th)],[])).
% 123.70/123.86 tff(9,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> ![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.86 inference(quant_intro,[status(thm)],[8])).
% 123.70/123.86 tff(10,plain,
% 123.70/123.86 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C)) | status(Ax, C, wca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))))),
% 123.70/123.86 inference(bind,[status(th)],[])).
% 123.70/123.86 tff(11,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C)) | status(Ax, C, wca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca)))) <=> ![Ax: $i, C: $i] : ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))))),
% 123.70/123.86 inference(quant_intro,[status(thm)],[10])).
% 123.70/123.86 tff(12,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))),
% 123.70/123.86 inference(rewrite,[status(thm)],[])).
% 123.70/123.86 tff(13,plain,
% 123.70/123.86 (^[Ax: $i, C: $i] : rewrite(((((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca)) <=> (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca)))),
% 123.70/123.86 inference(bind,[status(th)],[])).
% 123.70/123.86 tff(14,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : ((((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))),
% 123.70/123.86 inference(quant_intro,[status(thm)],[13])).
% 123.70/123.86 tff(15,axiom,(![Ax: $i, C: $i] : ((((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','wca')).
% 123.70/123.86 tff(16,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))),
% 123.70/123.86 inference(modus_ponens,[status(thm)],[15, 14])).
% 123.70/123.86 tff(17,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C) & ?[I3: $i] : (~model(I3, C))) <=> status(Ax, C, wca))),
% 123.70/123.86 inference(modus_ponens,[status(thm)],[16, 12])).
% 123.70/123.86 tff(18,plain,(
% 123.70/123.86 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C)) | status(Ax, C, wca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))))),
% 123.70/123.86 inference(skolemize,[status(sab)],[17])).
% 123.70/123.86 tff(19,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : ((![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C) & (~model(tptp_fun_I3_13(C), C))) | (~status(Ax, C, wca))))),
% 123.70/123.86 inference(modus_ponens,[status(thm)],[18, 11])).
% 123.70/123.86 tff(20,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.86 inference(modus_ponens,[status(thm)],[19, 9])).
% 123.70/123.86 tff(21,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (~((~(![I3: $i] : model(I3, C) | status(Ax, C, wca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.86 inference(modus_ponens,[status(thm)],[20, 7])).
% 123.70/123.86 tff(22,plain,
% 123.70/123.86 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.86 inference(modus_ponens,[status(thm)],[21, 2])).
% 123.70/123.86 tff(23,plain,
% 123.70/123.86 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))) | model(tptp_fun_I3_13(not(F!29)), not(F!29))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))) | model(tptp_fun_I3_13(not(F!29)), not(F!29)))))))))),
% 123.70/123.86 inference(rewrite,[status(thm)],[])).
% 123.70/123.86 tff(24,plain,
% 123.70/123.86 ((~((~(status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~(model(tptp_fun_I3_13(not(F!29)), not(F!29)) | (~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))))))))) <=> (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))) | model(tptp_fun_I3_13(not(F!29)), not(F!29))))))))),
% 123.70/123.86 inference(rewrite,[status(thm)],[])).
% 123.70/123.86 tff(25,plain,
% 123.70/123.86 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~(model(tptp_fun_I3_13(not(F!29)), not(F!29)) | (~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac)))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))) | model(tptp_fun_I3_13(not(F!29)), not(F!29)))))))))),
% 123.70/123.87 inference(monotonicity,[status(thm)],[24])).
% 123.70/123.87 tff(26,plain,
% 123.70/123.87 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~(model(tptp_fun_I3_13(not(F!29)), not(F!29)) | (~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac)))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))) | model(tptp_fun_I3_13(not(F!29)), not(F!29)))))))))),
% 123.70/123.87 inference(transitivity,[status(thm)],[25, 23])).
% 123.70/123.87 tff(27,plain,
% 123.70/123.87 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~(model(tptp_fun_I3_13(not(F!29)), not(F!29)) | (~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac)))))))))))),
% 123.70/123.87 inference(quant_inst,[status(thm)],[])).
% 123.70/123.87 tff(28,plain,
% 123.70/123.87 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)) | ![I3: $i] : model(I3, C))) | (~((~status(Ax, C, wca)) | (~(model(tptp_fun_I3_13(C), C) | (~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))) | model(tptp_fun_I3_13(not(F!29)), not(F!29))))))))),
% 123.70/123.87 inference(modus_ponens,[status(thm)],[27, 26])).
% 123.70/123.87 tff(29,plain,
% 123.70/123.87 (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))) | model(tptp_fun_I3_13(not(F!29)), not(F!29)))))))),
% 123.70/123.87 inference(unit_resolution,[status(thm)],[28, 22])).
% 123.70/123.87 tff(30,plain,
% 123.70/123.87 (((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))) | model(tptp_fun_I3_13(not(F!29)), not(F!29))))))) | (model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))),
% 123.70/123.87 inference(tautology,[status(thm)],[])).
% 123.70/123.87 tff(31,plain,
% 123.70/123.87 (model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)),
% 123.70/123.87 inference(unit_resolution,[status(thm)],[30, 29])).
% 123.70/123.87 tff(32,plain,
% 123.70/123.87 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 123.70/123.87 inference(bind,[status(th)],[])).
% 123.70/123.87 tff(33,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.87 inference(quant_intro,[status(thm)],[32])).
% 123.70/123.87 tff(34,plain,
% 123.70/123.87 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 123.70/123.87 inference(bind,[status(th)],[])).
% 123.70/123.87 tff(35,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.87 inference(quant_intro,[status(thm)],[34])).
% 123.70/123.87 tff(36,plain,
% 123.70/123.87 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 123.70/123.87 inference(bind,[status(th)],[])).
% 123.70/123.87 tff(37,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.87 inference(quant_intro,[status(thm)],[36])).
% 123.70/123.87 tff(38,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.87 inference(transitivity,[status(thm)],[37, 35])).
% 123.70/123.87 tff(39,plain,
% 123.70/123.87 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) <=> (status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))), trans(monotonicity(rewrite((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) <=> (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))) <=> ((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, sca))))), rewrite(((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, sca))) <=> ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))) <=> ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))), (((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))), rewrite(((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))), (((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))))),
% 123.70/123.87 inference(bind,[status(th)],[])).
% 123.70/123.87 tff(40,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.87 inference(quant_intro,[status(thm)],[39])).
% 123.70/123.87 tff(41,plain,
% 123.70/123.87 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))))),
% 123.70/123.87 inference(bind,[status(th)],[])).
% 123.70/123.87 tff(42,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 123.70/123.87 inference(quant_intro,[status(thm)],[41])).
% 123.70/123.87 tff(43,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))),
% 123.70/123.87 inference(rewrite,[status(thm)],[])).
% 123.70/123.87 tff(44,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','sca')).
% 123.70/123.87 tff(45,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))),
% 123.70/123.87 inference(modus_ponens,[status(thm)],[44, 43])).
% 123.70/123.87 tff(46,plain,(
% 123.70/123.87 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 123.70/123.87 inference(skolemize,[status(sab)],[45])).
% 123.70/123.87 tff(47,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 123.70/123.87 inference(modus_ponens,[status(thm)],[46, 42])).
% 123.70/123.87 tff(48,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.87 inference(modus_ponens,[status(thm)],[47, 40])).
% 123.70/123.87 tff(49,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.87 inference(modus_ponens,[status(thm)],[48, 38])).
% 123.70/123.87 tff(50,plain,
% 123.70/123.87 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 123.70/123.87 inference(modus_ponens,[status(thm)],[49, 33])).
% 123.70/123.87 tff(51,plain,
% 123.70/123.87 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))))))))),
% 123.70/123.87 inference(rewrite,[status(thm)],[])).
% 123.70/123.87 tff(52,plain,
% 123.70/123.87 ((~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))))))) <=> (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))))))),
% 123.70/123.87 inference(rewrite,[status(thm)],[])).
% 123.70/123.87 tff(53,plain,
% 123.70/123.87 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))))))))),
% 123.70/123.87 inference(monotonicity,[status(thm)],[52])).
% 123.70/123.87 tff(54,plain,
% 123.70/123.87 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))))))))),
% 123.70/123.87 inference(transitivity,[status(thm)],[53, 51])).
% 123.70/123.87 tff(55,plain,
% 123.70/123.87 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))))))),
% 123.70/123.87 inference(quant_inst,[status(thm)],[])).
% 123.70/123.87 tff(56,plain,
% 123.70/123.87 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))))))),
% 123.70/123.87 inference(modus_ponens,[status(thm)],[55, 54])).
% 123.70/123.87 tff(57,plain,
% 123.70/123.87 (~((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))))))),
% 123.70/123.87 inference(unit_resolution,[status(thm)],[56, 50])).
% 123.70/123.87 tff(58,plain,
% 123.70/123.87 (((~(status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca) | ![I2: $i] : (~model(I2, tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))))) | ((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))))),
% 123.70/123.87 inference(tautology,[status(thm)],[])).
% 123.70/123.87 tff(59,plain,
% 123.70/123.87 ((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))),
% 123.70/123.87 inference(unit_resolution,[status(thm)],[58, 57])).
% 123.70/123.87 tff(60,assumption,(~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))), introduced(assumption)).
% 123.70/123.87 tff(61,plain,
% 123.70/123.87 (((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)),
% 123.70/123.87 inference(tautology,[status(thm)],[])).
% 123.70/123.87 tff(62,plain,
% 123.70/123.87 (status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)),
% 123.70/123.87 inference(unit_resolution,[status(thm)],[61, 60])).
% 123.70/123.87 tff(63,plain,
% 123.70/123.87 ((~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))))) | (~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))),
% 123.70/123.87 inference(tautology,[status(thm)],[])).
% 123.70/123.87 tff(64,plain,
% 123.70/123.87 ((~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))))) | (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))))),
% 123.70/123.87 inference(unit_resolution,[status(thm)],[63, 62])).
% 123.70/123.87 tff(65,plain,
% 123.70/123.87 (~((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))))),
% 123.70/123.87 inference(unit_resolution,[status(thm)],[64, 59])).
% 123.70/123.87 tff(66,plain,
% 123.70/123.87 (((~model(tptp_fun_I2_1(tptp_fun_C_22(thm, sca)), tptp_fun_C_22(thm, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca))))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))),
% 123.70/123.87 inference(tautology,[status(thm)],[])).
% 123.70/123.87 tff(67,plain,
% 123.70/123.87 (![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))),
% 123.70/123.87 inference(unit_resolution,[status(thm)],[66, 65])).
% 123.70/123.87 tff(68,plain,
% 123.70/123.87 (^[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)))))))),
% 123.70/123.87 inference(bind,[status(th)],[])).
% 123.70/123.87 tff(69,plain,
% 123.70/123.87 (![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))))))),
% 123.70/123.87 inference(quant_intro,[status(thm)],[68])).
% 123.70/123.87 tff(70,plain,
% 123.70/123.87 (^[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)))))))),
% 123.70/123.87 inference(bind,[status(th)],[])).
% 123.70/123.87 tff(71,plain,
% 123.70/123.87 (![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))))))),
% 123.70/123.87 inference(quant_intro,[status(thm)],[70])).
% 123.70/123.87 tff(72,plain,
% 123.70/123.87 (^[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)))))))),
% 123.70/123.87 inference(bind,[status(th)],[])).
% 123.70/123.87 tff(73,plain,
% 123.70/123.87 (![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))))))),
% 123.70/123.87 inference(quant_intro,[status(thm)],[72])).
% 123.70/123.87 tff(74,plain,
% 123.70/123.87 (![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))))))),
% 123.70/123.87 inference(transitivity,[status(thm)],[73, 71])).
% 123.70/123.87 tff(75,plain,
% 123.70/123.87 (^[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))))))))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(76,plain,
% 123.70/123.88 (![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))))))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[75])).
% 123.70/123.88 tff(77,plain,
% 123.70/123.88 (![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))),
% 123.70/123.88 inference(rewrite,[status(thm)],[])).
% 123.70/123.88 tff(78,plain,
% 123.70/123.88 (^[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)))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(79,plain,
% 123.70/123.88 (![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))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[78])).
% 123.70/123.88 tff(80,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','thm')).
% 123.70/123.88 tff(81,plain,
% 123.70/123.88 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[80, 79])).
% 123.70/123.88 tff(82,plain,
% 123.70/123.88 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[81, 77])).
% 123.70/123.88 tff(83,plain,(
% 123.70/123.88 ![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))))),
% 123.70/123.88 inference(skolemize,[status(sab)],[82])).
% 123.70/123.88 tff(84,plain,
% 123.70/123.88 (![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))))))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[83, 76])).
% 123.70/123.88 tff(85,plain,
% 123.70/123.88 (![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))))))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[84, 74])).
% 123.70/123.88 tff(86,plain,
% 123.70/123.88 (![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))))))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[85, 69])).
% 123.70/123.88 tff(87,plain,
% 123.70/123.88 (((~![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, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), 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, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))))))),
% 123.70/123.88 inference(rewrite,[status(thm)],[])).
% 123.70/123.88 tff(88,plain,
% 123.70/123.88 ((~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))))) <=> (~((~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))))),
% 123.70/123.88 inference(rewrite,[status(thm)],[])).
% 123.70/123.88 tff(89,plain,
% 123.70/123.88 (((~![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, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca)))))))) <=> ((~![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, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))))))),
% 123.70/123.88 inference(monotonicity,[status(thm)],[88])).
% 123.70/123.88 tff(90,plain,
% 123.70/123.88 (((~![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, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca)))))))) <=> ((~![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, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))))))),
% 123.70/123.88 inference(transitivity,[status(thm)],[89, 87])).
% 123.70/123.88 tff(91,plain,
% 123.70/123.88 ((~![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, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca)))))))),
% 123.70/123.88 inference(quant_inst,[status(thm)],[])).
% 123.70/123.88 tff(92,plain,
% 123.70/123.88 ((~![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, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[91, 90])).
% 123.70/123.88 tff(93,plain,
% 123.70/123.88 (~((~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[92, 86])).
% 123.70/123.88 tff(94,plain,
% 123.70/123.88 (((~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, sca))) | model(I1, tptp_fun_C_22(thm, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))) | ((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))),
% 123.70/123.88 inference(tautology,[status(thm)],[])).
% 123.70/123.88 tff(95,plain,
% 123.70/123.88 ((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[94, 93])).
% 123.70/123.88 tff(96,plain,
% 123.70/123.88 (((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)) | (~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))),
% 123.70/123.88 inference(tautology,[status(thm)],[])).
% 123.70/123.88 tff(97,plain,
% 123.70/123.88 (~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[96, 60])).
% 123.70/123.88 tff(98,plain,
% 123.70/123.88 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)),
% 123.70/123.88 inference(tautology,[status(thm)],[])).
% 123.70/123.88 tff(99,plain,
% 123.70/123.88 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca))))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[98, 97])).
% 123.70/123.88 tff(100,plain,
% 123.70/123.88 (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca)))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[99, 95])).
% 123.70/123.88 tff(101,plain,
% 123.70/123.88 (((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_C_22(thm, sca))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))),
% 123.70/123.88 inference(tautology,[status(thm)],[])).
% 123.70/123.88 tff(102,plain,
% 123.70/123.88 (model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[101, 100])).
% 123.70/123.88 tff(103,plain,
% 123.70/123.88 ((~![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, sca)))) | (~model(tptp_fun_I1_3(tptp_fun_C_22(thm, sca), tptp_fun_Ax_23(thm, sca)), tptp_fun_Ax_23(thm, sca)))),
% 123.70/123.88 inference(quant_inst,[status(thm)],[])).
% 123.70/123.88 tff(104,plain,
% 123.70/123.88 ($false),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[103, 102, 67])).
% 123.70/123.88 tff(105,plain,((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)), inference(lemma,lemma(discharge,[]))).
% 123.70/123.88 tff(106,plain,
% 123.70/123.88 (^[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))))))))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(107,plain,
% 123.70/123.88 (![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)))))))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[106])).
% 123.70/123.88 tff(108,plain,
% 123.70/123.88 (^[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))))))))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(109,plain,
% 123.70/123.88 (![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)))))))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[108])).
% 123.70/123.88 tff(110,plain,
% 123.70/123.88 (![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)))))))),
% 123.70/123.88 inference(transitivity,[status(thm)],[109, 107])).
% 123.70/123.88 tff(111,plain,
% 123.70/123.88 (^[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)))))))))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(112,plain,
% 123.70/123.88 (![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)))))))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[111])).
% 123.70/123.88 tff(113,plain,
% 123.70/123.88 (^[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)))))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(114,plain,
% 123.70/123.88 (![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))))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[113])).
% 123.70/123.88 tff(115,plain,
% 123.70/123.88 (![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))),
% 123.70/123.88 inference(rewrite,[status(thm)],[])).
% 123.70/123.88 tff(116,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nota')).
% 123.70/123.88 tff(117,plain,
% 123.70/123.88 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[116, 115])).
% 123.70/123.88 tff(118,plain,(
% 123.70/123.88 ![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))))),
% 123.70/123.88 inference(skolemize,[status(sab)],[117])).
% 123.70/123.88 tff(119,plain,
% 123.70/123.88 (![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))))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[118, 114])).
% 123.70/123.88 tff(120,plain,
% 123.70/123.88 (![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)))))))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[119, 112])).
% 123.70/123.88 tff(121,plain,
% 123.70/123.88 (![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)))))))),
% 123.70/123.88 inference(modus_ponens,[status(thm)],[120, 110])).
% 123.70/123.88 tff(122,plain,
% 123.70/123.88 ((~![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(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm)))) | (~((~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))))))),
% 123.70/123.88 inference(quant_inst,[status(thm)],[])).
% 123.70/123.88 tff(123,plain,
% 123.70/123.88 (~((~(nota(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm)))) | (~((~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))))))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[122, 121])).
% 123.70/123.88 tff(124,plain,
% 123.70/123.88 (((~(nota(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm)))) | (~((~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))))) | ((~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))))),
% 123.70/123.88 inference(tautology,[status(thm)],[])).
% 123.70/123.88 tff(125,plain,
% 123.70/123.88 ((~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[124, 123])).
% 123.70/123.88 tff(126,plain,
% 123.70/123.88 ((~((~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm))))) | (~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))),
% 123.70/123.88 inference(tautology,[status(thm)],[])).
% 123.70/123.88 tff(127,plain,
% 123.70/123.88 ((~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[126, 125])).
% 123.70/123.88 tff(128,plain,
% 123.70/123.88 (~nota(sca, thm)),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[127, 105])).
% 123.70/123.88 tff(129,plain,
% 123.70/123.88 (((~(nota(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm)))) | (~((~nota(sca, thm)) | (~((~status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), sca)) | status(tptp_fun_Ax_23(thm, sca), tptp_fun_C_22(thm, sca), thm)))))) | (nota(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm)))),
% 123.70/123.88 inference(tautology,[status(thm)],[])).
% 123.70/123.88 tff(130,plain,
% 123.70/123.88 (nota(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[129, 123])).
% 123.70/123.88 tff(131,plain,
% 123.70/123.88 ((~(nota(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm)))) | nota(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm))),
% 123.70/123.88 inference(tautology,[status(thm)],[])).
% 123.70/123.88 tff(132,plain,
% 123.70/123.88 (nota(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[131, 130])).
% 123.70/123.88 tff(133,plain,
% 123.70/123.88 (![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm))),
% 123.70/123.88 inference(unit_resolution,[status(thm)],[132, 128])).
% 123.70/123.88 tff(134,assumption,((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28))))))), introduced(assumption)).
% 123.70/123.88 tff(135,plain,
% 123.70/123.88 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(136,plain,
% 123.70/123.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[135])).
% 123.70/123.88 tff(137,plain,
% 123.70/123.88 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(138,plain,
% 123.70/123.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[137])).
% 123.70/123.88 tff(139,plain,
% 123.70/123.88 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))))),
% 123.70/123.88 inference(bind,[status(th)],[])).
% 123.70/123.88 tff(140,plain,
% 123.70/123.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 123.70/123.88 inference(quant_intro,[status(thm)],[139])).
% 123.70/123.88 tff(141,plain,
% 123.70/123.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 123.70/123.88 inference(transitivity,[status(thm)],[140, 138])).
% 123.70/123.88 tff(142,plain,
% 123.70/123.88 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) <=> (status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) <=> (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))) <=> ((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))) | (~status(Ax, C, tac))))), rewrite(((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))) | (~status(Ax, C, tac))) <=> ((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))) <=> ((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))), (((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))), rewrite(((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))) <=> (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))), (((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(143,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[142])).
% 123.70/123.89 tff(144,plain,
% 123.70/123.89 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tac)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(145,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tac)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[144])).
% 123.70/123.89 tff(146,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(147,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','tac')).
% 123.70/123.89 tff(148,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[147, 146])).
% 123.70/123.89 tff(149,plain,(
% 123.70/123.89 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tac)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))))),
% 123.70/123.89 inference(skolemize,[status(sab)],[148])).
% 123.70/123.89 tff(150,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[149, 145])).
% 123.70/123.89 tff(151,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[150, 143])).
% 123.70/123.89 tff(152,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[151, 141])).
% 123.70/123.89 tff(153,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[152, 136])).
% 123.70/123.89 tff(154,plain,
% 123.70/123.89 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(155,plain,
% 123.70/123.89 ((~((~(status(F!29, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28)))))))) <=> (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28))))))))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(156,plain,
% 123.70/123.89 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(F!29, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 123.70/123.89 inference(monotonicity,[status(thm)],[155])).
% 123.70/123.89 tff(157,plain,
% 123.70/123.89 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(F!29, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 123.70/123.89 inference(transitivity,[status(thm)],[156, 154])).
% 123.70/123.89 tff(158,plain,
% 123.70/123.89 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(F!29, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28))))))))),
% 123.70/123.89 inference(quant_inst,[status(thm)],[])).
% 123.70/123.89 tff(159,plain,
% 123.70/123.89 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28))))))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[158, 157])).
% 123.70/123.89 tff(160,plain,
% 123.70/123.89 ($false),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[159, 153, 134])).
% 123.70/123.89 tff(161,plain,(~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28)))))))), inference(lemma,lemma(discharge,[]))).
% 123.70/123.89 tff(162,plain,
% 123.70/123.89 (((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | (~((~status(F!29, F!28, tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, F!28))))))) | (![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))),
% 123.70/123.89 inference(tautology,[status(thm)],[])).
% 123.70/123.89 tff(163,plain,
% 123.70/123.89 (![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac)),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[162, 161])).
% 123.70/123.89 tff(164,assumption,(~model(tptp_fun_I2_5(F!28), F!28)), introduced(assumption)).
% 123.70/123.89 tff(165,plain,
% 123.70/123.89 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(166,plain,
% 123.70/123.89 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 123.70/123.89 inference(quant_intro,[status(thm)],[165])).
% 123.70/123.89 tff(167,plain,
% 123.70/123.89 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(168,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','tautology')).
% 123.70/123.89 tff(169,plain,
% 123.70/123.89 (?[F: $i] : ![I: $i] : model(I, F)),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[168, 167])).
% 123.70/123.89 tff(170,plain,(
% 123.70/123.89 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 123.70/123.89 inference(transitivity,[status(sab)],[169])).
% 123.70/123.89 tff(171,plain,
% 123.70/123.89 (![I: $i] : model(I, F!28)),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[170, 166])).
% 123.70/123.89 tff(172,plain,
% 123.70/123.89 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I2_5(F!28), F!28)),
% 123.70/123.89 inference(quant_inst,[status(thm)],[])).
% 123.70/123.89 tff(173,plain,
% 123.70/123.89 ($false),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[172, 171, 164])).
% 123.70/123.89 tff(174,plain,(model(tptp_fun_I2_5(F!28), F!28)), inference(lemma,lemma(discharge,[]))).
% 123.70/123.89 tff(175,assumption,(![I1: $i] : (~model(I1, F!29))), introduced(assumption)).
% 123.70/123.89 tff(176,plain,
% 123.70/123.89 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(177,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 123.70/123.89 tff(178,plain,
% 123.70/123.89 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[177, 176])).
% 123.70/123.89 tff(179,plain,
% 123.70/123.89 (model(I1!30, F!29)),
% 123.70/123.89 inference(and_elim,[status(thm)],[178])).
% 123.70/123.89 tff(180,plain,
% 123.70/123.89 ((~![I1: $i] : (~model(I1, F!29))) | (~model(I1!30, F!29))),
% 123.70/123.89 inference(quant_inst,[status(thm)],[])).
% 123.70/123.89 tff(181,plain,
% 123.70/123.89 ($false),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[180, 179, 175])).
% 123.70/123.89 tff(182,plain,(~![I1: $i] : (~model(I1, F!29))), inference(lemma,lemma(discharge,[]))).
% 123.70/123.89 tff(183,plain,
% 123.70/123.89 ((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac)),
% 123.70/123.89 inference(tautology,[status(thm)],[])).
% 123.70/123.89 tff(184,plain,
% 123.70/123.89 ((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!29, F!28, tac))) | status(F!29, F!28, tac)),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[183, 182, 174])).
% 123.70/123.89 tff(185,plain,
% 123.70/123.89 (status(F!29, F!28, tac)),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[184, 163])).
% 123.70/123.89 tff(186,assumption,(![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))), introduced(assumption)).
% 123.70/123.89 tff(187,plain,
% 123.70/123.89 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C)))))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(188,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[187])).
% 123.70/123.89 tff(189,plain,
% 123.70/123.89 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(190,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[189])).
% 123.70/123.89 tff(191,plain,
% 123.70/123.89 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(192,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[191])).
% 123.70/123.89 tff(193,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 123.70/123.89 inference(transitivity,[status(thm)],[192, 190])).
% 123.70/123.89 tff(194,plain,
% 123.70/123.89 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite(((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) <=> ((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))), rewrite((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))) <=> (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))), rewrite((((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(195,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[194])).
% 123.70/123.89 tff(196,plain,
% 123.70/123.89 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(197,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[196])).
% 123.70/123.89 tff(198,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(199,plain,
% 123.70/123.89 (^[Ax: $i, C: $i] : rewrite((((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(200,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[199])).
% 123.70/123.89 tff(201,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','unp')).
% 123.70/123.89 tff(202,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[201, 200])).
% 123.70/123.89 tff(203,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[202, 198])).
% 123.70/123.89 tff(204,plain,(
% 123.70/123.89 ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp))))),
% 123.70/123.89 inference(skolemize,[status(sab)],[203])).
% 123.70/123.89 tff(205,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[204, 197])).
% 123.70/123.89 tff(206,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[205, 195])).
% 123.70/123.89 tff(207,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[206, 193])).
% 123.70/123.89 tff(208,plain,
% 123.70/123.89 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[207, 188])).
% 123.70/123.89 tff(209,plain,
% 123.70/123.89 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, F!28)) | (~status(F!29, F!28, unp)))) | (~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, F!28)) | (~status(F!29, F!28, unp)))) | (~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))))))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(210,plain,
% 123.70/123.89 ((~((~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))) | (~(model(tptp_fun_I1_0(F!29), F!29) | (~status(F!29, F!28, unp)) | ![I2: $i] : (~model(I2, F!28)))))) <=> (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, F!28)) | (~status(F!29, F!28, unp)))) | (~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp)))))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(211,plain,
% 123.70/123.89 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))) | (~(model(tptp_fun_I1_0(F!29), F!29) | (~status(F!29, F!28, unp)) | ![I2: $i] : (~model(I2, F!28))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, F!28)) | (~status(F!29, F!28, unp)))) | (~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))))))),
% 123.70/123.89 inference(monotonicity,[status(thm)],[210])).
% 123.70/123.89 tff(212,plain,
% 123.70/123.89 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))) | (~(model(tptp_fun_I1_0(F!29), F!29) | (~status(F!29, F!28, unp)) | ![I2: $i] : (~model(I2, F!28))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, F!28)) | (~status(F!29, F!28, unp)))) | (~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))))))),
% 123.70/123.89 inference(transitivity,[status(thm)],[211, 209])).
% 123.70/123.89 tff(213,plain,
% 123.70/123.89 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))) | (~(model(tptp_fun_I1_0(F!29), F!29) | (~status(F!29, F!28, unp)) | ![I2: $i] : (~model(I2, F!28))))))),
% 123.70/123.89 inference(quant_inst,[status(thm)],[])).
% 123.70/123.89 tff(214,plain,
% 123.70/123.89 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, F!28)) | (~status(F!29, F!28, unp)))) | (~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp)))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[213, 212])).
% 123.70/123.89 tff(215,plain,
% 123.70/123.89 (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, F!28)) | (~status(F!29, F!28, unp)))) | (~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))))),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[214, 208])).
% 123.70/123.89 tff(216,plain,
% 123.70/123.89 (((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, F!28)) | (~status(F!29, F!28, unp)))) | (~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp)))) | ((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))),
% 123.70/123.89 inference(tautology,[status(thm)],[])).
% 123.70/123.89 tff(217,plain,
% 123.70/123.89 ((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp)),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[216, 215])).
% 123.70/123.89 tff(218,plain,
% 123.70/123.89 (((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29)))) | ![I1: $i] : (~model(I1, F!29))),
% 123.70/123.89 inference(tautology,[status(thm)],[])).
% 123.70/123.89 tff(219,plain,
% 123.70/123.89 ((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29)))),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[218, 182])).
% 123.70/123.89 tff(220,plain,
% 123.70/123.89 ((~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))) | (~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp)),
% 123.70/123.89 inference(tautology,[status(thm)],[])).
% 123.70/123.89 tff(221,plain,
% 123.70/123.89 ((~((~((~model(tptp_fun_I2_1(F!28), F!28)) | (~![I1: $i] : (~model(I1, F!29))))) | status(F!29, F!28, unp))) | status(F!29, F!28, unp)),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[220, 219])).
% 123.70/123.89 tff(222,plain,
% 123.70/123.89 (status(F!29, F!28, unp)),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[221, 217])).
% 123.70/123.89 tff(223,plain,
% 123.70/123.89 (((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))) | ((~status(F!29, F!28, unp)) | (~status(F!29, F!28, tac)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))) | (~status(F!29, F!28, unp)) | (~status(F!29, F!28, tac)))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(224,plain,
% 123.70/123.89 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))) | ((~status(F!29, F!28, unp)) | (~status(F!29, F!28, tac)))),
% 123.70/123.89 inference(quant_inst,[status(thm)],[])).
% 123.70/123.89 tff(225,plain,
% 123.70/123.89 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))) | (~status(F!29, F!28, unp)) | (~status(F!29, F!28, tac))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[224, 223])).
% 123.70/123.89 tff(226,plain,
% 123.70/123.89 ($false),
% 123.70/123.89 inference(unit_resolution,[status(thm)],[225, 222, 186, 185])).
% 123.70/123.89 tff(227,plain,(~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))), inference(lemma,lemma(discharge,[]))).
% 123.70/123.89 tff(228,plain,
% 123.70/123.89 (^[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)))))))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(229,plain,
% 123.70/123.89 (![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))))))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[228])).
% 123.70/123.89 tff(230,plain,
% 123.70/123.89 (^[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)))))))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(231,plain,
% 123.70/123.89 (![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))))))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[230])).
% 123.70/123.89 tff(232,plain,
% 123.70/123.89 (![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))))))))),
% 123.70/123.89 inference(transitivity,[status(thm)],[231, 229])).
% 123.70/123.89 tff(233,plain,
% 123.70/123.89 (^[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))))))))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(234,plain,
% 123.70/123.89 (![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))))))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[233])).
% 123.70/123.89 tff(235,plain,
% 123.70/123.89 (^[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)))))),
% 123.70/123.89 inference(bind,[status(th)],[])).
% 123.70/123.89 tff(236,plain,
% 123.70/123.89 (![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))))),
% 123.70/123.89 inference(quant_intro,[status(thm)],[235])).
% 123.70/123.89 tff(237,plain,
% 123.70/123.89 (![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))),
% 123.70/123.89 inference(rewrite,[status(thm)],[])).
% 123.70/123.89 tff(238,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','mighta')).
% 123.70/123.89 tff(239,plain,
% 123.70/123.89 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[238, 237])).
% 123.70/123.89 tff(240,plain,(
% 123.70/123.89 ![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))))),
% 123.70/123.89 inference(skolemize,[status(sab)],[239])).
% 123.70/123.89 tff(241,plain,
% 123.70/123.89 (![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))))),
% 123.70/123.89 inference(modus_ponens,[status(thm)],[240, 236])).
% 123.70/123.89 tff(242,plain,
% 123.70/123.89 (![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))))))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[241, 234])).
% 123.70/123.90 tff(243,plain,
% 123.70/123.90 (![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))))))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[242, 232])).
% 123.70/123.90 tff(244,plain,
% 123.70/123.90 ((~![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(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp))))))))),
% 123.70/123.90 inference(quant_inst,[status(thm)],[])).
% 123.70/123.90 tff(245,plain,
% 123.70/123.90 (~((~(mighta(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp)))))))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[244, 243])).
% 123.70/123.90 tff(246,plain,
% 123.70/123.90 (((~(mighta(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp))))))) | (mighta(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac))))),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(247,plain,
% 123.70/123.90 (mighta(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[246, 245])).
% 123.70/123.90 tff(248,plain,
% 123.70/123.90 ((~(mighta(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac))))) | mighta(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(249,plain,
% 123.70/123.90 (mighta(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac)))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[248, 247])).
% 123.70/123.90 tff(250,plain,
% 123.70/123.90 (mighta(tac, unp)),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[249, 227])).
% 123.70/123.90 tff(251,plain,
% 123.70/123.90 (((~(mighta(tac, unp) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp))))))) | ((~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp)))))),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(252,plain,
% 123.70/123.90 ((~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp))))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[251, 245])).
% 123.70/123.90 tff(253,plain,
% 123.70/123.90 ((~((~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp)))))) | (~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp))))),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(254,plain,
% 123.70/123.90 ((~mighta(tac, unp)) | (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp))))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[253, 252])).
% 123.70/123.90 tff(255,plain,
% 123.70/123.90 (~((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp)))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[254, 250])).
% 123.70/123.90 tff(256,plain,
% 123.70/123.90 (((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), unp))) | status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(257,plain,
% 123.70/123.90 (status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[256, 255])).
% 123.70/123.90 tff(258,assumption,(status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)), introduced(assumption)).
% 123.70/123.90 tff(259,assumption,(![Ax: $i, C: $i] : (~status(Ax, C, tac))), introduced(assumption)).
% 123.70/123.90 tff(260,plain,
% 123.70/123.90 ((~![Ax: $i, C: $i] : (~status(Ax, C, tac))) | (~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac))),
% 123.70/123.90 inference(quant_inst,[status(thm)],[])).
% 123.70/123.90 tff(261,plain,
% 123.70/123.90 ($false),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[260, 259, 258])).
% 123.70/123.90 tff(262,plain,((~status(tptp_fun_Ax_19(unp, tac), tptp_fun_C_18(unp, tac), tac)) | (~![Ax: $i, C: $i] : (~status(Ax, C, tac)))), inference(lemma,lemma(discharge,[]))).
% 123.70/123.90 tff(263,plain,
% 123.70/123.90 (~![Ax: $i, C: $i] : (~status(Ax, C, tac))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[262, 257])).
% 123.70/123.90 tff(264,plain,
% 123.70/123.90 (((~![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(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))))) <=> ((~![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(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))))))),
% 123.70/123.90 inference(rewrite,[status(thm)],[])).
% 123.70/123.90 tff(265,plain,
% 123.70/123.90 ((~((~(mighta(tac, tac) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, tac)) | (~((~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))))))) <=> (~((~(mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))))),
% 123.70/123.90 inference(rewrite,[status(thm)],[])).
% 123.70/123.90 tff(266,plain,
% 123.70/123.90 (((~![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(tac, tac) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, tac)) | (~((~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))))))))) <=> ((~![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(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))))))),
% 123.70/123.90 inference(monotonicity,[status(thm)],[265])).
% 123.70/123.90 tff(267,plain,
% 123.70/123.90 (((~![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(tac, tac) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, tac)) | (~((~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))))))))) <=> ((~![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(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))))))),
% 123.70/123.90 inference(transitivity,[status(thm)],[266, 264])).
% 123.70/123.90 tff(268,plain,
% 123.70/123.90 ((~![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(tac, tac) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, tac)) | (~((~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))))))))),
% 123.70/123.90 inference(quant_inst,[status(thm)],[])).
% 123.70/123.90 tff(269,plain,
% 123.70/123.90 ((~![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(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[268, 267])).
% 123.70/123.90 tff(270,plain,
% 123.70/123.90 (~((~(mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[269, 243])).
% 123.70/123.90 tff(271,plain,
% 123.70/123.90 (((~(mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))) | (mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(272,plain,
% 123.70/123.90 (mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[271, 270])).
% 123.70/123.90 tff(273,plain,
% 123.70/123.90 ((~(mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac))),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(274,plain,
% 123.70/123.90 (mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[273, 272])).
% 123.70/123.90 tff(275,plain,
% 123.70/123.90 (mighta(tac, tac)),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[274, 263])).
% 123.70/123.90 tff(276,plain,
% 123.70/123.90 (((~(mighta(tac, tac) | ![Ax: $i, C: $i] : (~status(Ax, C, tac)))) | (~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))) | ((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(277,plain,
% 123.70/123.90 ((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[276, 270])).
% 123.70/123.90 tff(278,plain,
% 123.70/123.90 ((~((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))) | (~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)),
% 123.70/123.90 inference(tautology,[status(thm)],[])).
% 123.70/123.90 tff(279,plain,
% 123.70/123.90 ((~mighta(tac, tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[278, 277])).
% 123.70/123.90 tff(280,plain,
% 123.70/123.90 (status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[279, 275])).
% 123.70/123.90 tff(281,assumption,(status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)), introduced(assumption)).
% 123.70/123.90 tff(282,plain,
% 123.70/123.90 (^[I: $i, F: $i] : refl((~(model(I, F) <=> model(I, not(F)))) <=> (~(model(I, F) <=> model(I, not(F)))))),
% 123.70/123.90 inference(bind,[status(th)],[])).
% 123.70/123.90 tff(283,plain,
% 123.70/123.90 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 123.70/123.90 inference(quant_intro,[status(thm)],[282])).
% 123.70/123.90 tff(284,plain,
% 123.70/123.90 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 123.70/123.90 inference(rewrite,[status(thm)],[])).
% 123.70/123.90 tff(285,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','completeness')).
% 123.70/123.90 tff(286,plain,
% 123.70/123.90 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[285, 284])).
% 123.70/123.90 tff(287,plain,(
% 123.70/123.90 ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 123.70/123.90 inference(skolemize,[status(sab)],[286])).
% 123.70/123.90 tff(288,plain,
% 123.70/123.90 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[287, 283])).
% 123.70/123.90 tff(289,plain,
% 123.70/123.90 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))))),
% 123.70/123.90 inference(quant_inst,[status(thm)],[])).
% 123.70/123.90 tff(290,plain,
% 123.70/123.90 (~(model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac))))),
% 123.70/123.90 inference(unit_resolution,[status(thm)],[289, 288])).
% 123.70/123.90 tff(291,plain,
% 123.70/123.90 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))))))),
% 123.70/123.90 inference(bind,[status(th)],[])).
% 123.70/123.90 tff(292,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))),
% 123.70/123.90 inference(quant_intro,[status(thm)],[291])).
% 123.70/123.90 tff(293,plain,
% 123.70/123.90 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))))),
% 123.70/123.90 inference(bind,[status(th)],[])).
% 123.70/123.90 tff(294,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 123.70/123.90 inference(quant_intro,[status(thm)],[293])).
% 123.70/123.90 tff(295,plain,
% 123.70/123.90 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))))),
% 123.70/123.90 inference(bind,[status(th)],[])).
% 123.70/123.90 tff(296,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 123.70/123.90 inference(quant_intro,[status(thm)],[295])).
% 123.70/123.90 tff(297,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 123.70/123.90 inference(transitivity,[status(thm)],[296, 294])).
% 123.70/123.90 tff(298,plain,
% 123.70/123.90 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) <=> (status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))), rewrite(((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) <=> ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))), (((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> ((status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))) & ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))), rewrite(((status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))) & ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))), (((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))))),
% 123.70/123.90 inference(bind,[status(th)],[])).
% 123.70/123.90 tff(299,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 123.70/123.90 inference(quant_intro,[status(thm)],[298])).
% 123.70/123.90 tff(300,plain,
% 123.70/123.90 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc)))) <=> ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))))),
% 123.70/123.90 inference(bind,[status(th)],[])).
% 123.70/123.90 tff(301,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : (((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))))),
% 123.70/123.90 inference(quant_intro,[status(thm)],[300])).
% 123.70/123.90 tff(302,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))),
% 123.70/123.90 inference(rewrite,[status(thm)],[])).
% 123.70/123.90 tff(303,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','noc')).
% 123.70/123.90 tff(304,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[303, 302])).
% 123.70/123.90 tff(305,plain,(
% 123.70/123.90 ![Ax: $i, C: $i] : (((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc))))),
% 123.70/123.90 inference(skolemize,[status(sab)],[304])).
% 123.70/123.90 tff(306,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[305, 301])).
% 123.70/123.90 tff(307,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[306, 299])).
% 123.70/123.90 tff(308,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[307, 297])).
% 123.70/123.90 tff(309,plain,
% 123.70/123.90 (![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))),
% 123.70/123.90 inference(modus_ponens,[status(thm)],[308, 292])).
% 123.70/123.90 tff(310,plain,
% 123.70/123.90 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac))))))))))),
% 123.70/123.90 inference(rewrite,[status(thm)],[])).
% 123.70/123.90 tff(311,plain,
% 123.70/123.90 ((~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac))))))))) <=> (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac)))))))))),
% 123.70/123.90 inference(rewrite,[status(thm)],[])).
% 123.70/123.90 tff(312,plain,
% 123.70/123.90 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac))))))))))),
% 123.70/123.91 inference(monotonicity,[status(thm)],[311])).
% 123.70/123.91 tff(313,plain,
% 123.70/123.91 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac))))))))))),
% 123.70/123.91 inference(transitivity,[status(thm)],[312, 310])).
% 123.70/123.91 tff(314,plain,
% 123.70/123.91 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac)))))))))),
% 123.70/123.91 inference(quant_inst,[status(thm)],[])).
% 123.70/123.91 tff(315,plain,
% 123.70/123.91 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac)))))))))),
% 123.70/123.91 inference(modus_ponens,[status(thm)],[314, 313])).
% 123.70/123.91 tff(316,plain,
% 123.70/123.91 (~((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac))))))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[315, 309])).
% 123.70/123.91 tff(317,plain,
% 123.70/123.91 (((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(I1, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, tac))) | (~model(I2, not(tptp_fun_C_18(noc, tac)))))))) | ((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(318,plain,
% 123.70/123.91 ((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac)))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[317, 316])).
% 123.70/123.91 tff(319,assumption,(~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)))), introduced(assumption)).
% 123.70/123.91 tff(320,plain,
% 123.70/123.91 (((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))) | status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(321,plain,
% 123.70/123.91 (status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[320, 319])).
% 123.70/123.91 tff(322,plain,
% 123.70/123.91 ((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac)))))),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(323,plain,
% 123.70/123.91 ((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))))) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac)))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[322, 321])).
% 123.70/123.91 tff(324,plain,
% 123.70/123.91 (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[323, 318])).
% 123.70/123.91 tff(325,plain,
% 123.70/123.91 (((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac)))) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(326,plain,
% 123.70/123.91 (model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[325, 324])).
% 123.70/123.91 tff(327,plain,
% 123.70/123.91 ((model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac))))),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(328,plain,
% 123.70/123.91 ((model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), not(tptp_fun_C_18(noc, tac)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac)))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[327, 326])).
% 123.70/123.91 tff(329,plain,
% 123.70/123.91 (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[328, 290])).
% 123.70/123.91 tff(330,plain,
% 123.70/123.91 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))))))))),
% 123.70/123.91 inference(rewrite,[status(thm)],[])).
% 123.70/123.91 tff(331,plain,
% 123.70/123.91 ((~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))))))) <=> (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))))))),
% 123.70/123.91 inference(rewrite,[status(thm)],[])).
% 123.70/123.91 tff(332,plain,
% 123.70/123.91 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))))))))),
% 123.70/123.91 inference(monotonicity,[status(thm)],[331])).
% 123.70/123.91 tff(333,plain,
% 123.70/123.91 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))))))))),
% 123.70/123.91 inference(transitivity,[status(thm)],[332, 330])).
% 123.70/123.91 tff(334,plain,
% 123.70/123.91 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))))))),
% 123.70/123.91 inference(quant_inst,[status(thm)],[])).
% 123.70/123.91 tff(335,plain,
% 123.70/123.91 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))))))),
% 123.70/123.91 inference(modus_ponens,[status(thm)],[334, 333])).
% 123.70/123.91 tff(336,plain,
% 123.70/123.91 (~((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[335, 153])).
% 123.70/123.91 tff(337,plain,
% 123.70/123.91 (((~(status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(noc, tac))) | (~model(tptp_fun_I2_5(tptp_fun_C_18(noc, tac)), tptp_fun_C_18(noc, tac))))) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))))) | ((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))))),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(338,plain,
% 123.70/123.91 ((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[337, 336])).
% 123.70/123.91 tff(339,plain,
% 123.70/123.91 (((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))) | status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(340,plain,
% 123.70/123.91 (status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[339, 319])).
% 123.70/123.91 tff(341,plain,
% 123.70/123.91 ((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))))) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(342,plain,
% 123.70/123.91 ((~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))))) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[341, 340])).
% 123.70/123.91 tff(343,plain,
% 123.70/123.91 (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[342, 338])).
% 123.70/123.91 tff(344,plain,
% 123.70/123.91 (((~model(tptp_fun_I1_0(tptp_fun_Ax_19(noc, tac)), tptp_fun_Ax_19(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac)))) | ![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(345,plain,
% 123.70/123.91 (![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[344, 343])).
% 123.70/123.91 tff(346,plain,
% 123.70/123.91 ((~![I2: $i] : model(I2, tptp_fun_C_18(noc, tac))) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, tac), tptp_fun_Ax_19(noc, tac)), tptp_fun_C_18(noc, tac))),
% 123.70/123.91 inference(quant_inst,[status(thm)],[])).
% 123.70/123.91 tff(347,plain,
% 123.70/123.91 ($false),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[346, 345, 329])).
% 123.70/123.91 tff(348,plain,((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))), inference(lemma,lemma(discharge,[]))).
% 123.70/123.91 tff(349,plain,
% 123.70/123.91 ((~![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(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))))))))),
% 123.70/123.91 inference(quant_inst,[status(thm)],[])).
% 123.70/123.91 tff(350,plain,
% 123.70/123.91 (~((~(mighta(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)))))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[349, 243])).
% 123.70/123.91 tff(351,plain,
% 123.70/123.91 (((~(mighta(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))))))) | ((~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)))))),
% 123.70/123.91 inference(tautology,[status(thm)],[])).
% 123.70/123.91 tff(352,plain,
% 123.70/123.91 ((~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))))),
% 123.70/123.91 inference(unit_resolution,[status(thm)],[351, 350])).
% 123.70/123.91 tff(353,plain,
% 123.70/123.91 ((~((~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc)))))) | (~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))))),
% 123.70/123.92 inference(tautology,[status(thm)],[])).
% 123.70/123.92 tff(354,plain,
% 123.70/123.92 ((~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))))),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[353, 352])).
% 123.70/123.92 tff(355,plain,
% 123.70/123.92 (~mighta(tac, noc)),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[354, 348])).
% 123.70/123.92 tff(356,plain,
% 123.70/123.92 (((~(mighta(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, noc)) | (~((~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), tac)) | (~status(tptp_fun_Ax_19(noc, tac), tptp_fun_C_18(noc, tac), noc))))))) | (mighta(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac))))),
% 123.70/123.92 inference(tautology,[status(thm)],[])).
% 123.70/123.92 tff(357,plain,
% 123.70/123.92 (mighta(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac)))),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[356, 350])).
% 123.70/123.92 tff(358,plain,
% 123.70/123.92 ((~(mighta(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac))))) | mighta(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac)))),
% 123.70/123.92 inference(tautology,[status(thm)],[])).
% 123.70/123.92 tff(359,plain,
% 123.70/123.92 (mighta(tac, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac)))),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[358, 357])).
% 123.70/123.92 tff(360,plain,
% 123.70/123.92 (![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac)))),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[359, 355])).
% 123.70/123.92 tff(361,plain,
% 123.70/123.92 (((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac)))) | ((~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc)) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac)))) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc)) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))),
% 123.70/123.92 inference(rewrite,[status(thm)],[])).
% 123.70/123.92 tff(362,plain,
% 123.70/123.92 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac)))) | ((~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc)) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)))),
% 123.70/123.92 inference(quant_inst,[status(thm)],[])).
% 123.70/123.92 tff(363,plain,
% 123.70/123.92 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, tac)))) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc)) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))),
% 123.70/123.92 inference(modus_ponens,[status(thm)],[362, 361])).
% 123.70/123.92 tff(364,plain,
% 123.70/123.92 (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc)),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[363, 360, 281])).
% 123.70/123.92 tff(365,assumption,(![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))), introduced(assumption)).
% 123.70/123.92 tff(366,plain,
% 123.70/123.92 (((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))) | ((~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc))),
% 123.70/123.92 inference(rewrite,[status(thm)],[])).
% 123.70/123.92 tff(367,plain,
% 123.70/123.92 ((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))) | ((~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc))),
% 123.70/123.92 inference(quant_inst,[status(thm)],[])).
% 123.70/123.92 tff(368,plain,
% 123.70/123.92 ((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac)) | status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), noc)),
% 123.70/123.92 inference(modus_ponens,[status(thm)],[367, 366])).
% 123.70/123.92 tff(369,plain,
% 123.70/123.92 ($false),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[368, 365, 281, 364])).
% 123.70/123.92 tff(370,plain,((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))) | (~status(tptp_fun_Ax_19(tac, tac), tptp_fun_C_18(tac, tac), tac))), inference(lemma,lemma(discharge,[]))).
% 123.70/123.92 tff(371,plain,
% 123.70/123.92 (~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[370, 280])).
% 123.70/123.92 tff(372,plain,
% 123.70/123.92 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))))))),
% 123.70/123.92 inference(bind,[status(th)],[])).
% 123.70/123.92 tff(373,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))),
% 123.70/123.92 inference(quant_intro,[status(thm)],[372])).
% 123.70/123.92 tff(374,plain,
% 123.70/123.92 (^[S1: $i, S2: $i] : refl((~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))))),
% 123.70/123.92 inference(bind,[status(th)],[])).
% 123.70/123.92 tff(375,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 123.70/123.92 inference(quant_intro,[status(thm)],[374])).
% 123.70/123.92 tff(376,plain,
% 123.70/123.92 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))))),
% 123.70/123.92 inference(bind,[status(th)],[])).
% 123.70/123.92 tff(377,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 123.70/123.92 inference(quant_intro,[status(thm)],[376])).
% 123.70/123.92 tff(378,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 123.70/123.92 inference(transitivity,[status(thm)],[377, 375])).
% 123.70/123.92 tff(379,plain,
% 123.70/123.92 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))), ((((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))) <=> (((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))))), rewrite((((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))), ((((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))))),
% 123.70/123.92 inference(bind,[status(th)],[])).
% 123.70/123.92 tff(380,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 123.70/123.92 inference(quant_intro,[status(thm)],[379])).
% 123.70/123.92 tff(381,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 123.70/123.92 inference(rewrite,[status(thm)],[])).
% 123.70/123.92 tff(382,plain,
% 123.70/123.92 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (status(Ax, C, S1) => status(Ax, C, S2)) <=> isa(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2)))),
% 123.70/123.92 inference(bind,[status(th)],[])).
% 123.70/123.92 tff(383,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => status(Ax, C, S2)) <=> isa(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 123.70/123.92 inference(quant_intro,[status(thm)],[382])).
% 123.70/123.92 tff(384,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => status(Ax, C, S2)) <=> isa(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','isa')).
% 123.70/123.92 tff(385,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 123.70/123.92 inference(modus_ponens,[status(thm)],[384, 383])).
% 123.70/123.92 tff(386,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) <=> isa(S1, S2))),
% 123.70/123.92 inference(modus_ponens,[status(thm)],[385, 381])).
% 123.70/123.92 tff(387,plain,(
% 123.70/123.92 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))),
% 123.70/123.92 inference(skolemize,[status(sab)],[386])).
% 123.70/123.92 tff(388,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 123.70/123.92 inference(modus_ponens,[status(thm)],[387, 380])).
% 123.70/123.92 tff(389,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)) | (~isa(S1, S2))))))),
% 123.70/123.92 inference(modus_ponens,[status(thm)],[388, 378])).
% 123.70/123.92 tff(390,plain,
% 123.70/123.92 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))),
% 123.70/123.92 inference(modus_ponens,[status(thm)],[389, 373])).
% 123.70/123.92 tff(391,plain,
% 123.70/123.92 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S1)) | status(tptp_fun_Ax_21(S2, S1), tptp_fun_C_20(S2, S1), S2))) | isa(S1, S2))) | (~((~isa(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))))))) | (~((~((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc))) | (~((~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))))))),
% 123.70/123.92 inference(quant_inst,[status(thm)],[])).
% 123.70/123.92 tff(392,plain,
% 123.70/123.92 (~((~((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc))) | (~((~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc)))))),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[391, 390])).
% 123.70/123.92 tff(393,plain,
% 123.70/123.92 (((~((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc))) | (~((~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))))) | ((~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc)))),
% 123.70/123.92 inference(tautology,[status(thm)],[])).
% 123.70/123.92 tff(394,plain,
% 123.70/123.92 ((~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[393, 392])).
% 123.70/123.92 tff(395,plain,
% 123.70/123.92 ((~((~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc)))) | (~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))),
% 123.70/123.92 inference(tautology,[status(thm)],[])).
% 123.70/123.92 tff(396,plain,
% 123.70/123.92 ((~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[395, 394])).
% 123.70/123.92 tff(397,plain,
% 123.70/123.92 (~isa(tac, noc)),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[396, 371])).
% 123.70/123.92 tff(398,plain,
% 123.70/123.92 (((~((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc))) | (~((~isa(tac, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | status(Ax, C, noc))))) | ((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc))),
% 123.70/123.92 inference(tautology,[status(thm)],[])).
% 123.70/123.92 tff(399,plain,
% 123.70/123.92 ((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc)),
% 123.70/123.92 inference(unit_resolution,[status(thm)],[398, 392])).
% 123.70/123.92 tff(400,plain,
% 123.70/123.92 ((~((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc)),
% 123.77/123.92 inference(tautology,[status(thm)],[])).
% 123.77/123.92 tff(401,plain,
% 123.77/123.92 ((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))) | isa(tac, noc)),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[400, 399])).
% 123.77/123.92 tff(402,plain,
% 123.77/123.92 (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[401, 397])).
% 123.77/123.92 tff(403,plain,
% 123.77/123.92 (((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), noc)) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)),
% 123.77/123.92 inference(tautology,[status(thm)],[])).
% 123.77/123.92 tff(404,plain,
% 123.77/123.92 (status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[403, 402])).
% 123.77/123.92 tff(405,plain,
% 123.77/123.92 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~((~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~((~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))))))))))),
% 123.77/123.92 inference(rewrite,[status(thm)],[])).
% 123.77/123.92 tff(406,plain,
% 123.77/123.92 ((~((~(status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))))))))) <=> (~((~((~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))))))),
% 123.77/123.92 inference(rewrite,[status(thm)],[])).
% 123.77/123.92 tff(407,plain,
% 123.77/123.92 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~((~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))))))))))),
% 123.77/123.92 inference(monotonicity,[status(thm)],[406])).
% 123.77/123.92 tff(408,plain,
% 123.77/123.92 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~((~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))))))))))),
% 123.77/123.92 inference(transitivity,[status(thm)],[407, 405])).
% 123.77/123.92 tff(409,plain,
% 123.77/123.92 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))))))),
% 123.77/123.92 inference(quant_inst,[status(thm)],[])).
% 123.77/123.92 tff(410,plain,
% 123.77/123.92 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~((~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))))))),
% 123.77/123.92 inference(modus_ponens,[status(thm)],[409, 408])).
% 123.77/123.92 tff(411,plain,
% 123.77/123.92 (~((~((~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))))))))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[410, 153])).
% 123.77/123.92 tff(412,plain,
% 123.77/123.92 (((~((~model(tptp_fun_I2_5(tptp_fun_C_20(noc, tac)), tptp_fun_C_20(noc, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_21(noc, tac))) | status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac))) | (~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))))) | ((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))))))),
% 123.77/123.92 inference(tautology,[status(thm)],[])).
% 123.77/123.92 tff(413,plain,
% 123.77/123.92 ((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[412, 411])).
% 123.77/123.92 tff(414,plain,
% 123.77/123.92 ((~((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))))))) | (~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))),
% 123.77/123.92 inference(tautology,[status(thm)],[])).
% 123.77/123.92 tff(415,plain,
% 123.77/123.92 ((~status(tptp_fun_Ax_21(noc, tac), tptp_fun_C_20(noc, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[414, 413])).
% 123.77/123.92 tff(416,plain,
% 123.77/123.92 (~((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[415, 404])).
% 123.77/123.92 tff(417,plain,
% 123.77/123.92 (((~model(tptp_fun_I1_0(tptp_fun_Ax_21(noc, tac)), tptp_fun_Ax_21(noc, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))) | ![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))),
% 123.77/123.92 inference(tautology,[status(thm)],[])).
% 123.77/123.92 tff(418,plain,
% 123.77/123.92 (![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[417, 416])).
% 123.77/123.92 tff(419,assumption,(~model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac))), introduced(assumption)).
% 123.77/123.92 tff(420,assumption,(![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))), introduced(assumption)).
% 123.77/123.92 tff(421,plain,
% 123.77/123.92 ((~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac))) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac))),
% 123.77/123.92 inference(quant_inst,[status(thm)],[])).
% 123.77/123.92 tff(422,plain,
% 123.77/123.92 ($false),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[421, 420, 419])).
% 123.77/123.92 tff(423,plain,(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac)) | (~![I2: $i] : model(I2, tptp_fun_C_20(noc, tac)))), inference(lemma,lemma(discharge,[]))).
% 123.77/123.92 tff(424,plain,
% 123.77/123.92 (model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[423, 418])).
% 123.77/123.92 tff(425,assumption,(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac)) <=> model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac)))), introduced(assumption)).
% 123.77/123.92 tff(426,plain,
% 123.77/123.92 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac)) <=> model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac)))))),
% 123.77/123.92 inference(quant_inst,[status(thm)],[])).
% 123.77/123.92 tff(427,plain,
% 123.77/123.92 ($false),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[426, 288, 425])).
% 123.77/123.92 tff(428,plain,(~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac)) <=> model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))))), inference(lemma,lemma(discharge,[]))).
% 123.77/123.92 tff(429,plain,
% 123.77/123.92 ((model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac)) <=> model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac)))) | (~model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac))) | (~model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))))),
% 123.77/123.92 inference(tautology,[status(thm)],[])).
% 123.77/123.92 tff(430,plain,
% 123.77/123.92 ((~model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), tptp_fun_C_20(noc, tac))) | (~model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[429, 428])).
% 123.77/123.92 tff(431,plain,
% 123.77/123.92 (~model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac)))),
% 123.77/123.92 inference(unit_resolution,[status(thm)],[430, 424])).
% 123.77/123.92 tff(432,plain,
% 123.77/123.92 (^[I: $i, F: $i] : refl((~(model(I, not(F)) <=> model(I, F))) <=> (~(model(I, not(F)) <=> model(I, F))))),
% 123.77/123.92 inference(bind,[status(th)],[])).
% 123.77/123.92 tff(433,plain,
% 123.77/123.92 (![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F))) <=> ![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F)))),
% 123.77/123.92 inference(quant_intro,[status(thm)],[432])).
% 123.77/123.92 tff(434,plain,
% 123.77/123.92 (![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F))) <=> ![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F)))),
% 123.77/123.92 inference(rewrite,[status(thm)],[])).
% 123.77/123.92 tff(435,plain,
% 123.77/123.92 (^[I: $i, F: $i] : trans(rewrite((model(I, F) <=> (~model(I, not(F)))) <=> (~(model(I, not(F)) <=> model(I, F)))), rewrite((~(model(I, not(F)) <=> model(I, F))) <=> (~(model(I, not(F)) <=> model(I, F)))), ((model(I, F) <=> (~model(I, not(F)))) <=> (~(model(I, not(F)) <=> model(I, F)))))),
% 123.77/123.92 inference(bind,[status(th)],[])).
% 123.77/123.92 tff(436,plain,
% 123.77/123.92 (![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F)))),
% 123.77/123.92 inference(quant_intro,[status(thm)],[435])).
% 123.77/123.92 tff(437,axiom,(![I: $i, F: $i] : (model(I, F) <=> (~model(I, not(F))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','not')).
% 123.77/123.92 tff(438,plain,
% 123.77/123.92 (![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F)))),
% 123.77/123.92 inference(modus_ponens,[status(thm)],[437, 436])).
% 123.77/123.92 tff(439,plain,
% 123.77/123.92 (![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F)))),
% 123.77/123.92 inference(modus_ponens,[status(thm)],[438, 434])).
% 123.77/123.92 tff(440,plain,(
% 123.77/123.92 ![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F)))),
% 123.77/123.92 inference(skolemize,[status(sab)],[439])).
% 123.77/123.92 tff(441,plain,
% 123.77/123.92 (![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F)))),
% 123.77/123.92 inference(modus_ponens,[status(thm)],[440, 433])).
% 123.77/123.92 tff(442,plain,
% 123.77/123.92 ((~![I: $i, F: $i] : (~(model(I, not(F)) <=> model(I, F)))) | (~(model(I2!31, not(F!29)) <=> model(I2!31, F!29)))),
% 123.77/123.92 inference(quant_inst,[status(thm)],[])).
% 123.77/123.93 tff(443,plain,
% 123.77/123.93 (~(model(I2!31, not(F!29)) <=> model(I2!31, F!29))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[442, 441])).
% 123.77/123.93 tff(444,plain,
% 123.77/123.93 (~model(I2!31, F!29)),
% 123.77/123.93 inference(and_elim,[status(thm)],[178])).
% 123.77/123.93 tff(445,plain,
% 123.77/123.93 ((model(I2!31, not(F!29)) <=> model(I2!31, F!29)) | model(I2!31, not(F!29)) | model(I2!31, F!29)),
% 123.77/123.93 inference(tautology,[status(thm)],[])).
% 123.77/123.93 tff(446,plain,
% 123.77/123.93 ((model(I2!31, not(F!29)) <=> model(I2!31, F!29)) | model(I2!31, not(F!29))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[445, 444])).
% 123.77/123.93 tff(447,plain,
% 123.77/123.93 (model(I2!31, not(F!29))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[446, 443])).
% 123.77/123.93 tff(448,assumption,(![I2: $i] : (~model(I2, not(F!29)))), introduced(assumption)).
% 123.77/123.93 tff(449,plain,
% 123.77/123.93 ((~![I2: $i] : (~model(I2, not(F!29)))) | (~model(I2!31, not(F!29)))),
% 123.77/123.93 inference(quant_inst,[status(thm)],[])).
% 123.77/123.93 tff(450,plain,
% 123.77/123.93 ($false),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[449, 448, 447])).
% 123.77/123.93 tff(451,plain,(~![I2: $i] : (~model(I2, not(F!29)))), inference(lemma,lemma(discharge,[]))).
% 123.77/123.93 tff(452,plain,
% 123.77/123.93 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac)))))))))))),
% 123.77/123.93 inference(quant_inst,[status(thm)],[])).
% 123.77/123.93 tff(453,plain,
% 123.77/123.93 (~((~(status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac))))))))))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[452, 50])).
% 123.77/123.93 tff(454,plain,
% 123.77/123.93 (((~(status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))))) | (~((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca)) | (~((~model(tptp_fun_I2_1(not(F!29)), not(F!29))) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_20(noc, tac)))))))))) | (status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))))),
% 123.77/123.93 inference(tautology,[status(thm)],[])).
% 123.77/123.93 tff(455,plain,
% 123.77/123.93 (status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29)))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[454, 453])).
% 123.77/123.93 tff(456,plain,
% 123.77/123.93 ((~(status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))))) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29)))),
% 123.77/123.93 inference(tautology,[status(thm)],[])).
% 123.77/123.93 tff(457,plain,
% 123.77/123.93 (status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29)))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[456, 455])).
% 123.77/123.93 tff(458,plain,
% 123.77/123.93 (status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac)))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[457, 451])).
% 123.77/123.93 tff(459,plain,
% 123.77/123.93 (status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca)),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[458, 431])).
% 123.77/123.93 tff(460,plain,
% 123.77/123.93 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm))) | ((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm))) | (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm))),
% 123.77/123.93 inference(rewrite,[status(thm)],[])).
% 123.77/123.93 tff(461,plain,
% 123.77/123.93 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm))) | ((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm))),
% 123.77/123.93 inference(quant_inst,[status(thm)],[])).
% 123.77/123.93 tff(462,plain,
% 123.77/123.93 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | status(Ax, C, thm))) | (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), sca)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm)),
% 123.77/123.93 inference(modus_ponens,[status(thm)],[461, 460])).
% 123.77/123.93 tff(463,plain,
% 123.77/123.93 (status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm)),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[462, 459, 133])).
% 123.77/123.93 tff(464,plain,
% 123.77/123.93 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca))))))))) <=> ((~![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(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)))))))))),
% 123.77/123.93 inference(rewrite,[status(thm)],[])).
% 123.77/123.93 tff(465,plain,
% 123.77/123.93 ((~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)))))))) <=> (~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca))))))))),
% 123.77/123.93 inference(rewrite,[status(thm)],[])).
% 123.77/123.93 tff(466,plain,
% 123.77/123.93 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), 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(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)))))))))),
% 123.77/123.93 inference(monotonicity,[status(thm)],[465])).
% 123.77/123.93 tff(467,plain,
% 123.77/123.93 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), 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(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)))))))))),
% 123.77/123.93 inference(transitivity,[status(thm)],[466, 464])).
% 123.77/123.93 tff(468,plain,
% 123.77/123.93 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm))))))))),
% 123.77/123.93 inference(quant_inst,[status(thm)],[])).
% 123.77/123.93 tff(469,plain,
% 123.77/123.93 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca))))))))),
% 123.77/123.93 inference(modus_ponens,[status(thm)],[468, 467])).
% 123.77/123.93 tff(470,plain,
% 123.77/123.93 (~((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca)))))))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[469, 243])).
% 123.77/123.93 tff(471,plain,
% 123.77/123.93 (((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | (~((~mighta(wca, thm)) | (~((~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), thm)) | (~status(tptp_fun_Ax_19(thm, wca), tptp_fun_C_18(thm, wca), wca))))))) | (mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))),
% 123.77/123.93 inference(tautology,[status(thm)],[])).
% 123.77/123.93 tff(472,plain,
% 123.77/123.93 (mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[471, 470])).
% 123.77/123.93 tff(473,plain,
% 123.77/123.93 ((~mighta(wca, thm)) <=> (~mighta(wca, thm))),
% 123.77/123.93 inference(rewrite,[status(thm)],[])).
% 123.77/123.93 tff(474,axiom,(~mighta(wca, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_wca_thm')).
% 123.77/123.93 tff(475,plain,
% 123.77/123.93 (~mighta(wca, thm)),
% 123.77/123.93 inference(modus_ponens,[status(thm)],[474, 473])).
% 123.77/123.93 tff(476,plain,
% 123.77/123.93 ((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))),
% 123.77/123.93 inference(tautology,[status(thm)],[])).
% 123.77/123.93 tff(477,plain,
% 123.77/123.93 ((~(mighta(wca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[476, 475])).
% 123.77/123.93 tff(478,plain,
% 123.77/123.93 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[477, 472])).
% 123.77/123.93 tff(479,plain,
% 123.77/123.93 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))) | ((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm)) | (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))) | (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm)) | (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)))),
% 123.77/123.93 inference(rewrite,[status(thm)],[])).
% 123.77/123.93 tff(480,plain,
% 123.77/123.93 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))) | ((~status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm)) | (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)))),
% 123.77/123.93 inference(quant_inst,[status(thm)],[])).
% 123.77/123.93 tff(481,plain,
% 123.77/123.93 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wca)))) | (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), thm)) | (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))),
% 123.77/123.93 inference(modus_ponens,[status(thm)],[480, 479])).
% 123.77/123.93 tff(482,plain,
% 123.77/123.93 (~status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[481, 478, 463])).
% 123.77/123.93 tff(483,plain,
% 123.77/123.93 ((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca)),
% 123.77/123.93 inference(tautology,[status(thm)],[])).
% 123.77/123.93 tff(484,plain,
% 123.77/123.93 ((~(model(tptp_fun_I1_0(not(tptp_fun_C_20(noc, tac))), not(tptp_fun_C_20(noc, tac))) | ![I2: $i] : (~model(I2, not(F!29))) | ![I3: $i] : model(I3, not(F!29)) | status(not(tptp_fun_C_20(noc, tac)), not(F!29), wca))) | ![I3: $i] : model(I3, not(F!29))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[483, 451, 431, 482])).
% 123.77/123.93 tff(485,plain,
% 123.77/123.93 (![I3: $i] : model(I3, not(F!29))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[484, 31])).
% 123.77/123.93 tff(486,plain,
% 123.77/123.93 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I2_17(F!29, F!29), not(F!29))) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I2_17(F!29, F!29), not(F!29))) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29)))))))))),
% 123.77/123.93 inference(rewrite,[status(thm)],[])).
% 123.77/123.93 tff(487,plain,
% 123.77/123.93 ((~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), not(F!29))))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29)))))))) <=> (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I2_17(F!29, F!29), not(F!29))) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))))))),
% 123.77/123.93 inference(rewrite,[status(thm)],[])).
% 123.77/123.93 tff(488,plain,
% 123.77/123.93 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), not(F!29))))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I2_17(F!29, F!29), not(F!29))) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29)))))))))),
% 123.77/123.93 inference(monotonicity,[status(thm)],[487])).
% 123.77/123.93 tff(489,plain,
% 123.77/123.93 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), not(F!29))))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I2_17(F!29, F!29), not(F!29))) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29)))))))))),
% 123.77/123.93 inference(transitivity,[status(thm)],[488, 486])).
% 123.77/123.93 tff(490,plain,
% 123.77/123.93 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), not(F!29))))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))))))),
% 123.77/123.93 inference(quant_inst,[status(thm)],[])).
% 123.77/123.93 tff(491,plain,
% 123.77/123.93 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I2_17(F!29, F!29), not(F!29))) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))))))),
% 123.77/123.93 inference(modus_ponens,[status(thm)],[490, 489])).
% 123.77/123.93 tff(492,plain,
% 123.77/123.93 (~((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I2_17(F!29, F!29), not(F!29))) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29)))))))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[491, 309])).
% 123.77/123.93 tff(493,plain,
% 123.77/123.93 (((~((~status(F!29, F!29, noc)) | (~((~model(tptp_fun_I2_17(F!29, F!29), not(F!29))) | (~model(tptp_fun_I1_2(F!29, F!29), F!29)) | (~model(tptp_fun_I2_17(F!29, F!29), F!29)))))) | (~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))))) | (status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29)))))),
% 123.77/123.93 inference(tautology,[status(thm)],[])).
% 123.77/123.93 tff(494,plain,
% 123.77/123.93 (status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))),
% 123.77/123.93 inference(unit_resolution,[status(thm)],[493, 492])).
% 123.77/123.93 tff(495,plain,
% 123.77/123.93 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 123.77/123.93 inference(bind,[status(th)],[])).
% 123.77/123.93 tff(496,plain,
% 123.77/123.93 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 123.77/123.93 inference(quant_intro,[status(thm)],[495])).
% 123.77/123.93 tff(497,plain,
% 123.77/123.93 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 123.77/123.93 inference(bind,[status(th)],[])).
% 123.77/123.93 tff(498,plain,
% 123.77/123.93 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 123.77/123.93 inference(quant_intro,[status(thm)],[497])).
% 123.77/123.93 tff(499,plain,
% 123.77/123.93 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 123.77/123.93 inference(bind,[status(th)],[])).
% 123.77/123.93 tff(500,plain,
% 123.77/123.93 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 123.77/123.93 inference(quant_intro,[status(thm)],[499])).
% 123.77/123.93 tff(501,plain,
% 123.77/123.93 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 123.77/123.93 inference(transitivity,[status(thm)],[500, 498])).
% 123.77/123.93 tff(502,plain,
% 123.77/123.93 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) <=> (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))), ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) <=> (status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))))), rewrite((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) <=> (status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))), ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) <=> (status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))) <=> ((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))) | (~status(Ax, C, eqv))))), rewrite(((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))) | (~status(Ax, C, eqv))) <=> ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))) <=> ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))), (((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))), rewrite(((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))), (((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))))),
% 123.77/123.93 inference(bind,[status(th)],[])).
% 123.77/123.93 tff(503,plain,
% 123.77/123.93 (![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 123.77/123.93 inference(quant_intro,[status(thm)],[502])).
% 123.77/123.93 tff(504,plain,
% 123.77/123.93 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))))),
% 123.77/123.94 inference(bind,[status(th)],[])).
% 123.77/123.94 tff(505,plain,
% 123.77/123.94 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 123.77/123.94 inference(quant_intro,[status(thm)],[504])).
% 123.77/123.94 tff(506,plain,
% 123.77/123.94 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))),
% 123.77/123.94 inference(rewrite,[status(thm)],[])).
% 123.77/123.94 tff(507,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','eqv')).
% 123.77/123.94 tff(508,plain,
% 123.77/123.94 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))),
% 123.77/123.94 inference(modus_ponens,[status(thm)],[507, 506])).
% 123.77/123.94 tff(509,plain,(
% 123.77/123.94 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 123.77/123.94 inference(skolemize,[status(sab)],[508])).
% 123.77/123.94 tff(510,plain,
% 123.77/123.94 (![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 123.77/123.94 inference(modus_ponens,[status(thm)],[509, 505])).
% 123.77/123.94 tff(511,plain,
% 123.77/123.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 123.77/123.94 inference(modus_ponens,[status(thm)],[510, 503])).
% 123.77/123.94 tff(512,plain,
% 123.77/123.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 123.77/123.94 inference(modus_ponens,[status(thm)],[511, 501])).
% 123.77/123.94 tff(513,plain,
% 123.77/123.94 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 123.77/123.94 inference(modus_ponens,[status(thm)],[512, 496])).
% 123.77/123.94 tff(514,plain,
% 123.77/123.94 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv) | (~(model(tptp_fun_I2_4(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc)) <=> model(tptp_fun_I2_4(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(eqv, noc))))) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc))))))))))),
% 123.77/123.94 inference(quant_inst,[status(thm)],[])).
% 123.77/123.94 tff(515,plain,
% 123.77/123.94 (~((~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv) | (~(model(tptp_fun_I2_4(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc)) <=> model(tptp_fun_I2_4(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(eqv, noc))))) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc)))))))))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[514, 513])).
% 123.77/123.94 tff(516,plain,
% 123.77/123.94 (((~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv) | (~(model(tptp_fun_I2_4(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc)) <=> model(tptp_fun_I2_4(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(eqv, noc))))) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc))))))))) | ((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc)))))))),
% 123.77/123.94 inference(tautology,[status(thm)],[])).
% 123.77/123.94 tff(517,plain,
% 123.77/123.94 ((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc))))))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[516, 515])).
% 123.77/123.94 tff(518,assumption,(~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)))), introduced(assumption)).
% 123.77/123.94 tff(519,plain,
% 123.77/123.94 (((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))) | status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)),
% 123.77/123.94 inference(tautology,[status(thm)],[])).
% 123.77/123.94 tff(520,plain,
% 123.77/123.94 (status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[519, 518])).
% 123.77/123.94 tff(521,plain,
% 123.77/123.94 ((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc)))))))) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc))))))),
% 123.77/123.94 inference(tautology,[status(thm)],[])).
% 123.77/123.94 tff(522,plain,
% 123.77/123.94 ((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc)))))))) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc))))))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[521, 520])).
% 123.77/123.94 tff(523,plain,
% 123.77/123.94 (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc)))))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[522, 517])).
% 123.77/123.94 tff(524,plain,
% 123.77/123.94 (((~model(tptp_fun_I1_0(tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc))))) | ![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc)))),
% 123.77/123.94 inference(tautology,[status(thm)],[])).
% 123.77/123.94 tff(525,plain,
% 123.77/123.94 (![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc)))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[524, 523])).
% 123.77/123.94 tff(526,plain,
% 123.77/123.94 ((~![I2: $i] : (model(I2, tptp_fun_Ax_19(eqv, noc)) <=> model(I2, tptp_fun_C_18(eqv, noc)))) | (model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)))),
% 123.77/123.94 inference(quant_inst,[status(thm)],[])).
% 123.77/123.94 tff(527,plain,
% 123.77/123.94 (model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[526, 525])).
% 123.77/123.94 tff(528,plain,
% 123.77/123.94 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))),
% 123.77/123.94 inference(quant_inst,[status(thm)],[])).
% 123.77/123.94 tff(529,plain,
% 123.77/123.94 (~(model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc))))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[528, 288])).
% 123.77/123.94 tff(530,plain,
% 123.77/123.94 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc))))))))))),
% 123.77/123.94 inference(rewrite,[status(thm)],[])).
% 123.77/123.94 tff(531,plain,
% 123.77/123.94 ((~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc))))))))) <=> (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc)))))))))),
% 123.77/123.94 inference(rewrite,[status(thm)],[])).
% 123.77/123.94 tff(532,plain,
% 123.77/123.94 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc))))))))))),
% 123.77/123.94 inference(monotonicity,[status(thm)],[531])).
% 123.77/123.94 tff(533,plain,
% 123.77/123.94 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc))))))))))),
% 123.77/123.94 inference(transitivity,[status(thm)],[532, 530])).
% 123.77/123.94 tff(534,plain,
% 123.77/123.94 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc)))))))))),
% 123.77/123.94 inference(quant_inst,[status(thm)],[])).
% 123.77/123.94 tff(535,plain,
% 123.77/123.94 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc)))))))))),
% 123.77/123.94 inference(modus_ponens,[status(thm)],[534, 533])).
% 123.77/123.94 tff(536,plain,
% 123.77/123.94 (~((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc))))))))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[535, 309])).
% 123.77/123.94 tff(537,plain,
% 123.77/123.94 (((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~(status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(eqv, noc))) | (~model(I1, tptp_fun_C_18(eqv, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(eqv, noc))) | (~model(I2, not(tptp_fun_C_18(eqv, noc)))))))) | ((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))),
% 123.77/123.94 inference(tautology,[status(thm)],[])).
% 123.77/123.94 tff(538,plain,
% 123.77/123.94 ((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc))))))),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[537, 536])).
% 123.77/123.94 tff(539,plain,
% 123.77/123.94 (((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))) | status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)),
% 123.77/123.94 inference(tautology,[status(thm)],[])).
% 123.77/123.94 tff(540,plain,
% 123.77/123.94 (status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)),
% 123.77/123.94 inference(unit_resolution,[status(thm)],[539, 518])).
% 123.77/123.94 tff(541,plain,
% 123.77/123.94 ((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc))))))),
% 123.77/123.94 inference(tautology,[status(thm)],[])).
% 123.77/123.94 tff(542,plain,
% 123.77/123.95 ((~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))))) | (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc))))))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[541, 540])).
% 123.77/123.95 tff(543,plain,
% 123.77/123.95 (~((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[542, 538])).
% 123.77/123.95 tff(544,plain,
% 123.77/123.95 (((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc))))) | model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(545,plain,
% 123.77/123.95 (model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[544, 543])).
% 123.77/123.95 tff(546,plain,
% 123.77/123.95 ((model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc))))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(547,plain,
% 123.77/123.95 ((model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[546, 545])).
% 123.77/123.95 tff(548,plain,
% 123.77/123.95 (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[547, 529])).
% 123.77/123.95 tff(549,plain,
% 123.77/123.95 (((~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), not(tptp_fun_C_18(eqv, noc))))) | model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(550,plain,
% 123.77/123.95 (model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[549, 543])).
% 123.77/123.95 tff(551,plain,
% 123.77/123.95 ((~(model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc))) | model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(552,plain,
% 123.77/123.95 ((~(model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_Ax_19(eqv, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc)))) | model(tptp_fun_I2_17(tptp_fun_C_18(eqv, noc), tptp_fun_Ax_19(eqv, noc)), tptp_fun_C_18(eqv, noc))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[551, 550])).
% 123.77/123.95 tff(553,plain,
% 123.77/123.95 ($false),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[552, 548, 527])).
% 123.77/123.95 tff(554,plain,((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))), inference(lemma,lemma(discharge,[]))).
% 123.77/123.95 tff(555,plain,
% 123.77/123.95 ((~![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(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))))))))),
% 123.77/123.95 inference(quant_inst,[status(thm)],[])).
% 123.77/123.95 tff(556,plain,
% 123.77/123.95 (~((~(mighta(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)))))))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[555, 243])).
% 123.77/123.95 tff(557,plain,
% 123.77/123.95 (((~(mighta(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))))))) | ((~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)))))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(558,plain,
% 123.77/123.95 ((~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[557, 556])).
% 123.77/123.95 tff(559,plain,
% 123.77/123.95 ((~((~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv)))))) | (~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(560,plain,
% 123.77/123.95 ((~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[559, 558])).
% 123.77/123.95 tff(561,plain,
% 123.77/123.95 (~mighta(noc, eqv)),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[560, 554])).
% 123.77/123.95 tff(562,plain,
% 123.77/123.95 (((~(mighta(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, eqv)) | (~((~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), noc)) | (~status(tptp_fun_Ax_19(eqv, noc), tptp_fun_C_18(eqv, noc), eqv))))))) | (mighta(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc))))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(563,plain,
% 123.77/123.95 (mighta(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc)))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[562, 556])).
% 123.77/123.95 tff(564,plain,
% 123.77/123.95 ((~(mighta(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc))))) | mighta(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc)))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(565,plain,
% 123.77/123.95 (mighta(noc, eqv) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc)))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[564, 563])).
% 123.77/123.95 tff(566,plain,
% 123.77/123.95 (![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc)))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[565, 561])).
% 123.77/123.95 tff(567,plain,
% 123.77/123.95 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29)))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29))))))),
% 123.77/123.95 inference(rewrite,[status(thm)],[])).
% 123.77/123.95 tff(568,plain,
% 123.77/123.95 ((~((~(status(F!29, F!29, eqv) | (~(model(tptp_fun_I2_4(F!29, F!29), F!29) <=> model(tptp_fun_I2_4(F!29, F!29), F!29))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (model(I2, F!29) <=> model(I2, F!29))))))))) <=> (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29)))))),
% 123.77/123.95 inference(rewrite,[status(thm)],[])).
% 123.77/123.95 tff(569,plain,
% 123.77/123.95 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | (~(model(tptp_fun_I2_4(F!29, F!29), F!29) <=> model(tptp_fun_I2_4(F!29, F!29), F!29))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (model(I2, F!29) <=> model(I2, F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29))))))),
% 123.77/123.95 inference(monotonicity,[status(thm)],[568])).
% 123.77/123.95 tff(570,plain,
% 123.77/123.95 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | (~(model(tptp_fun_I2_4(F!29, F!29), F!29) <=> model(tptp_fun_I2_4(F!29, F!29), F!29))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (model(I2, F!29) <=> model(I2, F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29))))))),
% 123.77/123.95 inference(transitivity,[status(thm)],[569, 567])).
% 123.77/123.95 tff(571,plain,
% 123.77/123.95 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | (~(model(tptp_fun_I2_4(F!29, F!29), F!29) <=> model(tptp_fun_I2_4(F!29, F!29), F!29))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (model(I2, F!29) <=> model(I2, F!29)))))))))),
% 123.77/123.95 inference(quant_inst,[status(thm)],[])).
% 123.77/123.95 tff(572,plain,
% 123.77/123.95 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29)))))),
% 123.77/123.95 inference(modus_ponens,[status(thm)],[571, 570])).
% 123.77/123.95 tff(573,plain,
% 123.77/123.95 (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29))))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[572, 513])).
% 123.77/123.95 tff(574,plain,
% 123.77/123.95 (((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29)))) | (status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(575,plain,
% 123.77/123.95 (status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[574, 573])).
% 123.77/123.95 tff(576,plain,
% 123.77/123.95 ((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(577,plain,
% 123.77/123.95 (status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[576, 575])).
% 123.77/123.95 tff(578,plain,
% 123.77/123.95 (status(F!29, F!29, eqv)),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[577, 182])).
% 123.77/123.95 tff(579,plain,
% 123.77/123.95 (((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc)))) | ((~status(F!29, F!29, eqv)) | (~status(F!29, F!29, noc)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc)))) | (~status(F!29, F!29, eqv)) | (~status(F!29, F!29, noc)))),
% 123.77/123.95 inference(rewrite,[status(thm)],[])).
% 123.77/123.95 tff(580,plain,
% 123.77/123.95 ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc)))) | ((~status(F!29, F!29, eqv)) | (~status(F!29, F!29, noc)))),
% 123.77/123.95 inference(quant_inst,[status(thm)],[])).
% 123.77/123.95 tff(581,plain,
% 123.77/123.95 ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, noc)))) | (~status(F!29, F!29, eqv)) | (~status(F!29, F!29, noc))),
% 123.77/123.95 inference(modus_ponens,[status(thm)],[580, 579])).
% 123.77/123.95 tff(582,plain,
% 123.77/123.95 (~status(F!29, F!29, noc)),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[581, 578, 566])).
% 123.77/123.95 tff(583,plain,
% 123.77/123.95 ((~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29)))))) | status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))),
% 123.77/123.95 inference(tautology,[status(thm)],[])).
% 123.77/123.95 tff(584,plain,
% 123.77/123.95 ((~(status(F!29, F!29, noc) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29)))))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[583, 182, 582])).
% 123.77/123.95 tff(585,plain,
% 123.77/123.95 (![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))),
% 123.77/123.95 inference(unit_resolution,[status(thm)],[584, 494])).
% 123.77/123.95 tff(586,plain,
% 123.77/123.95 (((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))) | ((~model(I1!30, F!29)) | (~model(I1!30, not(F!29))))) <=> ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))) | (~model(I1!30, F!29)) | (~model(I1!30, not(F!29))))),
% 123.77/123.95 inference(rewrite,[status(thm)],[])).
% 123.77/123.95 tff(587,plain,
% 123.77/123.95 ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))) | ((~model(I1!30, F!29)) | (~model(I1!30, not(F!29))))),
% 123.82/123.97 inference(quant_inst,[status(thm)],[])).
% 123.82/123.97 tff(588,plain,
% 123.82/123.97 ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(F!29))))) | (~model(I1!30, F!29)) | (~model(I1!30, not(F!29)))),
% 123.82/123.97 inference(modus_ponens,[status(thm)],[587, 586])).
% 123.82/123.97 tff(589,plain,
% 123.82/123.97 (~model(I1!30, not(F!29))),
% 123.82/123.97 inference(unit_resolution,[status(thm)],[588, 179, 585])).
% 123.82/123.97 tff(590,plain,
% 123.82/123.97 ((~![I3: $i] : model(I3, not(F!29))) | model(I1!30, not(F!29))),
% 123.82/123.97 inference(quant_inst,[status(thm)],[])).
% 123.82/123.97 tff(591,plain,
% 123.82/123.97 ($false),
% 123.82/123.97 inference(unit_resolution,[status(thm)],[590, 589, 485])).
% 123.82/123.97 % SZS output end Proof
% 123.82/123.98 % E exiting
%------------------------------------------------------------------------------