%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS258+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.60s 0.76s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS258+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:17:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.60/0.76 % SZS status Theorem
% 0.60/0.76 % SZS output start Proof
% 0.60/0.76 tff(status_type, type, (
% 0.60/0.76 status: ( $i * $i * $i ) > $o)).
% 0.60/0.76 tff(thm_type, type, (
% 0.60/0.76 thm: $i)).
% 0.60/0.76 tff(tptp_fun_Ax_34_type, type, (
% 0.60/0.76 tptp_fun_Ax_34: $i)).
% 0.60/0.76 tff(eqv_type, type, (
% 0.60/0.76 eqv: $i)).
% 0.60/0.76 tff(model_type, type, (
% 0.60/0.76 model: ( $i * $i ) > $o)).
% 0.60/0.76 tff(tptp_fun_I1_0_type, type, (
% 0.60/0.76 tptp_fun_I1_0: $i > $i)).
% 0.60/0.76 tff(tptp_fun_I2_4_type, type, (
% 0.60/0.76 tptp_fun_I2_4: ( $i * $i ) > $i)).
% 0.60/0.76 tff(tptp_fun_I1_35_type, type, (
% 0.60/0.76 tptp_fun_I1_35: $i)).
% 0.60/0.76 tff(tptp_fun_C_33_type, type, (
% 0.60/0.76 tptp_fun_C_33: $i)).
% 0.60/0.76 tff(tptp_fun_I2_36_type, type, (
% 0.60/0.76 tptp_fun_I2_36: $i)).
% 0.60/0.76 tff(mighta_type, type, (
% 0.60/0.76 mighta: ( $i * $i ) > $o)).
% 0.60/0.76 tff(tptp_fun_C_18_type, type, (
% 0.60/0.76 tptp_fun_C_18: ( $i * $i ) > $i)).
% 0.60/0.76 tff(tptp_fun_Ax_19_type, type, (
% 0.60/0.76 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 0.60/0.76 tff(tptp_fun_I1_3_type, type, (
% 0.60/0.76 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 0.60/0.76 tff(1,plain,
% 0.60/0.76 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(2,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[1])).
% 0.60/0.76 tff(3,plain,
% 0.60/0.76 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(4,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[3])).
% 0.60/0.76 tff(5,plain,
% 0.60/0.76 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(6,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[5])).
% 0.60/0.76 tff(7,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 0.60/0.76 inference(transitivity,[status(thm)],[6, 4])).
% 0.60/0.76 tff(8,plain,
% 0.60/0.76 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) <=> (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))), ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) <=> (status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))))), rewrite((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) <=> (status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))), ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) <=> (status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))) <=> ((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))) | (~status(Ax, C, eqv))))), rewrite(((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))) | (~status(Ax, C, eqv))) <=> ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))) <=> ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))), (((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))), rewrite(((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))), (((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(9,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[8])).
% 0.60/0.76 tff(10,plain,
% 0.60/0.76 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(11,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[10])).
% 0.60/0.76 tff(12,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(13,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','eqv')).
% 0.60/0.76 tff(14,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.60/0.76 tff(15,plain,(
% 0.60/0.76 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 0.60/0.76 inference(skolemize,[status(sab)],[14])).
% 0.60/0.76 tff(16,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.60/0.76 tff(17,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.60/0.76 tff(18,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.60/0.76 tff(19,plain,
% 0.60/0.76 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.60/0.76 tff(20,plain,
% 0.60/0.76 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~((~status(Ax!34, Ax!34, eqv)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv)))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~((~status(Ax!34, Ax!34, eqv)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv))))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(21,plain,
% 0.60/0.76 ((~((~(status(Ax!34, Ax!34, eqv) | (~(model(tptp_fun_I2_4(Ax!34, Ax!34), Ax!34) <=> model(tptp_fun_I2_4(Ax!34, Ax!34), Ax!34))) | ![I1: $i] : (~model(I1, Ax!34)))) | (~((~status(Ax!34, Ax!34, eqv)) | (~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (model(I2, Ax!34) <=> model(I2, Ax!34))))))))) <=> (~((~((~status(Ax!34, Ax!34, eqv)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv)))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(22,plain,
% 0.60/0.76 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(Ax!34, Ax!34, eqv) | (~(model(tptp_fun_I2_4(Ax!34, Ax!34), Ax!34) <=> model(tptp_fun_I2_4(Ax!34, Ax!34), Ax!34))) | ![I1: $i] : (~model(I1, Ax!34)))) | (~((~status(Ax!34, Ax!34, eqv)) | (~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (model(I2, Ax!34) <=> model(I2, Ax!34)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~((~status(Ax!34, Ax!34, eqv)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv))))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[21])).
% 0.60/0.76 tff(23,plain,
% 0.60/0.76 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(Ax!34, Ax!34, eqv) | (~(model(tptp_fun_I2_4(Ax!34, Ax!34), Ax!34) <=> model(tptp_fun_I2_4(Ax!34, Ax!34), Ax!34))) | ![I1: $i] : (~model(I1, Ax!34)))) | (~((~status(Ax!34, Ax!34, eqv)) | (~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (model(I2, Ax!34) <=> model(I2, Ax!34)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~((~status(Ax!34, Ax!34, eqv)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv))))))),
% 0.60/0.76 inference(transitivity,[status(thm)],[22, 20])).
% 0.60/0.76 tff(24,plain,
% 0.60/0.76 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(Ax!34, Ax!34, eqv) | (~(model(tptp_fun_I2_4(Ax!34, Ax!34), Ax!34) <=> model(tptp_fun_I2_4(Ax!34, Ax!34), Ax!34))) | ![I1: $i] : (~model(I1, Ax!34)))) | (~((~status(Ax!34, Ax!34, eqv)) | (~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (model(I2, Ax!34) <=> model(I2, Ax!34)))))))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(25,plain,
% 0.60/0.76 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~((~status(Ax!34, Ax!34, eqv)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.60/0.76 tff(26,plain,
% 0.60/0.76 (~((~((~status(Ax!34, Ax!34, eqv)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.60/0.76 tff(27,plain,
% 0.60/0.76 (((~((~status(Ax!34, Ax!34, eqv)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv)))) | (![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(28,plain,
% 0.60/0.76 (![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.60/0.76 tff(29,assumption,(![I1: $i] : (~model(I1, Ax!34))), introduced(assumption)).
% 0.60/0.76 tff(30,plain,
% 0.60/0.76 (((model(I1!35, Ax!34) & model(I1!35, C!33)) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))) <=> (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(31,plain,
% 0.60/0.76 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C)))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(32,axiom,(?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','sat_non_taut_pair')).
% 0.60/0.76 tff(33,plain,
% 0.60/0.76 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.60/0.76 tff(34,plain,
% 0.60/0.76 (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.60/0.76 tff(35,plain,
% 0.60/0.76 (model(I1!35, Ax!34)),
% 0.60/0.76 inference(and_elim,[status(thm)],[34])).
% 0.60/0.76 tff(36,plain,
% 0.60/0.76 ((~![I1: $i] : (~model(I1, Ax!34))) | (~model(I1!35, Ax!34))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(37,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[36, 35, 29])).
% 0.60/0.76 tff(38,plain,(~![I1: $i] : (~model(I1, Ax!34))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(39,plain,
% 0.60/0.76 ((~(![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv))) | ![I1: $i] : (~model(I1, Ax!34)) | status(Ax!34, Ax!34, eqv)),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(40,plain,
% 0.60/0.76 (status(Ax!34, Ax!34, eqv)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[39, 38, 28])).
% 0.60/0.76 tff(41,plain,
% 0.60/0.76 (^[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)))))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(42,plain,
% 0.60/0.77 (![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))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[41])).
% 0.60/0.77 tff(43,plain,
% 0.60/0.77 (^[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)))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(44,plain,
% 0.60/0.77 (![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))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[43])).
% 0.60/0.77 tff(45,plain,
% 0.60/0.77 (![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))))))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[44, 42])).
% 0.60/0.77 tff(46,plain,
% 0.60/0.77 (^[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))))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(47,plain,
% 0.60/0.77 (![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))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[46])).
% 0.60/0.77 tff(48,plain,
% 0.60/0.77 (^[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)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(49,plain,
% 0.60/0.77 (![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))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[48])).
% 0.60/0.77 tff(50,plain,
% 0.60/0.77 (![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))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(51,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','mighta')).
% 0.60/0.77 tff(52,plain,
% 0.60/0.77 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.60/0.77 tff(53,plain,(
% 0.60/0.77 ![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))))),
% 0.60/0.77 inference(skolemize,[status(sab)],[52])).
% 0.60/0.77 tff(54,plain,
% 0.60/0.77 (![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))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.60/0.77 tff(55,plain,
% 0.60/0.77 (![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))))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.60/0.77 tff(56,plain,
% 0.60/0.77 (![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))))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.60/0.77 tff(57,plain,
% 0.60/0.77 ((~![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(eqv, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv))))) | (~((~mighta(eqv, thm)) | (~((~status(tptp_fun_Ax_19(thm, eqv), tptp_fun_C_18(thm, eqv), eqv)) | (~status(tptp_fun_Ax_19(thm, eqv), tptp_fun_C_18(thm, eqv), thm))))))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(58,plain,
% 0.60/0.77 (~((~(mighta(eqv, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv))))) | (~((~mighta(eqv, thm)) | (~((~status(tptp_fun_Ax_19(thm, eqv), tptp_fun_C_18(thm, eqv), eqv)) | (~status(tptp_fun_Ax_19(thm, eqv), tptp_fun_C_18(thm, eqv), thm)))))))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.60/0.77 tff(59,plain,
% 0.60/0.77 (((~(mighta(eqv, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv))))) | (~((~mighta(eqv, thm)) | (~((~status(tptp_fun_Ax_19(thm, eqv), tptp_fun_C_18(thm, eqv), eqv)) | (~status(tptp_fun_Ax_19(thm, eqv), tptp_fun_C_18(thm, eqv), thm))))))) | (mighta(eqv, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv))))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(60,plain,
% 0.60/0.77 (mighta(eqv, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.60/0.77 tff(61,plain,
% 0.60/0.77 ((~mighta(eqv, thm)) <=> (~mighta(eqv, thm))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(62,axiom,(~mighta(eqv, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mighta_eqv_thm')).
% 0.60/0.77 tff(63,plain,
% 0.60/0.77 (~mighta(eqv, thm)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.60/0.77 tff(64,plain,
% 0.60/0.77 ((~(mighta(eqv, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv))))) | mighta(eqv, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(65,plain,
% 0.60/0.77 ((~(mighta(eqv, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.60/0.77 tff(66,plain,
% 0.60/0.77 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[65, 60])).
% 0.60/0.77 tff(67,plain,
% 0.60/0.77 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))) | ((~status(Ax!34, Ax!34, eqv)) | (~status(Ax!34, Ax!34, thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))) | (~status(Ax!34, Ax!34, eqv)) | (~status(Ax!34, Ax!34, thm)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(68,plain,
% 0.60/0.77 (((~status(Ax!34, Ax!34, thm)) | (~status(Ax!34, Ax!34, eqv))) <=> ((~status(Ax!34, Ax!34, eqv)) | (~status(Ax!34, Ax!34, thm)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(69,plain,
% 0.60/0.77 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))) | ((~status(Ax!34, Ax!34, thm)) | (~status(Ax!34, Ax!34, eqv)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))) | ((~status(Ax!34, Ax!34, eqv)) | (~status(Ax!34, Ax!34, thm))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[68])).
% 0.60/0.77 tff(70,plain,
% 0.60/0.77 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))) | ((~status(Ax!34, Ax!34, thm)) | (~status(Ax!34, Ax!34, eqv)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))) | (~status(Ax!34, Ax!34, eqv)) | (~status(Ax!34, Ax!34, thm)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[69, 67])).
% 0.60/0.77 tff(71,plain,
% 0.60/0.77 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))) | ((~status(Ax!34, Ax!34, thm)) | (~status(Ax!34, Ax!34, eqv)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(72,plain,
% 0.60/0.77 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, eqv)))) | (~status(Ax!34, Ax!34, eqv)) | (~status(Ax!34, Ax!34, thm))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.60/0.77 tff(73,plain,
% 0.60/0.77 (~status(Ax!34, Ax!34, thm)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[72, 66, 40])).
% 0.60/0.77 tff(74,plain,
% 0.60/0.77 (^[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)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(75,plain,
% 0.60/0.77 (![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))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[74])).
% 0.60/0.77 tff(76,plain,
% 0.60/0.77 (^[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)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(77,plain,
% 0.60/0.77 (![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))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[76])).
% 0.60/0.77 tff(78,plain,
% 0.60/0.77 (^[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)))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(79,plain,
% 0.60/0.77 (![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))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[78])).
% 0.60/0.77 tff(80,plain,
% 0.60/0.77 (![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))))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[79, 77])).
% 0.60/0.77 tff(81,plain,
% 0.60/0.77 (^[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))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(82,plain,
% 0.60/0.77 (![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))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[81])).
% 0.60/0.77 tff(83,plain,
% 0.60/0.77 (![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))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(84,plain,
% 0.60/0.77 (^[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)))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(85,plain,
% 0.60/0.77 (![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))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[84])).
% 0.60/0.77 tff(86,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','thm')).
% 0.60/0.77 tff(87,plain,
% 0.60/0.77 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.60/0.77 tff(88,plain,
% 0.60/0.77 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.60/0.77 tff(89,plain,(
% 0.60/0.77 ![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))))),
% 0.60/0.77 inference(skolemize,[status(sab)],[88])).
% 0.60/0.77 tff(90,plain,
% 0.60/0.77 (![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))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.60/0.77 tff(91,plain,
% 0.60/0.77 (![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))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.60/0.77 tff(92,plain,
% 0.60/0.77 (![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))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[91, 75])).
% 0.60/0.77 tff(93,plain,
% 0.60/0.77 (((~![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!34, Ax!34, 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!34, Ax!34, thm))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(94,plain,
% 0.60/0.77 ((~(~status(Ax!34, Ax!34, thm))) <=> status(Ax!34, Ax!34, thm)),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(95,plain,
% 0.60/0.77 (((~status(Ax!34, Ax!34, thm)) | $false) <=> (~status(Ax!34, Ax!34, thm))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(96,plain,
% 0.60/0.77 ((~$true) <=> $false),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(97,plain,
% 0.60/0.77 (((~status(Ax!34, Ax!34, thm)) | $true) <=> $true),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(98,plain,
% 0.60/0.77 (![I1: $i] : $true <=> $true),
% 0.60/0.77 inference(elim_unused_vars,[status(thm)],[])).
% 0.60/0.77 tff(99,plain,
% 0.60/0.77 (![I1: $i] : $true <=> ![I1: $i] : $true),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(100,plain,
% 0.60/0.77 (![I1: $i] : $true <=> $true),
% 0.60/0.77 inference(transitivity,[status(thm)],[99, 98])).
% 0.60/0.77 tff(101,plain,
% 0.60/0.77 (^[I1: $i] : rewrite(((~model(I1, Ax!34)) | model(I1, Ax!34)) <=> $true)),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(102,plain,
% 0.60/0.77 (![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)) <=> ![I1: $i] : $true),
% 0.60/0.77 inference(quant_intro,[status(thm)],[101])).
% 0.60/0.77 tff(103,plain,
% 0.60/0.77 (![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)) <=> $true),
% 0.60/0.77 inference(transitivity,[status(thm)],[102, 100])).
% 0.60/0.77 tff(104,plain,
% 0.60/0.77 (((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))) <=> ((~status(Ax!34, Ax!34, thm)) | $true)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[103])).
% 0.60/0.77 tff(105,plain,
% 0.60/0.77 (((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))) <=> $true),
% 0.60/0.77 inference(transitivity,[status(thm)],[104, 97])).
% 0.60/0.77 tff(106,plain,
% 0.60/0.77 ((~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)))) <=> (~$true)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[105])).
% 0.60/0.77 tff(107,plain,
% 0.60/0.77 ((~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)))) <=> $false),
% 0.60/0.77 inference(transitivity,[status(thm)],[106, 96])).
% 0.60/0.77 tff(108,plain,
% 0.60/0.77 ((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) <=> (~status(Ax!34, Ax!34, thm))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(109,plain,
% 0.60/0.77 (((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))) <=> ((~status(Ax!34, Ax!34, thm)) | $false)),
% 0.60/0.77 inference(monotonicity,[status(thm)],[108, 107])).
% 0.60/0.77 tff(110,plain,
% 0.60/0.77 (((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))) <=> (~status(Ax!34, Ax!34, thm))),
% 0.60/0.77 inference(transitivity,[status(thm)],[109, 95])).
% 0.60/0.77 tff(111,plain,
% 0.60/0.77 ((~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)))))) <=> (~(~status(Ax!34, Ax!34, thm)))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[110])).
% 0.60/0.77 tff(112,plain,
% 0.60/0.77 ((~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)))))) <=> status(Ax!34, Ax!34, thm)),
% 0.60/0.77 inference(transitivity,[status(thm)],[111, 94])).
% 0.60/0.77 tff(113,plain,
% 0.60/0.77 (((~![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(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))))) <=> ((~![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!34, Ax!34, thm))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[112])).
% 0.60/0.78 tff(114,plain,
% 0.60/0.78 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))))) <=> ((~![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!34, Ax!34, thm))),
% 0.60/0.78 inference(transitivity,[status(thm)],[113, 93])).
% 0.60/0.78 tff(115,plain,
% 0.60/0.78 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(116,plain,
% 0.60/0.78 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(Ax!34, Ax!34, thm)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.60/0.78 tff(117,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[116, 92, 73])).
% 0.60/0.78 % SZS output end Proof
% 0.60/0.78 % E exiting
%------------------------------------------------------------------------------