%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS260+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:39 AM UTC 2025
% Result : Theorem 94.12s 94.28s
% Output : Proof 94.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KRS260+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 19:16:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 94.12/94.28 % SZS status Theorem
% 94.12/94.28 % SZS output start Proof
% 94.12/94.28 tff(model_type, type, (
% 94.12/94.28 model: ( $i * $i ) > $o)).
% 94.12/94.28 tff(tptp_fun_Ax_23_type, type, (
% 94.12/94.28 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 94.12/94.28 tff(eqv_type, type, (
% 94.12/94.28 eqv: $i)).
% 94.12/94.28 tff(uns_type, type, (
% 94.12/94.28 uns: $i)).
% 94.12/94.28 tff(tptp_fun_I3_40_type, type, (
% 94.12/94.28 tptp_fun_I3_40: $i)).
% 94.12/94.28 tff(tptp_fun_C_22_type, type, (
% 94.12/94.28 tptp_fun_C_22: ( $i * $i ) > $i)).
% 94.12/94.28 tff(tptp_fun_I1_0_type, type, (
% 94.12/94.28 tptp_fun_I1_0: $i > $i)).
% 94.12/94.28 tff(status_type, type, (
% 94.12/94.28 status: ( $i * $i * $i ) > $o)).
% 94.12/94.28 tff(tptp_fun_I2_4_type, type, (
% 94.12/94.28 tptp_fun_I2_4: ( $i * $i ) > $i)).
% 94.12/94.28 tff(nota_type, type, (
% 94.12/94.28 nota: ( $i * $i ) > $o)).
% 94.12/94.28 tff(tptp_fun_F_29_type, type, (
% 94.12/94.28 tptp_fun_F_29: $i)).
% 94.12/94.28 tff(not_type, type, (
% 94.12/94.28 not: $i > $i)).
% 94.12/94.28 tff(tptp_fun_I2_31_type, type, (
% 94.12/94.28 tptp_fun_I2_31: $i)).
% 94.12/94.28 tff(tptp_fun_I1_30_type, type, (
% 94.12/94.28 tptp_fun_I1_30: $i)).
% 94.12/94.28 tff(tptp_fun_I1_15_type, type, (
% 94.12/94.28 tptp_fun_I1_15: $i > $i)).
% 94.12/94.28 tff(tptp_fun_I2_16_type, type, (
% 94.12/94.28 tptp_fun_I2_16: $i > $i)).
% 94.12/94.28 tff(tptp_fun_F_28_type, type, (
% 94.12/94.28 tptp_fun_F_28: $i)).
% 94.12/94.28 tff(wec_type, type, (
% 94.12/94.28 wec: $i)).
% 94.12/94.28 tff(thm_type, type, (
% 94.12/94.28 thm: $i)).
% 94.12/94.28 tff(tptp_fun_I3_6_type, type, (
% 94.12/94.28 tptp_fun_I3_6: ( $i * $i ) > $i)).
% 94.12/94.28 tff(tptp_fun_I2_7_type, type, (
% 94.12/94.28 tptp_fun_I2_7: ( $i * $i ) > $i)).
% 94.12/94.28 tff(tptp_fun_I1_3_type, type, (
% 94.12/94.28 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 94.12/94.28 tff(mighta_type, type, (
% 94.12/94.28 mighta: ( $i * $i ) > $o)).
% 94.12/94.28 tff(tptp_fun_C_18_type, type, (
% 94.12/94.28 tptp_fun_C_18: ( $i * $i ) > $i)).
% 94.12/94.28 tff(tptp_fun_Ax_19_type, type, (
% 94.12/94.28 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 94.12/94.28 tff(tptp_fun_F_32_type, type, (
% 94.12/94.28 tptp_fun_F_32: $i)).
% 94.12/94.28 tff(tca_type, type, (
% 94.12/94.28 tca: $i)).
% 94.12/94.28 tff(tptp_fun_I2_5_type, type, (
% 94.12/94.28 tptp_fun_I2_5: $i > $i)).
% 94.12/94.28 tff(tptp_fun_Ax_38_type, type, (
% 94.12/94.28 tptp_fun_Ax_38: $i)).
% 94.12/94.28 tff(tptp_fun_I1_39_type, type, (
% 94.12/94.28 tptp_fun_I1_39: $i)).
% 94.12/94.28 tff(tptp_fun_C_37_type, type, (
% 94.12/94.28 tptp_fun_C_37: $i)).
% 94.12/94.28 tff(tptp_fun_I4_41_type, type, (
% 94.12/94.28 tptp_fun_I4_41: $i)).
% 94.12/94.28 tff(1,plain,
% 94.12/94.28 (^[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))))))))))),
% 94.12/94.28 inference(bind,[status(th)],[])).
% 94.12/94.28 tff(2,plain,
% 94.12/94.28 (![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)))))))))),
% 94.12/94.28 inference(quant_intro,[status(thm)],[1])).
% 94.12/94.28 tff(3,plain,
% 94.12/94.28 (^[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))))))))))),
% 94.12/94.28 inference(bind,[status(th)],[])).
% 94.12/94.28 tff(4,plain,
% 94.12/94.28 (![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)))))))))),
% 94.12/94.28 inference(quant_intro,[status(thm)],[3])).
% 94.12/94.28 tff(5,plain,
% 94.12/94.28 (^[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))))))))))),
% 94.12/94.28 inference(bind,[status(th)],[])).
% 94.12/94.28 tff(6,plain,
% 94.12/94.28 (![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)))))))))),
% 94.12/94.28 inference(quant_intro,[status(thm)],[5])).
% 94.12/94.28 tff(7,plain,
% 94.12/94.28 (![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)))))))))),
% 94.12/94.28 inference(transitivity,[status(thm)],[6, 4])).
% 94.12/94.28 tff(8,plain,
% 94.12/94.28 (^[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)))))))))))),
% 94.12/94.28 inference(bind,[status(th)],[])).
% 94.12/94.28 tff(9,plain,
% 94.12/94.28 (![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)))))))))),
% 94.12/94.28 inference(quant_intro,[status(thm)],[8])).
% 94.12/94.28 tff(10,plain,
% 94.12/94.28 (^[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)))))),
% 94.12/94.28 inference(bind,[status(th)],[])).
% 94.12/94.28 tff(11,plain,
% 94.12/94.28 (![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))))),
% 94.12/94.28 inference(quant_intro,[status(thm)],[10])).
% 94.12/94.28 tff(12,plain,
% 94.12/94.28 (![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))),
% 94.12/94.28 inference(rewrite,[status(thm)],[])).
% 94.12/94.28 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/sandbox2/benchmark/Axioms/KRS001+0.ax','eqv')).
% 94.12/94.28 tff(14,plain,
% 94.12/94.28 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))),
% 94.12/94.28 inference(modus_ponens,[status(thm)],[13, 12])).
% 94.12/94.28 tff(15,plain,(
% 94.12/94.28 ![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))))),
% 94.12/94.28 inference(skolemize,[status(sab)],[14])).
% 94.12/94.28 tff(16,plain,
% 94.12/94.28 (![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))))),
% 94.12/94.28 inference(modus_ponens,[status(thm)],[15, 11])).
% 94.12/94.28 tff(17,plain,
% 94.12/94.28 (![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)))))))))),
% 94.12/94.28 inference(modus_ponens,[status(thm)],[16, 9])).
% 94.12/94.28 tff(18,plain,
% 94.12/94.28 (![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)))))))))),
% 94.12/94.28 inference(modus_ponens,[status(thm)],[17, 7])).
% 94.12/94.28 tff(19,plain,
% 94.12/94.28 (![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)))))))))),
% 94.12/94.28 inference(modus_ponens,[status(thm)],[18, 2])).
% 94.12/94.28 tff(20,plain,
% 94.12/94.28 (((~![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)))))))))) | (~((~((~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, 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)))))))))) | (~((~((~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))))))))),
% 94.12/94.28 inference(rewrite,[status(thm)],[])).
% 94.12/94.28 tff(21,plain,
% 94.12/94.28 ((~((~(status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | (~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))))))) <=> (~((~((~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))))))))),
% 94.12/94.28 inference(rewrite,[status(thm)],[])).
% 94.12/94.28 tff(22,plain,
% 94.12/94.28 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | (~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, 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)))))))))) | (~((~((~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))))))))),
% 94.12/94.28 inference(monotonicity,[status(thm)],[21])).
% 94.12/94.28 tff(23,plain,
% 94.12/94.28 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | (~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, 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)))))))))) | (~((~((~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))))))))),
% 94.12/94.28 inference(transitivity,[status(thm)],[22, 20])).
% 94.12/94.28 tff(24,plain,
% 94.12/94.28 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | (~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))))))))),
% 94.12/94.29 inference(quant_inst,[status(thm)],[])).
% 94.12/94.29 tff(25,plain,
% 94.12/94.29 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~((~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))))))))),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[24, 23])).
% 94.12/94.29 tff(26,plain,
% 94.12/94.29 (~((~((~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))))))),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[25, 19])).
% 94.12/94.29 tff(27,plain,
% 94.12/94.29 (((~((~(model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_4(tptp_fun_C_22(uns, eqv), tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(uns, eqv))))) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))))))) | ((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))))),
% 94.12/94.29 inference(tautology,[status(thm)],[])).
% 94.12/94.29 tff(28,plain,
% 94.12/94.29 ((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))))),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[27, 26])).
% 94.12/94.29 tff(29,assumption,(![I1: $i] : model(I1, F!29)), introduced(assumption)).
% 94.12/94.29 tff(30,plain,
% 94.12/94.29 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 94.12/94.29 inference(rewrite,[status(thm)],[])).
% 94.12/94.29 tff(31,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 94.12/94.29 tff(32,plain,
% 94.12/94.29 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[31, 30])).
% 94.12/94.29 tff(33,plain,
% 94.12/94.29 (~model(I2!31, F!29)),
% 94.12/94.29 inference(and_elim,[status(thm)],[32])).
% 94.12/94.29 tff(34,plain,
% 94.12/94.29 ((~![I1: $i] : model(I1, F!29)) | model(I2!31, F!29)),
% 94.12/94.29 inference(quant_inst,[status(thm)],[])).
% 94.12/94.29 tff(35,plain,
% 94.12/94.29 ($false),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[34, 33, 29])).
% 94.12/94.29 tff(36,plain,(~![I1: $i] : model(I1, F!29)), inference(lemma,lemma(discharge,[]))).
% 94.12/94.29 tff(37,plain,
% 94.12/94.29 (((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))) | ![I1: $i] : model(I1, F!29)),
% 94.12/94.29 inference(tautology,[status(thm)],[])).
% 94.12/94.29 tff(38,plain,
% 94.12/94.29 ((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[37, 36])).
% 94.12/94.29 tff(39,assumption,((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))))), introduced(assumption)).
% 94.12/94.29 tff(40,plain,
% 94.12/94.29 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))))) <=> (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))))))),
% 94.12/94.29 inference(bind,[status(th)],[])).
% 94.12/94.29 tff(41,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))),
% 94.12/94.29 inference(quant_intro,[status(thm)],[40])).
% 94.12/94.29 tff(42,plain,
% 94.12/94.29 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))))) <=> (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))))))),
% 94.12/94.29 inference(bind,[status(th)],[])).
% 94.12/94.29 tff(43,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))),
% 94.12/94.29 inference(quant_intro,[status(thm)],[42])).
% 94.12/94.29 tff(44,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))),
% 94.12/94.29 inference(transitivity,[status(thm)],[43, 41])).
% 94.12/94.29 tff(45,plain,
% 94.12/94.29 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) <=> (status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))), trans(monotonicity(rewrite((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) <=> (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))), (((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns))) <=> ((~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))) | (~status(Ax, C, uns))))), rewrite(((~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))) | (~status(Ax, C, uns))) <=> ((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))), (((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns))) <=> ((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))), (((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns)))) <=> ((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) & ((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))))), rewrite(((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) & ((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C))))))) <=> (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))), (((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns)))) <=> (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))))),
% 94.12/94.29 inference(bind,[status(th)],[])).
% 94.12/94.29 tff(46,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : ((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))),
% 94.12/94.29 inference(quant_intro,[status(thm)],[45])).
% 94.12/94.29 tff(47,plain,
% 94.12/94.29 (^[Ax: $i, C: $i] : rewrite(((((~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) | status(Ax, C, uns)) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns)))) <=> ((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns)))))),
% 94.12/94.29 inference(bind,[status(th)],[])).
% 94.12/94.29 tff(48,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : ((((~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) | status(Ax, C, uns)) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns))))),
% 94.12/94.29 inference(quant_intro,[status(thm)],[47])).
% 94.12/94.29 tff(49,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) <=> status(Ax, C, uns)) <=> ![Ax: $i, C: $i] : ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) <=> status(Ax, C, uns))),
% 94.12/94.29 inference(rewrite,[status(thm)],[])).
% 94.12/94.29 tff(50,axiom,(![Ax: $i, C: $i] : ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) <=> status(Ax, C, uns))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','uns')).
% 94.12/94.29 tff(51,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) <=> status(Ax, C, uns))),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[50, 49])).
% 94.12/94.29 tff(52,plain,(
% 94.12/94.29 ![Ax: $i, C: $i] : ((((~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) | status(Ax, C, uns)) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns))))),
% 94.12/94.29 inference(skolemize,[status(sab)],[51])).
% 94.12/94.29 tff(53,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : ((status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C)))) & ((![I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, not(C))) | (~status(Ax, C, uns))))),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[52, 48])).
% 94.12/94.29 tff(54,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[53, 46])).
% 94.12/94.29 tff(55,plain,
% 94.12/94.29 (![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[54, 44])).
% 94.12/94.29 tff(56,plain,
% 94.12/94.29 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))) | (~((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))) | (~((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29))))))))))),
% 94.12/94.29 inference(rewrite,[status(thm)],[])).
% 94.12/94.29 tff(57,plain,
% 94.12/94.29 ((~((~(status(F!29, F!29, uns) | (~model(tptp_fun_I1_15(F!29), F!29)) | (~model(tptp_fun_I2_16(F!29), not(F!29))))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29))))))))) <=> (~((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))))))),
% 94.12/94.29 inference(rewrite,[status(thm)],[])).
% 94.12/94.29 tff(58,plain,
% 94.12/94.29 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))) | (~((~(status(F!29, F!29, uns) | (~model(tptp_fun_I1_15(F!29), F!29)) | (~model(tptp_fun_I2_16(F!29), not(F!29))))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))) | (~((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29))))))))))),
% 94.12/94.29 inference(monotonicity,[status(thm)],[57])).
% 94.12/94.29 tff(59,plain,
% 94.12/94.29 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))) | (~((~(status(F!29, F!29, uns) | (~model(tptp_fun_I1_15(F!29), F!29)) | (~model(tptp_fun_I2_16(F!29), not(F!29))))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))) | (~((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29))))))))))),
% 94.12/94.29 inference(transitivity,[status(thm)],[58, 56])).
% 94.12/94.29 tff(60,plain,
% 94.12/94.29 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))) | (~((~(status(F!29, F!29, uns) | (~model(tptp_fun_I1_15(F!29), F!29)) | (~model(tptp_fun_I2_16(F!29), not(F!29))))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))))))),
% 94.12/94.29 inference(quant_inst,[status(thm)],[])).
% 94.12/94.29 tff(61,plain,
% 94.12/94.29 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, uns) | (~model(tptp_fun_I1_15(Ax), Ax)) | (~model(tptp_fun_I2_16(C), not(C))))) | (~((~status(Ax, C, uns)) | (~((~![I1: $i] : model(I1, Ax)) | (~![I2: $i] : model(I2, not(C)))))))))) | (~((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))))))),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[60, 59])).
% 94.12/94.29 tff(62,plain,
% 94.12/94.29 ($false),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[61, 55, 39])).
% 94.12/94.29 tff(63,plain,(~((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29))))))))), inference(lemma,lemma(discharge,[]))).
% 94.12/94.29 tff(64,plain,
% 94.12/94.29 (((~((~model(tptp_fun_I2_16(F!29), not(F!29))) | (~model(tptp_fun_I1_15(F!29), F!29)) | status(F!29, F!29, uns))) | (~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))))) | ((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29))))))),
% 94.12/94.29 inference(tautology,[status(thm)],[])).
% 94.12/94.29 tff(65,plain,
% 94.12/94.29 ((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[64, 63])).
% 94.12/94.29 tff(66,plain,
% 94.12/94.29 ((~((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29))))))) | (~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))),
% 94.12/94.29 inference(tautology,[status(thm)],[])).
% 94.12/94.29 tff(67,plain,
% 94.12/94.29 ((~status(F!29, F!29, uns)) | (~((~![I1: $i] : model(I1, F!29)) | (~![I2: $i] : model(I2, not(F!29)))))),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[66, 65])).
% 94.12/94.29 tff(68,plain,
% 94.12/94.29 (~status(F!29, F!29, uns)),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[67, 38])).
% 94.12/94.29 tff(69,assumption,(![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))), introduced(assumption)).
% 94.12/94.29 tff(70,assumption,(![I1: $i] : (~model(I1, F!29))), introduced(assumption)).
% 94.12/94.29 tff(71,plain,
% 94.12/94.29 (model(I1!30, F!29)),
% 94.12/94.29 inference(and_elim,[status(thm)],[32])).
% 94.12/94.29 tff(72,plain,
% 94.12/94.29 ((~![I1: $i] : (~model(I1, F!29))) | (~model(I1!30, F!29))),
% 94.12/94.29 inference(quant_inst,[status(thm)],[])).
% 94.12/94.29 tff(73,plain,
% 94.12/94.29 ($false),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[72, 71, 70])).
% 94.12/94.29 tff(74,plain,(~![I1: $i] : (~model(I1, F!29))), inference(lemma,lemma(discharge,[]))).
% 94.12/94.29 tff(75,plain,
% 94.12/94.29 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29)))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29))))))),
% 94.12/94.29 inference(rewrite,[status(thm)],[])).
% 94.12/94.29 tff(76,plain,
% 94.12/94.29 ((~((~(status(F!29, F!29, eqv) | (~(model(tptp_fun_I2_4(F!29, F!29), F!29) <=> model(tptp_fun_I2_4(F!29, F!29), F!29))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (model(I2, F!29) <=> model(I2, F!29))))))))) <=> (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29)))))),
% 94.12/94.29 inference(rewrite,[status(thm)],[])).
% 94.12/94.29 tff(77,plain,
% 94.12/94.29 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | (~(model(tptp_fun_I2_4(F!29, F!29), F!29) <=> model(tptp_fun_I2_4(F!29, F!29), F!29))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (model(I2, F!29) <=> model(I2, F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29))))))),
% 94.12/94.29 inference(monotonicity,[status(thm)],[76])).
% 94.12/94.29 tff(78,plain,
% 94.12/94.29 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | (~(model(tptp_fun_I2_4(F!29, F!29), F!29) <=> model(tptp_fun_I2_4(F!29, F!29), F!29))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (model(I2, F!29) <=> model(I2, F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29))))))),
% 94.12/94.29 inference(transitivity,[status(thm)],[77, 75])).
% 94.12/94.29 tff(79,plain,
% 94.12/94.29 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | (~(model(tptp_fun_I2_4(F!29, F!29), F!29) <=> model(tptp_fun_I2_4(F!29, F!29), F!29))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (model(I2, F!29) <=> model(I2, F!29)))))))))),
% 94.12/94.29 inference(quant_inst,[status(thm)],[])).
% 94.12/94.29 tff(80,plain,
% 94.12/94.29 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29)))))),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[79, 78])).
% 94.12/94.29 tff(81,plain,
% 94.12/94.29 (~((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29))))),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[80, 19])).
% 94.12/94.29 tff(82,plain,
% 94.12/94.29 (((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, F!29, eqv)) | model(tptp_fun_I1_0(F!29), F!29)))) | (status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))),
% 94.12/94.29 inference(tautology,[status(thm)],[])).
% 94.12/94.29 tff(83,plain,
% 94.12/94.29 (status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29))),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[82, 81])).
% 94.12/94.29 tff(84,plain,
% 94.12/94.29 ((~(status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29)))) | status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29))),
% 94.12/94.29 inference(tautology,[status(thm)],[])).
% 94.12/94.29 tff(85,plain,
% 94.12/94.29 (status(F!29, F!29, eqv) | ![I1: $i] : (~model(I1, F!29))),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[84, 83])).
% 94.12/94.29 tff(86,plain,
% 94.12/94.29 (status(F!29, F!29, eqv)),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[85, 74])).
% 94.12/94.29 tff(87,plain,
% 94.12/94.29 (((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))) | ((~status(F!29, F!29, eqv)) | status(F!29, F!29, uns))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))) | (~status(F!29, F!29, eqv)) | status(F!29, F!29, uns))),
% 94.12/94.29 inference(rewrite,[status(thm)],[])).
% 94.12/94.29 tff(88,plain,
% 94.12/94.29 ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))) | ((~status(F!29, F!29, eqv)) | status(F!29, F!29, uns))),
% 94.12/94.29 inference(quant_inst,[status(thm)],[])).
% 94.12/94.29 tff(89,plain,
% 94.12/94.29 ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))) | (~status(F!29, F!29, eqv)) | status(F!29, F!29, uns)),
% 94.12/94.29 inference(modus_ponens,[status(thm)],[88, 87])).
% 94.12/94.29 tff(90,plain,
% 94.12/94.29 ($false),
% 94.12/94.29 inference(unit_resolution,[status(thm)],[89, 86, 69, 68])).
% 94.12/94.29 tff(91,plain,(~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))), inference(lemma,lemma(discharge,[]))).
% 94.12/94.29 tff(92,plain,
% 94.12/94.29 (^[S1: $i, S2: $i] : refl((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 94.12/94.29 inference(bind,[status(th)],[])).
% 94.12/94.29 tff(93,plain,
% 94.12/94.29 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 94.12/94.29 inference(quant_intro,[status(thm)],[92])).
% 94.12/94.29 tff(94,plain,
% 94.12/94.29 (^[S1: $i, S2: $i] : rewrite((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 94.12/94.29 inference(bind,[status(th)],[])).
% 94.12/94.29 tff(95,plain,
% 94.12/94.29 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 94.12/94.29 inference(quant_intro,[status(thm)],[94])).
% 94.12/94.29 tff(96,plain,
% 94.12/94.29 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 94.12/94.29 inference(transitivity,[status(thm)],[95, 93])).
% 94.12/94.29 tff(97,plain,
% 94.12/94.29 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) <=> (nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))), trans(monotonicity(rewrite((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) <=> (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))), rewrite(((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))))),
% 94.12/94.29 inference(bind,[status(th)],[])).
% 94.12/94.29 tff(98,plain,
% 94.12/94.29 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 94.12/94.29 inference(quant_intro,[status(thm)],[97])).
% 94.12/94.29 tff(99,plain,
% 94.12/94.29 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))))),
% 94.12/94.30 inference(bind,[status(th)],[])).
% 94.12/94.30 tff(100,plain,
% 94.12/94.30 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 94.12/94.30 inference(quant_intro,[status(thm)],[99])).
% 94.12/94.30 tff(101,plain,
% 94.12/94.30 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 94.12/94.30 inference(rewrite,[status(thm)],[])).
% 94.12/94.30 tff(102,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nota')).
% 94.12/94.30 tff(103,plain,
% 94.12/94.30 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[102, 101])).
% 94.12/94.30 tff(104,plain,(
% 94.12/94.30 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 94.12/94.30 inference(skolemize,[status(sab)],[103])).
% 94.12/94.30 tff(105,plain,
% 94.12/94.30 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[104, 100])).
% 94.12/94.30 tff(106,plain,
% 94.12/94.30 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[105, 98])).
% 94.12/94.30 tff(107,plain,
% 94.12/94.30 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[106, 96])).
% 94.12/94.30 tff(108,plain,
% 94.12/94.30 ((~![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))) | (~((~(nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns)))) | (~((~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns)))))))),
% 94.12/94.30 inference(quant_inst,[status(thm)],[])).
% 94.12/94.30 tff(109,plain,
% 94.12/94.30 (~((~(nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns)))) | (~((~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns))))))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[108, 107])).
% 94.12/94.30 tff(110,plain,
% 94.12/94.30 (((~(nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns)))) | (~((~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns)))))) | (nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns)))),
% 94.12/94.30 inference(tautology,[status(thm)],[])).
% 94.12/94.30 tff(111,plain,
% 94.12/94.30 (nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[110, 109])).
% 94.12/94.30 tff(112,plain,
% 94.12/94.30 ((~(nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns)))) | nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))),
% 94.12/94.30 inference(tautology,[status(thm)],[])).
% 94.12/94.30 tff(113,plain,
% 94.12/94.30 (nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[112, 111])).
% 94.12/94.30 tff(114,plain,
% 94.12/94.30 (nota(eqv, uns)),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[113, 91])).
% 94.12/94.30 tff(115,plain,
% 94.12/94.30 (((~(nota(eqv, uns) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | status(Ax, C, uns)))) | (~((~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns)))))) | ((~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns))))),
% 94.12/94.30 inference(tautology,[status(thm)],[])).
% 94.12/94.30 tff(116,plain,
% 94.12/94.30 ((~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns)))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[115, 109])).
% 94.12/94.30 tff(117,plain,
% 94.12/94.30 ((~((~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns))))) | (~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns)))),
% 94.12/94.30 inference(tautology,[status(thm)],[])).
% 94.12/94.30 tff(118,plain,
% 94.12/94.30 ((~nota(eqv, uns)) | (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns)))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[117, 116])).
% 94.12/94.30 tff(119,plain,
% 94.12/94.30 (~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[118, 114])).
% 94.12/94.30 tff(120,plain,
% 94.12/94.30 (((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), uns)) | status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)),
% 94.12/94.30 inference(tautology,[status(thm)],[])).
% 94.12/94.30 tff(121,plain,
% 94.12/94.30 (status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[120, 119])).
% 94.12/94.30 tff(122,plain,
% 94.12/94.30 ((~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))))) | (~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))))),
% 94.12/94.30 inference(tautology,[status(thm)],[])).
% 94.12/94.30 tff(123,plain,
% 94.12/94.30 ((~((~status(tptp_fun_Ax_23(uns, eqv), tptp_fun_C_22(uns, eqv), eqv)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))))) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[122, 121])).
% 94.12/94.30 tff(124,plain,
% 94.12/94.30 (~((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[123, 28])).
% 94.12/94.30 tff(125,plain,
% 94.12/94.30 (((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))) | ![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))),
% 94.12/94.30 inference(tautology,[status(thm)],[])).
% 94.12/94.30 tff(126,plain,
% 94.12/94.30 (![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[125, 124])).
% 94.12/94.30 tff(127,plain,
% 94.12/94.30 ((~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))) | (model(I3!40, tptp_fun_Ax_23(uns, eqv)) <=> model(I3!40, tptp_fun_C_22(uns, eqv)))),
% 94.12/94.30 inference(quant_inst,[status(thm)],[])).
% 94.12/94.30 tff(128,plain,
% 94.12/94.30 (model(I3!40, tptp_fun_Ax_23(uns, eqv)) <=> model(I3!40, tptp_fun_C_22(uns, eqv))),
% 94.12/94.30 inference(unit_resolution,[status(thm)],[127, 126])).
% 94.12/94.30 tff(129,assumption,(status(tptp_fun_C_22(uns, eqv), F!28, wec)), introduced(assumption)).
% 94.12/94.30 tff(130,plain,
% 94.12/94.30 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))))))))))),
% 94.12/94.30 inference(bind,[status(th)],[])).
% 94.12/94.30 tff(131,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))),
% 94.12/94.30 inference(quant_intro,[status(thm)],[130])).
% 94.12/94.30 tff(132,plain,
% 94.12/94.30 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))))),
% 94.12/94.30 inference(bind,[status(th)],[])).
% 94.12/94.30 tff(133,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 94.12/94.30 inference(quant_intro,[status(thm)],[132])).
% 94.12/94.30 tff(134,plain,
% 94.12/94.30 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))))),
% 94.12/94.30 inference(bind,[status(th)],[])).
% 94.12/94.30 tff(135,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 94.12/94.30 inference(quant_intro,[status(thm)],[134])).
% 94.12/94.30 tff(136,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 94.12/94.30 inference(transitivity,[status(thm)],[135, 133])).
% 94.12/94.30 tff(137,plain,
% 94.12/94.30 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[I3: $i] : trans(monotonicity(rewrite((model(I3, C) & (~model(I3, Ax))) <=> (~((~model(I3, C)) | model(I3, Ax)))), ((~(model(I3, C) & (~model(I3, Ax)))) <=> (~(~((~model(I3, C)) | model(I3, Ax)))))), rewrite((~(~((~model(I3, C)) | model(I3, Ax)))) <=> ((~model(I3, C)) | model(I3, Ax))), ((~(model(I3, C) & (~model(I3, Ax)))) <=> ((~model(I3, C)) | model(I3, Ax))))), (![I3: $i] : (~(model(I3, C) & (~model(I3, Ax)))) <=> ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))), ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) <=> (status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))))), rewrite((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))) <=> (status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))), ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) <=> (status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))))), rewrite(((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))) <=> ((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))), (((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax))))) <=> ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))) & ((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))), rewrite(((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))) & ((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))) <=> (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))), (((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax))))) <=> (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))))),
% 94.12/94.30 inference(bind,[status(th)],[])).
% 94.12/94.30 tff(138,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 94.12/94.30 inference(quant_intro,[status(thm)],[137])).
% 94.12/94.30 tff(139,plain,
% 94.12/94.30 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) | status(Ax, C, wec)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & (model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))) | (~status(Ax, C, wec)))) <=> ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax))))))),
% 94.12/94.30 inference(bind,[status(th)],[])).
% 94.12/94.30 tff(140,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) | status(Ax, C, wec)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & (model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))) | (~status(Ax, C, wec)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))))),
% 94.12/94.30 inference(quant_intro,[status(thm)],[139])).
% 94.12/94.30 tff(141,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))),
% 94.12/94.30 inference(rewrite,[status(thm)],[])).
% 94.12/94.30 tff(142,plain,
% 94.12/94.30 (^[Ax: $i, C: $i] : rewrite((((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec)) <=> ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec)))),
% 94.12/94.30 inference(bind,[status(th)],[])).
% 94.12/94.30 tff(143,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))),
% 94.12/94.30 inference(quant_intro,[status(thm)],[142])).
% 94.12/94.30 tff(144,axiom,(![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','wec')).
% 94.12/94.30 tff(145,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[144, 143])).
% 94.12/94.30 tff(146,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[145, 141])).
% 94.12/94.30 tff(147,plain,(
% 94.12/94.30 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) | status(Ax, C, wec)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & (model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))) | (~status(Ax, C, wec))))),
% 94.12/94.30 inference(skolemize,[status(sab)],[146])).
% 94.12/94.30 tff(148,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[147, 140])).
% 94.12/94.30 tff(149,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[148, 138])).
% 94.12/94.30 tff(150,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[149, 136])).
% 94.12/94.30 tff(151,plain,
% 94.12/94.30 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))),
% 94.12/94.30 inference(modus_ponens,[status(thm)],[150, 131])).
% 94.12/94.30 tff(152,plain,
% 94.12/94.30 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)))))))))),
% 94.12/94.30 inference(rewrite,[status(thm)],[])).
% 94.12/94.30 tff(153,plain,
% 94.12/94.30 ((~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~(model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))))))))) <=> (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))))))))),
% 94.12/94.30 inference(rewrite,[status(thm)],[])).
% 94.12/94.30 tff(154,plain,
% 94.12/94.30 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~(model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)))))))))),
% 94.12/94.31 inference(monotonicity,[status(thm)],[153])).
% 94.12/94.31 tff(155,plain,
% 94.12/94.31 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~(model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)))))))))),
% 94.12/94.31 inference(transitivity,[status(thm)],[154, 152])).
% 94.12/94.31 tff(156,plain,
% 94.12/94.31 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~(model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec))))))))))),
% 94.12/94.31 inference(quant_inst,[status(thm)],[])).
% 94.12/94.31 tff(157,plain,
% 94.12/94.31 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))))))))),
% 94.12/94.31 inference(modus_ponens,[status(thm)],[156, 155])).
% 94.12/94.31 tff(158,plain,
% 94.12/94.31 (~((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)))))))),
% 94.12/94.31 inference(unit_resolution,[status(thm)],[157, 151])).
% 94.12/94.31 tff(159,plain,
% 94.12/94.31 (((~(status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec) | ![I3: $i] : ((~model(I3, tptp_fun_C_22(thm, wec))) | model(I3, tptp_fun_Ax_23(thm, wec))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_23(thm, wec))) | (~((~model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I2_7(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))))))) | ((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)))))),
% 94.12/94.31 inference(tautology,[status(thm)],[])).
% 94.12/94.31 tff(160,plain,
% 94.12/94.31 ((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))))),
% 94.12/94.31 inference(unit_resolution,[status(thm)],[159, 158])).
% 94.12/94.31 tff(161,assumption,(~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))), introduced(assumption)).
% 94.12/94.31 tff(162,plain,
% 94.12/94.31 (((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)),
% 94.12/94.31 inference(tautology,[status(thm)],[])).
% 94.12/94.31 tff(163,plain,
% 94.12/94.31 (status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)),
% 94.12/94.31 inference(unit_resolution,[status(thm)],[162, 161])).
% 94.12/94.31 tff(164,plain,
% 94.12/94.31 ((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)))))) | (~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))))),
% 94.12/94.31 inference(tautology,[status(thm)],[])).
% 94.12/94.31 tff(165,plain,
% 94.12/94.31 ((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)))))) | (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))))),
% 94.12/94.31 inference(unit_resolution,[status(thm)],[164, 163])).
% 94.12/94.31 tff(166,plain,
% 94.12/94.31 (~((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec)))),
% 94.12/94.31 inference(unit_resolution,[status(thm)],[165, 160])).
% 94.12/94.31 tff(167,plain,
% 94.12/94.31 (((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I3_6(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))),
% 94.12/94.31 inference(tautology,[status(thm)],[])).
% 94.12/94.31 tff(168,plain,
% 94.12/94.31 (![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))),
% 94.12/94.31 inference(unit_resolution,[status(thm)],[167, 166])).
% 94.12/94.31 tff(169,plain,
% 94.12/94.31 (^[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)))))))),
% 94.12/94.31 inference(bind,[status(th)],[])).
% 94.12/94.31 tff(170,plain,
% 94.12/94.31 (![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))))))),
% 94.12/94.31 inference(quant_intro,[status(thm)],[169])).
% 94.12/94.31 tff(171,plain,
% 94.12/94.31 (^[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)))))))),
% 94.12/94.31 inference(bind,[status(th)],[])).
% 94.12/94.31 tff(172,plain,
% 94.12/94.31 (![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))))))),
% 94.12/94.31 inference(quant_intro,[status(thm)],[171])).
% 94.12/94.31 tff(173,plain,
% 94.12/94.31 (^[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)))))))),
% 94.12/94.31 inference(bind,[status(th)],[])).
% 94.12/94.31 tff(174,plain,
% 94.12/94.31 (![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))))))),
% 94.12/94.31 inference(quant_intro,[status(thm)],[173])).
% 94.12/94.31 tff(175,plain,
% 94.12/94.31 (![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))))))),
% 94.12/94.31 inference(transitivity,[status(thm)],[174, 172])).
% 94.12/94.31 tff(176,plain,
% 94.12/94.31 (^[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))))))))),
% 94.12/94.31 inference(bind,[status(th)],[])).
% 94.12/94.31 tff(177,plain,
% 94.12/94.31 (![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))))))),
% 94.12/94.31 inference(quant_intro,[status(thm)],[176])).
% 94.12/94.31 tff(178,plain,
% 94.12/94.31 (![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))),
% 94.12/94.31 inference(rewrite,[status(thm)],[])).
% 94.12/94.31 tff(179,plain,
% 94.12/94.31 (^[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)))),
% 94.12/94.31 inference(bind,[status(th)],[])).
% 94.12/94.31 tff(180,plain,
% 94.12/94.31 (![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))),
% 94.12/94.31 inference(quant_intro,[status(thm)],[179])).
% 94.12/94.31 tff(181,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')).
% 94.12/94.31 tff(182,plain,
% 94.12/94.31 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 94.12/94.31 inference(modus_ponens,[status(thm)],[181, 180])).
% 94.12/94.31 tff(183,plain,
% 94.12/94.31 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 94.12/94.31 inference(modus_ponens,[status(thm)],[182, 178])).
% 94.12/94.31 tff(184,plain,(
% 94.12/94.31 ![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))))),
% 94.12/94.31 inference(skolemize,[status(sab)],[183])).
% 94.12/94.31 tff(185,plain,
% 94.12/94.31 (![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))))))),
% 94.12/94.31 inference(modus_ponens,[status(thm)],[184, 177])).
% 94.12/94.31 tff(186,plain,
% 94.12/94.31 (![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))))))),
% 94.12/94.31 inference(modus_ponens,[status(thm)],[185, 175])).
% 94.12/94.31 tff(187,plain,
% 94.12/94.31 (![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))))))),
% 94.12/94.31 inference(modus_ponens,[status(thm)],[186, 170])).
% 94.12/94.31 tff(188,plain,
% 94.12/94.31 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))))))),
% 94.12/94.31 inference(rewrite,[status(thm)],[])).
% 94.12/94.31 tff(189,plain,
% 94.12/94.31 ((~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))))) <=> (~((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))))),
% 94.12/94.31 inference(rewrite,[status(thm)],[])).
% 94.12/94.31 tff(190,plain,
% 94.12/94.31 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))))))),
% 94.12/94.31 inference(monotonicity,[status(thm)],[189])).
% 94.12/94.31 tff(191,plain,
% 94.12/94.31 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))))))),
% 94.15/94.31 inference(transitivity,[status(thm)],[190, 188])).
% 94.15/94.31 tff(192,plain,
% 94.15/94.31 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec)))))))),
% 94.15/94.31 inference(quant_inst,[status(thm)],[])).
% 94.15/94.31 tff(193,plain,
% 94.15/94.31 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))))),
% 94.15/94.31 inference(modus_ponens,[status(thm)],[192, 191])).
% 94.15/94.31 tff(194,plain,
% 94.15/94.31 (~((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))))),
% 94.15/94.31 inference(unit_resolution,[status(thm)],[193, 187])).
% 94.15/94.31 tff(195,plain,
% 94.15/94.31 (((~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_23(thm, wec))) | model(I1, tptp_fun_C_22(thm, wec))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))) | ((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))),
% 94.15/94.31 inference(tautology,[status(thm)],[])).
% 94.15/94.31 tff(196,plain,
% 94.15/94.31 ((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[195, 194])).
% 94.15/94.32 tff(197,plain,
% 94.15/94.32 (((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)) | (~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(198,plain,
% 94.15/94.32 (~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[197, 161])).
% 94.15/94.32 tff(199,plain,
% 94.15/94.32 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(200,plain,
% 94.15/94.32 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[199, 198])).
% 94.15/94.32 tff(201,plain,
% 94.15/94.32 (~((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[200, 196])).
% 94.15/94.32 tff(202,plain,
% 94.15/94.32 (((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | (~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(203,plain,
% 94.15/94.32 (~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[202, 201])).
% 94.15/94.32 tff(204,plain,
% 94.15/94.32 (((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(205,plain,
% 94.15/94.32 (model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[204, 201])).
% 94.15/94.32 tff(206,plain,
% 94.15/94.32 (((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | ((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))) <=> ((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))),
% 94.15/94.32 inference(rewrite,[status(thm)],[])).
% 94.15/94.32 tff(207,plain,
% 94.15/94.32 ((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | ((~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec)))),
% 94.15/94.32 inference(quant_inst,[status(thm)],[])).
% 94.15/94.32 tff(208,plain,
% 94.15/94.32 ((~![I2: $i] : ((~model(I2, tptp_fun_Ax_23(thm, wec))) | model(I2, tptp_fun_C_22(thm, wec)))) | (~model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_Ax_23(thm, wec))) | model(tptp_fun_I1_3(tptp_fun_C_22(thm, wec), tptp_fun_Ax_23(thm, wec)), tptp_fun_C_22(thm, wec))),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[207, 206])).
% 94.15/94.32 tff(209,plain,
% 94.15/94.32 ($false),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[208, 205, 203, 168])).
% 94.15/94.32 tff(210,plain,((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)), inference(lemma,lemma(discharge,[]))).
% 94.15/94.32 tff(211,plain,
% 94.15/94.32 ((~![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))) | (~((~(nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm)))) | (~((~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))))))),
% 94.15/94.32 inference(quant_inst,[status(thm)],[])).
% 94.15/94.32 tff(212,plain,
% 94.15/94.32 (~((~(nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm)))) | (~((~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))))))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[211, 107])).
% 94.15/94.32 tff(213,plain,
% 94.15/94.32 (((~(nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm)))) | (~((~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))))) | ((~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(214,plain,
% 94.15/94.32 ((~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[213, 212])).
% 94.15/94.32 tff(215,plain,
% 94.15/94.32 ((~((~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm))))) | (~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(216,plain,
% 94.15/94.32 ((~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[215, 214])).
% 94.15/94.32 tff(217,plain,
% 94.15/94.32 (~nota(wec, thm)),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[216, 210])).
% 94.15/94.32 tff(218,plain,
% 94.15/94.32 (((~(nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm)))) | (~((~nota(wec, thm)) | (~((~status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), wec)) | status(tptp_fun_Ax_23(thm, wec), tptp_fun_C_22(thm, wec), thm)))))) | (nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm)))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(219,plain,
% 94.15/94.32 (nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[218, 212])).
% 94.15/94.32 tff(220,plain,
% 94.15/94.32 ((~(nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm)))) | nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(221,plain,
% 94.15/94.32 (nota(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[220, 219])).
% 94.15/94.32 tff(222,plain,
% 94.15/94.32 (![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[221, 217])).
% 94.15/94.32 tff(223,plain,
% 94.15/94.32 (((~![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))) | ((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | status(tptp_fun_C_22(uns, eqv), F!28, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))) | (~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | status(tptp_fun_C_22(uns, eqv), F!28, thm))),
% 94.15/94.32 inference(rewrite,[status(thm)],[])).
% 94.15/94.32 tff(224,plain,
% 94.15/94.32 ((~![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))) | ((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | status(tptp_fun_C_22(uns, eqv), F!28, thm))),
% 94.15/94.32 inference(quant_inst,[status(thm)],[])).
% 94.15/94.32 tff(225,plain,
% 94.15/94.32 ((~![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))) | (~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | status(tptp_fun_C_22(uns, eqv), F!28, thm)),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[224, 223])).
% 94.15/94.32 tff(226,plain,
% 94.15/94.32 (status(tptp_fun_C_22(uns, eqv), F!28, thm)),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[225, 222, 129])).
% 94.15/94.32 tff(227,plain,
% 94.15/94.32 (^[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)))))))))),
% 94.15/94.32 inference(bind,[status(th)],[])).
% 94.15/94.32 tff(228,plain,
% 94.15/94.32 (![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))))))))),
% 94.15/94.32 inference(quant_intro,[status(thm)],[227])).
% 94.15/94.32 tff(229,plain,
% 94.15/94.32 (^[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)))))))))),
% 94.15/94.32 inference(bind,[status(th)],[])).
% 94.15/94.32 tff(230,plain,
% 94.15/94.32 (![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))))))))),
% 94.15/94.32 inference(quant_intro,[status(thm)],[229])).
% 94.15/94.32 tff(231,plain,
% 94.15/94.32 (![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))))))))),
% 94.15/94.32 inference(transitivity,[status(thm)],[230, 228])).
% 94.15/94.32 tff(232,plain,
% 94.15/94.32 (^[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))))))))))),
% 94.15/94.32 inference(bind,[status(th)],[])).
% 94.15/94.32 tff(233,plain,
% 94.15/94.32 (![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))))))))),
% 94.15/94.32 inference(quant_intro,[status(thm)],[232])).
% 94.15/94.32 tff(234,plain,
% 94.15/94.32 (^[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)))))),
% 94.15/94.32 inference(bind,[status(th)],[])).
% 94.15/94.32 tff(235,plain,
% 94.15/94.32 (![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))))),
% 94.15/94.32 inference(quant_intro,[status(thm)],[234])).
% 94.15/94.32 tff(236,plain,
% 94.15/94.32 (![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))),
% 94.15/94.32 inference(rewrite,[status(thm)],[])).
% 94.15/94.32 tff(237,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')).
% 94.15/94.32 tff(238,plain,
% 94.15/94.32 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[237, 236])).
% 94.15/94.32 tff(239,plain,(
% 94.15/94.32 ![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))))),
% 94.15/94.32 inference(skolemize,[status(sab)],[238])).
% 94.15/94.32 tff(240,plain,
% 94.15/94.32 (![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))))),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[239, 235])).
% 94.15/94.32 tff(241,plain,
% 94.15/94.32 (![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))))))))),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[240, 233])).
% 94.15/94.32 tff(242,plain,
% 94.15/94.32 (![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))))))))),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[241, 231])).
% 94.15/94.32 tff(243,plain,
% 94.15/94.32 (((~![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(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec))))))))) <=> ((~![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(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec)))))))))),
% 94.15/94.32 inference(rewrite,[status(thm)],[])).
% 94.15/94.32 tff(244,plain,
% 94.15/94.32 ((~((~(mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)))))))) <=> (~((~(mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec))))))))),
% 94.15/94.32 inference(rewrite,[status(thm)],[])).
% 94.15/94.32 tff(245,plain,
% 94.15/94.32 (((~![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(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), 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(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec)))))))))),
% 94.15/94.32 inference(monotonicity,[status(thm)],[244])).
% 94.15/94.32 tff(246,plain,
% 94.15/94.32 (((~![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(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), 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(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec)))))))))),
% 94.15/94.32 inference(transitivity,[status(thm)],[245, 243])).
% 94.15/94.32 tff(247,plain,
% 94.15/94.32 ((~![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(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm))))))))),
% 94.15/94.32 inference(quant_inst,[status(thm)],[])).
% 94.15/94.32 tff(248,plain,
% 94.15/94.32 ((~![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(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec))))))))),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[247, 246])).
% 94.15/94.32 tff(249,plain,
% 94.15/94.32 (~((~(mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec)))))))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[248, 242])).
% 94.15/94.32 tff(250,plain,
% 94.15/94.32 (((~(mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | (~((~mighta(wec, thm)) | (~((~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), thm)) | (~status(tptp_fun_Ax_19(thm, wec), tptp_fun_C_18(thm, wec), wec))))))) | (mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(251,plain,
% 94.15/94.32 (mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[250, 249])).
% 94.15/94.32 tff(252,plain,
% 94.15/94.32 ((~mighta(wec, thm)) <=> (~mighta(wec, thm))),
% 94.15/94.32 inference(rewrite,[status(thm)],[])).
% 94.15/94.32 tff(253,axiom,(~mighta(wec, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_wec_thm')).
% 94.15/94.32 tff(254,plain,
% 94.15/94.32 (~mighta(wec, thm)),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[253, 252])).
% 94.15/94.32 tff(255,plain,
% 94.15/94.32 ((~(mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))),
% 94.15/94.32 inference(tautology,[status(thm)],[])).
% 94.15/94.32 tff(256,plain,
% 94.15/94.32 ((~(mighta(wec, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[255, 254])).
% 94.15/94.32 tff(257,plain,
% 94.15/94.32 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[256, 251])).
% 94.15/94.32 tff(258,plain,
% 94.15/94.32 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))) | ((~status(tptp_fun_C_22(uns, eqv), F!28, thm)) | (~status(tptp_fun_C_22(uns, eqv), F!28, wec)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))) | (~status(tptp_fun_C_22(uns, eqv), F!28, thm)) | (~status(tptp_fun_C_22(uns, eqv), F!28, wec)))),
% 94.15/94.32 inference(rewrite,[status(thm)],[])).
% 94.15/94.32 tff(259,plain,
% 94.15/94.32 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))) | ((~status(tptp_fun_C_22(uns, eqv), F!28, thm)) | (~status(tptp_fun_C_22(uns, eqv), F!28, wec)))),
% 94.15/94.32 inference(quant_inst,[status(thm)],[])).
% 94.15/94.32 tff(260,plain,
% 94.15/94.32 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))) | (~status(tptp_fun_C_22(uns, eqv), F!28, thm)) | (~status(tptp_fun_C_22(uns, eqv), F!28, wec))),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[259, 258])).
% 94.15/94.32 tff(261,plain,
% 94.15/94.32 ($false),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[260, 257, 129, 226])).
% 94.15/94.32 tff(262,plain,(~status(tptp_fun_C_22(uns, eqv), F!28, wec)), inference(lemma,lemma(discharge,[]))).
% 94.15/94.32 tff(263,assumption,(~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)), introduced(assumption)).
% 94.15/94.32 tff(264,assumption,(~model(tptp_fun_I2_5(F!28), F!28)), introduced(assumption)).
% 94.15/94.32 tff(265,plain,
% 94.15/94.32 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 94.15/94.32 inference(bind,[status(th)],[])).
% 94.15/94.32 tff(266,plain,
% 94.15/94.32 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 94.15/94.32 inference(quant_intro,[status(thm)],[265])).
% 94.15/94.32 tff(267,plain,
% 94.15/94.32 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 94.15/94.32 inference(rewrite,[status(thm)],[])).
% 94.15/94.32 tff(268,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','tautology')).
% 94.15/94.32 tff(269,plain,
% 94.15/94.32 (?[F: $i] : ![I: $i] : model(I, F)),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[268, 267])).
% 94.15/94.32 tff(270,plain,(
% 94.15/94.32 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 94.15/94.32 inference(transitivity,[status(sab)],[269])).
% 94.15/94.32 tff(271,plain,
% 94.15/94.32 (![I: $i] : model(I, F!28)),
% 94.15/94.32 inference(modus_ponens,[status(thm)],[270, 266])).
% 94.15/94.32 tff(272,plain,
% 94.15/94.32 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I2_5(F!28), F!28)),
% 94.15/94.32 inference(quant_inst,[status(thm)],[])).
% 94.15/94.32 tff(273,plain,
% 94.15/94.32 ($false),
% 94.15/94.32 inference(unit_resolution,[status(thm)],[272, 271, 264])).
% 94.15/94.32 tff(274,plain,(model(tptp_fun_I2_5(F!28), F!28)), inference(lemma,lemma(discharge,[]))).
% 94.15/94.32 tff(275,plain,
% 94.15/94.32 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 94.15/94.32 inference(bind,[status(th)],[])).
% 94.15/94.32 tff(276,plain,
% 94.15/94.32 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 94.15/94.32 inference(quant_intro,[status(thm)],[275])).
% 94.15/94.32 tff(277,plain,
% 94.15/94.32 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 94.15/94.32 inference(bind,[status(th)],[])).
% 94.15/94.32 tff(278,plain,
% 94.15/94.32 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 94.15/94.32 inference(quant_intro,[status(thm)],[277])).
% 94.15/94.32 tff(279,plain,
% 94.15/94.32 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 94.15/94.32 inference(transitivity,[status(thm)],[278, 276])).
% 94.15/94.32 tff(280,plain,
% 94.15/94.32 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) <=> (status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))), trans(monotonicity(rewrite((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) <=> (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))), (((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca))) <=> ((~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, tca))))), rewrite(((~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, tca))) <=> ((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))), (((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca))) <=> ((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))), (((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca)))) <=> ((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) & ((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))))), rewrite(((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) & ((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax))))))) <=> (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))), (((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca)))) <=> (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))))),
% 94.15/94.32 inference(bind,[status(th)],[])).
% 94.15/94.32 tff(281,plain,
% 94.15/94.32 (![Ax: $i, C: $i] : ((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 94.15/94.32 inference(quant_intro,[status(thm)],[280])).
% 94.15/94.32 tff(282,plain,
% 94.15/94.32 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tca)) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca)))) <=> ((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca)))))),
% 94.15/94.33 inference(bind,[status(th)],[])).
% 94.15/94.33 tff(283,plain,
% 94.15/94.33 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tca)) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca))))),
% 94.15/94.33 inference(quant_intro,[status(thm)],[282])).
% 94.15/94.33 tff(284,plain,
% 94.15/94.33 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tca)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tca))),
% 94.15/94.33 inference(rewrite,[status(thm)],[])).
% 94.15/94.33 tff(285,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tca))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','tca')).
% 94.15/94.33 tff(286,plain,
% 94.15/94.33 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tca))),
% 94.15/94.33 inference(modus_ponens,[status(thm)],[285, 284])).
% 94.15/94.33 tff(287,plain,(
% 94.15/94.33 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tca)) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca))))),
% 94.15/94.33 inference(skolemize,[status(sab)],[286])).
% 94.15/94.33 tff(288,plain,
% 94.15/94.33 (![Ax: $i, C: $i] : ((status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C))) & ((![I1: $i] : (~model(I1, Ax)) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tca))))),
% 94.15/94.33 inference(modus_ponens,[status(thm)],[287, 283])).
% 94.15/94.33 tff(289,plain,
% 94.15/94.33 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 94.15/94.33 inference(modus_ponens,[status(thm)],[288, 281])).
% 94.15/94.33 tff(290,plain,
% 94.15/94.33 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 94.15/94.33 inference(modus_ponens,[status(thm)],[289, 279])).
% 94.15/94.33 tff(291,plain,
% 94.15/94.33 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32))))))))))),
% 94.15/94.33 inference(rewrite,[status(thm)],[])).
% 94.15/94.33 tff(292,plain,
% 94.15/94.33 ((~((~(status(F!32, F!28, tca) | model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32))))))))) <=> (~((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))))))),
% 94.15/94.33 inference(rewrite,[status(thm)],[])).
% 94.15/94.33 tff(293,plain,
% 94.15/94.33 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(F!32, F!28, tca) | model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32))))))))))),
% 94.15/94.33 inference(monotonicity,[status(thm)],[292])).
% 94.15/94.33 tff(294,plain,
% 94.15/94.33 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(F!32, F!28, tca) | model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32))))))))))),
% 94.15/94.33 inference(transitivity,[status(thm)],[293, 291])).
% 94.15/94.33 tff(295,plain,
% 94.15/94.33 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(F!32, F!28, tca) | model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))))))),
% 94.15/94.33 inference(quant_inst,[status(thm)],[])).
% 94.15/94.33 tff(296,plain,
% 94.15/94.33 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tca) | model(tptp_fun_I1_0(Ax), Ax) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tca)) | (~((~![I2: $i] : model(I2, C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))))))),
% 94.15/94.33 inference(modus_ponens,[status(thm)],[295, 294])).
% 94.15/94.33 tff(297,plain,
% 94.15/94.33 (~((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32))))))))),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[296, 290])).
% 94.15/94.33 tff(298,plain,
% 94.15/94.33 (((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))))) | (model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))),
% 94.15/94.33 inference(tautology,[status(thm)],[])).
% 94.15/94.33 tff(299,plain,
% 94.15/94.33 (model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca)),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[298, 297])).
% 94.15/94.33 tff(300,assumption,(model(tptp_fun_I1_0(F!32), F!32)), introduced(assumption)).
% 94.15/94.33 tff(301,plain,
% 94.15/94.33 (^[I: $i] : refl((~model(I, F!32)) <=> (~model(I, F!32)))),
% 94.15/94.33 inference(bind,[status(th)],[])).
% 94.15/94.33 tff(302,plain,
% 94.15/94.33 (![I: $i] : (~model(I, F!32)) <=> ![I: $i] : (~model(I, F!32))),
% 94.15/94.33 inference(quant_intro,[status(thm)],[301])).
% 94.15/94.33 tff(303,plain,
% 94.15/94.33 (?[F: $i] : ![I: $i] : (~model(I, F)) <=> ?[F: $i] : ![I: $i] : (~model(I, F))),
% 94.15/94.33 inference(rewrite,[status(thm)],[])).
% 94.15/94.33 tff(304,axiom,(?[F: $i] : ![I: $i] : (~model(I, F))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','contradiction')).
% 94.15/94.33 tff(305,plain,
% 94.15/94.33 (?[F: $i] : ![I: $i] : (~model(I, F))),
% 94.15/94.33 inference(modus_ponens,[status(thm)],[304, 303])).
% 94.15/94.33 tff(306,plain,(
% 94.15/94.33 $oeq(![I: $i] : (~model(I, F!32)), ![I: $i] : (~model(I, F!32)))),
% 94.15/94.33 inference(transitivity,[status(sab)],[305])).
% 94.15/94.33 tff(307,plain,
% 94.15/94.33 (![I: $i] : (~model(I, F!32))),
% 94.15/94.33 inference(modus_ponens,[status(thm)],[306, 302])).
% 94.15/94.33 tff(308,plain,
% 94.15/94.33 ((~![I: $i] : (~model(I, F!32))) | (~model(tptp_fun_I1_0(F!32), F!32))),
% 94.15/94.33 inference(quant_inst,[status(thm)],[])).
% 94.15/94.33 tff(309,plain,
% 94.15/94.33 ($false),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[308, 307, 300])).
% 94.15/94.33 tff(310,plain,(~model(tptp_fun_I1_0(F!32), F!32)), inference(lemma,lemma(discharge,[]))).
% 94.15/94.33 tff(311,plain,
% 94.15/94.33 ((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca)),
% 94.15/94.33 inference(tautology,[status(thm)],[])).
% 94.15/94.33 tff(312,plain,
% 94.15/94.33 ((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca)),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[311, 310])).
% 94.15/94.33 tff(313,plain,
% 94.15/94.33 ((~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca)),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[312, 299])).
% 94.15/94.33 tff(314,plain,
% 94.15/94.33 (status(F!32, F!28, tca)),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[313, 274])).
% 94.15/94.33 tff(315,plain,
% 94.15/94.33 (((~(model(tptp_fun_I1_0(F!32), F!32) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(F!32, F!28, tca))) | (~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))))) | ((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32))))))),
% 94.15/94.33 inference(tautology,[status(thm)],[])).
% 94.15/94.33 tff(316,plain,
% 94.15/94.33 ((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[315, 297])).
% 94.15/94.33 tff(317,plain,
% 94.15/94.33 ((~((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32))))))) | (~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))),
% 94.15/94.33 inference(tautology,[status(thm)],[])).
% 94.15/94.33 tff(318,plain,
% 94.15/94.33 ((~status(F!32, F!28, tca)) | (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))))),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[317, 316])).
% 94.15/94.33 tff(319,plain,
% 94.15/94.33 (~((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32))))),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[318, 314])).
% 94.15/94.33 tff(320,plain,
% 94.15/94.33 (((~![I2: $i] : model(I2, F!28)) | (~![I1: $i] : (~model(I1, F!32)))) | ![I2: $i] : model(I2, F!28)),
% 94.15/94.33 inference(tautology,[status(thm)],[])).
% 94.15/94.33 tff(321,plain,
% 94.15/94.33 (![I2: $i] : model(I2, F!28)),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[320, 319])).
% 94.15/94.33 tff(322,plain,
% 94.15/94.33 ((~![I2: $i] : model(I2, F!28)) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)),
% 94.15/94.33 inference(quant_inst,[status(thm)],[])).
% 94.15/94.33 tff(323,plain,
% 94.15/94.33 ($false),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[322, 321, 263])).
% 94.15/94.33 tff(324,plain,(model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)), inference(lemma,lemma(discharge,[]))).
% 94.15/94.33 tff(325,plain,
% 94.15/94.33 (((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)) | (~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))),
% 94.15/94.33 inference(tautology,[status(thm)],[])).
% 94.15/94.33 tff(326,plain,
% 94.15/94.33 ((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)),
% 94.15/94.33 inference(unit_resolution,[status(thm)],[325, 324])).
% 94.15/94.33 tff(327,plain,
% 94.15/94.33 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28)))))))))),
% 94.17/94.33 inference(rewrite,[status(thm)],[])).
% 94.17/94.33 tff(328,plain,
% 94.17/94.33 ((~((~(status(tptp_fun_C_22(uns, eqv), F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))) | ![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28)) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))))))))) <=> (~((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28))))))))),
% 94.17/94.33 inference(rewrite,[status(thm)],[])).
% 94.17/94.33 tff(329,plain,
% 94.17/94.33 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_C_22(uns, eqv), F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))) | ![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28)) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28)))))))))),
% 94.17/94.33 inference(monotonicity,[status(thm)],[328])).
% 94.17/94.33 tff(330,plain,
% 94.17/94.33 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_C_22(uns, eqv), F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))) | ![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28)) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28)))))))))),
% 94.17/94.33 inference(transitivity,[status(thm)],[329, 327])).
% 94.17/94.33 tff(331,plain,
% 94.17/94.33 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(tptp_fun_C_22(uns, eqv), F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))) | ![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28)) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28)))))))))),
% 94.17/94.33 inference(quant_inst,[status(thm)],[])).
% 94.17/94.33 tff(332,plain,
% 94.17/94.33 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28))))))))),
% 94.17/94.33 inference(modus_ponens,[status(thm)],[331, 330])).
% 94.17/94.33 tff(333,plain,
% 94.17/94.33 (~((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28)))))))),
% 94.17/94.33 inference(unit_resolution,[status(thm)],[332, 151])).
% 94.17/94.33 tff(334,plain,
% 94.17/94.33 (((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | (~((~status(tptp_fun_C_22(uns, eqv), F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv)) | (~model(tptp_fun_I1_0(tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | (~![I2: $i] : ((~model(I2, tptp_fun_C_22(uns, eqv))) | model(I2, F!28))) | (~model(tptp_fun_I3_6(F!28, tptp_fun_C_22(uns, eqv)), F!28))))))) | (![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))),
% 94.17/94.33 inference(tautology,[status(thm)],[])).
% 94.17/94.33 tff(335,plain,
% 94.17/94.33 (![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)))),
% 94.17/94.33 inference(unit_resolution,[status(thm)],[334, 333])).
% 94.17/94.33 tff(336,assumption,(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv)))), introduced(assumption)).
% 94.17/94.33 tff(337,plain,
% 94.17/94.33 ((~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))) | (model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(338,plain,
% 94.17/94.34 (model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[337, 126])).
% 94.17/94.34 tff(339,plain,
% 94.17/94.34 (((~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv))))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))),
% 94.17/94.34 inference(tautology,[status(thm)],[])).
% 94.17/94.34 tff(340,plain,
% 94.17/94.34 (model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[339, 124])).
% 94.17/94.34 tff(341,plain,
% 94.17/94.34 ((~(model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(tautology,[status(thm)],[])).
% 94.17/94.34 tff(342,plain,
% 94.17/94.34 ((~(model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))) | model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[341, 340])).
% 94.17/94.34 tff(343,plain,
% 94.17/94.34 (model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[342, 338])).
% 94.17/94.34 tff(344,plain,
% 94.17/94.34 ((~![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv)))) | (~model(tptp_fun_I1_0(tptp_fun_Ax_23(uns, eqv)), tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(345,plain,
% 94.17/94.34 ($false),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[344, 343, 336])).
% 94.17/94.34 tff(346,plain,(~![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv)))), inference(lemma,lemma(discharge,[]))).
% 94.17/94.34 tff(347,plain,
% 94.17/94.34 ((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | ![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)))),
% 94.17/94.34 inference(tautology,[status(thm)],[])).
% 94.17/94.34 tff(348,plain,
% 94.17/94.34 ((~(![I1: $i] : (~model(I1, tptp_fun_C_22(uns, eqv))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28))))) | status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[347, 346])).
% 94.17/94.34 tff(349,plain,
% 94.17/94.34 (status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv))) | (~((~model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), tptp_fun_C_22(uns, eqv))) | model(tptp_fun_I2_7(F!28, tptp_fun_C_22(uns, eqv)), F!28)))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[348, 335])).
% 94.17/94.34 tff(350,plain,
% 94.17/94.34 (status(tptp_fun_C_22(uns, eqv), F!28, wec) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[349, 326])).
% 94.17/94.34 tff(351,plain,
% 94.17/94.34 (![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[350, 262])).
% 94.17/94.34 tff(352,plain,
% 94.17/94.34 ((~![I: $i] : model(I, F!28)) | model(I3!40, F!28)),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(353,plain,
% 94.17/94.34 (model(I3!40, F!28)),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[352, 271])).
% 94.17/94.34 tff(354,plain,
% 94.17/94.34 (((~![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))) | ((~model(I3!40, F!28)) | model(I3!40, tptp_fun_C_22(uns, eqv)))) <=> ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))) | (~model(I3!40, F!28)) | model(I3!40, tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(rewrite,[status(thm)],[])).
% 94.17/94.34 tff(355,plain,
% 94.17/94.34 ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))) | ((~model(I3!40, F!28)) | model(I3!40, tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(356,plain,
% 94.17/94.34 ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))) | (~model(I3!40, F!28)) | model(I3!40, tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(modus_ponens,[status(thm)],[355, 354])).
% 94.17/94.34 tff(357,plain,
% 94.17/94.34 (model(I3!40, tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[356, 353, 351])).
% 94.17/94.34 tff(358,plain,
% 94.17/94.34 ((~(model(I3!40, tptp_fun_Ax_23(uns, eqv)) <=> model(I3!40, tptp_fun_C_22(uns, eqv)))) | model(I3!40, tptp_fun_Ax_23(uns, eqv)) | (~model(I3!40, tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(tautology,[status(thm)],[])).
% 94.17/94.34 tff(359,plain,
% 94.17/94.34 ((~(model(I3!40, tptp_fun_Ax_23(uns, eqv)) <=> model(I3!40, tptp_fun_C_22(uns, eqv)))) | model(I3!40, tptp_fun_Ax_23(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[358, 357])).
% 94.17/94.34 tff(360,plain,
% 94.17/94.34 (model(I3!40, tptp_fun_Ax_23(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[359, 128])).
% 94.17/94.34 tff(361,plain,
% 94.17/94.34 ((~![I2: $i] : (model(I2, tptp_fun_Ax_23(uns, eqv)) <=> model(I2, tptp_fun_C_22(uns, eqv)))) | (model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(362,plain,
% 94.17/94.34 (model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[361, 126])).
% 94.17/94.34 tff(363,assumption,(~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), F!28)), introduced(assumption)).
% 94.17/94.34 tff(364,plain,
% 94.17/94.34 ((~![I2: $i] : model(I2, F!28)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), F!28)),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(365,plain,
% 94.17/94.34 ($false),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[364, 321, 363])).
% 94.17/94.34 tff(366,plain,(model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), F!28)), inference(lemma,lemma(discharge,[]))).
% 94.17/94.34 tff(367,plain,
% 94.17/94.34 (((~![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))) | ((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), F!28)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv)))) <=> ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))) | (~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), F!28)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(rewrite,[status(thm)],[])).
% 94.17/94.34 tff(368,plain,
% 94.17/94.34 ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))) | ((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), F!28)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(369,plain,
% 94.17/94.34 ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, tptp_fun_C_22(uns, eqv)))) | (~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), F!28)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(modus_ponens,[status(thm)],[368, 367])).
% 94.17/94.34 tff(370,plain,
% 94.17/94.34 (model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[369, 351, 366])).
% 94.17/94.34 tff(371,plain,
% 94.17/94.34 ((~(model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv)))) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)) | (~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv)))),
% 94.17/94.34 inference(tautology,[status(thm)],[])).
% 94.17/94.34 tff(372,plain,
% 94.17/94.34 ((~(model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)) <=> model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_C_22(uns, eqv)))) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[371, 370])).
% 94.17/94.34 tff(373,plain,
% 94.17/94.34 (model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[372, 362])).
% 94.17/94.34 tff(374,plain,
% 94.17/94.34 (((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))) | (~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))),
% 94.17/94.34 inference(tautology,[status(thm)],[])).
% 94.17/94.34 tff(375,plain,
% 94.17/94.34 ((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[374, 373])).
% 94.17/94.34 tff(376,assumption,(status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)), introduced(assumption)).
% 94.17/94.34 tff(377,plain,
% 94.17/94.34 (((~![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))) | ((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))) | (~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm))),
% 94.17/94.34 inference(rewrite,[status(thm)],[])).
% 94.17/94.34 tff(378,plain,
% 94.17/94.34 ((~![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))) | ((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(379,plain,
% 94.17/94.34 ((~![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | status(Ax, C, thm))) | (~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm)),
% 94.17/94.34 inference(modus_ponens,[status(thm)],[378, 377])).
% 94.17/94.34 tff(380,plain,
% 94.17/94.34 (status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm)),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[379, 222, 376])).
% 94.17/94.34 tff(381,plain,
% 94.17/94.34 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))) | ((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm)) | (~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))) | (~status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm)) | (~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)))),
% 94.17/94.34 inference(rewrite,[status(thm)],[])).
% 94.17/94.34 tff(382,plain,
% 94.17/94.34 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))) | ((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm)) | (~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(383,plain,
% 94.17/94.34 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, wec)))) | (~status(Ax!38, tptp_fun_Ax_23(uns, eqv), thm)) | (~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec))),
% 94.17/94.34 inference(modus_ponens,[status(thm)],[382, 381])).
% 94.17/94.34 tff(384,plain,
% 94.17/94.34 ($false),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[383, 257, 376, 380])).
% 94.17/94.34 tff(385,plain,(~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)), inference(lemma,lemma(discharge,[]))).
% 94.17/94.34 tff(386,plain,
% 94.17/94.34 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))))))))))),
% 94.17/94.34 inference(rewrite,[status(thm)],[])).
% 94.17/94.34 tff(387,plain,
% 94.17/94.34 ((~((~(status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~(model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~model(tptp_fun_I1_0(Ax!38), Ax!38)) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))))))))) <=> (~((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))))))))),
% 94.17/94.34 inference(rewrite,[status(thm)],[])).
% 94.17/94.34 tff(388,plain,
% 94.17/94.34 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~(model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~model(tptp_fun_I1_0(Ax!38), Ax!38)) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))))))))))),
% 94.17/94.34 inference(monotonicity,[status(thm)],[387])).
% 94.17/94.34 tff(389,plain,
% 94.17/94.34 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~(model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~model(tptp_fun_I1_0(Ax!38), Ax!38)) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))))))))))),
% 94.17/94.34 inference(transitivity,[status(thm)],[388, 386])).
% 94.17/94.34 tff(390,plain,
% 94.17/94.34 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~(model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~model(tptp_fun_I1_0(Ax!38), Ax!38)) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv))))))))))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(391,plain,
% 94.17/94.34 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))))))))),
% 94.17/94.34 inference(modus_ponens,[status(thm)],[390, 389])).
% 94.17/94.34 tff(392,plain,
% 94.17/94.34 (~((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv))))))))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[391, 151])).
% 94.17/94.34 tff(393,plain,
% 94.17/94.34 (((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | (~((~status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, tptp_fun_Ax_23(uns, eqv)))) | (~model(tptp_fun_I3_6(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))))))) | (![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))),
% 94.17/94.34 inference(tautology,[status(thm)],[])).
% 94.17/94.34 tff(394,plain,
% 94.17/94.34 (![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[393, 392])).
% 94.17/94.34 tff(395,assumption,(![I1: $i] : (~model(I1, Ax!38))), introduced(assumption)).
% 94.17/94.34 tff(396,plain,
% 94.17/94.34 ((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)))),
% 94.17/94.34 inference(rewrite,[status(thm)],[])).
% 94.17/94.34 tff(397,plain,
% 94.17/94.34 (?[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)))),
% 94.17/94.34 inference(rewrite,[status(thm)],[])).
% 94.17/94.34 tff(398,plain,
% 94.17/94.34 (^[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)))))),
% 94.17/94.34 inference(bind,[status(th)],[])).
% 94.17/94.34 tff(399,plain,
% 94.17/94.34 (?[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)))),
% 94.17/94.34 inference(quant_intro,[status(thm)],[398])).
% 94.17/94.34 tff(400,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')).
% 94.17/94.34 tff(401,plain,
% 94.17/94.34 (?[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)))),
% 94.17/94.34 inference(modus_ponens,[status(thm)],[400, 399])).
% 94.17/94.34 tff(402,plain,
% 94.17/94.34 (?[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)))),
% 94.17/94.34 inference(modus_ponens,[status(thm)],[401, 397])).
% 94.17/94.34 tff(403,plain,
% 94.17/94.34 (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))),
% 94.17/94.34 inference(modus_ponens,[status(thm)],[402, 396])).
% 94.17/94.34 tff(404,plain,
% 94.17/94.34 (model(I1!39, Ax!38)),
% 94.17/94.34 inference(and_elim,[status(thm)],[403])).
% 94.17/94.34 tff(405,plain,
% 94.17/94.34 ((~![I1: $i] : (~model(I1, Ax!38))) | (~model(I1!39, Ax!38))),
% 94.17/94.34 inference(quant_inst,[status(thm)],[])).
% 94.17/94.34 tff(406,plain,
% 94.17/94.34 ($false),
% 94.17/94.34 inference(unit_resolution,[status(thm)],[405, 404, 395])).
% 94.17/94.34 tff(407,plain,(~![I1: $i] : (~model(I1, Ax!38))), inference(lemma,lemma(discharge,[]))).
% 94.17/94.34 tff(408,plain,
% 94.17/94.34 ((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | ![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))),
% 94.17/94.37 inference(tautology,[status(thm)],[])).
% 94.17/94.37 tff(409,plain,
% 94.17/94.37 ((~(![I1: $i] : (~model(I1, Ax!38)) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38)))) | status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))),
% 94.17/94.37 inference(unit_resolution,[status(thm)],[408, 407])).
% 94.17/94.37 tff(410,plain,
% 94.17/94.37 (status(Ax!38, tptp_fun_Ax_23(uns, eqv), wec) | (~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))),
% 94.17/94.37 inference(unit_resolution,[status(thm)],[409, 394])).
% 94.17/94.37 tff(411,plain,
% 94.17/94.37 ((~((~model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), Ax!38)) | model(tptp_fun_I2_7(tptp_fun_Ax_23(uns, eqv), Ax!38), tptp_fun_Ax_23(uns, eqv)))) | ![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))),
% 94.17/94.37 inference(unit_resolution,[status(thm)],[410, 385])).
% 94.17/94.37 tff(412,plain,
% 94.17/94.37 (![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))),
% 94.17/94.37 inference(unit_resolution,[status(thm)],[411, 375])).
% 94.17/94.37 tff(413,plain,
% 94.17/94.37 (~model(I3!40, Ax!38)),
% 94.17/94.37 inference(and_elim,[status(thm)],[403])).
% 94.17/94.37 tff(414,plain,
% 94.17/94.37 (((~![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))) | ((~model(I3!40, tptp_fun_Ax_23(uns, eqv))) | model(I3!40, Ax!38))) <=> ((~![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))) | (~model(I3!40, tptp_fun_Ax_23(uns, eqv))) | model(I3!40, Ax!38))),
% 94.17/94.37 inference(rewrite,[status(thm)],[])).
% 94.17/94.37 tff(415,plain,
% 94.17/94.37 ((~![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))) | ((~model(I3!40, tptp_fun_Ax_23(uns, eqv))) | model(I3!40, Ax!38))),
% 94.17/94.37 inference(quant_inst,[status(thm)],[])).
% 94.17/94.37 tff(416,plain,
% 94.17/94.37 ((~![I3: $i] : ((~model(I3, tptp_fun_Ax_23(uns, eqv))) | model(I3, Ax!38))) | (~model(I3!40, tptp_fun_Ax_23(uns, eqv))) | model(I3!40, Ax!38)),
% 94.17/94.37 inference(modus_ponens,[status(thm)],[415, 414])).
% 94.17/94.37 tff(417,plain,
% 94.17/94.37 ($false),
% 94.17/94.37 inference(unit_resolution,[status(thm)],[416, 413, 412, 360])).
% 94.17/94.37 % SZS output end Proof
% 94.17/94.38 % E exiting
%------------------------------------------------------------------------------