%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS259+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 05:13:38 AM UTC 2025
% Result : Theorem 0.58s 0.78s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS259+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 19:17:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.58/0.78 % SZS status Theorem
% 0.58/0.78 % SZS output start Proof
% 0.58/0.78 tff(model_type, type, (
% 0.58/0.78 model: ( $i * $i ) > $o)).
% 0.58/0.78 tff(tptp_fun_C_42_type, type, (
% 0.58/0.78 tptp_fun_C_42: $i)).
% 0.58/0.78 tff(status_type, type, (
% 0.58/0.78 status: ( $i * $i * $i ) > $o)).
% 0.58/0.78 tff(tac_type, type, (
% 0.58/0.78 tac: $i)).
% 0.58/0.78 tff(tptp_fun_F_28_type, type, (
% 0.58/0.78 tptp_fun_F_28: $i)).
% 0.58/0.78 tff(thm_type, type, (
% 0.58/0.78 thm: $i)).
% 0.58/0.78 tff(tptp_fun_I1_3_type, type, (
% 0.58/0.78 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.58/0.78 tff(mighta_type, type, (
% 0.58/0.78 mighta: ( $i * $i ) > $o)).
% 0.58/0.78 tff(tptp_fun_C_18_type, type, (
% 0.58/0.78 tptp_fun_C_18: ( $i * $i ) > $i)).
% 0.58/0.78 tff(tptp_fun_Ax_19_type, type, (
% 0.58/0.78 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 0.58/0.78 tff(tptp_fun_I2_5_type, type, (
% 0.58/0.78 tptp_fun_I2_5: $i > $i)).
% 0.58/0.78 tff(tptp_fun_I1_0_type, type, (
% 0.58/0.78 tptp_fun_I1_0: $i > $i)).
% 0.58/0.78 tff(tptp_fun_I2_45_type, type, (
% 0.58/0.78 tptp_fun_I2_45: $i)).
% 0.58/0.78 tff(tptp_fun_I1_44_type, type, (
% 0.58/0.78 tptp_fun_I1_44: $i)).
% 0.58/0.78 tff(tptp_fun_Ax_43_type, type, (
% 0.58/0.78 tptp_fun_Ax_43: $i)).
% 0.58/0.78 tff(1,assumption,((~((~status(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm)))), introduced(assumption)).
% 0.58/0.78 tff(2,plain,
% 0.58/0.78 (^[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)))))))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(3,plain,
% 0.58/0.78 (![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))))))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[2])).
% 0.58/0.78 tff(4,plain,
% 0.58/0.78 (^[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)))))))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(5,plain,
% 0.58/0.78 (![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))))))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[4])).
% 0.58/0.78 tff(6,plain,
% 0.58/0.78 (^[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)))))))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(7,plain,
% 0.58/0.78 (![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))))))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[6])).
% 0.58/0.78 tff(8,plain,
% 0.58/0.78 (![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))))))),
% 0.58/0.78 inference(transitivity,[status(thm)],[7, 5])).
% 0.58/0.78 tff(9,plain,
% 0.58/0.78 (^[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))))))))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(10,plain,
% 0.58/0.78 (![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))))))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[9])).
% 0.58/0.78 tff(11,plain,
% 0.58/0.78 (![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))),
% 0.58/0.78 inference(rewrite,[status(thm)],[])).
% 0.58/0.78 tff(12,plain,
% 0.58/0.78 (^[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)))),
% 0.58/0.78 inference(bind,[status(th)],[])).
% 0.58/0.78 tff(13,plain,
% 0.58/0.78 (![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))),
% 0.58/0.78 inference(quant_intro,[status(thm)],[12])).
% 0.58/0.78 tff(14,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')).
% 0.58/0.78 tff(15,plain,
% 0.58/0.78 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.58/0.78 tff(16,plain,
% 0.58/0.78 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.58/0.78 tff(17,plain,(
% 0.58/0.78 ![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))))),
% 0.58/0.78 inference(skolemize,[status(sab)],[16])).
% 0.58/0.78 tff(18,plain,
% 0.58/0.78 (![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))))))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.58/0.78 tff(19,plain,
% 0.58/0.78 (![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))))))),
% 0.58/0.78 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.58/0.79 tff(20,plain,
% 0.58/0.79 (![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))))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[19, 3])).
% 0.58/0.79 tff(21,plain,
% 0.58/0.79 (((~![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(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, 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(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))))))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(22,plain,
% 0.58/0.79 ((~((~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))) | (~((~status(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))))) <=> (~((~((~status(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm)))))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(23,plain,
% 0.58/0.79 (((~![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, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))) | (~((~status(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | 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(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))))))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[22])).
% 0.58/0.79 tff(24,plain,
% 0.58/0.79 (((~![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, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))) | (~((~status(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | 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(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))))))),
% 0.58/0.79 inference(transitivity,[status(thm)],[23, 21])).
% 0.58/0.79 tff(25,plain,
% 0.58/0.79 ((~![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, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))) | (~((~status(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28))))))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(26,plain,
% 0.58/0.79 ((~![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(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm)))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.58/0.79 tff(27,plain,
% 0.58/0.79 ($false),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[26, 20, 1])).
% 0.58/0.79 tff(28,plain,(~((~((~status(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.79 tff(29,plain,
% 0.58/0.79 (((~((~status(C!42, F!28, thm)) | ![I1: $i] : ((~model(I1, C!42)) | model(I1, F!28)))) | (~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm)))) | ((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))),
% 0.58/0.79 inference(tautology,[status(thm)],[])).
% 0.58/0.79 tff(30,plain,
% 0.58/0.79 ((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.58/0.79 tff(31,assumption,(~model(tptp_fun_I1_3(F!28, C!42), F!28)), introduced(assumption)).
% 0.58/0.79 tff(32,plain,
% 0.58/0.79 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(33,plain,
% 0.58/0.79 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 0.58/0.79 inference(quant_intro,[status(thm)],[32])).
% 0.58/0.79 tff(34,plain,
% 0.58/0.79 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(35,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','tautology')).
% 0.58/0.79 tff(36,plain,
% 0.58/0.79 (?[F: $i] : ![I: $i] : model(I, F)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.58/0.79 tff(37,plain,(
% 0.58/0.79 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 0.58/0.79 inference(transitivity,[status(sab)],[36])).
% 0.58/0.79 tff(38,plain,
% 0.58/0.79 (![I: $i] : model(I, F!28)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.58/0.79 tff(39,plain,
% 0.58/0.79 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I1_3(F!28, C!42), F!28)),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(40,plain,
% 0.58/0.79 ($false),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[39, 38, 31])).
% 0.58/0.79 tff(41,plain,(model(tptp_fun_I1_3(F!28, C!42), F!28)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.79 tff(42,plain,
% 0.58/0.79 (((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28)) | (~model(tptp_fun_I1_3(F!28, C!42), F!28))),
% 0.58/0.79 inference(tautology,[status(thm)],[])).
% 0.58/0.79 tff(43,plain,
% 0.58/0.79 ((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.58/0.79 tff(44,plain,
% 0.58/0.79 ((~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))) | (~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm)),
% 0.58/0.79 inference(tautology,[status(thm)],[])).
% 0.58/0.79 tff(45,plain,
% 0.58/0.79 ((~((~((~model(tptp_fun_I1_3(F!28, C!42), C!42)) | model(tptp_fun_I1_3(F!28, C!42), F!28))) | status(C!42, F!28, thm))) | status(C!42, F!28, thm)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.58/0.79 tff(46,plain,
% 0.58/0.79 (status(C!42, F!28, thm)),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[45, 30])).
% 0.58/0.79 tff(47,assumption,(status(C!42, F!28, tac)), introduced(assumption)).
% 0.58/0.79 tff(48,plain,
% 0.58/0.79 (^[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)))))))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(49,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[48])).
% 0.58/0.79 tff(50,plain,
% 0.58/0.79 (^[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)))))))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(51,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[50])).
% 0.58/0.79 tff(52,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(transitivity,[status(thm)],[51, 49])).
% 0.58/0.79 tff(53,plain,
% 0.58/0.79 (^[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))))))))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(54,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[53])).
% 0.58/0.79 tff(55,plain,
% 0.58/0.79 (^[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)))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(56,plain,
% 0.58/0.79 (![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))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[55])).
% 0.58/0.79 tff(57,plain,
% 0.58/0.79 (![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))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(58,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')).
% 0.58/0.79 tff(59,plain,
% 0.58/0.79 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.58/0.79 tff(60,plain,(
% 0.58/0.79 ![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))))),
% 0.58/0.79 inference(skolemize,[status(sab)],[59])).
% 0.58/0.79 tff(61,plain,
% 0.58/0.79 (![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))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.58/0.79 tff(62,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.58/0.79 tff(63,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.58/0.79 tff(64,plain,
% 0.58/0.79 ((~![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, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, thm)) | (~((~status(tptp_fun_Ax_19(thm, tac), tptp_fun_C_18(thm, tac), tac)) | (~status(tptp_fun_Ax_19(thm, tac), tptp_fun_C_18(thm, tac), thm))))))))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(65,plain,
% 0.58/0.79 (~((~(mighta(tac, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, thm)) | (~((~status(tptp_fun_Ax_19(thm, tac), tptp_fun_C_18(thm, tac), tac)) | (~status(tptp_fun_Ax_19(thm, tac), tptp_fun_C_18(thm, tac), thm)))))))),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.58/0.79 tff(66,plain,
% 0.58/0.79 (((~(mighta(tac, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, thm)) | (~((~status(tptp_fun_Ax_19(thm, tac), tptp_fun_C_18(thm, tac), tac)) | (~status(tptp_fun_Ax_19(thm, tac), tptp_fun_C_18(thm, tac), thm))))))) | (mighta(tac, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac))))),
% 0.58/0.79 inference(tautology,[status(thm)],[])).
% 0.58/0.79 tff(67,plain,
% 0.58/0.79 (mighta(tac, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.58/0.79 tff(68,plain,
% 0.58/0.79 ((~mighta(tac, thm)) <=> (~mighta(tac, thm))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(69,axiom,(~mighta(tac, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_tac_thm')).
% 0.58/0.79 tff(70,plain,
% 0.58/0.79 (~mighta(tac, thm)),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.58/0.79 tff(71,plain,
% 0.58/0.79 ((~(mighta(tac, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac))))) | mighta(tac, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))),
% 0.58/0.79 inference(tautology,[status(thm)],[])).
% 0.58/0.79 tff(72,plain,
% 0.58/0.79 ((~(mighta(tac, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.58/0.79 tff(73,plain,
% 0.58/0.79 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[72, 67])).
% 0.58/0.79 tff(74,plain,
% 0.58/0.79 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))) | ((~status(C!42, F!28, tac)) | (~status(C!42, F!28, thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))) | (~status(C!42, F!28, tac)) | (~status(C!42, F!28, thm)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(75,plain,
% 0.58/0.79 (((~status(C!42, F!28, thm)) | (~status(C!42, F!28, tac))) <=> ((~status(C!42, F!28, tac)) | (~status(C!42, F!28, thm)))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(76,plain,
% 0.58/0.79 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))) | ((~status(C!42, F!28, thm)) | (~status(C!42, F!28, tac)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))) | ((~status(C!42, F!28, tac)) | (~status(C!42, F!28, thm))))),
% 0.58/0.79 inference(monotonicity,[status(thm)],[75])).
% 0.58/0.79 tff(77,plain,
% 0.58/0.79 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))) | ((~status(C!42, F!28, thm)) | (~status(C!42, F!28, tac)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))) | (~status(C!42, F!28, tac)) | (~status(C!42, F!28, thm)))),
% 0.58/0.79 inference(transitivity,[status(thm)],[76, 74])).
% 0.58/0.79 tff(78,plain,
% 0.58/0.79 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))) | ((~status(C!42, F!28, thm)) | (~status(C!42, F!28, tac)))),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(79,plain,
% 0.58/0.79 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tac)))) | (~status(C!42, F!28, tac)) | (~status(C!42, F!28, thm))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.58/0.79 tff(80,plain,
% 0.58/0.79 ($false),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[79, 73, 47, 46])).
% 0.58/0.79 tff(81,plain,(~status(C!42, F!28, tac)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.79 tff(82,assumption,(~model(tptp_fun_I2_5(F!28), F!28)), introduced(assumption)).
% 0.58/0.79 tff(83,plain,
% 0.58/0.79 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I2_5(F!28), F!28)),
% 0.58/0.79 inference(quant_inst,[status(thm)],[])).
% 0.58/0.79 tff(84,plain,
% 0.58/0.79 ($false),
% 0.58/0.79 inference(unit_resolution,[status(thm)],[83, 38, 82])).
% 0.58/0.79 tff(85,plain,(model(tptp_fun_I2_5(F!28), F!28)), inference(lemma,lemma(discharge,[]))).
% 0.58/0.79 tff(86,plain,
% 0.58/0.79 (^[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)))))))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(87,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[86])).
% 0.58/0.79 tff(88,plain,
% 0.58/0.79 (^[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)))))))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(89,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[88])).
% 0.58/0.79 tff(90,plain,
% 0.58/0.79 (^[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)))))))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(91,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[90])).
% 0.58/0.79 tff(92,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(transitivity,[status(thm)],[91, 89])).
% 0.58/0.79 tff(93,plain,
% 0.58/0.79 (^[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))))))))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(94,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[93])).
% 0.58/0.79 tff(95,plain,
% 0.58/0.79 (^[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)))))),
% 0.58/0.79 inference(bind,[status(th)],[])).
% 0.58/0.79 tff(96,plain,
% 0.58/0.79 (![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))))),
% 0.58/0.79 inference(quant_intro,[status(thm)],[95])).
% 0.58/0.79 tff(97,plain,
% 0.58/0.79 (![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))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(98,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')).
% 0.58/0.79 tff(99,plain,
% 0.58/0.79 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.58/0.79 tff(100,plain,(
% 0.58/0.79 ![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))))),
% 0.58/0.79 inference(skolemize,[status(sab)],[99])).
% 0.58/0.79 tff(101,plain,
% 0.58/0.79 (![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))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.58/0.79 tff(102,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.58/0.79 tff(103,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.58/0.79 tff(104,plain,
% 0.58/0.79 (![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))))))))),
% 0.58/0.79 inference(modus_ponens,[status(thm)],[103, 87])).
% 0.58/0.79 tff(105,plain,
% 0.58/0.79 (((~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(106,plain,
% 0.58/0.79 ((~((~(status(C!42, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))) <=> (~((~(![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))),
% 0.58/0.79 inference(rewrite,[status(thm)],[])).
% 0.58/0.79 tff(107,plain,
% 0.58/0.79 (((~![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(C!42, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 0.58/0.80 inference(monotonicity,[status(thm)],[106])).
% 0.58/0.80 tff(108,plain,
% 0.58/0.80 (((~![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(C!42, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 0.58/0.80 inference(transitivity,[status(thm)],[107, 105])).
% 0.58/0.80 tff(109,plain,
% 0.58/0.80 ((~![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(C!42, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))),
% 0.58/0.80 inference(quant_inst,[status(thm)],[])).
% 0.58/0.80 tff(110,plain,
% 0.58/0.80 ((~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))),
% 0.58/0.80 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.58/0.80 tff(111,plain,
% 0.58/0.80 (~((~(![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))),
% 0.58/0.80 inference(unit_resolution,[status(thm)],[110, 104])).
% 0.58/0.80 tff(112,plain,
% 0.58/0.80 (((~(![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))) | (![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))),
% 0.58/0.80 inference(tautology,[status(thm)],[])).
% 0.58/0.80 tff(113,plain,
% 0.58/0.80 (![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac)),
% 0.58/0.80 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.58/0.80 tff(114,plain,
% 0.58/0.80 ((~(![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | ![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac)),
% 0.58/0.80 inference(tautology,[status(thm)],[])).
% 0.58/0.80 tff(115,plain,
% 0.58/0.80 (![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac)),
% 0.58/0.80 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.58/0.80 tff(116,plain,
% 0.58/0.80 (![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, tac)),
% 0.58/0.80 inference(unit_resolution,[status(thm)],[115, 85])).
% 0.58/0.80 tff(117,plain,
% 0.58/0.80 (![I1: $i] : (~model(I1, C!42))),
% 0.58/0.80 inference(unit_resolution,[status(thm)],[116, 81])).
% 0.58/0.80 tff(118,plain,
% 0.58/0.80 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C)) <=> ?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 0.58/0.80 inference(rewrite,[status(thm)],[])).
% 0.58/0.80 tff(119,plain,
% 0.58/0.80 (^[I1: $i, Ax: $i, C: $i] : rewrite(((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C)) <=> (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C)))),
% 0.58/0.80 inference(bind,[status(th)],[])).
% 0.58/0.80 tff(120,plain,
% 0.58/0.80 (?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C)) <=> ?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 0.58/0.80 inference(quant_intro,[status(thm)],[119])).
% 0.58/0.80 tff(121,axiom,(?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','non_thm_spt')).
% 0.58/0.80 tff(122,plain,
% 0.58/0.80 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 0.58/0.80 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.58/0.80 tff(123,plain,
% 0.58/0.80 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 0.58/0.80 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.58/0.80 tff(124,plain,
% 0.58/0.80 (model(I2!45, C!42)),
% 0.58/0.80 inference(and_elim,[status(thm)],[123])).
% 0.58/0.80 tff(125,plain,
% 0.58/0.80 ((~![I1: $i] : (~model(I1, C!42))) | (~model(I2!45, C!42))),
% 0.58/0.80 inference(quant_inst,[status(thm)],[])).
% 0.58/0.80 tff(126,plain,
% 0.58/0.80 ($false),
% 0.58/0.80 inference(unit_resolution,[status(thm)],[125, 124, 117])).
% 0.58/0.80 % SZS output end Proof
% 0.58/0.80 % E exiting
%------------------------------------------------------------------------------