%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS257+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:38 AM UTC 2025
% Result : Theorem 0.61s 0.79s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : KRS257+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:17:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.61/0.79 % SZS status Theorem
% 0.61/0.79 % SZS output start Proof
% 0.61/0.79 tff(model_type, type, (
% 0.61/0.79 model: ( $i * $i ) > $o)).
% 0.61/0.79 tff(tptp_fun_F_28_type, type, (
% 0.61/0.79 tptp_fun_F_28: $i)).
% 0.61/0.79 tff(tptp_fun_Ax_38_type, type, (
% 0.61/0.79 tptp_fun_Ax_38: $i)).
% 0.61/0.79 tff(status_type, type, (
% 0.61/0.79 status: ( $i * $i * $i ) > $o)).
% 0.61/0.79 tff(sat_type, type, (
% 0.61/0.79 sat: $i)).
% 0.61/0.79 tff(tptp_fun_I1_2_type, type, (
% 0.61/0.79 tptp_fun_I1_2: ( $i * $i ) > $i)).
% 0.61/0.79 tff(thm_type, type, (
% 0.61/0.79 thm: $i)).
% 0.61/0.79 tff(tptp_fun_I1_3_type, type, (
% 0.61/0.79 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.61/0.79 tff(mighta_type, type, (
% 0.61/0.79 mighta: ( $i * $i ) > $o)).
% 0.61/0.79 tff(tptp_fun_C_18_type, type, (
% 0.61/0.79 tptp_fun_C_18: ( $i * $i ) > $i)).
% 0.61/0.79 tff(tptp_fun_Ax_19_type, type, (
% 0.61/0.79 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 0.61/0.79 tff(tptp_fun_I1_39_type, type, (
% 0.61/0.79 tptp_fun_I1_39: $i)).
% 0.61/0.79 tff(tptp_fun_C_37_type, type, (
% 0.61/0.79 tptp_fun_C_37: $i)).
% 0.61/0.79 tff(tptp_fun_I4_41_type, type, (
% 0.61/0.79 tptp_fun_I4_41: $i)).
% 0.61/0.79 tff(tptp_fun_I3_40_type, type, (
% 0.61/0.79 tptp_fun_I3_40: $i)).
% 0.61/0.79 tff(1,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(2,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[1])).
% 0.61/0.79 tff(3,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(4,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[3])).
% 0.61/0.79 tff(5,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 0.61/0.79 inference(transitivity,[status(thm)],[4, 2])).
% 0.61/0.79 tff(6,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) <=> (status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))), trans(monotonicity(rewrite((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) <=> (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))), (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))) <=> ((~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))) | (~status(Ax, C, sat))))), rewrite(((~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))) | (~status(Ax, C, sat))) <=> ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))), (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))) <=> ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))), (((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ((status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C)))) & ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))), rewrite(((status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C)))) & ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))), (((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(7,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[6])).
% 0.61/0.79 tff(8,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : rewrite(((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(9,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[8])).
% 0.61/0.79 tff(10,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat)) <=> ![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(11,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','sat')).
% 0.61/0.79 tff(12,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.61/0.79 tff(13,plain,(
% 0.61/0.79 ![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[12])).
% 0.61/0.79 tff(14,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.61/0.79 tff(15,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.61/0.79 tff(16,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.61/0.79 tff(17,plain,
% 0.61/0.79 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(Ax!38, F!28, sat) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28))))) | (~((~status(Ax!38, F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, Ax!38), Ax!38)) | (~model(tptp_fun_I1_2(F!28, Ax!38), F!28))))))))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(18,plain,
% 0.61/0.79 (~((~(status(Ax!38, F!28, sat) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28))))) | (~((~status(Ax!38, F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, Ax!38), Ax!38)) | (~model(tptp_fun_I1_2(F!28, Ax!38), F!28)))))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.61/0.79 tff(19,plain,
% 0.61/0.79 (((~(status(Ax!38, F!28, sat) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28))))) | (~((~status(Ax!38, F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, Ax!38), Ax!38)) | (~model(tptp_fun_I1_2(F!28, Ax!38), F!28))))))) | (status(Ax!38, F!28, sat) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28))))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(20,plain,
% 0.61/0.79 (status(Ax!38, F!28, sat) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28)))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.61/0.79 tff(21,assumption,(~model(tptp_fun_I1_3(F!28, Ax!38), F!28)), introduced(assumption)).
% 0.61/0.79 tff(22,plain,
% 0.61/0.79 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(23,plain,
% 0.61/0.79 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 0.61/0.79 inference(quant_intro,[status(thm)],[22])).
% 0.61/0.79 tff(24,plain,
% 0.61/0.79 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(25,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','tautology')).
% 0.61/0.79 tff(26,plain,
% 0.61/0.79 (?[F: $i] : ![I: $i] : model(I, F)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.61/0.79 tff(27,plain,(
% 0.61/0.79 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 0.61/0.79 inference(transitivity,[status(sab)],[26])).
% 0.61/0.79 tff(28,plain,
% 0.61/0.79 (![I: $i] : model(I, F!28)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.61/0.79 tff(29,plain,
% 0.61/0.79 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28)),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(30,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[29, 28, 21])).
% 0.61/0.79 tff(31,plain,(model(tptp_fun_I1_3(F!28, Ax!38), F!28)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(32,plain,
% 0.61/0.79 (((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28)) | (~model(tptp_fun_I1_3(F!28, Ax!38), F!28))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(33,plain,
% 0.61/0.79 ((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.61/0.79 tff(34,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C)))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(35,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[34])).
% 0.61/0.79 tff(36,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(37,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[36])).
% 0.61/0.79 tff(38,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(39,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[38])).
% 0.61/0.79 tff(40,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.61/0.79 inference(transitivity,[status(thm)],[39, 37])).
% 0.61/0.79 tff(41,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))), rewrite((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(42,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[41])).
% 0.61/0.79 tff(43,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(44,plain,
% 0.61/0.79 (^[Ax: $i, C: $i] : rewrite((![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(45,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[44])).
% 0.61/0.79 tff(46,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')).
% 0.61/0.79 tff(47,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.61/0.79 tff(48,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.61/0.79 tff(49,plain,(
% 0.61/0.79 ![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[48])).
% 0.61/0.79 tff(50,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.61/0.79 tff(51,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.61/0.79 tff(52,plain,
% 0.61/0.79 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[51, 35])).
% 0.61/0.79 tff(53,plain,
% 0.61/0.79 (((~![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(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, 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(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(54,plain,
% 0.61/0.79 ((~((~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))) | (~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))))) <=> (~((~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm)))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(55,plain,
% 0.61/0.79 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))) | (~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))))))) <=> ((~![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(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[54])).
% 0.61/0.79 tff(56,plain,
% 0.61/0.79 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))) | (~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))))))) <=> ((~![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(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))))))),
% 0.61/0.79 inference(transitivity,[status(thm)],[55, 53])).
% 0.61/0.79 tff(57,plain,
% 0.61/0.79 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))) | (~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))))))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(58,plain,
% 0.61/0.79 ((~![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(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm)))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.61/0.79 tff(59,plain,
% 0.61/0.79 (~((~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[58, 52])).
% 0.61/0.79 tff(60,plain,
% 0.61/0.79 (((~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm)))) | ((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(61,plain,
% 0.61/0.79 ((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.61/0.79 tff(62,plain,
% 0.61/0.79 ((~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm))) | (~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm)),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(63,plain,
% 0.61/0.79 ((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.61/0.79 tff(64,plain,
% 0.61/0.79 (status(Ax!38, F!28, thm)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[63, 33])).
% 0.61/0.79 tff(65,plain,
% 0.61/0.79 (^[S1: $i, S2: $i] : refl((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(66,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[65])).
% 0.61/0.80 tff(67,plain,
% 0.61/0.80 (^[S1: $i, S2: $i] : rewrite((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(68,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[67])).
% 0.61/0.80 tff(69,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[68, 66])).
% 0.61/0.80 tff(70,plain,
% 0.61/0.80 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) <=> (mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))), trans(monotonicity(rewrite((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) <=> (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))), rewrite(((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(71,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[70])).
% 0.61/0.80 tff(72,plain,
% 0.61/0.80 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(73,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[72])).
% 0.61/0.80 tff(74,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(75,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')).
% 0.61/0.80 tff(76,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.61/0.80 tff(77,plain,(
% 0.61/0.80 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.61/0.80 inference(skolemize,[status(sab)],[76])).
% 0.61/0.80 tff(78,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.61/0.80 tff(79,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.61/0.80 tff(80,plain,
% 0.61/0.80 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.61/0.80 tff(81,plain,
% 0.61/0.80 (((~![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(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), 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(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm)))))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(82,plain,
% 0.61/0.80 ((~((~(mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sat))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm)))))))) <=> (~((~(mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm))))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(83,plain,
% 0.61/0.80 (((~![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(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sat))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), 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(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm)))))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[82])).
% 0.61/0.80 tff(84,plain,
% 0.61/0.80 (((~![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(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sat))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), 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(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm)))))))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[83, 81])).
% 0.61/0.80 tff(85,plain,
% 0.61/0.80 ((~![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(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sat))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm))))))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(86,plain,
% 0.61/0.80 ((~![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(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm))))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.61/0.80 tff(87,plain,
% 0.61/0.80 (~((~(mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm)))))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[86, 80])).
% 0.61/0.80 tff(88,plain,
% 0.61/0.80 (((~(mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | (~((~mighta(sat, thm)) | (~((~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), sat)) | (~status(tptp_fun_Ax_19(thm, sat), tptp_fun_C_18(thm, sat), thm))))))) | (mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))),
% 0.61/0.80 inference(tautology,[status(thm)],[])).
% 0.61/0.80 tff(89,plain,
% 0.61/0.80 (mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.61/0.80 tff(90,plain,
% 0.61/0.80 ((~mighta(sat, thm)) <=> (~mighta(sat, thm))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(91,axiom,(~mighta(sat, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_sat_thm')).
% 0.61/0.80 tff(92,plain,
% 0.61/0.80 (~mighta(sat, thm)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.61/0.80 tff(93,plain,
% 0.61/0.80 ((~(mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm)))),
% 0.61/0.80 inference(tautology,[status(thm)],[])).
% 0.61/0.80 tff(94,plain,
% 0.61/0.80 ((~(mighta(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.61/0.80 tff(95,plain,
% 0.61/0.80 (![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[94, 89])).
% 0.61/0.80 tff(96,plain,
% 0.61/0.80 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm)))) | ((~status(Ax!38, F!28, sat)) | (~status(Ax!38, F!28, thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm)))) | (~status(Ax!38, F!28, sat)) | (~status(Ax!38, F!28, thm)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(97,plain,
% 0.61/0.80 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm)))) | ((~status(Ax!38, F!28, sat)) | (~status(Ax!38, F!28, thm)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(98,plain,
% 0.61/0.80 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, thm)))) | (~status(Ax!38, F!28, sat)) | (~status(Ax!38, F!28, thm))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.61/0.80 tff(99,plain,
% 0.61/0.80 (~status(Ax!38, F!28, sat)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[98, 95, 64])).
% 0.61/0.80 tff(100,plain,
% 0.61/0.80 ((~(status(Ax!38, F!28, sat) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28))))) | status(Ax!38, F!28, sat) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28)))),
% 0.61/0.80 inference(tautology,[status(thm)],[])).
% 0.61/0.80 tff(101,plain,
% 0.61/0.80 ((~(status(Ax!38, F!28, sat) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28))))) | ![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.61/0.80 tff(102,plain,
% 0.61/0.80 (![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[101, 20])).
% 0.61/0.80 tff(103,plain,
% 0.61/0.80 (((~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!28, Ax!38), F!28))) | status(Ax!38, F!28, thm)))) | ((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))),
% 0.61/0.80 inference(tautology,[status(thm)],[])).
% 0.61/0.80 tff(104,plain,
% 0.61/0.80 ((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[103, 59])).
% 0.61/0.80 tff(105,plain,
% 0.61/0.80 ((~((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28)))) | (~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))),
% 0.61/0.80 inference(tautology,[status(thm)],[])).
% 0.61/0.80 tff(106,plain,
% 0.61/0.80 ((~status(Ax!38, F!28, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.61/0.80 tff(107,plain,
% 0.61/0.80 (![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[106, 64])).
% 0.61/0.80 tff(108,plain,
% 0.61/0.80 ((model(I1!39, Ax!38) & ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) & ((~model(I3!40, Ax!38)) & model(I3!40, C!37)) & (~model(I4!41, C!37))) <=> (model(I1!39, Ax!38) & ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) & (~model(I3!40, Ax!38)) & model(I3!40, C!37) & (~model(I4!41, C!37)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(109,plain,
% 0.61/0.80 (?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(110,plain,
% 0.61/0.80 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))), (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) <=> ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))))), rewrite(((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)))), (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))))), ((((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))) <=> ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))))), rewrite(((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))), ((((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))) <=> (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(111,plain,
% 0.61/0.80 (?[Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[110])).
% 0.61/0.80 tff(112,axiom,(?[Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','mixed_pair')).
% 0.61/0.80 tff(113,plain,
% 0.61/0.80 (?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.61/0.80 tff(114,plain,
% 0.61/0.80 (?[Ax: $i, C: $i] : (?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C)) & ?[I4: $i] : (~model(I4, C)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.61/0.80 tff(115,plain,
% 0.61/0.80 (model(I1!39, Ax!38) & ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) & (~model(I3!40, Ax!38)) & model(I3!40, C!37) & (~model(I4!41, C!37))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[114, 108])).
% 0.61/0.80 tff(116,plain,
% 0.61/0.80 (model(I1!39, Ax!38)),
% 0.61/0.80 inference(and_elim,[status(thm)],[115])).
% 0.61/0.80 tff(117,plain,
% 0.61/0.80 (((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))) | ((~model(I1!39, Ax!38)) | model(I1!39, F!28))) <=> ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))) | (~model(I1!39, Ax!38)) | model(I1!39, F!28))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(118,plain,
% 0.61/0.80 ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))) | ((~model(I1!39, Ax!38)) | model(I1!39, F!28))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(119,plain,
% 0.61/0.80 ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!28))) | (~model(I1!39, Ax!38)) | model(I1!39, F!28)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.61/0.80 tff(120,plain,
% 0.61/0.80 (model(I1!39, F!28)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[119, 116, 107])).
% 0.61/0.80 tff(121,plain,
% 0.61/0.80 (((~![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28)))) | ((~model(I1!39, Ax!38)) | (~model(I1!39, F!28)))) <=> ((~![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28)))) | (~model(I1!39, Ax!38)) | (~model(I1!39, F!28)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(122,plain,
% 0.61/0.80 ((~![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28)))) | ((~model(I1!39, Ax!38)) | (~model(I1!39, F!28)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(123,plain,
% 0.61/0.80 ((~![I1: $i] : ((~model(I1, Ax!38)) | (~model(I1, F!28)))) | (~model(I1!39, Ax!38)) | (~model(I1!39, F!28))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.61/0.81 tff(124,plain,
% 0.61/0.81 ($false),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[123, 116, 120, 102])).
% 0.61/0.81 % SZS output end Proof
% 0.61/0.81 % E exiting
%------------------------------------------------------------------------------