%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS202+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 05:13:34 AM UTC 2025
% Result : Theorem 7.23s 7.43s
% Output : Proof 7.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS202+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:11:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 7.23/7.43 % SZS status Theorem
% 7.23/7.43 % SZS output start Proof
% 7.23/7.43 tff(model_type, type, (
% 7.23/7.43 model: ( $i * $i ) > $o)).
% 7.23/7.43 tff(not_type, type, (
% 7.23/7.43 not: $i > $i)).
% 7.23/7.43 tff(tptp_fun_C_33_type, type, (
% 7.23/7.43 tptp_fun_C_33: $i)).
% 7.23/7.43 tff(tptp_fun_Ax_34_type, type, (
% 7.23/7.43 tptp_fun_Ax_34: $i)).
% 7.23/7.43 tff(status_type, type, (
% 7.23/7.43 status: ( $i * $i * $i ) > $o)).
% 7.23/7.43 tff(thm_type, type, (
% 7.23/7.43 thm: $i)).
% 7.23/7.43 tff(esa_type, type, (
% 7.23/7.43 esa: $i)).
% 7.23/7.43 tff(tptp_fun_I2_1_type, type, (
% 7.23/7.43 tptp_fun_I2_1: $i > $i)).
% 7.23/7.43 tff(tptp_fun_I1_0_type, type, (
% 7.23/7.43 tptp_fun_I1_0: $i > $i)).
% 7.23/7.43 tff(tptp_fun_I1_35_type, type, (
% 7.23/7.43 tptp_fun_I1_35: $i)).
% 7.23/7.43 tff(tptp_fun_I2_36_type, type, (
% 7.23/7.43 tptp_fun_I2_36: $i)).
% 7.23/7.43 tff(tptp_fun_I2_17_type, type, (
% 7.23/7.43 tptp_fun_I2_17: ( $i * $i ) > $i)).
% 7.23/7.43 tff(tptp_fun_C_37_type, type, (
% 7.23/7.43 tptp_fun_C_37: $i)).
% 7.23/7.43 tff(tptp_fun_I1_2_type, type, (
% 7.23/7.43 tptp_fun_I1_2: ( $i * $i ) > $i)).
% 7.23/7.43 tff(noc_type, type, (
% 7.23/7.43 noc: $i)).
% 7.23/7.43 tff(tptp_fun_I2_7_type, type, (
% 7.23/7.43 tptp_fun_I2_7: ( $i * $i ) > $i)).
% 7.23/7.43 tff(tptp_fun_F_29_type, type, (
% 7.23/7.43 tptp_fun_F_29: $i)).
% 7.23/7.43 tff(tptp_fun_Ax_38_type, type, (
% 7.23/7.43 tptp_fun_Ax_38: $i)).
% 7.23/7.43 tff(tptp_fun_I2_31_type, type, (
% 7.23/7.43 tptp_fun_I2_31: $i)).
% 7.23/7.43 tff(nota_type, type, (
% 7.23/7.43 nota: ( $i * $i ) > $o)).
% 7.23/7.43 tff(tptp_fun_C_22_type, type, (
% 7.23/7.43 tptp_fun_C_22: ( $i * $i ) > $i)).
% 7.23/7.43 tff(tptp_fun_Ax_23_type, type, (
% 7.23/7.43 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 7.23/7.43 tff(tptp_fun_I1_39_type, type, (
% 7.23/7.43 tptp_fun_I1_39: $i)).
% 7.23/7.43 tff(tptp_fun_I4_41_type, type, (
% 7.23/7.43 tptp_fun_I4_41: $i)).
% 7.23/7.43 tff(tptp_fun_I3_40_type, type, (
% 7.23/7.43 tptp_fun_I3_40: $i)).
% 7.23/7.43 tff(tptp_fun_I1_3_type, type, (
% 7.23/7.43 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 7.23/7.43 tff(tptp_fun_I1_30_type, type, (
% 7.23/7.43 tptp_fun_I1_30: $i)).
% 7.23/7.43 tff(wth_type, type, (
% 7.23/7.43 wth: $i)).
% 7.23/7.43 tff(tptp_fun_I3_6_type, type, (
% 7.23/7.43 tptp_fun_I3_6: ( $i * $i ) > $i)).
% 7.23/7.43 tff(tptp_fun_I4_12_type, type, (
% 7.23/7.43 tptp_fun_I4_12: $i > $i)).
% 7.23/7.43 tff(1,assumption,((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa)))), introduced(assumption)).
% 7.23/7.43 tff(2,plain,
% 7.23/7.43 (^[Ax: $i, C: $i] : refl((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 7.23/7.43 inference(bind,[status(th)],[])).
% 7.23/7.43 tff(3,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.23/7.43 inference(quant_intro,[status(thm)],[2])).
% 7.23/7.43 tff(4,plain,
% 7.23/7.43 (^[Ax: $i, C: $i] : rewrite((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 7.23/7.43 inference(bind,[status(th)],[])).
% 7.23/7.43 tff(5,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.23/7.43 inference(quant_intro,[status(thm)],[4])).
% 7.23/7.43 tff(6,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.23/7.43 inference(transitivity,[status(thm)],[5, 3])).
% 7.23/7.43 tff(7,plain,
% 7.23/7.43 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) <=> ((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))), rewrite(((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))) <=> ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))), rewrite((((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))))),
% 7.23/7.43 inference(bind,[status(th)],[])).
% 7.23/7.43 tff(8,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.23/7.43 inference(quant_intro,[status(thm)],[7])).
% 7.23/7.43 tff(9,plain,
% 7.23/7.43 (^[Ax: $i, C: $i] : rewrite(((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))),
% 7.23/7.43 inference(bind,[status(th)],[])).
% 7.23/7.43 tff(10,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 7.23/7.43 inference(quant_intro,[status(thm)],[9])).
% 7.23/7.43 tff(11,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 7.23/7.43 inference(rewrite,[status(thm)],[])).
% 7.23/7.43 tff(12,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','esa')).
% 7.23/7.43 tff(13,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 7.23/7.43 inference(modus_ponens,[status(thm)],[12, 11])).
% 7.23/7.43 tff(14,plain,(
% 7.23/7.43 ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa))))),
% 7.23/7.43 inference(skolemize,[status(sab)],[13])).
% 7.23/7.43 tff(15,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 7.23/7.43 inference(modus_ponens,[status(thm)],[14, 10])).
% 7.23/7.43 tff(16,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.23/7.43 inference(modus_ponens,[status(thm)],[15, 8])).
% 7.23/7.43 tff(17,plain,
% 7.23/7.43 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.23/7.43 inference(modus_ponens,[status(thm)],[16, 6])).
% 7.23/7.43 tff(18,plain,
% 7.23/7.43 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))))))),
% 7.23/7.43 inference(rewrite,[status(thm)],[])).
% 7.23/7.43 tff(19,plain,
% 7.23/7.43 ((~((~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))) | (~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))))) <=> (~((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa)))))),
% 7.23/7.43 inference(rewrite,[status(thm)],[])).
% 7.23/7.43 tff(20,plain,
% 7.23/7.43 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))) | (~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33)))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))))))),
% 7.23/7.43 inference(monotonicity,[status(thm)],[19])).
% 7.23/7.43 tff(21,plain,
% 7.23/7.43 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))) | (~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33)))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))))))),
% 7.23/7.43 inference(transitivity,[status(thm)],[20, 18])).
% 7.23/7.43 tff(22,plain,
% 7.23/7.43 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))) | (~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33)))))))))))),
% 7.23/7.43 inference(quant_inst,[status(thm)],[])).
% 7.23/7.43 tff(23,plain,
% 7.23/7.43 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa)))))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[22, 21])).
% 7.23/7.44 tff(24,plain,
% 7.23/7.44 ($false),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[23, 17, 1])).
% 7.23/7.44 tff(25,plain,(~((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.44 tff(26,plain,
% 7.23/7.44 (((~((~status(Ax!34, not(C!33), esa)) | (~((~(model(tptp_fun_I2_1(not(C!33)), not(C!33)) | ![I1: $i] : (~model(I1, Ax!34)))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | ![I2: $i] : (~model(I2, not(C!33))))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa)))) | ((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))),
% 7.23/7.44 inference(tautology,[status(thm)],[])).
% 7.23/7.44 tff(27,plain,
% 7.23/7.44 ((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa)),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[26, 25])).
% 7.23/7.44 tff(28,assumption,(![I1: $i] : (~model(I1, Ax!34))), introduced(assumption)).
% 7.23/7.44 tff(29,plain,
% 7.23/7.44 (((model(I1!35, Ax!34) & model(I1!35, C!33)) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))) <=> (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33))))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(30,plain,
% 7.23/7.44 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C)))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(31,axiom,(?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','sat_non_taut_pair')).
% 7.23/7.44 tff(32,plain,
% 7.23/7.44 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 7.23/7.44 tff(33,plain,
% 7.23/7.44 (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[32, 29])).
% 7.23/7.44 tff(34,plain,
% 7.23/7.44 (model(I1!35, Ax!34)),
% 7.23/7.44 inference(and_elim,[status(thm)],[33])).
% 7.23/7.44 tff(35,plain,
% 7.23/7.44 ((~![I1: $i] : (~model(I1, Ax!34))) | (~model(I1!35, Ax!34))),
% 7.23/7.44 inference(quant_inst,[status(thm)],[])).
% 7.23/7.44 tff(36,plain,
% 7.23/7.44 ($false),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[35, 34, 28])).
% 7.23/7.44 tff(37,plain,(~![I1: $i] : (~model(I1, Ax!34))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.44 tff(38,assumption,(![I2: $i] : (~model(I2, not(C!33)))), introduced(assumption)).
% 7.23/7.44 tff(39,assumption,(~model(tptp_fun_I2_7(C!33, F!29), Ax!38)), introduced(assumption)).
% 7.23/7.44 tff(40,plain,
% 7.23/7.44 (^[I: $i, F: $i] : refl((~(model(I, F) <=> model(I, not(F)))) <=> (~(model(I, F) <=> model(I, not(F)))))),
% 7.23/7.44 inference(bind,[status(th)],[])).
% 7.23/7.44 tff(41,plain,
% 7.23/7.44 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 7.23/7.44 inference(quant_intro,[status(thm)],[40])).
% 7.23/7.44 tff(42,plain,
% 7.23/7.44 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(43,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','completeness')).
% 7.23/7.44 tff(44,plain,
% 7.23/7.44 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 7.23/7.44 tff(45,plain,(
% 7.23/7.44 ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 7.23/7.44 inference(skolemize,[status(sab)],[44])).
% 7.23/7.44 tff(46,plain,
% 7.23/7.44 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[45, 41])).
% 7.23/7.44 tff(47,plain,
% 7.23/7.44 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I2!31, C!33) <=> model(I2!31, not(C!33))))),
% 7.23/7.44 inference(quant_inst,[status(thm)],[])).
% 7.23/7.44 tff(48,plain,
% 7.23/7.44 (~(model(I2!31, C!33) <=> model(I2!31, not(C!33)))),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[47, 46])).
% 7.23/7.44 tff(49,assumption,(~status(not(C!33), Ax!38, thm)), introduced(assumption)).
% 7.23/7.44 tff(50,plain,
% 7.23/7.44 (^[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))))))))),
% 7.23/7.44 inference(bind,[status(th)],[])).
% 7.23/7.44 tff(51,plain,
% 7.23/7.44 (![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)))))))),
% 7.23/7.44 inference(quant_intro,[status(thm)],[50])).
% 7.23/7.44 tff(52,plain,
% 7.23/7.44 (^[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))))))))),
% 7.23/7.44 inference(bind,[status(th)],[])).
% 7.23/7.44 tff(53,plain,
% 7.23/7.44 (![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)))))))),
% 7.23/7.44 inference(quant_intro,[status(thm)],[52])).
% 7.23/7.44 tff(54,plain,
% 7.23/7.44 (![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)))))))),
% 7.23/7.44 inference(transitivity,[status(thm)],[53, 51])).
% 7.23/7.44 tff(55,plain,
% 7.23/7.44 (^[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)))))))))),
% 7.23/7.44 inference(bind,[status(th)],[])).
% 7.23/7.44 tff(56,plain,
% 7.23/7.44 (![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)))))))),
% 7.23/7.44 inference(quant_intro,[status(thm)],[55])).
% 7.23/7.44 tff(57,plain,
% 7.23/7.44 (^[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)))))),
% 7.23/7.44 inference(bind,[status(th)],[])).
% 7.23/7.44 tff(58,plain,
% 7.23/7.44 (![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))))),
% 7.23/7.44 inference(quant_intro,[status(thm)],[57])).
% 7.23/7.44 tff(59,plain,
% 7.23/7.44 (![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))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(60,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')).
% 7.23/7.44 tff(61,plain,
% 7.23/7.44 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 7.23/7.44 tff(62,plain,(
% 7.23/7.44 ![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))))),
% 7.23/7.44 inference(skolemize,[status(sab)],[61])).
% 7.23/7.44 tff(63,plain,
% 7.23/7.44 (![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))))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[62, 58])).
% 7.23/7.44 tff(64,plain,
% 7.23/7.44 (![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)))))))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[63, 56])).
% 7.23/7.44 tff(65,plain,
% 7.23/7.44 (![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)))))))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[64, 54])).
% 7.23/7.44 tff(66,plain,
% 7.23/7.44 ((~![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(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | (~((~nota(esa, thm)) | (~((~status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), esa)) | status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), thm)))))))),
% 7.23/7.44 inference(quant_inst,[status(thm)],[])).
% 7.23/7.44 tff(67,plain,
% 7.23/7.44 (~((~(nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | (~((~nota(esa, thm)) | (~((~status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), esa)) | status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), thm))))))),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[66, 65])).
% 7.23/7.44 tff(68,plain,
% 7.23/7.44 (((~(nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | (~((~nota(esa, thm)) | (~((~status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), esa)) | status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), thm)))))) | (nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))),
% 7.23/7.44 inference(tautology,[status(thm)],[])).
% 7.23/7.44 tff(69,plain,
% 7.23/7.44 (nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 7.23/7.44 tff(70,plain,
% 7.23/7.44 ((~nota(esa, thm)) <=> (~nota(esa, thm))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(71,axiom,(~nota(esa, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nota_esa_thm')).
% 7.23/7.44 tff(72,plain,
% 7.23/7.44 (~nota(esa, thm)),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 7.23/7.44 tff(73,plain,
% 7.23/7.44 ((~(nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))),
% 7.23/7.44 inference(tautology,[status(thm)],[])).
% 7.23/7.44 tff(74,plain,
% 7.23/7.44 ((~(nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[73, 72])).
% 7.23/7.44 tff(75,plain,
% 7.23/7.44 (![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[74, 69])).
% 7.23/7.44 tff(76,plain,
% 7.23/7.44 (((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(not(C!33), Ax!38, esa)) | status(not(C!33), Ax!38, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(not(C!33), Ax!38, esa)) | status(not(C!33), Ax!38, thm))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(77,plain,
% 7.23/7.44 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(not(C!33), Ax!38, esa)) | status(not(C!33), Ax!38, thm))),
% 7.23/7.44 inference(quant_inst,[status(thm)],[])).
% 7.23/7.44 tff(78,plain,
% 7.23/7.44 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(not(C!33), Ax!38, esa)) | status(not(C!33), Ax!38, thm)),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 7.23/7.44 tff(79,plain,
% 7.23/7.44 (~status(not(C!33), Ax!38, esa)),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[78, 75, 49])).
% 7.23/7.44 tff(80,assumption,((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33)))))))))), introduced(assumption)).
% 7.23/7.44 tff(81,plain,
% 7.23/7.44 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33)))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33))))))))))))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(82,plain,
% 7.23/7.44 ((~((~((~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33))))) | (~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))))))))) <=> (~((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33)))))))))))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(83,plain,
% 7.23/7.44 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33))))) | (~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33))))))))))))),
% 7.23/7.44 inference(monotonicity,[status(thm)],[82])).
% 7.23/7.44 tff(84,plain,
% 7.23/7.44 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33))))) | (~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33))))))))))))),
% 7.23/7.44 inference(transitivity,[status(thm)],[83, 81])).
% 7.23/7.44 tff(85,plain,
% 7.23/7.44 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33))))) | (~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38))))))))))),
% 7.23/7.44 inference(quant_inst,[status(thm)],[])).
% 7.23/7.44 tff(86,plain,
% 7.23/7.44 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33)))))))))))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 7.23/7.44 tff(87,plain,
% 7.23/7.44 ($false),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[86, 17, 80])).
% 7.23/7.44 tff(88,plain,(~((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33))))))))))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.44 tff(89,plain,
% 7.23/7.44 (((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~status(not(C!33), Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(not(C!33)), not(C!33)) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(C!33)))))))))) | ((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))),
% 7.23/7.44 inference(tautology,[status(thm)],[])).
% 7.23/7.44 tff(90,plain,
% 7.23/7.44 ((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa)),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[89, 88])).
% 7.23/7.44 tff(91,plain,
% 7.23/7.44 ((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa))) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa)),
% 7.23/7.44 inference(tautology,[status(thm)],[])).
% 7.23/7.44 tff(92,plain,
% 7.23/7.44 ((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(C!33), Ax!38, esa)),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[91, 90])).
% 7.23/7.44 tff(93,plain,
% 7.23/7.44 (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))))),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[92, 79])).
% 7.23/7.44 tff(94,plain,
% 7.23/7.44 (((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38))))) | (![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))),
% 7.23/7.44 inference(tautology,[status(thm)],[])).
% 7.23/7.44 tff(95,plain,
% 7.23/7.44 (![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38))),
% 7.23/7.44 inference(unit_resolution,[status(thm)],[94, 93])).
% 7.23/7.44 tff(96,assumption,(![I2: $i] : (~model(I2, Ax!38))), introduced(assumption)).
% 7.23/7.44 tff(97,plain,
% 7.23/7.44 ((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)))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(98,plain,
% 7.23/7.44 (?[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)))),
% 7.23/7.44 inference(rewrite,[status(thm)],[])).
% 7.23/7.44 tff(99,plain,
% 7.23/7.44 (^[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)))))),
% 7.23/7.44 inference(bind,[status(th)],[])).
% 7.23/7.44 tff(100,plain,
% 7.23/7.44 (?[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)))),
% 7.23/7.44 inference(quant_intro,[status(thm)],[99])).
% 7.23/7.44 tff(101,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')).
% 7.23/7.44 tff(102,plain,
% 7.23/7.44 (?[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)))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 7.23/7.44 tff(103,plain,
% 7.23/7.44 (?[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)))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[102, 98])).
% 7.23/7.44 tff(104,plain,
% 7.23/7.44 (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))),
% 7.23/7.44 inference(modus_ponens,[status(thm)],[103, 97])).
% 7.23/7.44 tff(105,plain,
% 7.23/7.44 (model(I1!39, Ax!38)),
% 7.23/7.44 inference(and_elim,[status(thm)],[104])).
% 7.23/7.44 tff(106,plain,
% 7.23/7.44 ((~![I2: $i] : (~model(I2, Ax!38))) | (~model(I1!39, Ax!38))),
% 7.23/7.45 inference(quant_inst,[status(thm)],[])).
% 7.23/7.45 tff(107,plain,
% 7.23/7.45 ($false),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[106, 105, 96])).
% 7.23/7.45 tff(108,plain,(~![I2: $i] : (~model(I2, Ax!38))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.45 tff(109,plain,
% 7.23/7.45 ((~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))) | ![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(110,plain,
% 7.23/7.45 ((~(![I1: $i] : (~model(I1, not(C!33))) | ![I2: $i] : (~model(I2, Ax!38)))) | ![I1: $i] : (~model(I1, not(C!33)))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[109, 108])).
% 7.23/7.45 tff(111,plain,
% 7.23/7.45 (![I1: $i] : (~model(I1, not(C!33)))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[110, 95])).
% 7.23/7.45 tff(112,plain,
% 7.23/7.45 (^[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)))))))),
% 7.23/7.45 inference(bind,[status(th)],[])).
% 7.23/7.45 tff(113,plain,
% 7.23/7.45 (![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))))))),
% 7.23/7.45 inference(quant_intro,[status(thm)],[112])).
% 7.23/7.45 tff(114,plain,
% 7.23/7.45 (^[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)))))))),
% 7.23/7.45 inference(bind,[status(th)],[])).
% 7.23/7.45 tff(115,plain,
% 7.23/7.45 (![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))))))),
% 7.23/7.45 inference(quant_intro,[status(thm)],[114])).
% 7.23/7.45 tff(116,plain,
% 7.23/7.45 (^[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)))))))),
% 7.23/7.45 inference(bind,[status(th)],[])).
% 7.23/7.45 tff(117,plain,
% 7.23/7.45 (![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))))))),
% 7.23/7.45 inference(quant_intro,[status(thm)],[116])).
% 7.23/7.45 tff(118,plain,
% 7.23/7.45 (![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))))))),
% 7.23/7.45 inference(transitivity,[status(thm)],[117, 115])).
% 7.23/7.45 tff(119,plain,
% 7.23/7.45 (^[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))))))))),
% 7.23/7.45 inference(bind,[status(th)],[])).
% 7.23/7.45 tff(120,plain,
% 7.23/7.45 (![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))))))),
% 7.23/7.45 inference(quant_intro,[status(thm)],[119])).
% 7.23/7.45 tff(121,plain,
% 7.23/7.45 (![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))),
% 7.23/7.45 inference(rewrite,[status(thm)],[])).
% 7.23/7.45 tff(122,plain,
% 7.23/7.45 (^[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)))),
% 7.23/7.45 inference(bind,[status(th)],[])).
% 7.23/7.45 tff(123,plain,
% 7.23/7.45 (![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))),
% 7.23/7.45 inference(quant_intro,[status(thm)],[122])).
% 7.23/7.45 tff(124,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')).
% 7.23/7.45 tff(125,plain,
% 7.23/7.45 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 7.23/7.45 inference(modus_ponens,[status(thm)],[124, 123])).
% 7.23/7.45 tff(126,plain,
% 7.23/7.45 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 7.23/7.45 inference(modus_ponens,[status(thm)],[125, 121])).
% 7.23/7.45 tff(127,plain,(
% 7.23/7.45 ![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))))),
% 7.23/7.45 inference(skolemize,[status(sab)],[126])).
% 7.23/7.45 tff(128,plain,
% 7.23/7.45 (![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))))))),
% 7.23/7.45 inference(modus_ponens,[status(thm)],[127, 120])).
% 7.23/7.45 tff(129,plain,
% 7.23/7.45 (![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))))))),
% 7.23/7.45 inference(modus_ponens,[status(thm)],[128, 118])).
% 7.23/7.45 tff(130,plain,
% 7.23/7.45 (![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))))))),
% 7.23/7.45 inference(modus_ponens,[status(thm)],[129, 113])).
% 7.23/7.45 tff(131,plain,
% 7.23/7.45 (((~![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(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, 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(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))))))),
% 7.23/7.45 inference(rewrite,[status(thm)],[])).
% 7.23/7.45 tff(132,plain,
% 7.23/7.45 ((~((~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))) | (~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))))) <=> (~((~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm)))))),
% 7.23/7.45 inference(rewrite,[status(thm)],[])).
% 7.23/7.45 tff(133,plain,
% 7.23/7.45 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))) | (~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))))))) <=> ((~![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(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))))))),
% 7.23/7.45 inference(monotonicity,[status(thm)],[132])).
% 7.23/7.45 tff(134,plain,
% 7.23/7.45 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))) | (~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))))))) <=> ((~![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(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))))))),
% 7.23/7.45 inference(transitivity,[status(thm)],[133, 131])).
% 7.23/7.45 tff(135,plain,
% 7.23/7.45 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))) | (~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))))))),
% 7.23/7.45 inference(quant_inst,[status(thm)],[])).
% 7.23/7.45 tff(136,plain,
% 7.23/7.45 ((~![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(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm)))))),
% 7.23/7.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 7.23/7.45 tff(137,plain,
% 7.23/7.45 (~((~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[136, 130])).
% 7.23/7.45 tff(138,plain,
% 7.23/7.45 (((~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm)))) | ((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(139,plain,
% 7.23/7.45 ((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm)),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[138, 137])).
% 7.23/7.45 tff(140,plain,
% 7.23/7.45 ((~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm))) | (~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm)),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(141,plain,
% 7.23/7.45 ((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm)),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[140, 139])).
% 7.23/7.45 tff(142,plain,
% 7.23/7.45 (~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[141, 49])).
% 7.23/7.45 tff(143,plain,
% 7.23/7.45 (((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38)) | model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(144,plain,
% 7.23/7.45 (model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[143, 142])).
% 7.23/7.45 tff(145,plain,
% 7.23/7.45 ((~![I1: $i] : (~model(I1, not(C!33)))) | (~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33)))),
% 7.23/7.45 inference(quant_inst,[status(thm)],[])).
% 7.23/7.45 tff(146,plain,
% 7.23/7.45 ($false),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[145, 144, 111])).
% 7.23/7.45 tff(147,plain,(status(not(C!33), Ax!38, thm)), inference(lemma,lemma(discharge,[]))).
% 7.23/7.45 tff(148,plain,
% 7.23/7.45 (((~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(C!33)), not(C!33))) | model(tptp_fun_I1_3(Ax!38, not(C!33)), Ax!38))) | status(not(C!33), Ax!38, thm)))) | ((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(149,plain,
% 7.23/7.45 ((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[148, 137])).
% 7.23/7.45 tff(150,plain,
% 7.23/7.45 ((~((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38)))) | (~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(151,plain,
% 7.23/7.45 ((~status(not(C!33), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[150, 149])).
% 7.23/7.45 tff(152,plain,
% 7.23/7.45 (![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[151, 147])).
% 7.23/7.45 tff(153,plain,
% 7.23/7.45 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!29, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!29, Ax!38), F!29))) | status(Ax!38, F!29, thm))) | (~((~status(Ax!38, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))))))),
% 7.23/7.45 inference(quant_inst,[status(thm)],[])).
% 7.23/7.45 tff(154,plain,
% 7.23/7.45 (~((~((~((~model(tptp_fun_I1_3(F!29, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!29, Ax!38), F!29))) | status(Ax!38, F!29, thm))) | (~((~status(Ax!38, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29)))))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[153, 130])).
% 7.23/7.45 tff(155,plain,
% 7.23/7.45 (((~((~((~model(tptp_fun_I1_3(F!29, Ax!38), Ax!38)) | model(tptp_fun_I1_3(F!29, Ax!38), F!29))) | status(Ax!38, F!29, thm))) | (~((~status(Ax!38, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))))) | ((~status(Ax!38, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29)))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(156,plain,
% 7.23/7.45 ((~status(Ax!38, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[155, 154])).
% 7.23/7.45 tff(157,assumption,(![I1: $i] : (~model(I1, Ax!38))), introduced(assumption)).
% 7.23/7.45 tff(158,plain,
% 7.23/7.45 ((~![I1: $i] : (~model(I1, Ax!38))) | (~model(I1!39, Ax!38))),
% 7.23/7.45 inference(quant_inst,[status(thm)],[])).
% 7.23/7.45 tff(159,plain,
% 7.23/7.45 ($false),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[158, 105, 157])).
% 7.23/7.45 tff(160,plain,(~![I1: $i] : (~model(I1, Ax!38))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.45 tff(161,assumption,(![I2: $i] : (~model(I2, F!29))), introduced(assumption)).
% 7.23/7.45 tff(162,plain,
% 7.23/7.45 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 7.23/7.45 inference(rewrite,[status(thm)],[])).
% 7.23/7.45 tff(163,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 7.23/7.45 tff(164,plain,
% 7.23/7.45 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 7.23/7.45 inference(modus_ponens,[status(thm)],[163, 162])).
% 7.23/7.45 tff(165,plain,
% 7.23/7.45 (model(I1!30, F!29)),
% 7.23/7.45 inference(and_elim,[status(thm)],[164])).
% 7.23/7.45 tff(166,plain,
% 7.23/7.45 ((~![I2: $i] : (~model(I2, F!29))) | (~model(I1!30, F!29))),
% 7.23/7.45 inference(quant_inst,[status(thm)],[])).
% 7.23/7.45 tff(167,plain,
% 7.23/7.45 ($false),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[166, 165, 161])).
% 7.23/7.45 tff(168,plain,(~![I2: $i] : (~model(I2, F!29))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.45 tff(169,plain,
% 7.23/7.45 ((~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(170,plain,
% 7.23/7.45 ((~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))) | ![I1: $i] : (~model(I1, Ax!38))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[169, 168])).
% 7.23/7.45 tff(171,plain,
% 7.23/7.45 (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[170, 160])).
% 7.23/7.45 tff(172,plain,
% 7.23/7.45 (((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29))))) | (![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(173,plain,
% 7.23/7.45 ((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29))))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[172, 171])).
% 7.23/7.45 tff(174,plain,
% 7.23/7.45 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))))))),
% 7.23/7.45 inference(rewrite,[status(thm)],[])).
% 7.23/7.45 tff(175,plain,
% 7.23/7.45 ((~((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))) | (~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))))) <=> (~((~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa)))))),
% 7.23/7.45 inference(rewrite,[status(thm)],[])).
% 7.23/7.45 tff(176,plain,
% 7.23/7.45 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))) | (~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))))))),
% 7.23/7.45 inference(monotonicity,[status(thm)],[175])).
% 7.23/7.45 tff(177,plain,
% 7.23/7.45 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))) | (~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))))))),
% 7.23/7.45 inference(transitivity,[status(thm)],[176, 174])).
% 7.23/7.45 tff(178,plain,
% 7.23/7.45 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))) | (~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29))))))))))),
% 7.23/7.45 inference(quant_inst,[status(thm)],[])).
% 7.23/7.45 tff(179,plain,
% 7.23/7.45 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa)))))),
% 7.23/7.45 inference(modus_ponens,[status(thm)],[178, 177])).
% 7.23/7.45 tff(180,plain,
% 7.23/7.45 (~((~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))))),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[179, 17])).
% 7.23/7.45 tff(181,plain,
% 7.23/7.45 (((~((~status(Ax!38, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, Ax!38)))) | (~(model(tptp_fun_I1_0(Ax!38), Ax!38) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa)))) | ((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))),
% 7.23/7.45 inference(tautology,[status(thm)],[])).
% 7.23/7.45 tff(182,plain,
% 7.23/7.45 ((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa)),
% 7.23/7.45 inference(unit_resolution,[status(thm)],[181, 180])).
% 7.23/7.45 tff(183,plain,
% 7.23/7.45 ((~((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa))) | (~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa)),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(184,plain,
% 7.23/7.46 ((~((~(model(tptp_fun_I1_0(Ax!38), Ax!38) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, Ax!38)) | ![I2: $i] : (~model(I2, F!29)))))) | status(Ax!38, F!29, esa)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[183, 182])).
% 7.23/7.46 tff(185,plain,
% 7.23/7.46 (status(Ax!38, F!29, esa)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[184, 173])).
% 7.23/7.46 tff(186,plain,
% 7.23/7.46 (((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(Ax!38, F!29, esa)) | status(Ax!38, F!29, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(Ax!38, F!29, esa)) | status(Ax!38, F!29, thm))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(187,plain,
% 7.23/7.46 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(Ax!38, F!29, esa)) | status(Ax!38, F!29, thm))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(188,plain,
% 7.23/7.46 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(Ax!38, F!29, esa)) | status(Ax!38, F!29, thm)),
% 7.23/7.46 inference(modus_ponens,[status(thm)],[187, 186])).
% 7.23/7.46 tff(189,plain,
% 7.23/7.46 (status(Ax!38, F!29, thm)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[188, 75, 185])).
% 7.23/7.46 tff(190,plain,
% 7.23/7.46 ((~((~status(Ax!38, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29)))) | (~status(Ax!38, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(191,plain,
% 7.23/7.46 ((~((~status(Ax!38, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29)))) | ![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[190, 189])).
% 7.23/7.46 tff(192,plain,
% 7.23/7.46 (![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[191, 156])).
% 7.23/7.46 tff(193,plain,
% 7.23/7.46 (~model(I2!31, F!29)),
% 7.23/7.46 inference(and_elim,[status(thm)],[164])).
% 7.23/7.46 tff(194,plain,
% 7.23/7.46 (((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | ((~model(I2!31, Ax!38)) | model(I2!31, F!29))) <=> ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | (~model(I2!31, Ax!38)) | model(I2!31, F!29))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(195,plain,
% 7.23/7.46 ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | ((~model(I2!31, Ax!38)) | model(I2!31, F!29))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(196,plain,
% 7.23/7.46 ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | (~model(I2!31, Ax!38)) | model(I2!31, F!29)),
% 7.23/7.46 inference(modus_ponens,[status(thm)],[195, 194])).
% 7.23/7.46 tff(197,plain,
% 7.23/7.46 (~model(I2!31, Ax!38)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[196, 193, 192])).
% 7.23/7.46 tff(198,plain,
% 7.23/7.46 (((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(I2!31, not(C!33))) | model(I2!31, Ax!38))) <=> ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(I2!31, not(C!33))) | model(I2!31, Ax!38))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(199,plain,
% 7.23/7.46 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(I2!31, not(C!33))) | model(I2!31, Ax!38))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(200,plain,
% 7.23/7.46 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(I2!31, not(C!33))) | model(I2!31, Ax!38)),
% 7.23/7.46 inference(modus_ponens,[status(thm)],[199, 198])).
% 7.23/7.46 tff(201,plain,
% 7.23/7.46 (~model(I2!31, not(C!33))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[200, 197, 152])).
% 7.23/7.46 tff(202,plain,
% 7.23/7.46 ((model(I2!31, C!33) <=> model(I2!31, not(C!33))) | model(I2!31, C!33) | model(I2!31, not(C!33))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(203,plain,
% 7.23/7.46 ((model(I2!31, C!33) <=> model(I2!31, not(C!33))) | model(I2!31, C!33)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[202, 201])).
% 7.23/7.46 tff(204,plain,
% 7.23/7.46 (model(I2!31, C!33)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[203, 48])).
% 7.23/7.46 tff(205,assumption,(![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29))), introduced(assumption)).
% 7.23/7.46 tff(206,plain,
% 7.23/7.46 (((~![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29))) | ((~model(I2!31, C!33)) | model(I2!31, F!29))) <=> ((~![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29))) | (~model(I2!31, C!33)) | model(I2!31, F!29))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(207,plain,
% 7.23/7.46 ((~![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29))) | ((~model(I2!31, C!33)) | model(I2!31, F!29))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(208,plain,
% 7.23/7.46 ((~![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29))) | (~model(I2!31, C!33)) | model(I2!31, F!29)),
% 7.23/7.46 inference(modus_ponens,[status(thm)],[207, 206])).
% 7.23/7.46 tff(209,plain,
% 7.23/7.46 ($false),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[208, 193, 205, 204])).
% 7.23/7.46 tff(210,plain,(~![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.46 tff(211,assumption,(![I4: $i] : model(I4, C!33)), introduced(assumption)).
% 7.23/7.46 tff(212,assumption,(~status(F!29, Ax!34, thm)), introduced(assumption)).
% 7.23/7.46 tff(213,plain,
% 7.23/7.46 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))) | (~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))))))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(214,plain,
% 7.23/7.46 (~((~((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))) | (~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34)))))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[213, 130])).
% 7.23/7.46 tff(215,plain,
% 7.23/7.46 (((~((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))) | (~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))))) | ((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(216,plain,
% 7.23/7.46 ((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[215, 214])).
% 7.23/7.46 tff(217,plain,
% 7.23/7.46 ((~((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))) | (~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm)),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(218,plain,
% 7.23/7.46 ((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[217, 216])).
% 7.23/7.46 tff(219,plain,
% 7.23/7.46 (~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[218, 212])).
% 7.23/7.46 tff(220,plain,
% 7.23/7.46 (((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34)) | model(tptp_fun_I1_3(Ax!34, F!29), F!29)),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(221,plain,
% 7.23/7.46 (model(tptp_fun_I1_3(Ax!34, F!29), F!29)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[220, 219])).
% 7.23/7.46 tff(222,assumption,(status(F!29, Ax!34, esa)), introduced(assumption)).
% 7.23/7.46 tff(223,plain,
% 7.23/7.46 (((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(F!29, Ax!34, esa)) | status(F!29, Ax!34, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(F!29, Ax!34, esa)) | status(F!29, Ax!34, thm))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(224,plain,
% 7.23/7.46 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(F!29, Ax!34, esa)) | status(F!29, Ax!34, thm))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(225,plain,
% 7.23/7.46 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(F!29, Ax!34, esa)) | status(F!29, Ax!34, thm)),
% 7.23/7.46 inference(modus_ponens,[status(thm)],[224, 223])).
% 7.23/7.46 tff(226,plain,
% 7.23/7.46 ($false),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[225, 75, 212, 222])).
% 7.23/7.46 tff(227,plain,(status(F!29, Ax!34, thm) | (~status(F!29, Ax!34, esa))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.46 tff(228,plain,
% 7.23/7.46 (~status(F!29, Ax!34, esa)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[227, 212])).
% 7.23/7.46 tff(229,assumption,((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29))))))))), introduced(assumption)).
% 7.23/7.46 tff(230,plain,
% 7.23/7.46 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29)))))))))))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(231,plain,
% 7.23/7.46 ((~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29)))) | (~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29))))))))))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(232,plain,
% 7.23/7.46 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29)))) | (~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29)))))))))))),
% 7.23/7.46 inference(monotonicity,[status(thm)],[231])).
% 7.23/7.46 tff(233,plain,
% 7.23/7.46 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29)))) | (~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29)))))))))))),
% 7.23/7.46 inference(transitivity,[status(thm)],[232, 230])).
% 7.23/7.46 tff(234,plain,
% 7.23/7.46 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29)))) | (~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34))))))))))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(235,plain,
% 7.23/7.46 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29))))))))))),
% 7.23/7.46 inference(modus_ponens,[status(thm)],[234, 233])).
% 7.23/7.46 tff(236,plain,
% 7.23/7.46 ($false),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[235, 17, 229])).
% 7.23/7.46 tff(237,plain,(~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29)))))))))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.46 tff(238,plain,
% 7.23/7.46 (((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~status(F!29, Ax!34, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!34)))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, F!29))))))))) | ((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(239,plain,
% 7.23/7.46 ((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[238, 237])).
% 7.23/7.46 tff(240,plain,
% 7.23/7.46 ((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa))) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa)),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(241,plain,
% 7.23/7.46 ((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))) | status(F!29, Ax!34, esa)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[240, 239])).
% 7.23/7.46 tff(242,plain,
% 7.23/7.46 (~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[241, 228])).
% 7.23/7.46 tff(243,plain,
% 7.23/7.46 (((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!34), Ax!34))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34))))) | (![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(244,plain,
% 7.23/7.46 (![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[243, 242])).
% 7.23/7.46 tff(245,assumption,(![I2: $i] : (~model(I2, Ax!34))), introduced(assumption)).
% 7.23/7.46 tff(246,plain,
% 7.23/7.46 ((~![I2: $i] : (~model(I2, Ax!34))) | (~model(I1!35, Ax!34))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(247,plain,
% 7.23/7.46 ($false),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[246, 34, 245])).
% 7.23/7.46 tff(248,plain,(~![I2: $i] : (~model(I2, Ax!34))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.46 tff(249,plain,
% 7.23/7.46 ((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(250,plain,
% 7.23/7.46 ((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!34)))) | ![I1: $i] : (~model(I1, F!29))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[249, 248])).
% 7.23/7.46 tff(251,plain,
% 7.23/7.46 (![I1: $i] : (~model(I1, F!29))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[250, 244])).
% 7.23/7.46 tff(252,plain,
% 7.23/7.46 ((~![I1: $i] : (~model(I1, F!29))) | (~model(tptp_fun_I1_3(Ax!34, F!29), F!29))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(253,plain,
% 7.23/7.46 ($false),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[252, 251, 221])).
% 7.23/7.46 tff(254,plain,(status(F!29, Ax!34, thm)), inference(lemma,lemma(discharge,[]))).
% 7.23/7.46 tff(255,plain,
% 7.23/7.46 (((~((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))) | (~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))))) | ((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34)))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(256,plain,
% 7.23/7.46 ((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[255, 214])).
% 7.23/7.46 tff(257,plain,
% 7.23/7.46 ((~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34)))) | (~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(258,plain,
% 7.23/7.46 ((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[257, 256])).
% 7.23/7.46 tff(259,plain,
% 7.23/7.46 (![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[258, 254])).
% 7.23/7.46 tff(260,assumption,(~model(I2!36, Ax!34)), introduced(assumption)).
% 7.23/7.46 tff(261,plain,
% 7.23/7.46 (((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | ((~model(I2!36, F!29)) | model(I2!36, Ax!34))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | (~model(I2!36, F!29)) | model(I2!36, Ax!34))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(262,plain,
% 7.23/7.46 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | ((~model(I2!36, F!29)) | model(I2!36, Ax!34))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(263,plain,
% 7.23/7.46 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | (~model(I2!36, F!29)) | model(I2!36, Ax!34)),
% 7.23/7.46 inference(modus_ponens,[status(thm)],[262, 261])).
% 7.23/7.46 tff(264,plain,
% 7.23/7.46 (~model(I2!36, F!29)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[263, 260, 259])).
% 7.23/7.46 tff(265,plain,
% 7.23/7.46 (((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | ((~model(I2!36, Ax!38)) | model(I2!36, F!29))) <=> ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | (~model(I2!36, Ax!38)) | model(I2!36, F!29))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(266,plain,
% 7.23/7.46 ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | ((~model(I2!36, Ax!38)) | model(I2!36, F!29))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(267,plain,
% 7.23/7.46 ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | (~model(I2!36, Ax!38)) | model(I2!36, F!29)),
% 7.23/7.46 inference(modus_ponens,[status(thm)],[266, 265])).
% 7.23/7.46 tff(268,plain,
% 7.23/7.46 (~model(I2!36, Ax!38)),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[267, 192, 264])).
% 7.23/7.46 tff(269,assumption,(model(I2!36, Ax!34) <=> model(I2!36, not(Ax!34))), introduced(assumption)).
% 7.23/7.46 tff(270,plain,
% 7.23/7.46 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I2!36, Ax!34) <=> model(I2!36, not(Ax!34))))),
% 7.23/7.46 inference(quant_inst,[status(thm)],[])).
% 7.23/7.46 tff(271,plain,
% 7.23/7.46 ($false),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[270, 46, 269])).
% 7.23/7.46 tff(272,plain,(~(model(I2!36, Ax!34) <=> model(I2!36, not(Ax!34)))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.46 tff(273,plain,
% 7.23/7.46 ((model(I2!36, Ax!34) <=> model(I2!36, not(Ax!34))) | model(I2!36, Ax!34) | model(I2!36, not(Ax!34))),
% 7.23/7.46 inference(tautology,[status(thm)],[])).
% 7.23/7.46 tff(274,plain,
% 7.23/7.46 (model(I2!36, not(Ax!34))),
% 7.23/7.46 inference(unit_resolution,[status(thm)],[273, 260, 272])).
% 7.23/7.46 tff(275,assumption,(~status(not(Ax!34), Ax!38, thm)), introduced(assumption)).
% 7.23/7.46 tff(276,plain,
% 7.23/7.46 (((~![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(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, 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(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))))))),
% 7.23/7.46 inference(rewrite,[status(thm)],[])).
% 7.23/7.46 tff(277,plain,
% 7.23/7.46 ((~((~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))) | (~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))))) <=> (~((~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm)))))),
% 7.23/7.47 inference(rewrite,[status(thm)],[])).
% 7.23/7.47 tff(278,plain,
% 7.23/7.47 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))) | (~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))))))) <=> ((~![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(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))))))),
% 7.23/7.47 inference(monotonicity,[status(thm)],[277])).
% 7.23/7.47 tff(279,plain,
% 7.23/7.47 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))) | (~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))))))) <=> ((~![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(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))))))),
% 7.23/7.47 inference(transitivity,[status(thm)],[278, 276])).
% 7.23/7.47 tff(280,plain,
% 7.23/7.47 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))) | (~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))))))),
% 7.23/7.47 inference(quant_inst,[status(thm)],[])).
% 7.23/7.47 tff(281,plain,
% 7.23/7.47 ((~![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(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm)))))),
% 7.23/7.47 inference(modus_ponens,[status(thm)],[280, 279])).
% 7.23/7.47 tff(282,plain,
% 7.23/7.47 (~((~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))))),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[281, 130])).
% 7.23/7.47 tff(283,plain,
% 7.23/7.47 (((~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm)))) | ((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))),
% 7.23/7.47 inference(tautology,[status(thm)],[])).
% 7.23/7.47 tff(284,plain,
% 7.23/7.47 ((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm)),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[283, 282])).
% 7.23/7.47 tff(285,plain,
% 7.23/7.47 ((~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm))) | (~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm)),
% 7.23/7.47 inference(tautology,[status(thm)],[])).
% 7.23/7.47 tff(286,plain,
% 7.23/7.47 ((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm)),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[285, 284])).
% 7.23/7.47 tff(287,plain,
% 7.23/7.47 (~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[286, 275])).
% 7.23/7.47 tff(288,plain,
% 7.23/7.47 (((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38)) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))),
% 7.23/7.47 inference(tautology,[status(thm)],[])).
% 7.23/7.47 tff(289,plain,
% 7.23/7.47 (model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[288, 287])).
% 7.23/7.47 tff(290,assumption,(![I1: $i] : (~model(I1, not(Ax!34)))), introduced(assumption)).
% 7.23/7.47 tff(291,assumption,(model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))), introduced(assumption)).
% 7.23/7.47 tff(292,plain,
% 7.23/7.47 ((~![I1: $i] : (~model(I1, not(Ax!34)))) | (~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34)))),
% 7.23/7.47 inference(quant_inst,[status(thm)],[])).
% 7.23/7.47 tff(293,plain,
% 7.23/7.47 ($false),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[292, 291, 290])).
% 7.23/7.47 tff(294,plain,((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | (~![I1: $i] : (~model(I1, not(Ax!34))))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.47 tff(295,plain,
% 7.23/7.47 (~![I1: $i] : (~model(I1, not(Ax!34)))),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[294, 289])).
% 7.23/7.47 tff(296,assumption,(status(not(Ax!34), Ax!38, esa)), introduced(assumption)).
% 7.23/7.47 tff(297,plain,
% 7.23/7.47 (((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(not(Ax!34), Ax!38, esa)) | status(not(Ax!34), Ax!38, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(not(Ax!34), Ax!38, esa)) | status(not(Ax!34), Ax!38, thm))),
% 7.23/7.47 inference(rewrite,[status(thm)],[])).
% 7.23/7.47 tff(298,plain,
% 7.23/7.47 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(not(Ax!34), Ax!38, esa)) | status(not(Ax!34), Ax!38, thm))),
% 7.23/7.47 inference(quant_inst,[status(thm)],[])).
% 7.23/7.47 tff(299,plain,
% 7.23/7.47 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(not(Ax!34), Ax!38, esa)) | status(not(Ax!34), Ax!38, thm)),
% 7.23/7.47 inference(modus_ponens,[status(thm)],[298, 297])).
% 7.23/7.47 tff(300,plain,
% 7.23/7.47 ($false),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[299, 75, 275, 296])).
% 7.23/7.47 tff(301,plain,(status(not(Ax!34), Ax!38, thm) | (~status(not(Ax!34), Ax!38, esa))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.47 tff(302,plain,
% 7.23/7.47 (~status(not(Ax!34), Ax!38, esa)),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[301, 275])).
% 7.23/7.47 tff(303,assumption,((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa)))), introduced(assumption)).
% 7.23/7.47 tff(304,plain,
% 7.23/7.47 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))))))),
% 7.23/7.47 inference(rewrite,[status(thm)],[])).
% 7.23/7.47 tff(305,plain,
% 7.23/7.47 ((~((~((~((~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))) | (~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))))) <=> (~((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa)))))),
% 7.23/7.47 inference(rewrite,[status(thm)],[])).
% 7.23/7.47 tff(306,plain,
% 7.23/7.47 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))) | (~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))))))),
% 7.23/7.47 inference(monotonicity,[status(thm)],[305])).
% 7.23/7.47 tff(307,plain,
% 7.23/7.47 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))) | (~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))))))),
% 7.23/7.47 inference(transitivity,[status(thm)],[306, 304])).
% 7.23/7.47 tff(308,plain,
% 7.23/7.47 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))) | (~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38))))))))))),
% 7.23/7.47 inference(quant_inst,[status(thm)],[])).
% 7.23/7.47 tff(309,plain,
% 7.23/7.47 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa)))))),
% 7.23/7.47 inference(modus_ponens,[status(thm)],[308, 307])).
% 7.23/7.47 tff(310,plain,
% 7.23/7.47 ($false),
% 7.23/7.47 inference(unit_resolution,[status(thm)],[309, 17, 303])).
% 7.23/7.47 tff(311,plain,(~((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))))), inference(lemma,lemma(discharge,[]))).
% 7.23/7.47 tff(312,plain,
% 7.23/7.47 (((~((~status(not(Ax!34), Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, not(Ax!34))))) | (~(model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)) | ![I2: $i] : (~model(I2, Ax!38)))))))) | (~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa)))) | ((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(313,plain,
% 7.31/7.47 ((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa)),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[312, 311])).
% 7.31/7.47 tff(314,plain,
% 7.31/7.47 ((~((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa))) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa)),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(315,plain,
% 7.31/7.47 ((~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(not(Ax!34), Ax!38, esa)),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[314, 313])).
% 7.31/7.47 tff(316,plain,
% 7.31/7.47 (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))))),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[315, 302])).
% 7.31/7.47 tff(317,plain,
% 7.31/7.47 (((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | model(tptp_fun_I1_0(not(Ax!34)), not(Ax!34)))) | (~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38))))) | (![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(318,plain,
% 7.31/7.47 (![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38))),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[317, 316])).
% 7.31/7.47 tff(319,plain,
% 7.31/7.47 ((~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))) | ![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38))),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(320,plain,
% 7.31/7.47 ((~(![I1: $i] : (~model(I1, not(Ax!34))) | ![I2: $i] : (~model(I2, Ax!38)))) | ![I1: $i] : (~model(I1, not(Ax!34)))),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[319, 108])).
% 7.31/7.47 tff(321,plain,
% 7.31/7.47 ($false),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[320, 318, 295])).
% 7.31/7.47 tff(322,plain,(status(not(Ax!34), Ax!38, thm)), inference(lemma,lemma(discharge,[]))).
% 7.31/7.47 tff(323,plain,
% 7.31/7.47 (((~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~((~((~model(tptp_fun_I1_3(Ax!38, not(Ax!34)), not(Ax!34))) | model(tptp_fun_I1_3(Ax!38, not(Ax!34)), Ax!38))) | status(not(Ax!34), Ax!38, thm)))) | ((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(324,plain,
% 7.31/7.47 ((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[323, 282])).
% 7.31/7.47 tff(325,plain,
% 7.31/7.47 ((~((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38)))) | (~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(326,plain,
% 7.31/7.47 ((~status(not(Ax!34), Ax!38, thm)) | ![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[325, 324])).
% 7.31/7.47 tff(327,plain,
% 7.31/7.47 (![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[326, 322])).
% 7.31/7.47 tff(328,plain,
% 7.31/7.47 (((~![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))) | ((~model(I2!36, not(Ax!34))) | model(I2!36, Ax!38))) <=> ((~![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))) | (~model(I2!36, not(Ax!34))) | model(I2!36, Ax!38))),
% 7.31/7.47 inference(rewrite,[status(thm)],[])).
% 7.31/7.47 tff(329,plain,
% 7.31/7.47 ((~![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))) | ((~model(I2!36, not(Ax!34))) | model(I2!36, Ax!38))),
% 7.31/7.47 inference(quant_inst,[status(thm)],[])).
% 7.31/7.47 tff(330,plain,
% 7.31/7.47 ((~![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))) | (~model(I2!36, not(Ax!34))) | model(I2!36, Ax!38)),
% 7.31/7.47 inference(modus_ponens,[status(thm)],[329, 328])).
% 7.31/7.47 tff(331,plain,
% 7.31/7.47 ($false),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[330, 327, 274, 268])).
% 7.31/7.47 tff(332,plain,(model(I2!36, Ax!34)), inference(lemma,lemma(discharge,[]))).
% 7.31/7.47 tff(333,plain,
% 7.31/7.47 ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33))),
% 7.31/7.47 inference(and_elim,[status(thm)],[33])).
% 7.31/7.47 tff(334,plain,
% 7.31/7.47 (~model(I2!36, C!33)),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[333, 332])).
% 7.31/7.47 tff(335,plain,
% 7.31/7.47 ((~![I4: $i] : model(I4, C!33)) | model(I2!36, C!33)),
% 7.31/7.47 inference(quant_inst,[status(thm)],[])).
% 7.31/7.47 tff(336,plain,
% 7.31/7.47 ($false),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[335, 334, 211])).
% 7.31/7.47 tff(337,plain,(~![I4: $i] : model(I4, C!33)), inference(lemma,lemma(discharge,[]))).
% 7.31/7.47 tff(338,assumption,(~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))))), introduced(assumption)).
% 7.31/7.47 tff(339,plain,
% 7.31/7.47 (((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))) | ![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(340,plain,
% 7.31/7.47 (![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[339, 338])).
% 7.31/7.47 tff(341,plain,
% 7.31/7.47 (((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))) | (~model(tptp_fun_I4_12(C!33), C!33))),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(342,plain,
% 7.31/7.47 (~model(tptp_fun_I4_12(C!33), C!33)),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[341, 338])).
% 7.31/7.47 tff(343,plain,
% 7.31/7.47 (((~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))) | ((~model(tptp_fun_I4_12(C!33), F!29)) | model(tptp_fun_I4_12(C!33), C!33))) <=> ((~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))) | (~model(tptp_fun_I4_12(C!33), F!29)) | model(tptp_fun_I4_12(C!33), C!33))),
% 7.31/7.47 inference(rewrite,[status(thm)],[])).
% 7.31/7.47 tff(344,plain,
% 7.31/7.47 ((~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))) | ((~model(tptp_fun_I4_12(C!33), F!29)) | model(tptp_fun_I4_12(C!33), C!33))),
% 7.31/7.47 inference(quant_inst,[status(thm)],[])).
% 7.31/7.47 tff(345,plain,
% 7.31/7.47 ((~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))) | (~model(tptp_fun_I4_12(C!33), F!29)) | model(tptp_fun_I4_12(C!33), C!33)),
% 7.31/7.47 inference(modus_ponens,[status(thm)],[344, 343])).
% 7.31/7.47 tff(346,plain,
% 7.31/7.47 (~model(tptp_fun_I4_12(C!33), F!29)),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[345, 342, 340])).
% 7.31/7.47 tff(347,plain,
% 7.31/7.47 (((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | ((~model(tptp_fun_I4_12(C!33), Ax!38)) | model(tptp_fun_I4_12(C!33), F!29))) <=> ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | (~model(tptp_fun_I4_12(C!33), Ax!38)) | model(tptp_fun_I4_12(C!33), F!29))),
% 7.31/7.47 inference(rewrite,[status(thm)],[])).
% 7.31/7.47 tff(348,plain,
% 7.31/7.47 ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | ((~model(tptp_fun_I4_12(C!33), Ax!38)) | model(tptp_fun_I4_12(C!33), F!29))),
% 7.31/7.47 inference(quant_inst,[status(thm)],[])).
% 7.31/7.47 tff(349,plain,
% 7.31/7.47 ((~![I1: $i] : ((~model(I1, Ax!38)) | model(I1, F!29))) | (~model(tptp_fun_I4_12(C!33), Ax!38)) | model(tptp_fun_I4_12(C!33), F!29)),
% 7.31/7.47 inference(modus_ponens,[status(thm)],[348, 347])).
% 7.31/7.47 tff(350,plain,
% 7.31/7.47 (~model(tptp_fun_I4_12(C!33), Ax!38)),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[349, 192, 346])).
% 7.31/7.47 tff(351,assumption,(model(tptp_fun_I4_12(C!33), C!33) <=> model(tptp_fun_I4_12(C!33), not(C!33))), introduced(assumption)).
% 7.31/7.47 tff(352,plain,
% 7.31/7.47 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I4_12(C!33), C!33) <=> model(tptp_fun_I4_12(C!33), not(C!33))))),
% 7.31/7.47 inference(quant_inst,[status(thm)],[])).
% 7.31/7.47 tff(353,plain,
% 7.31/7.47 ($false),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[352, 46, 351])).
% 7.31/7.47 tff(354,plain,(~(model(tptp_fun_I4_12(C!33), C!33) <=> model(tptp_fun_I4_12(C!33), not(C!33)))), inference(lemma,lemma(discharge,[]))).
% 7.31/7.47 tff(355,plain,
% 7.31/7.47 ((model(tptp_fun_I4_12(C!33), C!33) <=> model(tptp_fun_I4_12(C!33), not(C!33))) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I4_12(C!33), not(C!33))),
% 7.31/7.47 inference(tautology,[status(thm)],[])).
% 7.31/7.47 tff(356,plain,
% 7.31/7.47 (model(tptp_fun_I4_12(C!33), not(C!33))),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[355, 342, 354])).
% 7.31/7.47 tff(357,plain,
% 7.31/7.47 (((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(tptp_fun_I4_12(C!33), not(C!33))) | model(tptp_fun_I4_12(C!33), Ax!38))) <=> ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(tptp_fun_I4_12(C!33), not(C!33))) | model(tptp_fun_I4_12(C!33), Ax!38))),
% 7.31/7.47 inference(rewrite,[status(thm)],[])).
% 7.31/7.47 tff(358,plain,
% 7.31/7.47 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(tptp_fun_I4_12(C!33), not(C!33))) | model(tptp_fun_I4_12(C!33), Ax!38))),
% 7.31/7.47 inference(quant_inst,[status(thm)],[])).
% 7.31/7.47 tff(359,plain,
% 7.31/7.47 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(tptp_fun_I4_12(C!33), not(C!33))) | model(tptp_fun_I4_12(C!33), Ax!38)),
% 7.31/7.47 inference(modus_ponens,[status(thm)],[358, 357])).
% 7.31/7.47 tff(360,plain,
% 7.31/7.47 ($false),
% 7.31/7.47 inference(unit_resolution,[status(thm)],[359, 152, 356, 350])).
% 7.31/7.47 tff(361,plain,((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))), inference(lemma,lemma(discharge,[]))).
% 7.31/7.47 tff(362,plain,
% 7.31/7.47 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))))))))))),
% 7.31/7.47 inference(bind,[status(th)],[])).
% 7.31/7.47 tff(363,plain,
% 7.31/7.47 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))),
% 7.31/7.47 inference(quant_intro,[status(thm)],[362])).
% 7.31/7.47 tff(364,plain,
% 7.31/7.47 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))))),
% 7.31/7.48 inference(bind,[status(th)],[])).
% 7.31/7.48 tff(365,plain,
% 7.31/7.48 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 7.31/7.48 inference(quant_intro,[status(thm)],[364])).
% 7.31/7.48 tff(366,plain,
% 7.31/7.48 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))))),
% 7.31/7.48 inference(bind,[status(th)],[])).
% 7.31/7.48 tff(367,plain,
% 7.31/7.48 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 7.31/7.48 inference(quant_intro,[status(thm)],[366])).
% 7.31/7.48 tff(368,plain,
% 7.31/7.48 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 7.31/7.48 inference(transitivity,[status(thm)],[367, 365])).
% 7.31/7.48 tff(369,plain,
% 7.31/7.48 (^[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, wth) | ![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)))) | ![I4: $i] : model(I4, C)) <=> (status(Ax, C, wth) | ![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)) | ![I4: $i] : model(I4, C)))), rewrite((status(Ax, C, wth) | ![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)) | ![I4: $i] : model(I4, C)) <=> (status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))), ((status(Ax, C, wth) | ![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)))) | ![I4: $i] : model(I4, C)) <=> (status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))))), rewrite(((~status(Ax, C, wth)) | (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)) & (~model(tptp_fun_I4_12(C), C)))) <=> ((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))), (((status(Ax, C, wth) | ![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)))) | ![I4: $i] : model(I4, C)) & ((~status(Ax, C, wth)) | (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)) & (~model(tptp_fun_I4_12(C), C))))) <=> ((status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))) & ((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))), rewrite(((status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))) & ((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))) <=> (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))), (((status(Ax, C, wth) | ![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)))) | ![I4: $i] : model(I4, C)) & ((~status(Ax, C, wth)) | (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)) & (~model(tptp_fun_I4_12(C), C))))) <=> (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))))),
% 7.31/7.48 inference(bind,[status(th)],[])).
% 7.31/7.48 tff(370,plain,
% 7.31/7.48 (![Ax: $i, C: $i] : ((status(Ax, C, wth) | ![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)))) | ![I4: $i] : model(I4, C)) & ((~status(Ax, C, wth)) | (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)) & (~model(tptp_fun_I4_12(C), C))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 7.31/7.48 inference(quant_intro,[status(thm)],[369])).
% 7.31/7.48 tff(371,plain,
% 7.31/7.48 (^[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)))) | ![I4: $i] : model(I4, C)) | status(Ax, C, wth)) & ((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))) & (~model(tptp_fun_I4_12(C), C))) | (~status(Ax, C, wth)))) <=> ((status(Ax, C, wth) | ![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)))) | ![I4: $i] : model(I4, C)) & ((~status(Ax, C, wth)) | (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)) & (~model(tptp_fun_I4_12(C), C))))))),
% 7.31/7.48 inference(bind,[status(th)],[])).
% 7.31/7.48 tff(372,plain,
% 7.31/7.48 (![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)))) | ![I4: $i] : model(I4, C)) | status(Ax, C, wth)) & ((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))) & (~model(tptp_fun_I4_12(C), C))) | (~status(Ax, C, wth)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, wth) | ![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)))) | ![I4: $i] : model(I4, C)) & ((~status(Ax, C, wth)) | (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)) & (~model(tptp_fun_I4_12(C), C)))))),
% 7.31/7.48 inference(quant_intro,[status(thm)],[371])).
% 7.31/7.48 tff(373,plain,
% 7.31/7.48 (![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))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth)) <=> ![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))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth))),
% 7.31/7.48 inference(rewrite,[status(thm)],[])).
% 7.31/7.48 tff(374,plain,
% 7.31/7.48 (^[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)))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth)) <=> ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth)))),
% 7.31/7.48 inference(bind,[status(th)],[])).
% 7.31/7.48 tff(375,plain,
% 7.31/7.48 (![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)))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth)) <=> ![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))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth))),
% 7.31/7.48 inference(quant_intro,[status(thm)],[374])).
% 7.31/7.48 tff(376,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)))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','wth')).
% 7.31/7.48 tff(377,plain,
% 7.31/7.48 (![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))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth))),
% 7.31/7.48 inference(modus_ponens,[status(thm)],[376, 375])).
% 7.31/7.48 tff(378,plain,
% 7.31/7.48 (![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))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth))),
% 7.31/7.48 inference(modus_ponens,[status(thm)],[377, 373])).
% 7.31/7.48 tff(379,plain,(
% 7.31/7.48 ![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)))) | ![I4: $i] : model(I4, C)) | status(Ax, C, wth)) & ((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))) & (~model(tptp_fun_I4_12(C), C))) | (~status(Ax, C, wth))))),
% 7.31/7.48 inference(skolemize,[status(sab)],[378])).
% 7.31/7.48 tff(380,plain,
% 7.31/7.48 (![Ax: $i, C: $i] : ((status(Ax, C, wth) | ![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)))) | ![I4: $i] : model(I4, C)) & ((~status(Ax, C, wth)) | (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)) & (~model(tptp_fun_I4_12(C), C)))))),
% 7.31/7.48 inference(modus_ponens,[status(thm)],[379, 372])).
% 7.31/7.48 tff(381,plain,
% 7.31/7.48 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 7.31/7.48 inference(modus_ponens,[status(thm)],[380, 370])).
% 7.31/7.48 tff(382,plain,
% 7.31/7.48 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I4: $i] : model(I4, C) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 7.31/7.48 inference(modus_ponens,[status(thm)],[381, 368])).
% 7.31/7.48 tff(383,plain,
% 7.31/7.48 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))),
% 7.31/7.48 inference(modus_ponens,[status(thm)],[382, 363])).
% 7.31/7.48 tff(384,plain,
% 7.31/7.48 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))))))))))),
% 7.31/7.48 inference(rewrite,[status(thm)],[])).
% 7.31/7.48 tff(385,plain,
% 7.31/7.48 ((~((~(status(F!29, C!33, wth) | (~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33))) | (~((~status(F!29, C!33, wth)) | (~(model(tptp_fun_I3_6(C!33, F!29), F!29) | model(tptp_fun_I4_12(C!33), C!33) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))))))))) <=> (~((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))))))),
% 7.31/7.48 inference(rewrite,[status(thm)],[])).
% 7.31/7.48 tff(386,plain,
% 7.31/7.48 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(F!29, C!33, wth) | (~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33))) | (~((~status(F!29, C!33, wth)) | (~(model(tptp_fun_I3_6(C!33, F!29), F!29) | model(tptp_fun_I4_12(C!33), C!33) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))))))))))),
% 7.31/7.48 inference(monotonicity,[status(thm)],[385])).
% 7.31/7.48 tff(387,plain,
% 7.31/7.48 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(F!29, C!33, wth) | (~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33))) | (~((~status(F!29, C!33, wth)) | (~(model(tptp_fun_I3_6(C!33, F!29), F!29) | model(tptp_fun_I4_12(C!33), C!33) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))))))))))),
% 7.31/7.48 inference(transitivity,[status(thm)],[386, 384])).
% 7.31/7.48 tff(388,plain,
% 7.31/7.48 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(F!29, C!33, wth) | (~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33))) | (~((~status(F!29, C!33, wth)) | (~(model(tptp_fun_I3_6(C!33, F!29), F!29) | model(tptp_fun_I4_12(C!33), C!33) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))))))),
% 7.31/7.48 inference(quant_inst,[status(thm)],[])).
% 7.31/7.48 tff(389,plain,
% 7.31/7.48 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~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)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))))))),
% 7.31/7.48 inference(modus_ponens,[status(thm)],[388, 387])).
% 7.31/7.48 tff(390,plain,
% 7.31/7.48 (~((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))))))))),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[389, 383])).
% 7.31/7.48 tff(391,plain,
% 7.31/7.48 (((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))))) | ((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))))))),
% 7.31/7.48 inference(tautology,[status(thm)],[])).
% 7.31/7.48 tff(392,plain,
% 7.31/7.48 ((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[391, 390])).
% 7.31/7.48 tff(393,plain,
% 7.31/7.48 ((~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33))))))) | (~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))),
% 7.31/7.48 inference(tautology,[status(thm)],[])).
% 7.31/7.48 tff(394,plain,
% 7.31/7.48 ((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[393, 392])).
% 7.31/7.48 tff(395,plain,
% 7.31/7.48 (~status(F!29, C!33, wth)),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[394, 361])).
% 7.31/7.48 tff(396,assumption,(![I1: $i] : (~model(I1, F!29))), introduced(assumption)).
% 7.31/7.48 tff(397,plain,
% 7.31/7.48 ((~![I1: $i] : (~model(I1, F!29))) | (~model(I1!30, F!29))),
% 7.31/7.48 inference(quant_inst,[status(thm)],[])).
% 7.31/7.48 tff(398,plain,
% 7.31/7.48 ($false),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[397, 165, 396])).
% 7.31/7.48 tff(399,plain,(~![I1: $i] : (~model(I1, F!29))), inference(lemma,lemma(discharge,[]))).
% 7.31/7.48 tff(400,plain,
% 7.31/7.48 (((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~status(F!29, C!33, wth)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~model(tptp_fun_I3_6(C!33, F!29), C!33)) | model(tptp_fun_I4_12(C!33), C!33) | model(tptp_fun_I3_6(C!33, F!29), F!29) | (~![I2: $i] : ((~model(I2, F!29)) | model(I2, C!33)))))))) | ((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))),
% 7.31/7.48 inference(tautology,[status(thm)],[])).
% 7.31/7.48 tff(401,plain,
% 7.31/7.48 ((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth)),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[400, 390])).
% 7.31/7.48 tff(402,plain,
% 7.31/7.48 ((~((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth))) | (~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth)),
% 7.31/7.48 inference(tautology,[status(thm)],[])).
% 7.31/7.48 tff(403,plain,
% 7.31/7.48 ((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I1: $i] : (~model(I1, F!29)) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth)),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[402, 401])).
% 7.31/7.48 tff(404,plain,
% 7.31/7.48 ((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33) | status(F!29, C!33, wth)),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[403, 399])).
% 7.31/7.48 tff(405,plain,
% 7.31/7.48 ((~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))) | ![I3: $i] : ((~model(I3, C!33)) | model(I3, F!29)) | ![I4: $i] : model(I4, C!33)),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[404, 395])).
% 7.31/7.48 tff(406,plain,
% 7.31/7.48 (~((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33))),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[405, 337, 210])).
% 7.31/7.48 tff(407,plain,
% 7.31/7.48 (((~model(tptp_fun_I2_7(C!33, F!29), F!29)) | model(tptp_fun_I2_7(C!33, F!29), C!33)) | (~model(tptp_fun_I2_7(C!33, F!29), C!33))),
% 7.31/7.48 inference(tautology,[status(thm)],[])).
% 7.31/7.48 tff(408,plain,
% 7.31/7.48 (~model(tptp_fun_I2_7(C!33, F!29), C!33)),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[407, 406])).
% 7.31/7.48 tff(409,assumption,(model(tptp_fun_I2_7(C!33, F!29), C!33) <=> model(tptp_fun_I2_7(C!33, F!29), not(C!33))), introduced(assumption)).
% 7.31/7.48 tff(410,plain,
% 7.31/7.48 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_7(C!33, F!29), C!33) <=> model(tptp_fun_I2_7(C!33, F!29), not(C!33))))),
% 7.31/7.48 inference(quant_inst,[status(thm)],[])).
% 7.31/7.48 tff(411,plain,
% 7.31/7.48 ($false),
% 7.31/7.48 inference(unit_resolution,[status(thm)],[410, 46, 409])).
% 7.31/7.48 tff(412,plain,(~(model(tptp_fun_I2_7(C!33, F!29), C!33) <=> model(tptp_fun_I2_7(C!33, F!29), not(C!33)))), inference(lemma,lemma(discharge,[]))).
% 7.31/7.48 tff(413,plain,
% 7.31/7.48 ((model(tptp_fun_I2_7(C!33, F!29), C!33) <=> model(tptp_fun_I2_7(C!33, F!29), not(C!33))) | model(tptp_fun_I2_7(C!33, F!29), C!33) | model(tptp_fun_I2_7(C!33, F!29), not(C!33))),
% 7.31/7.49 inference(tautology,[status(thm)],[])).
% 7.31/7.49 tff(414,plain,
% 7.31/7.49 (model(tptp_fun_I2_7(C!33, F!29), C!33) | model(tptp_fun_I2_7(C!33, F!29), not(C!33))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[413, 412])).
% 7.31/7.49 tff(415,plain,
% 7.31/7.49 (model(tptp_fun_I2_7(C!33, F!29), not(C!33))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[414, 408])).
% 7.31/7.49 tff(416,plain,
% 7.31/7.49 (((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(tptp_fun_I2_7(C!33, F!29), not(C!33))) | model(tptp_fun_I2_7(C!33, F!29), Ax!38))) <=> ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(tptp_fun_I2_7(C!33, F!29), not(C!33))) | model(tptp_fun_I2_7(C!33, F!29), Ax!38))),
% 7.31/7.49 inference(rewrite,[status(thm)],[])).
% 7.31/7.49 tff(417,plain,
% 7.31/7.49 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(tptp_fun_I2_7(C!33, F!29), not(C!33))) | model(tptp_fun_I2_7(C!33, F!29), Ax!38))),
% 7.31/7.49 inference(quant_inst,[status(thm)],[])).
% 7.31/7.49 tff(418,plain,
% 7.31/7.49 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(tptp_fun_I2_7(C!33, F!29), not(C!33))) | model(tptp_fun_I2_7(C!33, F!29), Ax!38)),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[417, 416])).
% 7.31/7.49 tff(419,plain,
% 7.31/7.49 ($false),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[418, 152, 415, 39])).
% 7.31/7.49 tff(420,plain,(model(tptp_fun_I2_7(C!33, F!29), Ax!38)), inference(lemma,lemma(discharge,[]))).
% 7.31/7.49 tff(421,assumption,(model(tptp_fun_I2_7(C!33, F!29), Ax!38)), introduced(assumption)).
% 7.31/7.49 tff(422,assumption,(~model(tptp_fun_I2_7(C!33, F!29), C!37)), introduced(assumption)).
% 7.31/7.49 tff(423,plain,
% 7.31/7.49 (^[I2: $i] : refl(((~model(I2, Ax!38)) | model(I2, C!37)) <=> ((~model(I2, Ax!38)) | model(I2, C!37)))),
% 7.31/7.49 inference(bind,[status(th)],[])).
% 7.31/7.49 tff(424,plain,
% 7.31/7.49 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) <=> ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 7.31/7.49 inference(quant_intro,[status(thm)],[423])).
% 7.31/7.49 tff(425,plain,
% 7.31/7.49 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 7.31/7.49 inference(and_elim,[status(thm)],[104])).
% 7.31/7.49 tff(426,plain,
% 7.31/7.49 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[425, 424])).
% 7.31/7.49 tff(427,plain,
% 7.31/7.49 (((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(tptp_fun_I2_7(C!33, F!29), Ax!38)) | model(tptp_fun_I2_7(C!33, F!29), C!37))) <=> ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(tptp_fun_I2_7(C!33, F!29), Ax!38)) | model(tptp_fun_I2_7(C!33, F!29), C!37))),
% 7.31/7.49 inference(rewrite,[status(thm)],[])).
% 7.31/7.49 tff(428,plain,
% 7.31/7.49 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(tptp_fun_I2_7(C!33, F!29), Ax!38)) | model(tptp_fun_I2_7(C!33, F!29), C!37))),
% 7.31/7.49 inference(quant_inst,[status(thm)],[])).
% 7.31/7.49 tff(429,plain,
% 7.31/7.49 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(tptp_fun_I2_7(C!33, F!29), Ax!38)) | model(tptp_fun_I2_7(C!33, F!29), C!37)),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[428, 427])).
% 7.31/7.49 tff(430,plain,
% 7.31/7.49 ($false),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[429, 426, 422, 421])).
% 7.31/7.49 tff(431,plain,((~model(tptp_fun_I2_7(C!33, F!29), Ax!38)) | model(tptp_fun_I2_7(C!33, F!29), C!37)), inference(lemma,lemma(discharge,[]))).
% 7.31/7.49 tff(432,plain,
% 7.31/7.49 (model(tptp_fun_I2_7(C!33, F!29), C!37)),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[431, 420])).
% 7.31/7.49 tff(433,assumption,(model(tptp_fun_I2_7(C!33, F!29), C!37)), introduced(assumption)).
% 7.31/7.49 tff(434,assumption,(model(tptp_fun_I2_7(C!33, F!29), not(C!33))), introduced(assumption)).
% 7.31/7.49 tff(435,assumption,(![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))), introduced(assumption)).
% 7.31/7.49 tff(436,plain,
% 7.31/7.49 (((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | ((~model(tptp_fun_I2_7(C!33, F!29), C!37)) | (~model(tptp_fun_I2_7(C!33, F!29), not(C!33))))) <=> ((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | (~model(tptp_fun_I2_7(C!33, F!29), C!37)) | (~model(tptp_fun_I2_7(C!33, F!29), not(C!33))))),
% 7.31/7.49 inference(rewrite,[status(thm)],[])).
% 7.31/7.49 tff(437,plain,
% 7.31/7.49 ((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | ((~model(tptp_fun_I2_7(C!33, F!29), C!37)) | (~model(tptp_fun_I2_7(C!33, F!29), not(C!33))))),
% 7.31/7.49 inference(quant_inst,[status(thm)],[])).
% 7.31/7.49 tff(438,plain,
% 7.31/7.49 ((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | (~model(tptp_fun_I2_7(C!33, F!29), C!37)) | (~model(tptp_fun_I2_7(C!33, F!29), not(C!33)))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[437, 436])).
% 7.31/7.49 tff(439,plain,
% 7.31/7.49 ($false),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[438, 435, 434, 433])).
% 7.31/7.49 tff(440,plain,((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | (~model(tptp_fun_I2_7(C!33, F!29), not(C!33))) | (~model(tptp_fun_I2_7(C!33, F!29), C!37))), inference(lemma,lemma(discharge,[]))).
% 7.31/7.49 tff(441,plain,
% 7.31/7.49 ((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | (~model(tptp_fun_I2_7(C!33, F!29), C!37))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[440, 415])).
% 7.31/7.49 tff(442,plain,
% 7.31/7.49 (~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[441, 432])).
% 7.31/7.49 tff(443,plain,
% 7.31/7.49 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I3!40, C!33) <=> model(I3!40, not(C!33))))),
% 7.31/7.49 inference(quant_inst,[status(thm)],[])).
% 7.31/7.49 tff(444,plain,
% 7.31/7.49 (~(model(I3!40, C!33) <=> model(I3!40, not(C!33)))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[443, 46])).
% 7.31/7.49 tff(445,plain,
% 7.31/7.49 (~model(I3!40, Ax!38)),
% 7.31/7.49 inference(and_elim,[status(thm)],[104])).
% 7.31/7.49 tff(446,plain,
% 7.31/7.49 (((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(I3!40, not(C!33))) | model(I3!40, Ax!38))) <=> ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(I3!40, not(C!33))) | model(I3!40, Ax!38))),
% 7.31/7.49 inference(rewrite,[status(thm)],[])).
% 7.31/7.49 tff(447,plain,
% 7.31/7.49 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(I3!40, not(C!33))) | model(I3!40, Ax!38))),
% 7.31/7.49 inference(quant_inst,[status(thm)],[])).
% 7.31/7.49 tff(448,plain,
% 7.31/7.49 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(I3!40, not(C!33))) | model(I3!40, Ax!38)),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[447, 446])).
% 7.31/7.49 tff(449,plain,
% 7.31/7.49 (~model(I3!40, not(C!33))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[448, 445, 152])).
% 7.31/7.49 tff(450,plain,
% 7.31/7.49 ((model(I3!40, C!33) <=> model(I3!40, not(C!33))) | model(I3!40, C!33) | model(I3!40, not(C!33))),
% 7.31/7.49 inference(tautology,[status(thm)],[])).
% 7.31/7.49 tff(451,plain,
% 7.31/7.49 ((model(I3!40, C!33) <=> model(I3!40, not(C!33))) | model(I3!40, C!33)),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[450, 449])).
% 7.31/7.49 tff(452,plain,
% 7.31/7.49 (model(I3!40, C!33)),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[451, 444])).
% 7.31/7.49 tff(453,assumption,(![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))), introduced(assumption)).
% 7.31/7.49 tff(454,plain,
% 7.31/7.49 (model(I3!40, C!37)),
% 7.31/7.49 inference(and_elim,[status(thm)],[104])).
% 7.31/7.49 tff(455,plain,
% 7.31/7.49 (((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | ((~model(I3!40, C!33)) | (~model(I3!40, C!37)))) <=> ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | (~model(I3!40, C!33)) | (~model(I3!40, C!37)))),
% 7.31/7.49 inference(rewrite,[status(thm)],[])).
% 7.31/7.49 tff(456,plain,
% 7.31/7.49 ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | ((~model(I3!40, C!33)) | (~model(I3!40, C!37)))),
% 7.31/7.49 inference(quant_inst,[status(thm)],[])).
% 7.31/7.49 tff(457,plain,
% 7.31/7.49 ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | (~model(I3!40, C!33)) | (~model(I3!40, C!37))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[456, 455])).
% 7.31/7.49 tff(458,plain,
% 7.31/7.49 ($false),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[457, 454, 453, 452])).
% 7.31/7.49 tff(459,plain,(~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))), inference(lemma,lemma(discharge,[]))).
% 7.31/7.49 tff(460,plain,
% 7.31/7.49 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))))))),
% 7.31/7.49 inference(bind,[status(th)],[])).
% 7.31/7.49 tff(461,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))),
% 7.31/7.49 inference(quant_intro,[status(thm)],[460])).
% 7.31/7.49 tff(462,plain,
% 7.31/7.49 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))))),
% 7.31/7.49 inference(bind,[status(th)],[])).
% 7.31/7.49 tff(463,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 7.31/7.49 inference(quant_intro,[status(thm)],[462])).
% 7.31/7.49 tff(464,plain,
% 7.31/7.49 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))))),
% 7.31/7.49 inference(bind,[status(th)],[])).
% 7.31/7.49 tff(465,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 7.31/7.49 inference(quant_intro,[status(thm)],[464])).
% 7.31/7.49 tff(466,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 7.31/7.49 inference(transitivity,[status(thm)],[465, 463])).
% 7.31/7.49 tff(467,plain,
% 7.31/7.49 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) <=> (status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))), rewrite(((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) <=> ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))), (((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> ((status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))) & ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))), rewrite(((status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))) & ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))), (((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))))),
% 7.31/7.49 inference(bind,[status(th)],[])).
% 7.31/7.49 tff(468,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 7.31/7.49 inference(quant_intro,[status(thm)],[467])).
% 7.31/7.49 tff(469,plain,
% 7.31/7.49 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc)))) <=> ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))))),
% 7.31/7.49 inference(bind,[status(th)],[])).
% 7.31/7.49 tff(470,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : (((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))))),
% 7.31/7.49 inference(quant_intro,[status(thm)],[469])).
% 7.31/7.49 tff(471,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))),
% 7.31/7.49 inference(rewrite,[status(thm)],[])).
% 7.31/7.49 tff(472,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','noc')).
% 7.31/7.49 tff(473,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[472, 471])).
% 7.31/7.49 tff(474,plain,(
% 7.31/7.49 ![Ax: $i, C: $i] : (((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc))))),
% 7.31/7.49 inference(skolemize,[status(sab)],[473])).
% 7.31/7.49 tff(475,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[474, 470])).
% 7.31/7.49 tff(476,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[475, 468])).
% 7.31/7.49 tff(477,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[476, 466])).
% 7.31/7.49 tff(478,plain,
% 7.31/7.49 (![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[477, 461])).
% 7.31/7.49 tff(479,plain,
% 7.31/7.49 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))))),
% 7.31/7.49 inference(rewrite,[status(thm)],[])).
% 7.31/7.49 tff(480,plain,
% 7.31/7.49 ((~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I1_2(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33))))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, C!33))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))) <=> (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))),
% 7.31/7.49 inference(rewrite,[status(thm)],[])).
% 7.31/7.49 tff(481,plain,
% 7.31/7.49 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I1_2(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33))))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, C!33))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))))),
% 7.31/7.49 inference(monotonicity,[status(thm)],[480])).
% 7.31/7.49 tff(482,plain,
% 7.31/7.49 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I1_2(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33))))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, C!33))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))))),
% 7.31/7.49 inference(transitivity,[status(thm)],[481, 479])).
% 7.31/7.49 tff(483,plain,
% 7.31/7.49 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I1_2(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33))))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, C!33))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))),
% 7.31/7.49 inference(quant_inst,[status(thm)],[])).
% 7.31/7.49 tff(484,plain,
% 7.31/7.49 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))),
% 7.31/7.49 inference(modus_ponens,[status(thm)],[483, 482])).
% 7.31/7.49 tff(485,plain,
% 7.31/7.49 (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[484, 478])).
% 7.31/7.49 tff(486,plain,
% 7.31/7.49 (((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))) | (status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))),
% 7.31/7.49 inference(tautology,[status(thm)],[])).
% 7.31/7.49 tff(487,plain,
% 7.31/7.49 (status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[486, 485])).
% 7.31/7.49 tff(488,plain,
% 7.31/7.49 ((~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))) | status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))),
% 7.31/7.49 inference(tautology,[status(thm)],[])).
% 7.31/7.49 tff(489,plain,
% 7.31/7.49 (status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[488, 487])).
% 7.31/7.49 tff(490,plain,
% 7.31/7.49 (status(C!37, C!33, noc) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[489, 459])).
% 7.31/7.49 tff(491,plain,
% 7.31/7.49 (status(C!37, C!33, noc)),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[490, 442])).
% 7.31/7.49 tff(492,plain,
% 7.31/7.49 (((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))) | ((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))),
% 7.31/7.49 inference(tautology,[status(thm)],[])).
% 7.31/7.49 tff(493,plain,
% 7.31/7.49 ((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37))))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[492, 485])).
% 7.31/7.49 tff(494,plain,
% 7.31/7.49 ((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37))))),
% 7.31/7.49 inference(tautology,[status(thm)],[])).
% 7.31/7.49 tff(495,plain,
% 7.31/7.49 ((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37))))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[494, 493])).
% 7.31/7.49 tff(496,plain,
% 7.31/7.49 (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))),
% 7.31/7.49 inference(unit_resolution,[status(thm)],[495, 491])).
% 7.31/7.49 tff(497,plain,
% 7.31/7.49 (((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37))) | model(tptp_fun_I2_17(C!33, C!37), not(C!33))),
% 7.31/7.50 inference(tautology,[status(thm)],[])).
% 7.31/7.50 tff(498,plain,
% 7.31/7.50 (model(tptp_fun_I2_17(C!33, C!37), not(C!33))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[497, 496])).
% 7.31/7.50 tff(499,plain,
% 7.31/7.50 ((~![I2: $i] : (~model(I2, not(C!33)))) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33)))),
% 7.31/7.50 inference(quant_inst,[status(thm)],[])).
% 7.31/7.50 tff(500,plain,
% 7.31/7.50 ($false),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[499, 498, 38])).
% 7.31/7.50 tff(501,plain,(~![I2: $i] : (~model(I2, not(C!33)))), inference(lemma,lemma(discharge,[]))).
% 7.31/7.50 tff(502,plain,
% 7.31/7.50 ((~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))) | ![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33)))),
% 7.31/7.50 inference(tautology,[status(thm)],[])).
% 7.31/7.50 tff(503,plain,
% 7.31/7.50 (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[502, 501, 37])).
% 7.31/7.50 tff(504,plain,
% 7.31/7.50 (((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33)))))) | (![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))),
% 7.31/7.50 inference(tautology,[status(thm)],[])).
% 7.31/7.50 tff(505,plain,
% 7.31/7.50 ((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33)))))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[504, 503])).
% 7.31/7.50 tff(506,plain,
% 7.31/7.50 ((~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))) | (~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa)),
% 7.31/7.50 inference(tautology,[status(thm)],[])).
% 7.31/7.50 tff(507,plain,
% 7.31/7.50 ((~((~((~(model(tptp_fun_I1_0(Ax!34), Ax!34) | model(tptp_fun_I2_1(not(C!33)), not(C!33)))) | (~(![I1: $i] : (~model(I1, Ax!34)) | ![I2: $i] : (~model(I2, not(C!33))))))) | status(Ax!34, not(C!33), esa))) | status(Ax!34, not(C!33), esa)),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[506, 505])).
% 7.31/7.50 tff(508,plain,
% 7.31/7.50 (status(Ax!34, not(C!33), esa)),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[507, 27])).
% 7.31/7.50 tff(509,assumption,(~status(Ax!34, not(C!33), thm)), introduced(assumption)).
% 7.31/7.50 tff(510,plain,
% 7.31/7.50 (((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(Ax!34, not(C!33), esa)) | status(Ax!34, not(C!33), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(Ax!34, not(C!33), esa)) | status(Ax!34, not(C!33), thm))),
% 7.31/7.50 inference(rewrite,[status(thm)],[])).
% 7.31/7.50 tff(511,plain,
% 7.31/7.50 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(Ax!34, not(C!33), esa)) | status(Ax!34, not(C!33), thm))),
% 7.31/7.50 inference(quant_inst,[status(thm)],[])).
% 7.31/7.50 tff(512,plain,
% 7.31/7.50 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(Ax!34, not(C!33), esa)) | status(Ax!34, not(C!33), thm)),
% 7.31/7.50 inference(modus_ponens,[status(thm)],[511, 510])).
% 7.31/7.50 tff(513,plain,
% 7.31/7.50 ($false),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[512, 75, 509, 508])).
% 7.31/7.50 tff(514,plain,(status(Ax!34, not(C!33), thm)), inference(lemma,lemma(discharge,[]))).
% 7.31/7.50 tff(515,plain,
% 7.31/7.50 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm))))))),
% 7.31/7.50 inference(rewrite,[status(thm)],[])).
% 7.31/7.50 tff(516,plain,
% 7.31/7.50 ((~((~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm))) | (~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))))) <=> (~((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm)))))),
% 7.31/7.50 inference(rewrite,[status(thm)],[])).
% 7.31/7.50 tff(517,plain,
% 7.31/7.50 (((~![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(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm))) | (~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm))))))),
% 7.31/7.50 inference(monotonicity,[status(thm)],[516])).
% 7.31/7.50 tff(518,plain,
% 7.31/7.50 (((~![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(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm))) | (~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm))))))),
% 7.31/7.50 inference(transitivity,[status(thm)],[517, 515])).
% 7.31/7.50 tff(519,plain,
% 7.31/7.50 ((~![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(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm))) | (~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))))))),
% 7.31/7.50 inference(quant_inst,[status(thm)],[])).
% 7.31/7.50 tff(520,plain,
% 7.31/7.50 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm)))))),
% 7.31/7.50 inference(modus_ponens,[status(thm)],[519, 518])).
% 7.31/7.50 tff(521,plain,
% 7.31/7.50 (~((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm))))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[520, 130])).
% 7.31/7.50 tff(522,plain,
% 7.31/7.50 (((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~((~((~model(tptp_fun_I1_3(not(C!33), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!33), Ax!34), not(C!33)))) | status(Ax!34, not(C!33), thm)))) | ((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))),
% 7.31/7.50 inference(tautology,[status(thm)],[])).
% 7.31/7.50 tff(523,plain,
% 7.31/7.50 ((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[522, 521])).
% 7.31/7.50 tff(524,plain,
% 7.31/7.50 ((~((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33))))) | (~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))),
% 7.31/7.50 inference(tautology,[status(thm)],[])).
% 7.31/7.50 tff(525,plain,
% 7.31/7.50 ((~status(Ax!34, not(C!33), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[524, 523])).
% 7.31/7.50 tff(526,plain,
% 7.31/7.50 (![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[525, 514])).
% 7.31/7.50 tff(527,plain,
% 7.31/7.50 (~model(I4!41, C!37)),
% 7.31/7.50 inference(and_elim,[status(thm)],[104])).
% 7.31/7.50 tff(528,plain,
% 7.31/7.50 (((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(I4!41, Ax!38)) | model(I4!41, C!37))) <=> ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(I4!41, Ax!38)) | model(I4!41, C!37))),
% 7.31/7.50 inference(rewrite,[status(thm)],[])).
% 7.31/7.50 tff(529,plain,
% 7.31/7.50 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(I4!41, Ax!38)) | model(I4!41, C!37))),
% 7.31/7.50 inference(quant_inst,[status(thm)],[])).
% 7.31/7.50 tff(530,plain,
% 7.31/7.50 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(I4!41, Ax!38)) | model(I4!41, C!37)),
% 7.31/7.50 inference(modus_ponens,[status(thm)],[529, 528])).
% 7.31/7.50 tff(531,plain,
% 7.31/7.50 (~model(I4!41, Ax!38)),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[530, 426, 527])).
% 7.31/7.50 tff(532,plain,
% 7.31/7.50 (((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(I4!41, not(C!33))) | model(I4!41, Ax!38))) <=> ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(I4!41, not(C!33))) | model(I4!41, Ax!38))),
% 7.31/7.50 inference(rewrite,[status(thm)],[])).
% 7.31/7.50 tff(533,plain,
% 7.31/7.50 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | ((~model(I4!41, not(C!33))) | model(I4!41, Ax!38))),
% 7.31/7.50 inference(quant_inst,[status(thm)],[])).
% 7.31/7.50 tff(534,plain,
% 7.31/7.50 ((~![I1: $i] : ((~model(I1, not(C!33))) | model(I1, Ax!38))) | (~model(I4!41, not(C!33))) | model(I4!41, Ax!38)),
% 7.31/7.50 inference(modus_ponens,[status(thm)],[533, 532])).
% 7.31/7.50 tff(535,plain,
% 7.31/7.50 (~model(I4!41, not(C!33))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[534, 531, 152])).
% 7.31/7.50 tff(536,plain,
% 7.31/7.50 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I4!41, Ax!34) <=> model(I4!41, not(Ax!34))))),
% 7.31/7.50 inference(quant_inst,[status(thm)],[])).
% 7.31/7.50 tff(537,plain,
% 7.31/7.50 (~(model(I4!41, Ax!34) <=> model(I4!41, not(Ax!34)))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[536, 46])).
% 7.31/7.50 tff(538,plain,
% 7.31/7.50 (((~![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))) | ((~model(I4!41, not(Ax!34))) | model(I4!41, Ax!38))) <=> ((~![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))) | (~model(I4!41, not(Ax!34))) | model(I4!41, Ax!38))),
% 7.31/7.50 inference(rewrite,[status(thm)],[])).
% 7.31/7.50 tff(539,plain,
% 7.31/7.50 ((~![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))) | ((~model(I4!41, not(Ax!34))) | model(I4!41, Ax!38))),
% 7.31/7.50 inference(quant_inst,[status(thm)],[])).
% 7.31/7.50 tff(540,plain,
% 7.31/7.50 ((~![I1: $i] : ((~model(I1, not(Ax!34))) | model(I1, Ax!38))) | (~model(I4!41, not(Ax!34))) | model(I4!41, Ax!38)),
% 7.31/7.50 inference(modus_ponens,[status(thm)],[539, 538])).
% 7.31/7.50 tff(541,plain,
% 7.31/7.50 (~model(I4!41, not(Ax!34))),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[540, 531, 327])).
% 7.31/7.50 tff(542,plain,
% 7.31/7.50 ((model(I4!41, Ax!34) <=> model(I4!41, not(Ax!34))) | model(I4!41, Ax!34) | model(I4!41, not(Ax!34))),
% 7.31/7.50 inference(tautology,[status(thm)],[])).
% 7.31/7.50 tff(543,plain,
% 7.31/7.50 ((model(I4!41, Ax!34) <=> model(I4!41, not(Ax!34))) | model(I4!41, Ax!34)),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[542, 541])).
% 7.31/7.50 tff(544,plain,
% 7.31/7.50 (model(I4!41, Ax!34)),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[543, 537])).
% 7.31/7.50 tff(545,plain,
% 7.31/7.50 (((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))) | ((~model(I4!41, Ax!34)) | model(I4!41, not(C!33)))) <=> ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))) | (~model(I4!41, Ax!34)) | model(I4!41, not(C!33)))),
% 7.31/7.50 inference(rewrite,[status(thm)],[])).
% 7.31/7.50 tff(546,plain,
% 7.31/7.50 ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))) | ((~model(I4!41, Ax!34)) | model(I4!41, not(C!33)))),
% 7.31/7.50 inference(quant_inst,[status(thm)],[])).
% 7.31/7.50 tff(547,plain,
% 7.31/7.50 ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!33)))) | (~model(I4!41, Ax!34)) | model(I4!41, not(C!33))),
% 7.31/7.50 inference(modus_ponens,[status(thm)],[546, 545])).
% 7.31/7.50 tff(548,plain,
% 7.31/7.50 ($false),
% 7.31/7.50 inference(unit_resolution,[status(thm)],[547, 544, 535, 526])).
% 7.31/7.50 % SZS output end Proof
% 7.31/7.51 % E exiting
%------------------------------------------------------------------------------