%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS217+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:13:35 AM UTC 2025
% Result : Theorem 51.82s 51.98s
% Output : Proof 51.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : KRS217+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.04/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:12:39 EDT 2025
% 0.11/0.32 % CPUTime :
% 51.82/51.98 % SZS status Theorem
% 51.82/51.98 % SZS output start Proof
% 51.82/51.98 tff(model_type, type, (
% 51.82/51.98 model: ( $i * $i ) > $o)).
% 51.82/51.98 tff(tptp_fun_C_42_type, type, (
% 51.82/51.98 tptp_fun_C_42: $i)).
% 51.82/51.98 tff(tptp_fun_F_29_type, type, (
% 51.82/51.98 tptp_fun_F_29: $i)).
% 51.82/51.98 tff(tptp_fun_I2_45_type, type, (
% 51.82/51.98 tptp_fun_I2_45: $i)).
% 51.82/51.98 tff(not_type, type, (
% 51.82/51.98 not: $i > $i)).
% 51.82/51.98 tff(tptp_fun_C_33_type, type, (
% 51.82/51.98 tptp_fun_C_33: $i)).
% 51.82/51.98 tff(tptp_fun_I2_1_type, type, (
% 51.82/51.98 tptp_fun_I2_1: $i > $i)).
% 51.82/51.98 tff(status_type, type, (
% 51.82/51.98 status: ( $i * $i * $i ) > $o)).
% 51.82/51.98 tff(sca_type, type, (
% 51.82/51.98 sca: $i)).
% 51.82/51.98 tff(tptp_fun_I1_0_type, type, (
% 51.82/51.98 tptp_fun_I1_0: $i > $i)).
% 51.82/51.98 tff(tptp_fun_F_28_type, type, (
% 51.82/51.98 tptp_fun_F_28: $i)).
% 51.82/51.98 tff(noc_type, type, (
% 51.82/51.98 noc: $i)).
% 51.82/51.98 tff(nevera_type, type, (
% 51.82/51.98 nevera: ( $i * $i ) > $o)).
% 51.82/51.98 tff(tptp_fun_C_24_type, type, (
% 51.82/51.98 tptp_fun_C_24: ( $i * $i ) > $i)).
% 51.82/51.98 tff(tptp_fun_Ax_25_type, type, (
% 51.82/51.98 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 51.82/51.98 tff(tptp_fun_I2_17_type, type, (
% 51.82/51.98 tptp_fun_I2_17: ( $i * $i ) > $i)).
% 51.82/51.98 tff(tptp_fun_I1_2_type, type, (
% 51.82/51.98 tptp_fun_I1_2: ( $i * $i ) > $i)).
% 51.82/51.98 tff(thm_type, type, (
% 51.82/51.98 thm: $i)).
% 51.82/51.98 tff(tptp_fun_I1_3_type, type, (
% 51.82/51.98 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 51.82/51.98 tff(nota_type, type, (
% 51.82/51.98 nota: ( $i * $i ) > $o)).
% 51.82/51.98 tff(tptp_fun_C_22_type, type, (
% 51.82/51.98 tptp_fun_C_22: ( $i * $i ) > $i)).
% 51.82/51.98 tff(tptp_fun_Ax_23_type, type, (
% 51.82/51.98 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 51.82/51.98 tff(tptp_fun_I1_30_type, type, (
% 51.82/51.98 tptp_fun_I1_30: $i)).
% 51.82/51.98 tff(tptp_fun_I2_31_type, type, (
% 51.82/51.98 tptp_fun_I2_31: $i)).
% 51.82/51.98 tff(tptp_fun_I1_35_type, type, (
% 51.82/51.98 tptp_fun_I1_35: $i)).
% 51.82/51.98 tff(tptp_fun_I2_36_type, type, (
% 51.82/51.98 tptp_fun_I2_36: $i)).
% 51.82/51.98 tff(tptp_fun_Ax_34_type, type, (
% 51.82/51.98 tptp_fun_Ax_34: $i)).
% 51.82/51.98 tff(tptp_fun_I1_44_type, type, (
% 51.82/51.98 tptp_fun_I1_44: $i)).
% 51.82/51.98 tff(tptp_fun_Ax_43_type, type, (
% 51.82/51.98 tptp_fun_Ax_43: $i)).
% 51.82/51.98 tff(tptp_fun_C_37_type, type, (
% 51.82/51.98 tptp_fun_C_37: $i)).
% 51.82/51.98 tff(tptp_fun_I4_41_type, type, (
% 51.82/51.98 tptp_fun_I4_41: $i)).
% 51.82/51.98 tff(tptp_fun_I3_40_type, type, (
% 51.82/51.98 tptp_fun_I3_40: $i)).
% 51.82/51.98 tff(tptp_fun_Ax_38_type, type, (
% 51.82/51.98 tptp_fun_Ax_38: $i)).
% 51.82/51.98 tff(tptp_fun_I1_39_type, type, (
% 51.82/51.98 tptp_fun_I1_39: $i)).
% 51.82/51.98 tff(wth_type, type, (
% 51.82/51.98 wth: $i)).
% 51.82/51.98 tff(tptp_fun_I3_6_type, type, (
% 51.82/51.98 tptp_fun_I3_6: ( $i * $i ) > $i)).
% 51.82/51.98 tff(tptp_fun_I4_12_type, type, (
% 51.82/51.98 tptp_fun_I4_12: $i > $i)).
% 51.82/51.98 tff(tptp_fun_I2_7_type, type, (
% 51.82/51.98 tptp_fun_I2_7: ( $i * $i ) > $i)).
% 51.82/51.98 tff(sap_type, type, (
% 51.82/51.98 sap: $i)).
% 51.82/51.98 tff(mighta_type, type, (
% 51.82/51.98 mighta: ( $i * $i ) > $o)).
% 51.82/51.98 tff(tptp_fun_C_18_type, type, (
% 51.82/51.98 tptp_fun_C_18: ( $i * $i ) > $i)).
% 51.82/51.98 tff(tptp_fun_Ax_19_type, type, (
% 51.82/51.98 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 51.82/51.98 tff(1,assumption,(status(F!28, F!29, noc)), introduced(assumption)).
% 51.82/51.98 tff(2,plain,
% 51.82/51.98 (^[I: $i, F: $i] : refl((~(model(I, F) <=> model(I, not(F)))) <=> (~(model(I, F) <=> model(I, not(F)))))),
% 51.82/51.98 inference(bind,[status(th)],[])).
% 51.82/51.98 tff(3,plain,
% 51.82/51.98 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 51.82/51.98 inference(quant_intro,[status(thm)],[2])).
% 51.82/51.98 tff(4,plain,
% 51.82/51.98 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 51.82/51.98 inference(rewrite,[status(thm)],[])).
% 51.82/51.98 tff(5,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','completeness')).
% 51.82/51.98 tff(6,plain,
% 51.82/51.98 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 51.82/51.98 inference(modus_ponens,[status(thm)],[5, 4])).
% 51.82/51.98 tff(7,plain,(
% 51.82/51.98 ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 51.82/51.98 inference(skolemize,[status(sab)],[6])).
% 51.82/51.98 tff(8,plain,
% 51.82/51.98 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 51.82/51.98 inference(modus_ponens,[status(thm)],[7, 3])).
% 51.82/51.98 tff(9,plain,
% 51.82/51.98 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))))),
% 51.82/51.98 inference(quant_inst,[status(thm)],[])).
% 51.82/51.98 tff(10,plain,
% 51.82/51.98 (~(model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc))))),
% 51.82/51.98 inference(unit_resolution,[status(thm)],[9, 8])).
% 51.82/51.98 tff(11,plain,
% 51.82/51.98 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))))))),
% 51.82/51.98 inference(bind,[status(th)],[])).
% 51.82/51.98 tff(12,plain,
% 51.82/51.98 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))),
% 51.82/51.98 inference(quant_intro,[status(thm)],[11])).
% 51.82/51.98 tff(13,plain,
% 51.82/51.98 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))))),
% 51.82/51.98 inference(bind,[status(th)],[])).
% 51.82/51.98 tff(14,plain,
% 51.82/51.98 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 51.82/51.98 inference(quant_intro,[status(thm)],[13])).
% 51.82/51.98 tff(15,plain,
% 51.82/51.98 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))))),
% 51.82/51.98 inference(bind,[status(th)],[])).
% 51.82/51.98 tff(16,plain,
% 51.82/51.98 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 51.82/51.98 inference(quant_intro,[status(thm)],[15])).
% 51.82/51.98 tff(17,plain,
% 51.82/51.98 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 51.82/51.98 inference(transitivity,[status(thm)],[16, 14])).
% 51.82/51.98 tff(18,plain,
% 51.82/51.98 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) <=> (status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))), rewrite(((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) <=> ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))), (((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> ((status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))) & ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))))), rewrite(((status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))) & ((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))), (((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))))),
% 51.82/51.98 inference(bind,[status(th)],[])).
% 51.82/51.98 tff(19,plain,
% 51.82/51.98 (![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 51.82/51.99 inference(quant_intro,[status(thm)],[18])).
% 51.82/51.99 tff(20,plain,
% 51.82/51.99 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc)))) <=> ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C))))))),
% 51.82/51.99 inference(bind,[status(th)],[])).
% 51.82/51.99 tff(21,plain,
% 51.82/51.99 (![Ax: $i, C: $i] : (((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))))),
% 51.82/51.99 inference(quant_intro,[status(thm)],[20])).
% 51.82/51.99 tff(22,plain,
% 51.82/51.99 (![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))),
% 51.82/51.99 inference(rewrite,[status(thm)],[])).
% 51.82/51.99 tff(23,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','noc')).
% 51.82/51.99 tff(24,plain,
% 51.82/51.99 (![Ax: $i, C: $i] : ((?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : (model(I2, Ax) & model(I2, not(C)))) <=> status(Ax, C, noc))),
% 51.82/51.99 inference(modus_ponens,[status(thm)],[23, 22])).
% 51.82/51.99 tff(25,plain,(
% 51.82/51.99 ![Ax: $i, C: $i] : (((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) | status(Ax, C, noc)) & (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) & (model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))) | (~status(Ax, C, noc))))),
% 51.82/51.99 inference(skolemize,[status(sab)],[24])).
% 51.82/51.99 tff(26,plain,
% 51.82/51.99 (![Ax: $i, C: $i] : ((status(Ax, C, noc) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | ![I2: $i] : (~(model(I2, Ax) & model(I2, not(C))))) & ((~status(Ax, C, noc)) | (model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C) & model(tptp_fun_I2_17(C, Ax), Ax) & model(tptp_fun_I2_17(C, Ax), not(C)))))),
% 51.82/51.99 inference(modus_ponens,[status(thm)],[25, 21])).
% 51.82/51.99 tff(27,plain,
% 51.82/51.99 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 51.82/51.99 inference(modus_ponens,[status(thm)],[26, 19])).
% 51.82/51.99 tff(28,plain,
% 51.82/51.99 (![Ax: $i, C: $i] : (~((~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C)))))) | (~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C)))))))))),
% 51.82/51.99 inference(modus_ponens,[status(thm)],[27, 17])).
% 51.82/51.99 tff(29,plain,
% 51.82/51.99 (![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))),
% 51.82/51.99 inference(modus_ponens,[status(thm)],[28, 12])).
% 51.82/51.99 tff(30,plain,
% 51.82/51.99 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc))))))))))),
% 51.82/51.99 inference(rewrite,[status(thm)],[])).
% 51.82/51.99 tff(31,plain,
% 51.82/51.99 ((~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc))))))))) <=> (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc)))))))))),
% 51.82/51.99 inference(rewrite,[status(thm)],[])).
% 51.82/51.99 tff(32,plain,
% 51.82/51.99 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc))))))))))),
% 51.82/51.99 inference(monotonicity,[status(thm)],[31])).
% 51.82/51.99 tff(33,plain,
% 51.82/51.99 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc))))))))))),
% 51.82/51.99 inference(transitivity,[status(thm)],[32, 30])).
% 51.82/51.99 tff(34,plain,
% 51.82/51.99 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc)))))))))),
% 51.82/51.99 inference(quant_inst,[status(thm)],[])).
% 51.82/51.99 tff(35,plain,
% 51.82/51.99 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc)))))))))),
% 51.82/51.99 inference(modus_ponens,[status(thm)],[34, 33])).
% 51.82/51.99 tff(36,plain,
% 51.82/51.99 (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc))))))))),
% 51.82/51.99 inference(unit_resolution,[status(thm)],[35, 29])).
% 51.82/51.99 tff(37,plain,
% 51.82/51.99 (((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | (~model(I1, tptp_fun_C_24(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_25(noc, noc))) | (~model(I2, not(tptp_fun_C_24(noc, noc)))))))) | ((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))),
% 51.82/51.99 inference(tautology,[status(thm)],[])).
% 51.82/51.99 tff(38,plain,
% 51.82/51.99 ((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc)))))),
% 51.82/51.99 inference(unit_resolution,[status(thm)],[37, 36])).
% 51.82/51.99 tff(39,assumption,(status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)), introduced(assumption)).
% 51.82/51.99 tff(40,plain,
% 51.82/51.99 ((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc)))))),
% 51.82/51.99 inference(tautology,[status(thm)],[])).
% 51.82/51.99 tff(41,plain,
% 51.82/51.99 ((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))))) | (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc)))))),
% 51.82/51.99 inference(unit_resolution,[status(thm)],[40, 39])).
% 51.82/51.99 tff(42,plain,
% 51.82/51.99 (~((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))))),
% 51.82/51.99 inference(unit_resolution,[status(thm)],[41, 38])).
% 51.82/51.99 tff(43,plain,
% 51.82/51.99 (((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc)))) | model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))),
% 51.82/51.99 inference(tautology,[status(thm)],[])).
% 51.82/51.99 tff(44,plain,
% 51.82/51.99 (model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))),
% 51.82/51.99 inference(unit_resolution,[status(thm)],[43, 42])).
% 51.82/51.99 tff(45,plain,
% 51.82/51.99 ((model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc))))),
% 51.82/51.99 inference(tautology,[status(thm)],[])).
% 51.82/51.99 tff(46,plain,
% 51.82/51.99 ((model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))),
% 51.82/51.99 inference(unit_resolution,[status(thm)],[45, 44])).
% 51.82/51.99 tff(47,plain,
% 51.82/51.99 (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))),
% 51.82/51.99 inference(unit_resolution,[status(thm)],[46, 10])).
% 51.82/51.99 tff(48,plain,
% 51.82/51.99 (^[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)))))))),
% 51.82/51.99 inference(bind,[status(th)],[])).
% 51.82/51.99 tff(49,plain,
% 51.82/51.99 (![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))))))),
% 51.82/51.99 inference(quant_intro,[status(thm)],[48])).
% 51.82/51.99 tff(50,plain,
% 51.82/51.99 (^[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)))))))),
% 51.82/51.99 inference(bind,[status(th)],[])).
% 51.82/51.99 tff(51,plain,
% 51.82/51.99 (![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))))))),
% 51.82/51.99 inference(quant_intro,[status(thm)],[50])).
% 51.82/51.99 tff(52,plain,
% 51.82/51.99 (^[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)))))))),
% 51.82/51.99 inference(bind,[status(th)],[])).
% 51.82/51.99 tff(53,plain,
% 51.82/51.99 (![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))))))),
% 51.82/51.99 inference(quant_intro,[status(thm)],[52])).
% 51.82/51.99 tff(54,plain,
% 51.82/51.99 (![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))))))),
% 51.82/51.99 inference(transitivity,[status(thm)],[53, 51])).
% 51.82/51.99 tff(55,plain,
% 51.82/51.99 (^[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))))))))),
% 51.82/51.99 inference(bind,[status(th)],[])).
% 51.82/51.99 tff(56,plain,
% 51.82/51.99 (![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))))))),
% 51.82/51.99 inference(quant_intro,[status(thm)],[55])).
% 51.82/51.99 tff(57,plain,
% 51.82/51.99 (![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))),
% 51.82/51.99 inference(rewrite,[status(thm)],[])).
% 51.82/51.99 tff(58,plain,
% 51.82/51.99 (^[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)))),
% 51.82/51.99 inference(bind,[status(th)],[])).
% 51.82/51.99 tff(59,plain,
% 51.82/51.99 (![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))),
% 51.82/51.99 inference(quant_intro,[status(thm)],[58])).
% 51.82/51.99 tff(60,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','thm')).
% 51.82/52.00 tff(61,plain,
% 51.82/52.00 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[60, 59])).
% 51.82/52.00 tff(62,plain,
% 51.82/52.00 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[61, 57])).
% 51.82/52.00 tff(63,plain,(
% 51.82/52.00 ![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))))),
% 51.82/52.00 inference(skolemize,[status(sab)],[62])).
% 51.82/52.00 tff(64,plain,
% 51.82/52.00 (![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))))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[63, 56])).
% 51.82/52.00 tff(65,plain,
% 51.82/52.00 (![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))))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[64, 54])).
% 51.82/52.00 tff(66,plain,
% 51.82/52.00 (![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))))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[65, 49])).
% 51.82/52.00 tff(67,plain,
% 51.82/52.00 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))))))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(68,plain,
% 51.82/52.00 ((~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))) | (~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))))) <=> (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)))))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(69,plain,
% 51.82/52.00 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))) | (~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))))))),
% 51.82/52.00 inference(monotonicity,[status(thm)],[68])).
% 51.82/52.00 tff(70,plain,
% 51.82/52.00 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))) | (~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))))))),
% 51.82/52.00 inference(transitivity,[status(thm)],[69, 67])).
% 51.82/52.00 tff(71,plain,
% 51.82/52.00 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))) | (~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))))))),
% 51.82/52.00 inference(quant_inst,[status(thm)],[])).
% 51.82/52.00 tff(72,plain,
% 51.82/52.00 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[71, 70])).
% 51.82/52.00 tff(73,plain,
% 51.82/52.00 (~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[72, 66])).
% 51.82/52.00 tff(74,plain,
% 51.82/52.00 (((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I1_3(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)))) | ((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))),
% 51.82/52.00 inference(tautology,[status(thm)],[])).
% 51.82/52.00 tff(75,plain,
% 51.82/52.00 ((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[74, 73])).
% 51.82/52.00 tff(76,plain,
% 51.82/52.00 (^[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))))))))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(77,plain,
% 51.82/52.00 (![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)))))))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[76])).
% 51.82/52.00 tff(78,plain,
% 51.82/52.00 (^[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))))))))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(79,plain,
% 51.82/52.00 (![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)))))))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[78])).
% 51.82/52.00 tff(80,plain,
% 51.82/52.00 (![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)))))))),
% 51.82/52.00 inference(transitivity,[status(thm)],[79, 77])).
% 51.82/52.00 tff(81,plain,
% 51.82/52.00 (^[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)))))))))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(82,plain,
% 51.82/52.00 (![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)))))))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[81])).
% 51.82/52.00 tff(83,plain,
% 51.82/52.00 (^[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)))))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(84,plain,
% 51.82/52.00 (![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))))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[83])).
% 51.82/52.00 tff(85,plain,
% 51.82/52.00 (![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))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(86,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nota')).
% 51.82/52.00 tff(87,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[86, 85])).
% 51.82/52.00 tff(88,plain,(
% 51.82/52.00 ![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))))),
% 51.82/52.00 inference(skolemize,[status(sab)],[87])).
% 51.82/52.00 tff(89,plain,
% 51.82/52.00 (![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))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[88, 84])).
% 51.82/52.00 tff(90,plain,
% 51.82/52.00 (![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)))))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[89, 82])).
% 51.82/52.00 tff(91,plain,
% 51.82/52.00 (![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)))))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[90, 80])).
% 51.82/52.00 tff(92,plain,
% 51.82/52.00 ((~![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(noc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm)))) | (~((~nota(noc, thm)) | (~((~status(tptp_fun_Ax_23(thm, noc), tptp_fun_C_22(thm, noc), noc)) | status(tptp_fun_Ax_23(thm, noc), tptp_fun_C_22(thm, noc), thm)))))))),
% 51.82/52.00 inference(quant_inst,[status(thm)],[])).
% 51.82/52.00 tff(93,plain,
% 51.82/52.00 (~((~(nota(noc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm)))) | (~((~nota(noc, thm)) | (~((~status(tptp_fun_Ax_23(thm, noc), tptp_fun_C_22(thm, noc), noc)) | status(tptp_fun_Ax_23(thm, noc), tptp_fun_C_22(thm, noc), thm))))))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[92, 91])).
% 51.82/52.00 tff(94,plain,
% 51.82/52.00 (((~(nota(noc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm)))) | (~((~nota(noc, thm)) | (~((~status(tptp_fun_Ax_23(thm, noc), tptp_fun_C_22(thm, noc), noc)) | status(tptp_fun_Ax_23(thm, noc), tptp_fun_C_22(thm, noc), thm)))))) | (nota(noc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm)))),
% 51.82/52.00 inference(tautology,[status(thm)],[])).
% 51.82/52.00 tff(95,plain,
% 51.82/52.00 (nota(noc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[94, 93])).
% 51.82/52.00 tff(96,plain,
% 51.82/52.00 ((~nota(noc, thm)) <=> (~nota(noc, thm))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(97,axiom,(~nota(noc, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nota_noc_thm')).
% 51.82/52.00 tff(98,plain,
% 51.82/52.00 (~nota(noc, thm)),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[97, 96])).
% 51.82/52.00 tff(99,plain,
% 51.82/52.00 ((~(nota(noc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm)))) | nota(noc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm))),
% 51.82/52.00 inference(tautology,[status(thm)],[])).
% 51.82/52.00 tff(100,plain,
% 51.82/52.00 ((~(nota(noc, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[99, 98])).
% 51.82/52.00 tff(101,plain,
% 51.82/52.00 (![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[100, 95])).
% 51.82/52.00 tff(102,plain,
% 51.82/52.00 (((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(103,plain,
% 51.82/52.00 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm))),
% 51.82/52.00 inference(quant_inst,[status(thm)],[])).
% 51.82/52.00 tff(104,plain,
% 51.82/52.00 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[103, 102])).
% 51.82/52.00 tff(105,plain,
% 51.82/52.00 (status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[104, 101, 39])).
% 51.82/52.00 tff(106,plain,
% 51.82/52.00 ((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | (~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))),
% 51.82/52.00 inference(tautology,[status(thm)],[])).
% 51.82/52.00 tff(107,plain,
% 51.82/52.00 ((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc))))) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[106, 105])).
% 51.82/52.00 tff(108,plain,
% 51.82/52.00 (![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[107, 75])).
% 51.82/52.00 tff(109,plain,
% 51.82/52.00 (((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), not(tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc)))) | model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))),
% 51.82/52.00 inference(tautology,[status(thm)],[])).
% 51.82/52.00 tff(110,plain,
% 51.82/52.00 (model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[109, 42])).
% 51.82/52.00 tff(111,plain,
% 51.82/52.00 (((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))) | ((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))) <=> ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(112,plain,
% 51.82/52.00 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))) | ((~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc)))),
% 51.82/52.00 inference(quant_inst,[status(thm)],[])).
% 51.82/52.00 tff(113,plain,
% 51.82/52.00 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(noc, noc))) | model(I1, tptp_fun_C_24(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_Ax_25(noc, noc))) | model(tptp_fun_I2_17(tptp_fun_C_24(noc, noc), tptp_fun_Ax_25(noc, noc)), tptp_fun_C_24(noc, noc))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[112, 111])).
% 51.82/52.00 tff(114,plain,
% 51.82/52.00 ($false),
% 51.82/52.00 inference(unit_resolution,[status(thm)],[113, 110, 108, 47])).
% 51.82/52.00 tff(115,plain,(~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)), inference(lemma,lemma(discharge,[]))).
% 51.82/52.00 tff(116,plain,
% 51.82/52.00 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))))))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(117,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[116])).
% 51.82/52.00 tff(118,plain,
% 51.82/52.00 (^[S1: $i, S2: $i] : refl((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(119,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[118])).
% 51.82/52.00 tff(120,plain,
% 51.82/52.00 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(121,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[120])).
% 51.82/52.00 tff(122,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 51.82/52.00 inference(transitivity,[status(thm)],[121, 119])).
% 51.82/52.00 tff(123,plain,
% 51.82/52.00 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))), rewrite((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(124,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[123])).
% 51.82/52.00 tff(125,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(126,plain,
% 51.82/52.00 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)))),
% 51.82/52.00 inference(bind,[status(th)],[])).
% 51.82/52.00 tff(127,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 51.82/52.00 inference(quant_intro,[status(thm)],[126])).
% 51.82/52.00 tff(128,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nevera')).
% 51.82/52.00 tff(129,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[128, 127])).
% 51.82/52.00 tff(130,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[129, 125])).
% 51.82/52.00 tff(131,plain,(
% 51.82/52.00 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))),
% 51.82/52.00 inference(skolemize,[status(sab)],[130])).
% 51.82/52.00 tff(132,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[131, 124])).
% 51.82/52.00 tff(133,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[132, 122])).
% 51.82/52.00 tff(134,plain,
% 51.82/52.00 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 51.82/52.00 inference(modus_ponens,[status(thm)],[133, 117])).
% 51.82/52.00 tff(135,plain,
% 51.82/52.00 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))))))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(136,plain,
% 51.82/52.00 ((~((~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)))) | nevera(noc, noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, noc))))))) <=> (~((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))))))),
% 51.82/52.00 inference(rewrite,[status(thm)],[])).
% 51.82/52.00 tff(137,plain,
% 51.82/52.00 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)))) | nevera(noc, noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, noc)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))))))),
% 51.82/52.01 inference(monotonicity,[status(thm)],[136])).
% 51.82/52.01 tff(138,plain,
% 51.82/52.01 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)))) | nevera(noc, noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, noc)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))))))),
% 51.82/52.01 inference(transitivity,[status(thm)],[137, 135])).
% 51.82/52.01 tff(139,plain,
% 51.82/52.01 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)) | (~status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)))) | nevera(noc, noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, noc)))))))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(140,plain,
% 51.82/52.01 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))))))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[139, 138])).
% 51.82/52.01 tff(141,plain,
% 51.82/52.01 (~((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[140, 134])).
% 51.82/52.01 tff(142,plain,
% 51.82/52.01 (((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))))) | (nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(143,plain,
% 51.82/52.01 (nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[142, 141])).
% 51.82/52.01 tff(144,plain,
% 51.82/52.01 ((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(145,plain,
% 51.82/52.01 (nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc)),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[144, 143])).
% 51.82/52.01 tff(146,plain,
% 51.82/52.01 (nevera(noc, noc)),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[145, 115])).
% 51.82/52.01 tff(147,plain,
% 51.82/52.01 (((~(nevera(noc, noc) | status(tptp_fun_Ax_25(noc, noc), tptp_fun_C_24(noc, noc), noc))) | (~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))))) | ((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(148,plain,
% 51.82/52.01 ((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[147, 141])).
% 51.82/52.01 tff(149,plain,
% 51.82/52.01 ((~((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(150,plain,
% 51.82/52.01 ((~nevera(noc, noc)) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[149, 148])).
% 51.82/52.01 tff(151,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (~status(Ax, C, noc))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[150, 146])).
% 51.82/52.01 tff(152,plain,
% 51.82/52.01 ((~![Ax: $i, C: $i] : (~status(Ax, C, noc))) | (~status(F!28, F!29, noc))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(153,plain,
% 51.82/52.01 ($false),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[152, 151, 1])).
% 51.82/52.01 tff(154,plain,(~status(F!28, F!29, noc)), inference(lemma,lemma(discharge,[]))).
% 51.82/52.01 tff(155,assumption,(![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))), introduced(assumption)).
% 51.82/52.01 tff(156,assumption,(~model(I1!30, F!28)), introduced(assumption)).
% 51.82/52.01 tff(157,plain,
% 51.82/52.01 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 51.82/52.01 inference(bind,[status(th)],[])).
% 51.82/52.01 tff(158,plain,
% 51.82/52.01 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 51.82/52.01 inference(quant_intro,[status(thm)],[157])).
% 51.82/52.01 tff(159,plain,
% 51.82/52.01 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(160,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','tautology')).
% 51.82/52.01 tff(161,plain,
% 51.82/52.01 (?[F: $i] : ![I: $i] : model(I, F)),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[160, 159])).
% 51.82/52.01 tff(162,plain,(
% 51.82/52.01 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 51.82/52.01 inference(transitivity,[status(sab)],[161])).
% 51.82/52.01 tff(163,plain,
% 51.82/52.01 (![I: $i] : model(I, F!28)),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[162, 158])).
% 51.82/52.01 tff(164,plain,
% 51.82/52.01 ((~![I: $i] : model(I, F!28)) | model(I1!30, F!28)),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(165,plain,
% 51.82/52.01 ($false),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[164, 163, 156])).
% 51.82/52.01 tff(166,plain,(model(I1!30, F!28)), inference(lemma,lemma(discharge,[]))).
% 51.82/52.01 tff(167,plain,
% 51.82/52.01 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(168,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 51.82/52.01 tff(169,plain,
% 51.82/52.01 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[168, 167])).
% 51.82/52.01 tff(170,plain,
% 51.82/52.01 (model(I1!30, F!29)),
% 51.82/52.01 inference(and_elim,[status(thm)],[169])).
% 51.82/52.01 tff(171,plain,
% 51.82/52.01 (((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))) | ((~model(I1!30, F!28)) | (~model(I1!30, F!29)))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))) | (~model(I1!30, F!28)) | (~model(I1!30, F!29)))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(172,plain,
% 51.82/52.01 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))) | ((~model(I1!30, F!28)) | (~model(I1!30, F!29)))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(173,plain,
% 51.82/52.01 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))) | (~model(I1!30, F!28)) | (~model(I1!30, F!29))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[172, 171])).
% 51.82/52.01 tff(174,plain,
% 51.82/52.01 ($false),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[173, 170, 166, 155])).
% 51.82/52.01 tff(175,plain,(~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.01 tff(176,plain,
% 51.82/52.01 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!28, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, F!28), F!28)) | (~model(tptp_fun_I1_2(F!29, F!28), F!29)) | (~model(tptp_fun_I2_17(F!29, F!28), F!28)) | (~model(tptp_fun_I2_17(F!29, F!28), not(F!29))))))) | (~(status(F!28, F!29, noc) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))))))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(177,plain,
% 51.82/52.01 (~((~((~status(F!28, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, F!28), F!28)) | (~model(tptp_fun_I1_2(F!29, F!28), F!29)) | (~model(tptp_fun_I2_17(F!29, F!28), F!28)) | (~model(tptp_fun_I2_17(F!29, F!28), not(F!29))))))) | (~(status(F!28, F!29, noc) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29)))))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[176, 29])).
% 51.82/52.01 tff(178,plain,
% 51.82/52.01 (((~((~status(F!28, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, F!28), F!28)) | (~model(tptp_fun_I1_2(F!29, F!28), F!29)) | (~model(tptp_fun_I2_17(F!29, F!28), F!28)) | (~model(tptp_fun_I2_17(F!29, F!28), not(F!29))))))) | (~(status(F!28, F!29, noc) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))))) | (status(F!28, F!29, noc) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29)))))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(179,plain,
% 51.82/52.01 (status(F!28, F!29, noc) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[178, 177])).
% 51.82/52.01 tff(180,plain,
% 51.82/52.01 ((~(status(F!28, F!29, noc) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29)))))) | status(F!28, F!29, noc) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(181,plain,
% 51.82/52.01 (status(F!28, F!29, noc) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[180, 179])).
% 51.82/52.01 tff(182,plain,
% 51.82/52.01 (status(F!28, F!29, noc) | ![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[181, 175])).
% 51.82/52.01 tff(183,plain,
% 51.82/52.01 (![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[182, 154])).
% 51.82/52.01 tff(184,plain,
% 51.82/52.01 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I1_0(not(F!29)), F!28)),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(185,plain,
% 51.82/52.01 (model(tptp_fun_I1_0(not(F!29)), F!28)),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[184, 163])).
% 51.82/52.01 tff(186,plain,
% 51.82/52.01 (((~![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))) | ((~model(tptp_fun_I1_0(not(F!29)), F!28)) | (~model(tptp_fun_I1_0(not(F!29)), not(F!29))))) <=> ((~![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))) | (~model(tptp_fun_I1_0(not(F!29)), F!28)) | (~model(tptp_fun_I1_0(not(F!29)), not(F!29))))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(187,plain,
% 51.82/52.01 ((~![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))) | ((~model(tptp_fun_I1_0(not(F!29)), F!28)) | (~model(tptp_fun_I1_0(not(F!29)), not(F!29))))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(188,plain,
% 51.82/52.01 ((~![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))) | (~model(tptp_fun_I1_0(not(F!29)), F!28)) | (~model(tptp_fun_I1_0(not(F!29)), not(F!29)))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[187, 186])).
% 51.82/52.01 tff(189,plain,
% 51.82/52.01 (~model(tptp_fun_I1_0(not(F!29)), not(F!29))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[188, 185, 183])).
% 51.82/52.01 tff(190,assumption,(![I2: $i] : (~model(I2, C!33))), introduced(assumption)).
% 51.82/52.01 tff(191,plain,
% 51.82/52.01 (((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))))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(192,plain,
% 51.82/52.01 (?[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))))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(193,axiom,(?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','sat_non_taut_pair')).
% 51.82/52.01 tff(194,plain,
% 51.82/52.01 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[193, 192])).
% 51.82/52.01 tff(195,plain,
% 51.82/52.01 (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[194, 191])).
% 51.82/52.01 tff(196,plain,
% 51.82/52.01 (model(I1!35, C!33)),
% 51.82/52.01 inference(and_elim,[status(thm)],[195])).
% 51.82/52.01 tff(197,plain,
% 51.82/52.01 ((~![I2: $i] : (~model(I2, C!33))) | (~model(I1!35, C!33))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(198,plain,
% 51.82/52.01 ($false),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[197, 196, 190])).
% 51.82/52.01 tff(199,plain,(~![I2: $i] : (~model(I2, C!33))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.01 tff(200,plain,
% 51.82/52.01 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 51.82/52.01 inference(bind,[status(th)],[])).
% 51.82/52.01 tff(201,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 51.82/52.01 inference(quant_intro,[status(thm)],[200])).
% 51.82/52.01 tff(202,plain,
% 51.82/52.01 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 51.82/52.01 inference(bind,[status(th)],[])).
% 51.82/52.01 tff(203,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 51.82/52.01 inference(quant_intro,[status(thm)],[202])).
% 51.82/52.01 tff(204,plain,
% 51.82/52.01 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 51.82/52.01 inference(bind,[status(th)],[])).
% 51.82/52.01 tff(205,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 51.82/52.01 inference(quant_intro,[status(thm)],[204])).
% 51.82/52.01 tff(206,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 51.82/52.01 inference(transitivity,[status(thm)],[205, 203])).
% 51.82/52.01 tff(207,plain,
% 51.82/52.01 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) <=> (status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))), trans(monotonicity(rewrite((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) <=> (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))) <=> ((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, sca))))), rewrite(((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, sca))) <=> ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))) <=> ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))), (((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))), rewrite(((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))), (((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))))),
% 51.82/52.01 inference(bind,[status(th)],[])).
% 51.82/52.01 tff(208,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 51.82/52.01 inference(quant_intro,[status(thm)],[207])).
% 51.82/52.01 tff(209,plain,
% 51.82/52.01 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))))),
% 51.82/52.01 inference(bind,[status(th)],[])).
% 51.82/52.01 tff(210,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 51.82/52.01 inference(quant_intro,[status(thm)],[209])).
% 51.82/52.01 tff(211,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(212,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','sca')).
% 51.82/52.01 tff(213,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[212, 211])).
% 51.82/52.01 tff(214,plain,(
% 51.82/52.01 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 51.82/52.01 inference(skolemize,[status(sab)],[213])).
% 51.82/52.01 tff(215,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[214, 210])).
% 51.82/52.01 tff(216,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[215, 208])).
% 51.82/52.01 tff(217,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[216, 206])).
% 51.82/52.01 tff(218,plain,
% 51.82/52.01 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[217, 201])).
% 51.82/52.01 tff(219,plain,
% 51.82/52.01 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33)))) | (~((~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29))))))))))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(220,plain,
% 51.82/52.01 (~((~(status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33)))) | (~((~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29)))))))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[219, 218])).
% 51.82/52.01 tff(221,plain,
% 51.82/52.01 (((~(status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33)))) | (~((~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29))))))))) | (status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33)))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(222,plain,
% 51.82/52.01 (status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[221, 220])).
% 51.82/52.01 tff(223,plain,
% 51.82/52.01 ((~(status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33)))) | status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(224,plain,
% 51.82/52.01 (status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[223, 222])).
% 51.82/52.01 tff(225,plain,
% 51.82/52.01 (status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[224, 199])).
% 51.82/52.01 tff(226,plain,
% 51.82/52.01 (status(not(F!29), C!33, sca)),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[225, 189])).
% 51.82/52.01 tff(227,plain,
% 51.82/52.01 (((~(status(not(F!29), C!33, sca) | model(tptp_fun_I1_0(not(F!29)), not(F!29)) | ![I2: $i] : (~model(I2, C!33)))) | (~((~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29))))))))) | ((~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29)))))))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(228,plain,
% 51.82/52.01 ((~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29))))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[227, 220])).
% 51.82/52.01 tff(229,plain,
% 51.82/52.01 ((~((~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29)))))))) | (~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29))))))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(230,plain,
% 51.82/52.01 ((~status(not(F!29), C!33, sca)) | (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29))))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[229, 228])).
% 51.82/52.01 tff(231,plain,
% 51.82/52.01 (~((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29)))))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[230, 226])).
% 51.82/52.01 tff(232,plain,
% 51.82/52.01 (((~model(tptp_fun_I2_1(C!33), C!33)) | (~![I1: $i] : (~model(I1, not(F!29))))) | ![I1: $i] : (~model(I1, not(F!29)))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(233,plain,
% 51.82/52.01 (![I1: $i] : (~model(I1, not(F!29)))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[232, 231])).
% 51.82/52.01 tff(234,assumption,(![I1: $i] : (~model(I1, not(F!29)))), introduced(assumption)).
% 51.82/52.01 tff(235,assumption,(model(I2!45, not(F!29))), introduced(assumption)).
% 51.82/52.01 tff(236,plain,
% 51.82/52.01 ((~![I1: $i] : (~model(I1, not(F!29)))) | (~model(I2!45, not(F!29)))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(237,plain,
% 51.82/52.01 ($false),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[236, 235, 234])).
% 51.82/52.01 tff(238,plain,((~![I1: $i] : (~model(I1, not(F!29)))) | (~model(I2!45, not(F!29)))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.01 tff(239,plain,
% 51.82/52.01 (~model(I2!45, not(F!29))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[238, 233])).
% 51.82/52.01 tff(240,plain,
% 51.82/52.01 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I2!45, F!29) <=> model(I2!45, not(F!29))))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(241,plain,
% 51.82/52.01 (~(model(I2!45, F!29) <=> model(I2!45, not(F!29)))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[240, 8])).
% 51.82/52.01 tff(242,plain,
% 51.82/52.01 ((model(I2!45, F!29) <=> model(I2!45, not(F!29))) | model(I2!45, F!29) | model(I2!45, not(F!29))),
% 51.82/52.01 inference(tautology,[status(thm)],[])).
% 51.82/52.01 tff(243,plain,
% 51.82/52.01 (model(I2!45, F!29) | model(I2!45, not(F!29))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[242, 241])).
% 51.82/52.01 tff(244,plain,
% 51.82/52.01 (model(I2!45, F!29)),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[243, 239])).
% 51.82/52.01 tff(245,assumption,(![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42)))), introduced(assumption)).
% 51.82/52.01 tff(246,assumption,(model(I2!45, F!29)), introduced(assumption)).
% 51.82/52.01 tff(247,plain,
% 51.82/52.01 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C)) <=> ?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(248,plain,
% 51.82/52.01 (^[I1: $i, Ax: $i, C: $i] : rewrite(((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C)) <=> (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C)))),
% 51.82/52.01 inference(bind,[status(th)],[])).
% 51.82/52.01 tff(249,plain,
% 51.82/52.01 (?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C)) <=> ?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 51.82/52.01 inference(quant_intro,[status(thm)],[248])).
% 51.82/52.01 tff(250,axiom,(?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','non_thm_spt')).
% 51.82/52.01 tff(251,plain,
% 51.82/52.01 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[250, 249])).
% 51.82/52.01 tff(252,plain,
% 51.82/52.01 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[251, 247])).
% 51.82/52.01 tff(253,plain,
% 51.82/52.01 (model(I2!45, C!42)),
% 51.82/52.01 inference(and_elim,[status(thm)],[252])).
% 51.82/52.01 tff(254,plain,
% 51.82/52.01 (((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42)))) | ((~model(I2!45, F!29)) | (~model(I2!45, C!42)))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42)))) | (~model(I2!45, F!29)) | (~model(I2!45, C!42)))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(255,plain,
% 51.82/52.01 ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42)))) | ((~model(I2!45, F!29)) | (~model(I2!45, C!42)))),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(256,plain,
% 51.82/52.01 ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42)))) | (~model(I2!45, F!29)) | (~model(I2!45, C!42))),
% 51.82/52.01 inference(modus_ponens,[status(thm)],[255, 254])).
% 51.82/52.01 tff(257,plain,
% 51.82/52.01 ($false),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[256, 253, 246, 245])).
% 51.82/52.01 tff(258,plain,((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42)))) | (~model(I2!45, F!29))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.01 tff(259,plain,
% 51.82/52.01 (~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42)))),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[258, 244])).
% 51.82/52.01 tff(260,assumption,(~model(I4!41, F!28)), introduced(assumption)).
% 51.82/52.01 tff(261,plain,
% 51.82/52.01 ((~![I: $i] : model(I, F!28)) | model(I4!41, F!28)),
% 51.82/52.01 inference(quant_inst,[status(thm)],[])).
% 51.82/52.01 tff(262,plain,
% 51.82/52.01 ($false),
% 51.82/52.01 inference(unit_resolution,[status(thm)],[261, 163, 260])).
% 51.82/52.01 tff(263,plain,(model(I4!41, F!28)), inference(lemma,lemma(discharge,[]))).
% 51.82/52.01 tff(264,assumption,(![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37))), introduced(assumption)).
% 51.82/52.01 tff(265,plain,
% 51.82/52.01 ((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)))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(266,plain,
% 51.82/52.01 (?[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)))),
% 51.82/52.01 inference(rewrite,[status(thm)],[])).
% 51.82/52.01 tff(267,plain,
% 51.82/52.01 (^[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)))))),
% 51.82/52.02 inference(bind,[status(th)],[])).
% 51.82/52.02 tff(268,plain,
% 51.82/52.02 (?[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)))),
% 51.82/52.02 inference(quant_intro,[status(thm)],[267])).
% 51.82/52.02 tff(269,axiom,(?[Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : ((~model(I3, Ax)) & model(I3, C))) & ?[I4: $i] : (~model(I4, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','mixed_pair')).
% 51.82/52.02 tff(270,plain,
% 51.82/52.02 (?[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)))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[269, 268])).
% 51.82/52.02 tff(271,plain,
% 51.82/52.02 (?[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)))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[270, 266])).
% 51.82/52.02 tff(272,plain,
% 51.82/52.02 (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))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[271, 265])).
% 51.82/52.02 tff(273,plain,
% 51.82/52.02 (~model(I4!41, C!37)),
% 51.82/52.02 inference(and_elim,[status(thm)],[272])).
% 51.82/52.02 tff(274,plain,
% 51.82/52.02 (((~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37))) | ((~model(I4!41, F!28)) | model(I4!41, C!37))) <=> ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37))) | (~model(I4!41, F!28)) | model(I4!41, C!37))),
% 51.82/52.02 inference(rewrite,[status(thm)],[])).
% 51.82/52.02 tff(275,plain,
% 51.82/52.02 ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37))) | ((~model(I4!41, F!28)) | model(I4!41, C!37))),
% 51.82/52.02 inference(quant_inst,[status(thm)],[])).
% 51.82/52.02 tff(276,plain,
% 51.82/52.02 ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37))) | (~model(I4!41, F!28)) | model(I4!41, C!37)),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[275, 274])).
% 51.82/52.02 tff(277,plain,
% 51.82/52.02 ($false),
% 51.82/52.02 inference(unit_resolution,[status(thm)],[276, 273, 264, 263])).
% 51.82/52.02 tff(278,plain,(~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.02 tff(279,assumption,(![I1: $i] : (~model(I1, C!37))), introduced(assumption)).
% 51.82/52.02 tff(280,plain,
% 51.82/52.02 (model(I3!40, C!37)),
% 51.82/52.02 inference(and_elim,[status(thm)],[272])).
% 51.82/52.02 tff(281,plain,
% 51.82/52.02 ((~![I1: $i] : (~model(I1, C!37))) | (~model(I3!40, C!37))),
% 51.82/52.02 inference(quant_inst,[status(thm)],[])).
% 51.82/52.02 tff(282,plain,
% 51.82/52.02 ($false),
% 51.82/52.02 inference(unit_resolution,[status(thm)],[281, 280, 279])).
% 51.82/52.02 tff(283,plain,(~![I1: $i] : (~model(I1, C!37))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.02 tff(284,assumption,(~model(tptp_fun_I4_12(F!28), F!28)), introduced(assumption)).
% 51.82/52.02 tff(285,plain,
% 51.82/52.02 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I4_12(F!28), F!28)),
% 51.82/52.02 inference(quant_inst,[status(thm)],[])).
% 51.82/52.02 tff(286,plain,
% 51.82/52.02 ($false),
% 51.82/52.02 inference(unit_resolution,[status(thm)],[285, 163, 284])).
% 51.82/52.02 tff(287,plain,(model(tptp_fun_I4_12(F!28), F!28)), inference(lemma,lemma(discharge,[]))).
% 51.82/52.02 tff(288,plain,
% 51.82/52.02 ((model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))) | (~model(tptp_fun_I4_12(F!28), F!28))),
% 51.82/52.02 inference(tautology,[status(thm)],[])).
% 51.82/52.02 tff(289,plain,
% 51.82/52.02 (model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))),
% 51.82/52.02 inference(unit_resolution,[status(thm)],[288, 287])).
% 51.82/52.02 tff(290,plain,
% 51.82/52.02 (^[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))))))))))),
% 51.82/52.02 inference(bind,[status(th)],[])).
% 51.82/52.02 tff(291,plain,
% 51.82/52.02 (![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)))))))))),
% 51.82/52.02 inference(quant_intro,[status(thm)],[290])).
% 51.82/52.02 tff(292,plain,
% 51.82/52.02 (^[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)))))))))),
% 51.82/52.02 inference(bind,[status(th)],[])).
% 51.82/52.02 tff(293,plain,
% 51.82/52.02 (![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))))))))),
% 51.82/52.02 inference(quant_intro,[status(thm)],[292])).
% 51.82/52.02 tff(294,plain,
% 51.82/52.02 (^[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)))))))))),
% 51.82/52.02 inference(bind,[status(th)],[])).
% 51.82/52.02 tff(295,plain,
% 51.82/52.02 (![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))))))))),
% 51.82/52.02 inference(quant_intro,[status(thm)],[294])).
% 51.82/52.02 tff(296,plain,
% 51.82/52.02 (![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))))))))),
% 51.82/52.02 inference(transitivity,[status(thm)],[295, 293])).
% 51.82/52.02 tff(297,plain,
% 51.82/52.02 (^[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))))))))))),
% 51.82/52.02 inference(bind,[status(th)],[])).
% 51.82/52.02 tff(298,plain,
% 51.82/52.02 (![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))))))))),
% 51.82/52.02 inference(quant_intro,[status(thm)],[297])).
% 51.82/52.02 tff(299,plain,
% 51.82/52.02 (^[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))))))),
% 51.82/52.02 inference(bind,[status(th)],[])).
% 51.82/52.02 tff(300,plain,
% 51.82/52.02 (![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)))))),
% 51.82/52.02 inference(quant_intro,[status(thm)],[299])).
% 51.82/52.02 tff(301,plain,
% 51.82/52.02 (![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))),
% 51.82/52.02 inference(rewrite,[status(thm)],[])).
% 51.82/52.02 tff(302,plain,
% 51.82/52.02 (^[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)))),
% 51.82/52.02 inference(bind,[status(th)],[])).
% 51.82/52.02 tff(303,plain,
% 51.82/52.02 (![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))),
% 51.82/52.02 inference(quant_intro,[status(thm)],[302])).
% 51.82/52.02 tff(304,axiom,(![Ax: $i, C: $i] : ((((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) & ?[I4: $i] : (~model(I4, C))) <=> status(Ax, C, wth))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','wth')).
% 51.82/52.02 tff(305,plain,
% 51.82/52.02 (![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))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[304, 303])).
% 51.82/52.02 tff(306,plain,
% 51.82/52.02 (![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))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[305, 301])).
% 51.82/52.02 tff(307,plain,(
% 51.82/52.02 ![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))))),
% 51.82/52.02 inference(skolemize,[status(sab)],[306])).
% 51.82/52.02 tff(308,plain,
% 51.82/52.02 (![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)))))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[307, 300])).
% 51.82/52.02 tff(309,plain,
% 51.82/52.02 (![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))))))))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[308, 298])).
% 51.82/52.02 tff(310,plain,
% 51.82/52.02 (![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))))))))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[309, 296])).
% 51.82/52.02 tff(311,plain,
% 51.82/52.02 (![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)))))))))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[310, 291])).
% 51.82/52.02 tff(312,plain,
% 51.82/52.02 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28))))))))))),
% 51.82/52.02 inference(rewrite,[status(thm)],[])).
% 51.82/52.02 tff(313,plain,
% 51.82/52.02 ((~((~(status(C!37, F!28, wth) | (~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | ![I1: $i] : (~model(I1, C!37)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I4: $i] : model(I4, F!28))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I3_6(F!28, C!37), C!37) | model(tptp_fun_I4_12(F!28), F!28) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28))))))))) <=> (~((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))))))),
% 51.82/52.02 inference(rewrite,[status(thm)],[])).
% 51.82/52.02 tff(314,plain,
% 51.82/52.02 (((~![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(C!37, F!28, wth) | (~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | ![I1: $i] : (~model(I1, C!37)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I4: $i] : model(I4, F!28))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I3_6(F!28, C!37), C!37) | model(tptp_fun_I4_12(F!28), F!28) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28))))))))))),
% 51.82/52.02 inference(monotonicity,[status(thm)],[313])).
% 51.82/52.02 tff(315,plain,
% 51.82/52.02 (((~![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(C!37, F!28, wth) | (~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | ![I1: $i] : (~model(I1, C!37)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I4: $i] : model(I4, F!28))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I3_6(F!28, C!37), C!37) | model(tptp_fun_I4_12(F!28), F!28) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28))))))))))),
% 51.82/52.02 inference(transitivity,[status(thm)],[314, 312])).
% 51.82/52.02 tff(316,plain,
% 51.82/52.02 ((~![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(C!37, F!28, wth) | (~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | ![I1: $i] : (~model(I1, C!37)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I4: $i] : model(I4, F!28))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I3_6(F!28, C!37), C!37) | model(tptp_fun_I4_12(F!28), F!28) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))))))),
% 51.82/52.02 inference(quant_inst,[status(thm)],[])).
% 51.82/52.02 tff(317,plain,
% 51.82/52.02 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wth) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)) | ![I4: $i] : model(I4, C))) | (~((~status(Ax, C, wth)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | model(tptp_fun_I4_12(C), C) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))))))),
% 51.82/52.02 inference(modus_ponens,[status(thm)],[316, 315])).
% 51.82/52.02 tff(318,plain,
% 51.82/52.02 (~((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28))))))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[317, 311])).
% 51.82/52.03 tff(319,plain,
% 51.82/52.03 (((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))))) | ((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28))))))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(320,plain,
% 51.82/52.03 ((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[319, 318])).
% 51.82/52.03 tff(321,plain,
% 51.82/52.03 ((~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28))))))) | (~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(322,plain,
% 51.82/52.03 ((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[321, 320])).
% 51.82/52.03 tff(323,plain,
% 51.82/52.03 (~status(C!37, F!28, wth)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[322, 289])).
% 51.82/52.03 tff(324,assumption,(~model(tptp_fun_I2_7(F!28, C!37), F!28)), introduced(assumption)).
% 51.82/52.03 tff(325,plain,
% 51.82/52.03 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I2_7(F!28, C!37), F!28)),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(326,plain,
% 51.82/52.03 ($false),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[325, 163, 324])).
% 51.82/52.03 tff(327,plain,(model(tptp_fun_I2_7(F!28, C!37), F!28)), inference(lemma,lemma(discharge,[]))).
% 51.82/52.03 tff(328,plain,
% 51.82/52.03 (((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28)) | (~model(tptp_fun_I2_7(F!28, C!37), F!28))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(329,plain,
% 51.82/52.03 ((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[328, 327])).
% 51.82/52.03 tff(330,plain,
% 51.82/52.03 (((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~status(C!37, F!28, wth)) | (~(model(tptp_fun_I4_12(F!28), F!28) | model(tptp_fun_I3_6(F!28, C!37), C!37) | (~model(tptp_fun_I3_6(F!28, C!37), F!28)) | (~model(tptp_fun_I1_0(C!37), C!37)) | (~![I2: $i] : ((~model(I2, C!37)) | model(I2, F!28)))))))) | ((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(331,plain,
% 51.82/52.03 ((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[330, 318])).
% 51.82/52.03 tff(332,plain,
% 51.82/52.03 ((~((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37)))) | (~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(333,plain,
% 51.82/52.03 ((~((~model(tptp_fun_I2_7(F!28, C!37), C!37)) | model(tptp_fun_I2_7(F!28, C!37), F!28))) | status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[332, 331])).
% 51.82/52.03 tff(334,plain,
% 51.82/52.03 (status(C!37, F!28, wth) | ![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[333, 329])).
% 51.82/52.03 tff(335,plain,
% 51.82/52.03 (![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37)) | ![I1: $i] : (~model(I1, C!37))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[334, 323])).
% 51.82/52.03 tff(336,plain,
% 51.82/52.03 (![I4: $i] : model(I4, F!28) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!37))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[335, 283])).
% 51.82/52.03 tff(337,plain,
% 51.82/52.03 (![I4: $i] : model(I4, F!28)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[336, 278])).
% 51.82/52.03 tff(338,plain,
% 51.82/52.03 ((~![I4: $i] : model(I4, F!28)) | model(tptp_fun_I1_3(F!29, Ax!43), F!28)),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(339,plain,
% 51.82/52.03 (model(tptp_fun_I1_3(F!29, Ax!43), F!28)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[338, 337])).
% 51.82/52.03 tff(340,plain,
% 51.82/52.03 (((~![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))) | ((~model(tptp_fun_I1_3(F!29, Ax!43), F!28)) | (~model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))))) <=> ((~![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))) | (~model(tptp_fun_I1_3(F!29, Ax!43), F!28)) | (~model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))))),
% 51.82/52.03 inference(rewrite,[status(thm)],[])).
% 51.82/52.03 tff(341,plain,
% 51.82/52.03 ((~![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))) | ((~model(tptp_fun_I1_3(F!29, Ax!43), F!28)) | (~model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(342,plain,
% 51.82/52.03 ((~![I2: $i] : ((~model(I2, F!28)) | (~model(I2, not(F!29))))) | (~model(tptp_fun_I1_3(F!29, Ax!43), F!28)) | (~model(tptp_fun_I1_3(F!29, Ax!43), not(F!29)))),
% 51.82/52.03 inference(modus_ponens,[status(thm)],[341, 340])).
% 51.82/52.03 tff(343,plain,
% 51.82/52.03 (~model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[342, 339, 183])).
% 51.82/52.03 tff(344,assumption,(model(tptp_fun_I1_3(F!29, Ax!43), F!29) <=> model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))), introduced(assumption)).
% 51.82/52.03 tff(345,plain,
% 51.82/52.03 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I1_3(F!29, Ax!43), F!29) <=> model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(346,plain,
% 51.82/52.03 ($false),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[345, 8, 344])).
% 51.82/52.03 tff(347,plain,(~(model(tptp_fun_I1_3(F!29, Ax!43), F!29) <=> model(tptp_fun_I1_3(F!29, Ax!43), not(F!29)))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.03 tff(348,plain,
% 51.82/52.03 ((model(tptp_fun_I1_3(F!29, Ax!43), F!29) <=> model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))) | model(tptp_fun_I1_3(F!29, Ax!43), F!29) | model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(349,plain,
% 51.82/52.03 (model(tptp_fun_I1_3(F!29, Ax!43), F!29) | model(tptp_fun_I1_3(F!29, Ax!43), not(F!29))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[348, 347])).
% 51.82/52.03 tff(350,plain,
% 51.82/52.03 (model(tptp_fun_I1_3(F!29, Ax!43), F!29)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[349, 343])).
% 51.82/52.03 tff(351,plain,
% 51.82/52.03 (((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29)) | (~model(tptp_fun_I1_3(F!29, Ax!43), F!29))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(352,plain,
% 51.82/52.03 ((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[351, 350])).
% 51.82/52.03 tff(353,plain,
% 51.82/52.03 ((~![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!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm))) | (~((~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))))))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(354,plain,
% 51.82/52.03 (~((~((~((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm))) | (~((~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29)))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[353, 66])).
% 51.82/52.03 tff(355,plain,
% 51.82/52.03 (((~((~((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm))) | (~((~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))))) | ((~((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(356,plain,
% 51.82/52.03 ((~((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[355, 354])).
% 51.82/52.03 tff(357,plain,
% 51.82/52.03 ((~((~((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm))) | (~((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm)),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(358,plain,
% 51.82/52.03 ((~((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[357, 356])).
% 51.82/52.03 tff(359,plain,
% 51.82/52.03 (status(Ax!43, F!29, thm)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[358, 352])).
% 51.82/52.03 tff(360,plain,
% 51.82/52.03 (((~((~((~model(tptp_fun_I1_3(F!29, Ax!43), Ax!43)) | model(tptp_fun_I1_3(F!29, Ax!43), F!29))) | status(Ax!43, F!29, thm))) | (~((~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))))) | ((~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29)))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(361,plain,
% 51.82/52.03 ((~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[360, 354])).
% 51.82/52.03 tff(362,plain,
% 51.82/52.03 ((~((~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29)))) | (~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(363,plain,
% 51.82/52.03 ((~status(Ax!43, F!29, thm)) | ![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[362, 361])).
% 51.82/52.03 tff(364,plain,
% 51.82/52.03 (![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[363, 359])).
% 51.82/52.03 tff(365,assumption,(~model(I1!44, F!29)), introduced(assumption)).
% 51.82/52.03 tff(366,assumption,(![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))), introduced(assumption)).
% 51.82/52.03 tff(367,plain,
% 51.82/52.03 (model(I1!44, Ax!43)),
% 51.82/52.03 inference(and_elim,[status(thm)],[252])).
% 51.82/52.03 tff(368,plain,
% 51.82/52.03 (((~![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))) | ((~model(I1!44, Ax!43)) | model(I1!44, F!29))) <=> ((~![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))) | (~model(I1!44, Ax!43)) | model(I1!44, F!29))),
% 51.82/52.03 inference(rewrite,[status(thm)],[])).
% 51.82/52.03 tff(369,plain,
% 51.82/52.03 ((~![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))) | ((~model(I1!44, Ax!43)) | model(I1!44, F!29))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(370,plain,
% 51.82/52.03 ((~![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))) | (~model(I1!44, Ax!43)) | model(I1!44, F!29)),
% 51.82/52.03 inference(modus_ponens,[status(thm)],[369, 368])).
% 51.82/52.03 tff(371,plain,
% 51.82/52.03 ($false),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[370, 367, 366, 365])).
% 51.82/52.03 tff(372,plain,((~![I1: $i] : ((~model(I1, Ax!43)) | model(I1, F!29))) | model(I1!44, F!29)), inference(lemma,lemma(discharge,[]))).
% 51.82/52.03 tff(373,plain,
% 51.82/52.03 (model(I1!44, F!29)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[372, 364])).
% 51.82/52.03 tff(374,assumption,(model(I1!44, C!42) <=> model(I1!44, not(C!42))), introduced(assumption)).
% 51.82/52.03 tff(375,plain,
% 51.82/52.03 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I1!44, C!42) <=> model(I1!44, not(C!42))))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(376,plain,
% 51.82/52.03 ($false),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[375, 8, 374])).
% 51.82/52.03 tff(377,plain,(~(model(I1!44, C!42) <=> model(I1!44, not(C!42)))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.03 tff(378,plain,
% 51.82/52.03 (~model(I1!44, C!42)),
% 51.82/52.03 inference(and_elim,[status(thm)],[252])).
% 51.82/52.03 tff(379,plain,
% 51.82/52.03 ((model(I1!44, C!42) <=> model(I1!44, not(C!42))) | model(I1!44, C!42) | model(I1!44, not(C!42))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(380,plain,
% 51.82/52.03 ((model(I1!44, C!42) <=> model(I1!44, not(C!42))) | model(I1!44, not(C!42))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[379, 378])).
% 51.82/52.03 tff(381,plain,
% 51.82/52.03 (model(I1!44, not(C!42))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[380, 377])).
% 51.82/52.03 tff(382,assumption,(![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))), introduced(assumption)).
% 51.82/52.03 tff(383,assumption,(model(I1!44, F!29)), introduced(assumption)).
% 51.82/52.03 tff(384,plain,
% 51.82/52.03 (((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))) | ((~model(I1!44, F!29)) | (~model(I1!44, not(C!42))))) <=> ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))) | (~model(I1!44, F!29)) | (~model(I1!44, not(C!42))))),
% 51.82/52.03 inference(rewrite,[status(thm)],[])).
% 51.82/52.03 tff(385,plain,
% 51.82/52.03 ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))) | ((~model(I1!44, F!29)) | (~model(I1!44, not(C!42))))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(386,plain,
% 51.82/52.03 ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))) | (~model(I1!44, F!29)) | (~model(I1!44, not(C!42)))),
% 51.82/52.03 inference(modus_ponens,[status(thm)],[385, 384])).
% 51.82/52.03 tff(387,plain,
% 51.82/52.03 ($false),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[386, 383, 382, 381])).
% 51.82/52.03 tff(388,plain,((~model(I1!44, F!29)) | (~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42)))))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.03 tff(389,plain,
% 51.82/52.03 (~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[388, 373])).
% 51.82/52.03 tff(390,plain,
% 51.82/52.03 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(F!29, C!42, noc)) | (~((~model(tptp_fun_I1_2(C!42, F!29), F!29)) | (~model(tptp_fun_I1_2(C!42, F!29), C!42)) | (~model(tptp_fun_I2_17(C!42, F!29), F!29)) | (~model(tptp_fun_I2_17(C!42, F!29), not(C!42))))))) | (~(status(F!29, C!42, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))))))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(391,plain,
% 51.82/52.03 (~((~((~status(F!29, C!42, noc)) | (~((~model(tptp_fun_I1_2(C!42, F!29), F!29)) | (~model(tptp_fun_I1_2(C!42, F!29), C!42)) | (~model(tptp_fun_I2_17(C!42, F!29), F!29)) | (~model(tptp_fun_I2_17(C!42, F!29), not(C!42))))))) | (~(status(F!29, C!42, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42)))))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[390, 29])).
% 51.82/52.03 tff(392,plain,
% 51.82/52.03 (((~((~status(F!29, C!42, noc)) | (~((~model(tptp_fun_I1_2(C!42, F!29), F!29)) | (~model(tptp_fun_I1_2(C!42, F!29), C!42)) | (~model(tptp_fun_I2_17(C!42, F!29), F!29)) | (~model(tptp_fun_I2_17(C!42, F!29), not(C!42))))))) | (~(status(F!29, C!42, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))))) | (status(F!29, C!42, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42)))))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(393,plain,
% 51.82/52.03 (status(F!29, C!42, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[392, 391])).
% 51.82/52.03 tff(394,assumption,(status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)), introduced(assumption)).
% 51.82/52.03 tff(395,plain,
% 51.82/52.03 ((~![Ax: $i, C: $i] : (~status(Ax, C, noc))) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(396,plain,
% 51.82/52.03 ($false),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[395, 151, 394])).
% 51.82/52.03 tff(397,plain,(~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)), inference(lemma,lemma(discharge,[]))).
% 51.82/52.03 tff(398,plain,
% 51.82/52.03 (((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap))) | status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(399,plain,
% 51.82/52.03 ((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[398, 397])).
% 51.82/52.03 tff(400,plain,
% 51.82/52.03 (^[S1: $i, S2: $i] : refl((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 51.82/52.03 inference(bind,[status(th)],[])).
% 51.82/52.03 tff(401,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 51.82/52.03 inference(quant_intro,[status(thm)],[400])).
% 51.82/52.03 tff(402,plain,
% 51.82/52.03 (^[S1: $i, S2: $i] : rewrite((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 51.82/52.03 inference(bind,[status(th)],[])).
% 51.82/52.03 tff(403,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 51.82/52.03 inference(quant_intro,[status(thm)],[402])).
% 51.82/52.03 tff(404,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 51.82/52.03 inference(transitivity,[status(thm)],[403, 401])).
% 51.82/52.03 tff(405,plain,
% 51.82/52.03 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) <=> (mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))), trans(monotonicity(rewrite((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) <=> (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))), rewrite(((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))))),
% 51.82/52.03 inference(bind,[status(th)],[])).
% 51.82/52.03 tff(406,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 51.82/52.03 inference(quant_intro,[status(thm)],[405])).
% 51.82/52.03 tff(407,plain,
% 51.82/52.03 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))))),
% 51.82/52.03 inference(bind,[status(th)],[])).
% 51.82/52.03 tff(408,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 51.82/52.03 inference(quant_intro,[status(thm)],[407])).
% 51.82/52.03 tff(409,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 51.82/52.03 inference(rewrite,[status(thm)],[])).
% 51.82/52.03 tff(410,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','mighta')).
% 51.82/52.03 tff(411,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 51.82/52.03 inference(modus_ponens,[status(thm)],[410, 409])).
% 51.82/52.03 tff(412,plain,(
% 51.82/52.03 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 51.82/52.03 inference(skolemize,[status(sab)],[411])).
% 51.82/52.03 tff(413,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 51.82/52.03 inference(modus_ponens,[status(thm)],[412, 408])).
% 51.82/52.03 tff(414,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 51.82/52.03 inference(modus_ponens,[status(thm)],[413, 406])).
% 51.82/52.03 tff(415,plain,
% 51.82/52.03 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 51.82/52.03 inference(modus_ponens,[status(thm)],[414, 404])).
% 51.82/52.03 tff(416,plain,
% 51.82/52.03 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap))))))))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(417,plain,
% 51.82/52.03 (~((~(mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap)))))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[416, 415])).
% 51.82/52.03 tff(418,plain,
% 51.82/52.03 (((~(mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap))))))) | ((~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap)))))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(419,plain,
% 51.82/52.03 ((~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[418, 417])).
% 51.82/52.03 tff(420,plain,
% 51.82/52.03 ((~((~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap)))))) | (~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap))))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(421,plain,
% 51.82/52.03 ((~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap))))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[420, 419])).
% 51.82/52.03 tff(422,plain,
% 51.82/52.03 (~mighta(noc, sap)),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[421, 399])).
% 51.82/52.03 tff(423,plain,
% 51.82/52.03 (((~(mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, sap)) | (~((~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), noc)) | (~status(tptp_fun_Ax_19(sap, noc), tptp_fun_C_18(sap, noc), sap))))))) | (mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc))))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(424,plain,
% 51.82/52.03 (mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc)))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[423, 417])).
% 51.82/52.03 tff(425,plain,
% 51.82/52.03 ((~(mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc))))) | mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc)))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(426,plain,
% 51.82/52.03 (mighta(noc, sap) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc)))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[425, 424])).
% 51.82/52.03 tff(427,plain,
% 51.82/52.03 (![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc)))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[426, 422])).
% 51.82/52.03 tff(428,assumption,(![I2: $i] : (~model(I2, C!42))), introduced(assumption)).
% 51.82/52.03 tff(429,plain,
% 51.82/52.03 ((~![I2: $i] : (~model(I2, C!42))) | (~model(I2!45, C!42))),
% 51.82/52.03 inference(quant_inst,[status(thm)],[])).
% 51.82/52.03 tff(430,plain,
% 51.82/52.03 ($false),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[429, 253, 428])).
% 51.82/52.03 tff(431,plain,(~![I2: $i] : (~model(I2, C!42))), inference(lemma,lemma(discharge,[]))).
% 51.82/52.03 tff(432,plain,
% 51.82/52.03 (((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42)))) | ![I2: $i] : (~model(I2, C!42))),
% 51.82/52.03 inference(tautology,[status(thm)],[])).
% 51.82/52.03 tff(433,plain,
% 51.82/52.03 ((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42)))),
% 51.82/52.03 inference(unit_resolution,[status(thm)],[432, 431])).
% 51.82/52.03 tff(434,plain,
% 51.82/52.03 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax)))))))),
% 51.82/52.03 inference(bind,[status(th)],[])).
% 51.82/52.03 tff(435,plain,
% 51.82/52.03 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))),
% 51.82/52.04 inference(quant_intro,[status(thm)],[434])).
% 51.82/52.04 tff(436,plain,
% 51.82/52.04 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))))),
% 51.82/52.04 inference(bind,[status(th)],[])).
% 51.82/52.04 tff(437,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 51.82/52.04 inference(quant_intro,[status(thm)],[436])).
% 51.82/52.04 tff(438,plain,
% 51.82/52.04 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))))),
% 51.82/52.04 inference(bind,[status(th)],[])).
% 51.82/52.04 tff(439,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 51.82/52.04 inference(quant_intro,[status(thm)],[438])).
% 51.82/52.04 tff(440,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 51.82/52.04 inference(transitivity,[status(thm)],[439, 437])).
% 51.82/52.04 tff(441,plain,
% 51.82/52.04 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite(((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) <=> ((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))), rewrite((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))) <=> (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))), ((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))), rewrite((((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))), ((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))))),
% 51.82/52.04 inference(bind,[status(th)],[])).
% 51.82/52.04 tff(442,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 51.82/52.04 inference(quant_intro,[status(thm)],[441])).
% 51.82/52.04 tff(443,plain,
% 51.82/52.04 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap)))) <=> (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap)))))),
% 51.82/52.04 inference(bind,[status(th)],[])).
% 51.82/52.04 tff(444,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap)))) <=> ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))),
% 51.82/52.04 inference(quant_intro,[status(thm)],[443])).
% 51.82/52.04 tff(445,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 51.82/52.04 inference(rewrite,[status(thm)],[])).
% 51.82/52.04 tff(446,plain,
% 51.82/52.04 (^[Ax: $i, C: $i] : rewrite(((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)))),
% 51.82/52.04 inference(bind,[status(th)],[])).
% 51.82/52.04 tff(447,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 51.82/52.04 inference(quant_intro,[status(thm)],[446])).
% 51.82/52.04 tff(448,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) => ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','sap')).
% 51.82/52.04 tff(449,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 51.82/52.04 inference(modus_ponens,[status(thm)],[448, 447])).
% 51.82/52.04 tff(450,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 51.82/52.04 inference(modus_ponens,[status(thm)],[449, 445])).
% 51.82/52.04 tff(451,plain,(
% 51.82/52.04 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & ((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sap))))),
% 51.82/52.04 inference(skolemize,[status(sab)],[450])).
% 51.82/52.04 tff(452,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (~model(I2, C))) | status(Ax, C, sap)) & (model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))),
% 51.82/52.04 inference(modus_ponens,[status(thm)],[451, 444])).
% 51.82/52.04 tff(453,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 51.82/52.04 inference(modus_ponens,[status(thm)],[452, 442])).
% 51.82/52.04 tff(454,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)) | (~status(Ax, C, sap))))))),
% 51.82/52.04 inference(modus_ponens,[status(thm)],[453, 440])).
% 51.82/52.04 tff(455,plain,
% 51.82/52.04 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))),
% 51.82/52.04 inference(modus_ponens,[status(thm)],[454, 435])).
% 51.82/52.04 tff(456,plain,
% 51.82/52.04 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(C!42), C!42)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(C!42), C!42))))))),
% 51.82/52.04 inference(rewrite,[status(thm)],[])).
% 51.82/52.04 tff(457,plain,
% 51.82/52.04 ((~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~(model(tptp_fun_I2_1(C!42), C!42) | (~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)))))) <=> (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(C!42), C!42)))))),
% 51.82/52.04 inference(rewrite,[status(thm)],[])).
% 51.82/52.04 tff(458,plain,
% 51.82/52.04 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~(model(tptp_fun_I2_1(C!42), C!42) | (~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(C!42), C!42))))))),
% 51.82/52.04 inference(monotonicity,[status(thm)],[457])).
% 51.82/52.04 tff(459,plain,
% 51.82/52.04 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~(model(tptp_fun_I2_1(C!42), C!42) | (~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(C!42), C!42))))))),
% 51.82/52.04 inference(transitivity,[status(thm)],[458, 456])).
% 51.82/52.04 tff(460,plain,
% 51.82/52.04 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~(model(tptp_fun_I2_1(C!42), C!42) | (~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29))))))),
% 51.82/52.04 inference(quant_inst,[status(thm)],[])).
% 51.82/52.04 tff(461,plain,
% 51.82/52.04 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (~model(I2, C))))) | status(Ax, C, sap))) | (~(model(tptp_fun_I2_1(C), C) | (~status(Ax, C, sap)) | ![I1: $i] : (~model(I1, Ax))))))) | (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(C!42), C!42)))))),
% 51.90/52.05 inference(modus_ponens,[status(thm)],[460, 459])).
% 51.90/52.05 tff(462,plain,
% 51.90/52.05 (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(C!42), C!42))))),
% 51.90/52.05 inference(unit_resolution,[status(thm)],[461, 455])).
% 51.90/52.05 tff(463,plain,
% 51.90/52.05 (((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~status(F!29, C!42, sap)) | ![I1: $i] : (~model(I1, F!29)) | model(tptp_fun_I2_1(C!42), C!42)))) | ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))),
% 51.90/52.05 inference(tautology,[status(thm)],[])).
% 51.90/52.05 tff(464,plain,
% 51.90/52.05 ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap)),
% 51.90/52.05 inference(unit_resolution,[status(thm)],[463, 462])).
% 51.90/52.05 tff(465,plain,
% 51.90/52.05 ((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap))) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap)),
% 51.90/52.05 inference(tautology,[status(thm)],[])).
% 51.90/52.05 tff(466,plain,
% 51.90/52.05 ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap)),
% 51.90/52.05 inference(unit_resolution,[status(thm)],[465, 464])).
% 51.90/52.05 tff(467,plain,
% 51.90/52.05 (status(F!29, C!42, sap)),
% 51.90/52.05 inference(unit_resolution,[status(thm)],[466, 433])).
% 51.90/52.05 tff(468,plain,
% 51.90/52.05 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc)))) | ((~status(F!29, C!42, sap)) | (~status(F!29, C!42, noc)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc)))) | (~status(F!29, C!42, sap)) | (~status(F!29, C!42, noc)))),
% 51.90/52.05 inference(rewrite,[status(thm)],[])).
% 51.90/52.05 tff(469,plain,
% 51.90/52.05 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc)))) | ((~status(F!29, C!42, sap)) | (~status(F!29, C!42, noc)))),
% 51.90/52.05 inference(quant_inst,[status(thm)],[])).
% 51.90/52.05 tff(470,plain,
% 51.90/52.05 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | (~status(Ax, C, noc)))) | (~status(F!29, C!42, sap)) | (~status(F!29, C!42, noc))),
% 51.90/52.05 inference(modus_ponens,[status(thm)],[469, 468])).
% 51.90/52.05 tff(471,plain,
% 51.90/52.05 (~status(F!29, C!42, noc)),
% 51.90/52.05 inference(unit_resolution,[status(thm)],[470, 467, 427])).
% 51.90/52.05 tff(472,plain,
% 51.90/52.05 ((~(status(F!29, C!42, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42)))))) | status(F!29, C!42, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))),
% 51.90/52.05 inference(tautology,[status(thm)],[])).
% 51.90/52.05 tff(473,plain,
% 51.90/52.05 ((~(status(F!29, C!42, noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42)))))) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))),
% 51.90/52.05 inference(unit_resolution,[status(thm)],[472, 471])).
% 51.90/52.05 tff(474,plain,
% 51.90/52.05 (![I1: $i] : ((~model(I1, F!29)) | (~model(I1, C!42))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(C!42))))),
% 51.90/52.05 inference(unit_resolution,[status(thm)],[473, 393])).
% 51.90/52.05 tff(475,plain,
% 51.90/52.05 ($false),
% 51.90/52.05 inference(unit_resolution,[status(thm)],[474, 389, 259])).
% 51.90/52.05 % SZS output end Proof
% 51.90/52.06 % E exiting
%------------------------------------------------------------------------------