%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS200+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 1.84s 2.06s
% Output : Proof 1.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS200+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:13:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.84/2.06 % SZS status Theorem
% 1.84/2.06 % SZS output start Proof
% 1.84/2.06 tff(model_type, type, (
% 1.84/2.06 model: ( $i * $i ) > $o)).
% 1.84/2.06 tff(tptp_fun_Ax_34_type, type, (
% 1.84/2.06 tptp_fun_Ax_34: $i)).
% 1.84/2.06 tff(tptp_fun_I2_31_type, type, (
% 1.84/2.06 tptp_fun_I2_31: $i)).
% 1.84/2.06 tff(tptp_fun_F_29_type, type, (
% 1.84/2.06 tptp_fun_F_29: $i)).
% 1.84/2.06 tff(status_type, type, (
% 1.84/2.06 status: ( $i * $i * $i ) > $o)).
% 1.84/2.06 tff(thm_type, type, (
% 1.84/2.06 thm: $i)).
% 1.84/2.06 tff(unp_type, type, (
% 1.84/2.06 unp: $i)).
% 1.84/2.06 tff(tptp_fun_I2_1_type, type, (
% 1.84/2.06 tptp_fun_I2_1: $i > $i)).
% 1.84/2.06 tff(tptp_fun_I1_0_type, type, (
% 1.84/2.06 tptp_fun_I1_0: $i > $i)).
% 1.84/2.06 tff(tptp_fun_I1_35_type, type, (
% 1.84/2.06 tptp_fun_I1_35: $i)).
% 1.84/2.06 tff(tptp_fun_C_33_type, type, (
% 1.84/2.06 tptp_fun_C_33: $i)).
% 1.84/2.06 tff(tptp_fun_I2_36_type, type, (
% 1.84/2.06 tptp_fun_I2_36: $i)).
% 1.84/2.06 tff(nota_type, type, (
% 1.84/2.06 nota: ( $i * $i ) > $o)).
% 1.84/2.06 tff(tptp_fun_C_22_type, type, (
% 1.84/2.06 tptp_fun_C_22: ( $i * $i ) > $i)).
% 1.84/2.06 tff(tptp_fun_Ax_23_type, type, (
% 1.84/2.06 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 1.84/2.06 tff(tptp_fun_I1_3_type, type, (
% 1.84/2.06 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 1.84/2.06 tff(tptp_fun_I1_30_type, type, (
% 1.84/2.06 tptp_fun_I1_30: $i)).
% 1.84/2.06 tff(tptp_fun_Ax_38_type, type, (
% 1.84/2.06 tptp_fun_Ax_38: $i)).
% 1.84/2.06 tff(tptp_fun_I3_40_type, type, (
% 1.84/2.06 tptp_fun_I3_40: $i)).
% 1.84/2.06 tff(tptp_fun_F_28_type, type, (
% 1.84/2.06 tptp_fun_F_28: $i)).
% 1.84/2.06 tff(tptp_fun_C_37_type, type, (
% 1.84/2.06 tptp_fun_C_37: $i)).
% 1.84/2.06 tff(tptp_fun_I4_41_type, type, (
% 1.84/2.06 tptp_fun_I4_41: $i)).
% 1.84/2.06 tff(tptp_fun_I1_39_type, type, (
% 1.84/2.06 tptp_fun_I1_39: $i)).
% 1.84/2.06 tff(tptp_fun_I2_7_type, type, (
% 1.84/2.06 tptp_fun_I2_7: ( $i * $i ) > $i)).
% 1.84/2.06 tff(wth_type, type, (
% 1.84/2.06 wth: $i)).
% 1.84/2.06 tff(tptp_fun_I3_6_type, type, (
% 1.84/2.06 tptp_fun_I3_6: ( $i * $i ) > $i)).
% 1.84/2.06 tff(tptp_fun_I4_12_type, type, (
% 1.84/2.06 tptp_fun_I4_12: $i > $i)).
% 1.84/2.06 tff(1,assumption,((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp)))), introduced(assumption)).
% 1.84/2.06 tff(2,plain,
% 1.84/2.06 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C)))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(3,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[2])).
% 1.84/2.06 tff(4,plain,
% 1.84/2.06 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(5,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[4])).
% 1.84/2.06 tff(6,plain,
% 1.84/2.06 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(7,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[6])).
% 1.84/2.06 tff(8,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[7, 5])).
% 1.84/2.06 tff(9,plain,
% 1.84/2.06 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite(((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) <=> ((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))), rewrite((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))) <=> (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))), rewrite((((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(10,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[9])).
% 1.84/2.06 tff(11,plain,
% 1.84/2.06 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(12,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[11])).
% 1.84/2.06 tff(13,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(14,plain,
% 1.84/2.06 (^[Ax: $i, C: $i] : rewrite((((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(15,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[14])).
% 1.84/2.06 tff(16,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','unp')).
% 1.84/2.06 tff(17,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.84/2.06 tff(18,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.84/2.06 tff(19,plain,(
% 1.84/2.06 ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp))))),
% 1.84/2.06 inference(skolemize,[status(sab)],[18])).
% 1.84/2.06 tff(20,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.84/2.06 tff(21,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[20, 10])).
% 1.84/2.06 tff(22,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[21, 8])).
% 1.84/2.06 tff(23,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[22, 3])).
% 1.84/2.06 tff(24,plain,
% 1.84/2.06 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(25,plain,
% 1.84/2.06 ((~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, F!29, unp)) | ![I2: $i] : (~model(I2, F!29)))))) <=> (~((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(26,plain,
% 1.84/2.06 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, F!29, unp)) | ![I2: $i] : (~model(I2, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[25])).
% 1.84/2.06 tff(27,plain,
% 1.84/2.06 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, F!29, unp)) | ![I2: $i] : (~model(I2, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[26, 24])).
% 1.84/2.06 tff(28,plain,
% 1.84/2.06 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, F!29, unp)) | ![I2: $i] : (~model(I2, F!29))))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(29,plain,
% 1.84/2.06 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp)))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.84/2.06 tff(30,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[29, 23, 1])).
% 1.84/2.06 tff(31,plain,(~((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(32,plain,
% 1.84/2.06 (((~(![I2: $i] : (~model(I2, F!29)) | (~status(Ax!34, F!29, unp)) | model(tptp_fun_I1_0(Ax!34), Ax!34))) | (~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp)))) | ((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))),
% 1.84/2.06 inference(tautology,[status(thm)],[])).
% 1.84/2.06 tff(33,plain,
% 1.84/2.06 ((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.84/2.06 tff(34,assumption,(![I1: $i] : (~model(I1, Ax!34))), introduced(assumption)).
% 1.84/2.06 tff(35,plain,
% 1.84/2.06 (((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))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(36,plain,
% 1.84/2.06 (?[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))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(37,axiom,(?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','sat_non_taut_pair')).
% 1.84/2.06 tff(38,plain,
% 1.84/2.06 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.84/2.06 tff(39,plain,
% 1.84/2.06 (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[38, 35])).
% 1.84/2.06 tff(40,plain,
% 1.84/2.06 (model(I1!35, Ax!34)),
% 1.84/2.06 inference(and_elim,[status(thm)],[39])).
% 1.84/2.06 tff(41,plain,
% 1.84/2.06 ((~![I1: $i] : (~model(I1, Ax!34))) | (~model(I1!35, Ax!34))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(42,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[41, 40, 34])).
% 1.84/2.06 tff(43,plain,(~![I1: $i] : (~model(I1, Ax!34))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(44,plain,
% 1.84/2.06 (((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34)))) | ![I1: $i] : (~model(I1, Ax!34))),
% 1.84/2.06 inference(tautology,[status(thm)],[])).
% 1.84/2.06 tff(45,plain,
% 1.84/2.06 ((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[44, 43])).
% 1.84/2.06 tff(46,plain,
% 1.84/2.06 ((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))) | (~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp)),
% 1.84/2.06 inference(tautology,[status(thm)],[])).
% 1.84/2.06 tff(47,plain,
% 1.84/2.06 ((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, F!29, unp))) | status(Ax!34, F!29, unp)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.84/2.06 tff(48,plain,
% 1.84/2.06 (status(Ax!34, F!29, unp)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[47, 33])).
% 1.84/2.06 tff(49,assumption,(~status(Ax!34, F!29, thm)), introduced(assumption)).
% 1.84/2.06 tff(50,plain,
% 1.84/2.06 (^[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))))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(51,plain,
% 1.84/2.06 (![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)))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[50])).
% 1.84/2.06 tff(52,plain,
% 1.84/2.06 (^[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))))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(53,plain,
% 1.84/2.06 (![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)))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[52])).
% 1.84/2.06 tff(54,plain,
% 1.84/2.06 (![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)))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[53, 51])).
% 1.84/2.06 tff(55,plain,
% 1.84/2.06 (^[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)))))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(56,plain,
% 1.84/2.06 (![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)))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[55])).
% 1.84/2.06 tff(57,plain,
% 1.84/2.06 (^[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)))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(58,plain,
% 1.84/2.06 (![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))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[57])).
% 1.84/2.06 tff(59,plain,
% 1.84/2.06 (![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))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 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/sandbox/benchmark/Axioms/KRS001+1.ax','nota')).
% 1.84/2.06 tff(61,plain,
% 1.84/2.06 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.84/2.06 tff(62,plain,(
% 1.84/2.06 ![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))))),
% 1.84/2.06 inference(skolemize,[status(sab)],[61])).
% 1.84/2.06 tff(63,plain,
% 1.84/2.06 (![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))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[62, 58])).
% 1.84/2.06 tff(64,plain,
% 1.84/2.06 (![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)))))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[63, 56])).
% 1.84/2.06 tff(65,plain,
% 1.84/2.06 (![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)))))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[64, 54])).
% 1.84/2.06 tff(66,plain,
% 1.84/2.06 ((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | (~((~nota(unp, thm)) | (~((~status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), unp)) | status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), thm)))))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(67,plain,
% 1.84/2.06 (~((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | (~((~nota(unp, thm)) | (~((~status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), unp)) | status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), thm))))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[66, 65])).
% 1.84/2.06 tff(68,plain,
% 1.84/2.06 (((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | (~((~nota(unp, thm)) | (~((~status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), unp)) | status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), thm)))))) | (nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))),
% 1.84/2.06 inference(tautology,[status(thm)],[])).
% 1.84/2.06 tff(69,plain,
% 1.84/2.06 (nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[68, 67])).
% 1.84/2.06 tff(70,plain,
% 1.84/2.06 ((~nota(unp, thm)) <=> (~nota(unp, thm))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(71,axiom,(~nota(unp, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nota_unp_thm')).
% 1.84/2.06 tff(72,plain,
% 1.84/2.06 (~nota(unp, thm)),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.84/2.06 tff(73,plain,
% 1.84/2.06 ((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))),
% 1.84/2.06 inference(tautology,[status(thm)],[])).
% 1.84/2.06 tff(74,plain,
% 1.84/2.06 ((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[73, 72])).
% 1.84/2.06 tff(75,plain,
% 1.84/2.06 (![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[74, 69])).
% 1.84/2.06 tff(76,plain,
% 1.84/2.06 (((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | ((~status(Ax!34, F!29, unp)) | status(Ax!34, F!29, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | (~status(Ax!34, F!29, unp)) | status(Ax!34, F!29, thm))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(77,plain,
% 1.84/2.06 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | ((~status(Ax!34, F!29, unp)) | status(Ax!34, F!29, thm))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(78,plain,
% 1.84/2.06 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | (~status(Ax!34, F!29, unp)) | status(Ax!34, F!29, thm)),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.84/2.06 tff(79,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[78, 75, 49, 48])).
% 1.84/2.06 tff(80,plain,(status(Ax!34, F!29, thm)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(81,plain,
% 1.84/2.06 (^[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)))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(82,plain,
% 1.84/2.06 (![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))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[81])).
% 1.84/2.06 tff(83,plain,
% 1.84/2.06 (^[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)))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(84,plain,
% 1.84/2.06 (![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))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[83])).
% 1.84/2.06 tff(85,plain,
% 1.84/2.06 (^[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)))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(86,plain,
% 1.84/2.06 (![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))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[85])).
% 1.84/2.06 tff(87,plain,
% 1.84/2.06 (![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))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[86, 84])).
% 1.84/2.06 tff(88,plain,
% 1.84/2.06 (^[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))))))))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(89,plain,
% 1.84/2.06 (![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))))))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[88])).
% 1.84/2.06 tff(90,plain,
% 1.84/2.06 (![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))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(91,plain,
% 1.84/2.06 (^[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)))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(92,plain,
% 1.84/2.07 (![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))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[91])).
% 1.84/2.07 tff(93,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','thm')).
% 1.84/2.07 tff(94,plain,
% 1.84/2.07 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.84/2.07 tff(95,plain,
% 1.84/2.07 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[94, 90])).
% 1.84/2.07 tff(96,plain,(
% 1.84/2.07 ![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))))),
% 1.84/2.07 inference(skolemize,[status(sab)],[95])).
% 1.84/2.07 tff(97,plain,
% 1.84/2.07 (![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))))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[96, 89])).
% 1.84/2.07 tff(98,plain,
% 1.84/2.07 (![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))))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[97, 87])).
% 1.84/2.07 tff(99,plain,
% 1.84/2.07 (![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))))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[98, 82])).
% 1.84/2.07 tff(100,plain,
% 1.84/2.07 ((~![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!34), Ax!34)) | model(tptp_fun_I1_3(F!29, Ax!34), F!29))) | status(Ax!34, F!29, thm))) | (~((~status(Ax!34, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(101,plain,
% 1.84/2.07 (~((~((~((~model(tptp_fun_I1_3(F!29, Ax!34), Ax!34)) | model(tptp_fun_I1_3(F!29, Ax!34), F!29))) | status(Ax!34, F!29, thm))) | (~((~status(Ax!34, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[100, 99])).
% 1.84/2.07 tff(102,plain,
% 1.84/2.07 (((~((~((~model(tptp_fun_I1_3(F!29, Ax!34), Ax!34)) | model(tptp_fun_I1_3(F!29, Ax!34), F!29))) | status(Ax!34, F!29, thm))) | (~((~status(Ax!34, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))))) | ((~status(Ax!34, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29)))),
% 1.84/2.07 inference(tautology,[status(thm)],[])).
% 1.84/2.07 tff(103,plain,
% 1.84/2.07 ((~status(Ax!34, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[102, 101])).
% 1.84/2.07 tff(104,plain,
% 1.84/2.07 ((~((~status(Ax!34, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29)))) | (~status(Ax!34, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))),
% 1.84/2.07 inference(tautology,[status(thm)],[])).
% 1.84/2.07 tff(105,plain,
% 1.84/2.07 ((~status(Ax!34, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[104, 103])).
% 1.84/2.07 tff(106,plain,
% 1.84/2.07 (![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[105, 80])).
% 1.84/2.07 tff(107,plain,
% 1.84/2.07 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(108,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 1.84/2.07 tff(109,plain,
% 1.84/2.07 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.84/2.07 tff(110,plain,
% 1.84/2.07 (~model(I2!31, F!29)),
% 1.84/2.07 inference(and_elim,[status(thm)],[109])).
% 1.84/2.07 tff(111,plain,
% 1.84/2.07 (((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))) | ((~model(I2!31, Ax!34)) | model(I2!31, F!29))) <=> ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))) | (~model(I2!31, Ax!34)) | model(I2!31, F!29))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(112,plain,
% 1.84/2.07 ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))) | ((~model(I2!31, Ax!34)) | model(I2!31, F!29))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(113,plain,
% 1.84/2.07 ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, F!29))) | (~model(I2!31, Ax!34)) | model(I2!31, F!29)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.84/2.07 tff(114,plain,
% 1.84/2.07 (~model(I2!31, Ax!34)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[113, 110, 106])).
% 1.84/2.07 tff(115,assumption,(~model(I3!40, F!28)), introduced(assumption)).
% 1.84/2.07 tff(116,plain,
% 1.84/2.07 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(117,plain,
% 1.84/2.07 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 1.84/2.07 inference(quant_intro,[status(thm)],[116])).
% 1.84/2.07 tff(118,plain,
% 1.84/2.07 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(119,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','tautology')).
% 1.84/2.07 tff(120,plain,
% 1.84/2.07 (?[F: $i] : ![I: $i] : model(I, F)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.84/2.07 tff(121,plain,(
% 1.84/2.07 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 1.84/2.07 inference(transitivity,[status(sab)],[120])).
% 1.84/2.07 tff(122,plain,
% 1.84/2.07 (![I: $i] : model(I, F!28)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[121, 117])).
% 1.84/2.07 tff(123,plain,
% 1.84/2.07 ((~![I: $i] : model(I, F!28)) | model(I3!40, F!28)),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(124,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[123, 122, 115])).
% 1.84/2.07 tff(125,plain,(model(I3!40, F!28)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(126,assumption,((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp))))), introduced(assumption)).
% 1.84/2.07 tff(127,plain,
% 1.84/2.07 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(128,plain,
% 1.84/2.07 ((~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp)) | ![I2: $i] : (~model(I2, Ax!34)))))) <=> (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(129,plain,
% 1.84/2.07 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp)) | ![I2: $i] : (~model(I2, Ax!34))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp)))))))),
% 1.93/2.07 inference(monotonicity,[status(thm)],[128])).
% 1.93/2.07 tff(130,plain,
% 1.93/2.07 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp)) | ![I2: $i] : (~model(I2, Ax!34))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp)))))))),
% 1.93/2.07 inference(transitivity,[status(thm)],[129, 127])).
% 1.93/2.07 tff(131,plain,
% 1.93/2.07 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp)) | ![I2: $i] : (~model(I2, Ax!34))))))),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(132,plain,
% 1.93/2.07 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp))))))),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.93/2.07 tff(133,plain,
% 1.93/2.07 ($false),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[132, 23, 126])).
% 1.93/2.07 tff(134,plain,(~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp)))))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.07 tff(135,plain,
% 1.93/2.07 (((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, Ax!34, unp))))) | ((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))),
% 1.93/2.07 inference(tautology,[status(thm)],[])).
% 1.93/2.07 tff(136,plain,
% 1.93/2.07 ((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp)),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[135, 134])).
% 1.93/2.07 tff(137,assumption,(![I1: $i] : (~model(I1, F!28))), introduced(assumption)).
% 1.93/2.07 tff(138,plain,
% 1.93/2.07 ((~![I: $i] : model(I, F!28)) | model(I2!36, F!28)),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(139,plain,
% 1.93/2.07 (model(I2!36, F!28)),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[138, 122])).
% 1.93/2.07 tff(140,plain,
% 1.93/2.07 ((~![I1: $i] : (~model(I1, F!28))) | (~model(I2!36, F!28))),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(141,plain,
% 1.93/2.07 ($false),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[140, 139, 137])).
% 1.93/2.07 tff(142,plain,(~![I1: $i] : (~model(I1, F!28))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.07 tff(143,plain,
% 1.93/2.07 (((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28)))) | ![I1: $i] : (~model(I1, F!28))),
% 1.93/2.07 inference(tautology,[status(thm)],[])).
% 1.93/2.07 tff(144,plain,
% 1.93/2.07 ((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28)))),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[143, 142])).
% 1.93/2.07 tff(145,plain,
% 1.93/2.07 ((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | (~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp)),
% 1.93/2.07 inference(tautology,[status(thm)],[])).
% 1.93/2.07 tff(146,plain,
% 1.93/2.07 ((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, Ax!34, unp))) | status(F!28, Ax!34, unp)),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[145, 144])).
% 1.93/2.07 tff(147,plain,
% 1.93/2.07 (status(F!28, Ax!34, unp)),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[146, 136])).
% 1.93/2.07 tff(148,assumption,(~status(F!28, Ax!34, thm)), introduced(assumption)).
% 1.93/2.07 tff(149,plain,
% 1.93/2.07 (((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | ((~status(F!28, Ax!34, unp)) | status(F!28, Ax!34, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | (~status(F!28, Ax!34, unp)) | status(F!28, Ax!34, thm))),
% 1.93/2.07 inference(rewrite,[status(thm)],[])).
% 1.93/2.07 tff(150,plain,
% 1.93/2.07 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | ((~status(F!28, Ax!34, unp)) | status(F!28, Ax!34, thm))),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(151,plain,
% 1.93/2.07 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | (~status(F!28, Ax!34, unp)) | status(F!28, Ax!34, thm)),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.93/2.07 tff(152,plain,
% 1.93/2.07 ($false),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[151, 75, 148, 147])).
% 1.93/2.07 tff(153,plain,(status(F!28, Ax!34, thm)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.07 tff(154,plain,
% 1.93/2.07 ((~![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!28), F!28)) | model(tptp_fun_I1_3(Ax!34, F!28), Ax!34))) | status(F!28, Ax!34, thm))) | (~((~status(F!28, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))))))),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(155,plain,
% 1.93/2.07 (~((~((~((~model(tptp_fun_I1_3(Ax!34, F!28), F!28)) | model(tptp_fun_I1_3(Ax!34, F!28), Ax!34))) | status(F!28, Ax!34, thm))) | (~((~status(F!28, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34)))))),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[154, 99])).
% 1.93/2.07 tff(156,plain,
% 1.93/2.07 (((~((~((~model(tptp_fun_I1_3(Ax!34, F!28), F!28)) | model(tptp_fun_I1_3(Ax!34, F!28), Ax!34))) | status(F!28, Ax!34, thm))) | (~((~status(F!28, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))))) | ((~status(F!28, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34)))),
% 1.93/2.07 inference(tautology,[status(thm)],[])).
% 1.93/2.07 tff(157,plain,
% 1.93/2.07 ((~status(F!28, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[156, 155])).
% 1.93/2.07 tff(158,plain,
% 1.93/2.07 ((~((~status(F!28, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34)))) | (~status(F!28, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))),
% 1.93/2.07 inference(tautology,[status(thm)],[])).
% 1.93/2.07 tff(159,plain,
% 1.93/2.07 ((~status(F!28, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[158, 157])).
% 1.93/2.07 tff(160,plain,
% 1.93/2.07 (![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[159, 153])).
% 1.93/2.07 tff(161,plain,
% 1.93/2.07 (((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | ((~model(I3!40, F!28)) | model(I3!40, Ax!34))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | (~model(I3!40, F!28)) | model(I3!40, Ax!34))),
% 1.93/2.07 inference(rewrite,[status(thm)],[])).
% 1.93/2.07 tff(162,plain,
% 1.93/2.07 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | ((~model(I3!40, F!28)) | model(I3!40, Ax!34))),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(163,plain,
% 1.93/2.07 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | (~model(I3!40, F!28)) | model(I3!40, Ax!34)),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.93/2.07 tff(164,plain,
% 1.93/2.07 (model(I3!40, Ax!34)),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[163, 160, 125])).
% 1.93/2.07 tff(165,assumption,(![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))), introduced(assumption)).
% 1.93/2.07 tff(166,plain,
% 1.93/2.07 ((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)))),
% 1.93/2.07 inference(rewrite,[status(thm)],[])).
% 1.93/2.07 tff(167,plain,
% 1.93/2.07 (?[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)))),
% 1.93/2.07 inference(rewrite,[status(thm)],[])).
% 1.93/2.07 tff(168,plain,
% 1.93/2.07 (^[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)))))),
% 1.93/2.07 inference(bind,[status(th)],[])).
% 1.93/2.07 tff(169,plain,
% 1.93/2.07 (?[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)))),
% 1.93/2.07 inference(quant_intro,[status(thm)],[168])).
% 1.93/2.07 tff(170,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/sandbox/benchmark/Axioms/KRS001+1.ax','mixed_pair')).
% 1.93/2.07 tff(171,plain,
% 1.93/2.07 (?[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)))),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.93/2.07 tff(172,plain,
% 1.93/2.07 (?[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)))),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.93/2.07 tff(173,plain,
% 1.93/2.07 (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))),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[172, 166])).
% 1.93/2.07 tff(174,plain,
% 1.93/2.07 (~model(I3!40, Ax!38)),
% 1.93/2.07 inference(and_elim,[status(thm)],[173])).
% 1.93/2.07 tff(175,plain,
% 1.93/2.07 (((~![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))) | ((~model(I3!40, Ax!34)) | model(I3!40, Ax!38))) <=> ((~![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))) | (~model(I3!40, Ax!34)) | model(I3!40, Ax!38))),
% 1.93/2.07 inference(rewrite,[status(thm)],[])).
% 1.93/2.07 tff(176,plain,
% 1.93/2.07 ((~![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))) | ((~model(I3!40, Ax!34)) | model(I3!40, Ax!38))),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(177,plain,
% 1.93/2.07 ((~![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))) | (~model(I3!40, Ax!34)) | model(I3!40, Ax!38)),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.93/2.07 tff(178,plain,
% 1.93/2.07 ($false),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[177, 174, 165, 164])).
% 1.93/2.07 tff(179,plain,(~![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))), inference(lemma,lemma(discharge,[]))).
% 1.93/2.07 tff(180,assumption,(~model(tptp_fun_I2_7(Ax!34, Ax!38), F!28)), introduced(assumption)).
% 1.93/2.07 tff(181,plain,
% 1.93/2.07 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I2_7(Ax!34, Ax!38), F!28)),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(182,plain,
% 1.93/2.07 ($false),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[181, 122, 180])).
% 1.93/2.07 tff(183,plain,(model(tptp_fun_I2_7(Ax!34, Ax!38), F!28)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.07 tff(184,plain,
% 1.93/2.07 (((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | ((~model(tptp_fun_I2_7(Ax!34, Ax!38), F!28)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | (~model(tptp_fun_I2_7(Ax!34, Ax!38), F!28)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))),
% 1.93/2.07 inference(rewrite,[status(thm)],[])).
% 1.93/2.07 tff(185,plain,
% 1.93/2.07 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | ((~model(tptp_fun_I2_7(Ax!34, Ax!38), F!28)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(186,plain,
% 1.93/2.07 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | (~model(tptp_fun_I2_7(Ax!34, Ax!38), F!28)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34)),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.93/2.07 tff(187,plain,
% 1.93/2.07 (model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34)),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[186, 160, 183])).
% 1.93/2.07 tff(188,plain,
% 1.93/2.07 (((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34)) | (~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))),
% 1.93/2.07 inference(tautology,[status(thm)],[])).
% 1.93/2.07 tff(189,plain,
% 1.93/2.07 ((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34)),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[188, 187])).
% 1.93/2.07 tff(190,assumption,(~model(tptp_fun_I4_12(Ax!34), F!28)), introduced(assumption)).
% 1.93/2.07 tff(191,plain,
% 1.93/2.07 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I4_12(Ax!34), F!28)),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(192,plain,
% 1.93/2.07 ($false),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[191, 122, 190])).
% 1.93/2.07 tff(193,plain,(model(tptp_fun_I4_12(Ax!34), F!28)), inference(lemma,lemma(discharge,[]))).
% 1.93/2.07 tff(194,plain,
% 1.93/2.07 (((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | ((~model(tptp_fun_I4_12(Ax!34), F!28)) | model(tptp_fun_I4_12(Ax!34), Ax!34))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | (~model(tptp_fun_I4_12(Ax!34), F!28)) | model(tptp_fun_I4_12(Ax!34), Ax!34))),
% 1.93/2.07 inference(rewrite,[status(thm)],[])).
% 1.93/2.07 tff(195,plain,
% 1.93/2.07 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | ((~model(tptp_fun_I4_12(Ax!34), F!28)) | model(tptp_fun_I4_12(Ax!34), Ax!34))),
% 1.93/2.07 inference(quant_inst,[status(thm)],[])).
% 1.93/2.07 tff(196,plain,
% 1.93/2.07 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, Ax!34))) | (~model(tptp_fun_I4_12(Ax!34), F!28)) | model(tptp_fun_I4_12(Ax!34), Ax!34)),
% 1.93/2.07 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.93/2.07 tff(197,plain,
% 1.93/2.07 (model(tptp_fun_I4_12(Ax!34), Ax!34)),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[196, 160, 193])).
% 1.93/2.07 tff(198,plain,
% 1.93/2.07 (((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))) | (~model(tptp_fun_I4_12(Ax!34), Ax!34))),
% 1.93/2.07 inference(tautology,[status(thm)],[])).
% 1.93/2.07 tff(199,plain,
% 1.93/2.07 ((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))),
% 1.93/2.07 inference(unit_resolution,[status(thm)],[198, 197])).
% 1.93/2.07 tff(200,plain,
% 1.93/2.07 (^[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))))))))))),
% 1.93/2.07 inference(bind,[status(th)],[])).
% 1.93/2.07 tff(201,plain,
% 1.93/2.07 (![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)))))))))),
% 1.93/2.07 inference(quant_intro,[status(thm)],[200])).
% 1.93/2.07 tff(202,plain,
% 1.93/2.07 (^[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)))))))))),
% 1.93/2.07 inference(bind,[status(th)],[])).
% 1.93/2.07 tff(203,plain,
% 1.93/2.07 (![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))))))))),
% 1.93/2.07 inference(quant_intro,[status(thm)],[202])).
% 1.93/2.07 tff(204,plain,
% 1.93/2.07 (^[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)))))))))),
% 1.93/2.07 inference(bind,[status(th)],[])).
% 1.93/2.07 tff(205,plain,
% 1.93/2.07 (![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))))))))),
% 1.93/2.07 inference(quant_intro,[status(thm)],[204])).
% 1.93/2.07 tff(206,plain,
% 1.93/2.07 (![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))))))))),
% 1.93/2.07 inference(transitivity,[status(thm)],[205, 203])).
% 1.93/2.07 tff(207,plain,
% 1.93/2.07 (^[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))))))))))),
% 1.93/2.08 inference(bind,[status(th)],[])).
% 1.93/2.08 tff(208,plain,
% 1.93/2.08 (![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))))))))),
% 1.93/2.08 inference(quant_intro,[status(thm)],[207])).
% 1.93/2.08 tff(209,plain,
% 1.93/2.08 (^[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))))))),
% 1.93/2.08 inference(bind,[status(th)],[])).
% 1.93/2.08 tff(210,plain,
% 1.93/2.08 (![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)))))),
% 1.93/2.08 inference(quant_intro,[status(thm)],[209])).
% 1.93/2.08 tff(211,plain,
% 1.93/2.08 (![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))),
% 1.93/2.08 inference(rewrite,[status(thm)],[])).
% 1.93/2.08 tff(212,plain,
% 1.93/2.08 (^[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)))),
% 1.93/2.08 inference(bind,[status(th)],[])).
% 1.93/2.08 tff(213,plain,
% 1.93/2.08 (![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))),
% 1.93/2.08 inference(quant_intro,[status(thm)],[212])).
% 1.93/2.08 tff(214,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/sandbox/benchmark/Axioms/KRS001+0.ax','wth')).
% 1.93/2.08 tff(215,plain,
% 1.93/2.08 (![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))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.93/2.08 tff(216,plain,
% 1.93/2.08 (![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))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[215, 211])).
% 1.93/2.08 tff(217,plain,(
% 1.93/2.08 ![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))))),
% 1.93/2.08 inference(skolemize,[status(sab)],[216])).
% 1.93/2.08 tff(218,plain,
% 1.93/2.08 (![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)))))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[217, 210])).
% 1.93/2.08 tff(219,plain,
% 1.93/2.08 (![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))))))))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[218, 208])).
% 1.93/2.08 tff(220,plain,
% 1.93/2.08 (![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))))))))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[219, 206])).
% 1.93/2.08 tff(221,plain,
% 1.93/2.08 (![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)))))))))),
% 1.93/2.08 inference(modus_ponens,[status(thm)],[220, 201])).
% 1.94/2.08 tff(222,plain,
% 1.94/2.08 (((~![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)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))))))))) <=> ((~![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)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)))))))))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(223,plain,
% 1.94/2.08 ((~((~(status(Ax!38, Ax!34, wth) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)) | ![I4: $i] : model(I4, Ax!34))) | (~((~status(Ax!38, Ax!34, wth)) | (~(model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I1_0(Ax!38), Ax!38)) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))))))))) <=> (~((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))))))))),
% 1.94/2.08 inference(rewrite,[status(thm)],[])).
% 1.94/2.08 tff(224,plain,
% 1.94/2.08 (((~![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(Ax!38, Ax!34, wth) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)) | ![I4: $i] : model(I4, Ax!34))) | (~((~status(Ax!38, Ax!34, wth)) | (~(model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I1_0(Ax!38), Ax!38)) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34)))))))))) <=> ((~![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)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)))))))))),
% 1.94/2.08 inference(monotonicity,[status(thm)],[223])).
% 1.94/2.08 tff(225,plain,
% 1.94/2.08 (((~![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(Ax!38, Ax!34, wth) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)) | ![I4: $i] : model(I4, Ax!34))) | (~((~status(Ax!38, Ax!34, wth)) | (~(model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I1_0(Ax!38), Ax!38)) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34)))))))))) <=> ((~![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)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)))))))))),
% 1.94/2.08 inference(transitivity,[status(thm)],[224, 222])).
% 1.94/2.08 tff(226,plain,
% 1.94/2.08 ((~![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(Ax!38, Ax!34, wth) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)) | ![I4: $i] : model(I4, Ax!34))) | (~((~status(Ax!38, Ax!34, wth)) | (~(model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I1_0(Ax!38), Ax!38)) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34)))))))))),
% 1.94/2.08 inference(quant_inst,[status(thm)],[])).
% 1.94/2.08 tff(227,plain,
% 1.94/2.08 ((~![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)))))))))) | (~((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))))))))),
% 1.94/2.08 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.94/2.08 tff(228,plain,
% 1.94/2.08 (~((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)))))))),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[227, 221])).
% 1.94/2.08 tff(229,plain,
% 1.94/2.08 (((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))))))) | ((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)))))),
% 1.94/2.08 inference(tautology,[status(thm)],[])).
% 1.94/2.08 tff(230,plain,
% 1.94/2.08 ((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))))),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[229, 228])).
% 1.94/2.08 tff(231,plain,
% 1.94/2.08 ((~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34)))))) | (~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))))),
% 1.94/2.08 inference(tautology,[status(thm)],[])).
% 1.94/2.08 tff(232,plain,
% 1.94/2.08 ((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))))),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[231, 230])).
% 1.94/2.08 tff(233,plain,
% 1.94/2.08 (~status(Ax!38, Ax!34, wth)),
% 1.94/2.08 inference(unit_resolution,[status(thm)],[232, 199])).
% 1.94/2.08 tff(234,plain,
% 1.94/2.08 (((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | (~((~status(Ax!38, Ax!34, wth)) | (~((~model(tptp_fun_I1_0(Ax!38), Ax!38)) | model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!38) | (~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, Ax!34))) | model(tptp_fun_I4_12(Ax!34), Ax!34) | (~model(tptp_fun_I3_6(Ax!34, Ax!38), Ax!34))))))) | (![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))),
% 1.94/2.09 inference(tautology,[status(thm)],[])).
% 1.94/2.09 tff(235,plain,
% 1.94/2.09 (![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[234, 228])).
% 1.94/2.09 tff(236,assumption,(![I1: $i] : (~model(I1, Ax!38))), introduced(assumption)).
% 1.94/2.09 tff(237,plain,
% 1.94/2.09 (model(I1!39, Ax!38)),
% 1.94/2.09 inference(and_elim,[status(thm)],[173])).
% 1.94/2.09 tff(238,plain,
% 1.94/2.09 ((~![I1: $i] : (~model(I1, Ax!38))) | (~model(I1!39, Ax!38))),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(239,plain,
% 1.94/2.09 ($false),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[238, 237, 236])).
% 1.94/2.09 tff(240,plain,(~![I1: $i] : (~model(I1, Ax!38))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.09 tff(241,plain,
% 1.94/2.09 ((~(![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38)))) | ![I1: $i] : (~model(I1, Ax!38)) | ![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))),
% 1.94/2.09 inference(tautology,[status(thm)],[])).
% 1.94/2.09 tff(242,plain,
% 1.94/2.09 (![I4: $i] : model(I4, Ax!34) | (~((~model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!38)) | model(tptp_fun_I2_7(Ax!34, Ax!38), Ax!34))) | status(Ax!38, Ax!34, wth) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[241, 240, 235])).
% 1.94/2.09 tff(243,plain,
% 1.94/2.09 (![I4: $i] : model(I4, Ax!34) | ![I3: $i] : ((~model(I3, Ax!34)) | model(I3, Ax!38))),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[242, 233, 189])).
% 1.94/2.09 tff(244,plain,
% 1.94/2.09 (![I4: $i] : model(I4, Ax!34)),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[243, 179])).
% 1.94/2.09 tff(245,plain,
% 1.94/2.09 ((~![I4: $i] : model(I4, Ax!34)) | model(I2!31, Ax!34)),
% 1.94/2.09 inference(quant_inst,[status(thm)],[])).
% 1.94/2.09 tff(246,plain,
% 1.94/2.09 ($false),
% 1.94/2.09 inference(unit_resolution,[status(thm)],[245, 244, 114])).
% 1.94/2.09 % SZS output end Proof
% 1.94/2.09 % E exiting
%------------------------------------------------------------------------------