%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS256+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.56s 0.73s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS256+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 19:19:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.56/0.73 % SZS status Theorem
% 0.56/0.73 % SZS output start Proof
% 0.56/0.73 tff(model_type, type, (
% 0.56/0.73 model: ( $i * $i ) > $o)).
% 0.56/0.73 tff(tptp_fun_C_37_type, type, (
% 0.56/0.73 tptp_fun_C_37: $i)).
% 0.56/0.73 tff(tptp_fun_Ax_38_type, type, (
% 0.56/0.73 tptp_fun_Ax_38: $i)).
% 0.56/0.73 tff(tptp_fun_I2_1_type, type, (
% 0.56/0.73 tptp_fun_I2_1: $i > $i)).
% 0.56/0.73 tff(tptp_fun_I1_0_type, type, (
% 0.56/0.73 tptp_fun_I1_0: $i > $i)).
% 0.56/0.73 tff(status_type, type, (
% 0.56/0.73 status: ( $i * $i * $i ) > $o)).
% 0.56/0.73 tff(esa_type, type, (
% 0.56/0.73 esa: $i)).
% 0.56/0.73 tff(thm_type, type, (
% 0.56/0.73 thm: $i)).
% 0.56/0.73 tff(tptp_fun_I1_3_type, type, (
% 0.56/0.73 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.56/0.73 tff(tptp_fun_I4_41_type, type, (
% 0.56/0.73 tptp_fun_I4_41: $i)).
% 0.56/0.73 tff(tptp_fun_I3_40_type, type, (
% 0.56/0.73 tptp_fun_I3_40: $i)).
% 0.56/0.73 tff(tptp_fun_I1_39_type, type, (
% 0.56/0.73 tptp_fun_I1_39: $i)).
% 0.56/0.73 tff(mighta_type, type, (
% 0.56/0.73 mighta: ( $i * $i ) > $o)).
% 0.56/0.73 tff(tptp_fun_C_18_type, type, (
% 0.56/0.73 tptp_fun_C_18: ( $i * $i ) > $i)).
% 0.56/0.73 tff(tptp_fun_Ax_19_type, type, (
% 0.56/0.73 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 0.56/0.73 tff(1,plain,
% 0.56/0.73 (^[Ax: $i, C: $i] : refl((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(2,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.56/0.73 tff(3,plain,
% 0.56/0.73 (^[Ax: $i, C: $i] : rewrite((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(4,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[3])).
% 0.56/0.73 tff(5,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[4, 2])).
% 0.56/0.73 tff(6,plain,
% 0.56/0.73 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) <=> ((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))), rewrite(((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))) <=> ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))), rewrite((((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(7,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[6])).
% 0.56/0.73 tff(8,plain,
% 0.56/0.73 (^[Ax: $i, C: $i] : rewrite(((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(9,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[8])).
% 0.56/0.73 tff(10,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(11,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','esa')).
% 0.56/0.73 tff(12,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.56/0.73 tff(13,plain,(
% 0.56/0.73 ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa))))),
% 0.56/0.73 inference(skolemize,[status(sab)],[12])).
% 0.56/0.73 tff(14,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.56/0.73 tff(15,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.56/0.73 tff(16,plain,
% 0.56/0.73 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.56/0.73 tff(17,plain,
% 0.56/0.73 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))) | (~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))) | (~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(18,plain,
% 0.56/0.74 ((~((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))) | (~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))))))))) <=> (~((~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))) | (~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa)))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(19,plain,
% 0.56/0.74 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))) | (~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))) | (~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[18])).
% 0.56/0.74 tff(20,plain,
% 0.56/0.74 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))) | (~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))) | (~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[19, 17])).
% 0.56/0.74 tff(21,plain,
% 0.56/0.74 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))) | (~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37))))))))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(22,plain,
% 0.56/0.74 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))) | (~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa)))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.56/0.74 tff(23,plain,
% 0.56/0.74 (~((~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))) | (~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.56/0.74 tff(24,plain,
% 0.56/0.74 (((~((~status(Ax!38, C!37, esa)) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, C!37)))) | (~(model(tptp_fun_I2_1(C!37), C!37) | ![I1: $i] : (~model(I1, Ax!38)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa)))) | ((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(25,plain,
% 0.56/0.74 ((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.56/0.74 tff(26,assumption,(~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))), introduced(assumption)).
% 0.56/0.74 tff(27,plain,
% 0.56/0.74 (((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37)) | (~model(tptp_fun_I1_3(C!37, Ax!38), C!37))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(28,plain,
% 0.56/0.74 (~model(tptp_fun_I1_3(C!37, Ax!38), C!37)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.56/0.74 tff(29,plain,
% 0.56/0.74 (((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37)) | model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(30,plain,
% 0.56/0.74 (model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.56/0.74 tff(31,plain,
% 0.56/0.74 (^[I2: $i] : refl(((~model(I2, Ax!38)) | model(I2, C!37)) <=> ((~model(I2, Ax!38)) | model(I2, C!37)))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(32,plain,
% 0.56/0.74 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) <=> ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[31])).
% 0.56/0.74 tff(33,plain,
% 0.56/0.74 ((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)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(34,plain,
% 0.56/0.74 (?[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)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(35,plain,
% 0.56/0.74 (^[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)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(36,plain,
% 0.56/0.74 (?[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)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[35])).
% 0.56/0.74 tff(37,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')).
% 0.56/0.74 tff(38,plain,
% 0.56/0.74 (?[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)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.56/0.74 tff(39,plain,
% 0.56/0.74 (?[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)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.56/0.74 tff(40,plain,
% 0.56/0.74 (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))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.56/0.74 tff(41,plain,
% 0.56/0.74 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 0.56/0.74 inference(and_elim,[status(thm)],[40])).
% 0.56/0.74 tff(42,plain,
% 0.56/0.74 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[41, 32])).
% 0.56/0.74 tff(43,plain,
% 0.56/0.74 (((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) <=> ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(44,plain,
% 0.56/0.74 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(45,plain,
% 0.56/0.74 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.56/0.74 tff(46,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[45, 42, 30, 28])).
% 0.56/0.74 tff(47,plain,((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(48,plain,
% 0.56/0.74 (^[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)))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(49,plain,
% 0.56/0.74 (![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))))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[48])).
% 0.56/0.74 tff(50,plain,
% 0.56/0.74 (^[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)))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(51,plain,
% 0.56/0.74 (![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))))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[50])).
% 0.56/0.74 tff(52,plain,
% 0.56/0.74 (^[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)))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(53,plain,
% 0.56/0.74 (![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))))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[52])).
% 0.56/0.74 tff(54,plain,
% 0.56/0.74 (![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))))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[53, 51])).
% 0.56/0.74 tff(55,plain,
% 0.56/0.74 (^[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))))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(56,plain,
% 0.56/0.74 (![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))))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[55])).
% 0.56/0.74 tff(57,plain,
% 0.56/0.74 (![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))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(58,plain,
% 0.56/0.74 (^[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)))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(59,plain,
% 0.56/0.74 (![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))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[58])).
% 0.56/0.74 tff(60,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')).
% 0.56/0.74 tff(61,plain,
% 0.56/0.74 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.56/0.75 tff(62,plain,
% 0.56/0.75 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.56/0.75 tff(63,plain,(
% 0.56/0.75 ![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))),
% 0.56/0.75 inference(skolemize,[status(sab)],[62])).
% 0.56/0.75 tff(64,plain,
% 0.56/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.56/0.75 tff(65,plain,
% 0.56/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.56/0.75 tff(66,plain,
% 0.56/0.75 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[65, 49])).
% 0.56/0.75 tff(67,plain,
% 0.56/0.75 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))) | (~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, 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, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))) | (~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(68,plain,
% 0.56/0.75 ((~((~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))) | (~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))))) <=> (~((~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))) | (~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm)))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(69,plain,
% 0.56/0.75 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))) | (~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37))))))) <=> ((~![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, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))) | (~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[68])).
% 0.56/0.75 tff(70,plain,
% 0.56/0.75 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))) | (~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37))))))) <=> ((~![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, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))) | (~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[69, 67])).
% 0.56/0.75 tff(71,plain,
% 0.56/0.75 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))) | (~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37))))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(72,plain,
% 0.56/0.75 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))) | (~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm)))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.56/0.75 tff(73,plain,
% 0.56/0.75 (~((~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))) | (~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[72, 66])).
% 0.56/0.75 tff(74,plain,
% 0.56/0.75 (((~((~status(Ax!38, C!37, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, C!37)))) | (~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm)))) | ((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(75,plain,
% 0.56/0.75 ((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.56/0.75 tff(76,plain,
% 0.56/0.75 ((~((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm))) | (~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm)),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(77,plain,
% 0.56/0.75 ((~((~model(tptp_fun_I1_3(C!37, Ax!38), Ax!38)) | model(tptp_fun_I1_3(C!37, Ax!38), C!37))) | status(Ax!38, C!37, thm)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.56/0.75 tff(78,plain,
% 0.56/0.75 (status(Ax!38, C!37, thm)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[77, 47])).
% 0.56/0.75 tff(79,plain,
% 0.56/0.75 (^[S1: $i, S2: $i] : refl((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(80,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[79])).
% 0.56/0.75 tff(81,plain,
% 0.56/0.75 (^[S1: $i, S2: $i] : rewrite((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(82,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[81])).
% 0.56/0.75 tff(83,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[82, 80])).
% 0.56/0.75 tff(84,plain,
% 0.56/0.75 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) <=> (mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))), trans(monotonicity(rewrite((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) <=> (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))), rewrite(((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(85,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[84])).
% 0.56/0.75 tff(86,plain,
% 0.56/0.75 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(87,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[86])).
% 0.56/0.75 tff(88,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(89,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')).
% 0.56/0.75 tff(90,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.56/0.75 tff(91,plain,(
% 0.56/0.75 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.56/0.75 inference(skolemize,[status(sab)],[90])).
% 0.56/0.75 tff(92,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.56/0.75 tff(93,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.56/0.75 tff(94,plain,
% 0.56/0.75 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.56/0.75 tff(95,plain,
% 0.56/0.75 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), 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(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(96,plain,
% 0.56/0.75 ((~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, esa))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))) <=> (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(97,plain,
% 0.56/0.75 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, esa))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), 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(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[96])).
% 0.56/0.75 tff(98,plain,
% 0.56/0.75 (((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, esa))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), 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(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[97, 95])).
% 0.56/0.75 tff(99,plain,
% 0.56/0.75 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, esa))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(100,plain,
% 0.56/0.75 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.56/0.75 tff(101,plain,
% 0.56/0.75 (~((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm)))))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[100, 94])).
% 0.56/0.75 tff(102,plain,
% 0.56/0.75 (((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | (~((~mighta(esa, thm)) | (~((~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), esa)) | (~status(tptp_fun_Ax_19(thm, esa), tptp_fun_C_18(thm, esa), thm))))))) | (mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(103,plain,
% 0.56/0.75 (mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.56/0.75 tff(104,plain,
% 0.56/0.75 ((~mighta(esa, thm)) <=> (~mighta(esa, thm))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(105,axiom,(~mighta(esa, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_esa_thm')).
% 0.56/0.75 tff(106,plain,
% 0.56/0.75 (~mighta(esa, thm)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.56/0.75 tff(107,plain,
% 0.56/0.75 ((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(108,plain,
% 0.56/0.75 ((~(mighta(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.56/0.75 tff(109,plain,
% 0.56/0.75 (![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[108, 103])).
% 0.56/0.75 tff(110,plain,
% 0.56/0.75 (((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))) | ((~status(Ax!38, C!37, esa)) | (~status(Ax!38, C!37, thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))) | (~status(Ax!38, C!37, esa)) | (~status(Ax!38, C!37, thm)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(111,plain,
% 0.56/0.75 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))) | ((~status(Ax!38, C!37, esa)) | (~status(Ax!38, C!37, thm)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(112,plain,
% 0.56/0.75 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | (~status(Ax, C, thm)))) | (~status(Ax!38, C!37, esa)) | (~status(Ax!38, C!37, thm))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.56/0.75 tff(113,plain,
% 0.56/0.75 (~status(Ax!38, C!37, esa)),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[112, 109, 78])).
% 0.56/0.76 tff(114,plain,
% 0.56/0.76 ((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa)),
% 0.56/0.76 inference(tautology,[status(thm)],[])).
% 0.56/0.76 tff(115,plain,
% 0.56/0.76 ((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))) | status(Ax!38, C!37, esa))) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37))))))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.56/0.76 tff(116,plain,
% 0.56/0.76 (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[115, 25])).
% 0.56/0.76 tff(117,plain,
% 0.56/0.76 (((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(C!37), C!37))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37))))) | (![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))),
% 0.56/0.76 inference(tautology,[status(thm)],[])).
% 0.56/0.76 tff(118,plain,
% 0.56/0.76 (![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.56/0.76 tff(119,assumption,(![I1: $i] : (~model(I1, Ax!38))), introduced(assumption)).
% 0.56/0.76 tff(120,plain,
% 0.56/0.76 (model(I1!39, Ax!38)),
% 0.56/0.76 inference(and_elim,[status(thm)],[40])).
% 0.56/0.76 tff(121,plain,
% 0.56/0.76 ((~![I1: $i] : (~model(I1, Ax!38))) | (~model(I1!39, Ax!38))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(122,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[121, 120, 119])).
% 0.56/0.76 tff(123,plain,(~![I1: $i] : (~model(I1, Ax!38))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.76 tff(124,plain,
% 0.56/0.76 ((~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37))),
% 0.56/0.76 inference(tautology,[status(thm)],[])).
% 0.56/0.76 tff(125,plain,
% 0.56/0.76 ((~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, C!37)))) | ![I2: $i] : (~model(I2, C!37))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.56/0.76 tff(126,plain,
% 0.56/0.76 (![I2: $i] : (~model(I2, C!37))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[125, 118])).
% 0.56/0.76 tff(127,plain,
% 0.56/0.76 (model(I3!40, C!37)),
% 0.56/0.76 inference(and_elim,[status(thm)],[40])).
% 0.56/0.76 tff(128,plain,
% 0.56/0.76 ((~![I2: $i] : (~model(I2, C!37))) | (~model(I3!40, C!37))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(129,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[128, 127, 126])).
% 0.56/0.76 % SZS output end Proof
% 0.56/0.76 % E exiting
%------------------------------------------------------------------------------