%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS201+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:34 AM UTC 2025
% Result : Theorem 5.94s 6.09s
% Output : Proof 6.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS201+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:12:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.94/6.09 % SZS status Theorem
% 5.94/6.09 % SZS output start Proof
% 5.94/6.09 tff(model_type, type, (
% 5.94/6.09 model: ( $i * $i ) > $o)).
% 5.94/6.09 tff(tptp_fun_F_28_type, type, (
% 5.94/6.09 tptp_fun_F_28: $i)).
% 5.94/6.09 tff(tptp_fun_I1_0_type, type, (
% 5.94/6.09 tptp_fun_I1_0: $i > $i)).
% 5.94/6.09 tff(tptp_fun_C_33_type, type, (
% 5.94/6.09 tptp_fun_C_33: $i)).
% 5.94/6.09 tff(not_type, type, (
% 5.94/6.09 not: $i > $i)).
% 5.94/6.09 tff(tptp_fun_C_42_type, type, (
% 5.94/6.09 tptp_fun_C_42: $i)).
% 5.94/6.09 tff(tptp_fun_F_29_type, type, (
% 5.94/6.09 tptp_fun_F_29: $i)).
% 5.94/6.09 tff(tptp_fun_I2_8_type, type, (
% 5.94/6.09 tptp_fun_I2_8: $i > $i)).
% 5.94/6.09 tff(status_type, type, (
% 5.94/6.09 status: ( $i * $i * $i ) > $o)).
% 5.94/6.09 tff(eth_type, type, (
% 5.94/6.09 eth: $i)).
% 5.94/6.09 tff(tptp_fun_I3_9_type, type, (
% 5.94/6.09 tptp_fun_I3_9: ( $i * $i ) > $i)).
% 5.94/6.09 tff(noc_type, type, (
% 5.94/6.09 noc: $i)).
% 5.94/6.09 tff(tptp_fun_I2_17_type, type, (
% 5.94/6.09 tptp_fun_I2_17: ( $i * $i ) > $i)).
% 5.94/6.09 tff(tptp_fun_I1_2_type, type, (
% 5.94/6.09 tptp_fun_I1_2: ( $i * $i ) > $i)).
% 5.94/6.09 tff(wtc_type, type, (
% 5.94/6.09 wtc: $i)).
% 5.94/6.09 tff(nota_type, type, (
% 5.94/6.09 nota: ( $i * $i ) > $o)).
% 5.94/6.09 tff(tptp_fun_C_22_type, type, (
% 5.94/6.09 tptp_fun_C_22: ( $i * $i ) > $i)).
% 5.94/6.09 tff(tptp_fun_Ax_23_type, type, (
% 5.94/6.09 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 5.94/6.09 tff(mighta_type, type, (
% 5.94/6.09 mighta: ( $i * $i ) > $o)).
% 5.94/6.09 tff(tptp_fun_C_18_type, type, (
% 5.94/6.09 tptp_fun_C_18: ( $i * $i ) > $i)).
% 5.94/6.09 tff(tptp_fun_Ax_19_type, type, (
% 5.94/6.09 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 5.94/6.09 tff(tptp_fun_Ax_34_type, type, (
% 5.94/6.09 tptp_fun_Ax_34: $i)).
% 5.94/6.09 tff(thm_type, type, (
% 5.94/6.09 thm: $i)).
% 5.94/6.09 tff(tptp_fun_I1_3_type, type, (
% 5.94/6.09 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 5.94/6.09 tff(sap_type, type, (
% 5.94/6.09 sap: $i)).
% 5.94/6.09 tff(tptp_fun_I2_1_type, type, (
% 5.94/6.09 tptp_fun_I2_1: $i > $i)).
% 5.94/6.09 tff(tptp_fun_I1_35_type, type, (
% 5.94/6.09 tptp_fun_I1_35: $i)).
% 5.94/6.09 tff(tptp_fun_I2_36_type, type, (
% 5.94/6.09 tptp_fun_I2_36: $i)).
% 5.94/6.09 tff(tptp_fun_I2_31_type, type, (
% 5.94/6.09 tptp_fun_I2_31: $i)).
% 5.94/6.09 tff(tptp_fun_I1_30_type, type, (
% 5.94/6.09 tptp_fun_I1_30: $i)).
% 5.94/6.09 tff(tptp_fun_I3_11_type, type, (
% 5.94/6.09 tptp_fun_I3_11: $i > $i)).
% 5.94/6.09 tff(tptp_fun_I2_45_type, type, (
% 5.94/6.09 tptp_fun_I2_45: $i)).
% 5.94/6.09 tff(tptp_fun_I1_44_type, type, (
% 5.94/6.09 tptp_fun_I1_44: $i)).
% 5.94/6.09 tff(tptp_fun_Ax_43_type, type, (
% 5.94/6.09 tptp_fun_Ax_43: $i)).
% 5.94/6.09 tff(tptp_fun_Ax_38_type, type, (
% 5.94/6.09 tptp_fun_Ax_38: $i)).
% 5.94/6.09 tff(tptp_fun_C_37_type, type, (
% 5.94/6.09 tptp_fun_C_37: $i)).
% 5.94/6.09 tff(csa_type, type, (
% 5.94/6.09 csa: $i)).
% 5.94/6.09 tff(tptp_fun_I1_14_type, type, (
% 5.94/6.09 tptp_fun_I1_14: ( $i * $i ) > $i)).
% 5.94/6.09 tff(sat_type, type, (
% 5.94/6.09 sat: $i)).
% 5.94/6.09 tff(tptp_fun_I2_5_type, type, (
% 5.94/6.09 tptp_fun_I2_5: $i > $i)).
% 5.94/6.09 tff(tac_type, type, (
% 5.94/6.09 tac: $i)).
% 5.94/6.09 tff(tptp_fun_I1_39_type, type, (
% 5.94/6.09 tptp_fun_I1_39: $i)).
% 5.94/6.09 tff(tptp_fun_I4_41_type, type, (
% 5.94/6.09 tptp_fun_I4_41: $i)).
% 5.94/6.09 tff(tptp_fun_I3_40_type, type, (
% 5.94/6.09 tptp_fun_I3_40: $i)).
% 5.94/6.09 tff(esa_type, type, (
% 5.94/6.09 esa: $i)).
% 5.94/6.09 tff(unp_type, type, (
% 5.94/6.09 unp: $i)).
% 5.94/6.09 tff(1,assumption,(model(tptp_fun_I1_0(C!33), C!42) <=> model(tptp_fun_I1_0(C!33), not(C!42))), introduced(assumption)).
% 5.94/6.09 tff(2,plain,
% 5.94/6.09 (^[I: $i, F: $i] : refl((~(model(I, F) <=> model(I, not(F)))) <=> (~(model(I, F) <=> model(I, not(F)))))),
% 5.94/6.09 inference(bind,[status(th)],[])).
% 5.94/6.09 tff(3,plain,
% 5.94/6.09 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.94/6.09 inference(quant_intro,[status(thm)],[2])).
% 5.94/6.09 tff(4,plain,
% 5.94/6.09 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.94/6.09 inference(rewrite,[status(thm)],[])).
% 5.94/6.09 tff(5,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','completeness')).
% 5.94/6.09 tff(6,plain,
% 5.94/6.09 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.94/6.09 inference(modus_ponens,[status(thm)],[5, 4])).
% 5.94/6.09 tff(7,plain,(
% 5.94/6.09 ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.94/6.09 inference(skolemize,[status(sab)],[6])).
% 5.94/6.09 tff(8,plain,
% 5.94/6.09 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.94/6.09 inference(modus_ponens,[status(thm)],[7, 3])).
% 5.94/6.09 tff(9,plain,
% 5.94/6.09 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I1_0(C!33), C!42) <=> model(tptp_fun_I1_0(C!33), not(C!42))))),
% 5.94/6.09 inference(quant_inst,[status(thm)],[])).
% 5.94/6.09 tff(10,plain,
% 5.94/6.09 ($false),
% 5.94/6.09 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 5.94/6.09 tff(11,plain,(~(model(tptp_fun_I1_0(C!33), C!42) <=> model(tptp_fun_I1_0(C!33), not(C!42)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.09 tff(12,plain,
% 5.94/6.09 (^[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)))))))))),
% 5.94/6.09 inference(bind,[status(th)],[])).
% 5.94/6.09 tff(13,plain,
% 5.94/6.09 (![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))))))))),
% 5.94/6.09 inference(quant_intro,[status(thm)],[12])).
% 5.94/6.09 tff(14,plain,
% 5.94/6.09 (^[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))))))))))),
% 5.94/6.09 inference(bind,[status(th)],[])).
% 5.94/6.09 tff(15,plain,
% 5.94/6.09 (![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)))))))))),
% 5.94/6.09 inference(quant_intro,[status(thm)],[14])).
% 5.94/6.09 tff(16,plain,
% 5.94/6.09 (^[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))))))))))),
% 5.94/6.09 inference(bind,[status(th)],[])).
% 5.94/6.09 tff(17,plain,
% 5.94/6.09 (![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)))))))))),
% 5.94/6.09 inference(quant_intro,[status(thm)],[16])).
% 5.94/6.09 tff(18,plain,
% 5.94/6.09 (![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)))))))))),
% 5.94/6.09 inference(transitivity,[status(thm)],[17, 15])).
% 5.94/6.09 tff(19,plain,
% 5.94/6.09 (^[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)))))))))))),
% 5.94/6.09 inference(bind,[status(th)],[])).
% 5.94/6.09 tff(20,plain,
% 5.94/6.09 (![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)))))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[19])).
% 5.94/6.10 tff(21,plain,
% 5.94/6.10 (^[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))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(22,plain,
% 5.94/6.10 (![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)))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[21])).
% 5.94/6.10 tff(23,plain,
% 5.94/6.10 (![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))),
% 5.94/6.10 inference(rewrite,[status(thm)],[])).
% 5.94/6.10 tff(24,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')).
% 5.94/6.10 tff(25,plain,
% 5.94/6.10 (![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))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[24, 23])).
% 5.94/6.10 tff(26,plain,(
% 5.94/6.10 ![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))))),
% 5.94/6.10 inference(skolemize,[status(sab)],[25])).
% 5.94/6.10 tff(27,plain,
% 5.94/6.10 (![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)))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[26, 22])).
% 5.94/6.10 tff(28,plain,
% 5.94/6.10 (![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)))))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[27, 20])).
% 5.94/6.10 tff(29,plain,
% 5.94/6.10 (![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)))))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[28, 18])).
% 5.94/6.10 tff(30,plain,
% 5.94/6.10 (![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))))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[29, 13])).
% 5.94/6.10 tff(31,plain,
% 5.94/6.10 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!42, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, C!42), C!42)) | (~model(tptp_fun_I1_2(F!29, C!42), F!29)) | (~model(tptp_fun_I2_17(F!29, C!42), C!42)) | (~model(tptp_fun_I2_17(F!29, C!42), not(F!29))))))) | (~(status(C!42, F!29, noc) | ![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))))))),
% 5.94/6.10 inference(quant_inst,[status(thm)],[])).
% 5.94/6.10 tff(32,plain,
% 5.94/6.10 (~((~((~status(C!42, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, C!42), C!42)) | (~model(tptp_fun_I1_2(F!29, C!42), F!29)) | (~model(tptp_fun_I2_17(F!29, C!42), C!42)) | (~model(tptp_fun_I2_17(F!29, C!42), not(F!29))))))) | (~(status(C!42, F!29, noc) | ![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29)))))))),
% 5.94/6.10 inference(unit_resolution,[status(thm)],[31, 30])).
% 5.94/6.10 tff(33,plain,
% 5.94/6.10 (((~((~status(C!42, F!29, noc)) | (~((~model(tptp_fun_I1_2(F!29, C!42), C!42)) | (~model(tptp_fun_I1_2(F!29, C!42), F!29)) | (~model(tptp_fun_I2_17(F!29, C!42), C!42)) | (~model(tptp_fun_I2_17(F!29, C!42), not(F!29))))))) | (~(status(C!42, F!29, noc) | ![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))))) | (status(C!42, F!29, noc) | ![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29)))))),
% 5.94/6.10 inference(tautology,[status(thm)],[])).
% 5.94/6.10 tff(34,plain,
% 5.94/6.10 (status(C!42, F!29, noc) | ![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))),
% 5.94/6.10 inference(unit_resolution,[status(thm)],[33, 32])).
% 5.94/6.10 tff(35,plain,
% 5.94/6.10 (^[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)))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(36,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[35])).
% 5.94/6.10 tff(37,plain,
% 5.94/6.10 (^[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)))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(38,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[37])).
% 5.94/6.10 tff(39,plain,
% 5.94/6.10 (^[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)))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(40,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[39])).
% 5.94/6.10 tff(41,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(transitivity,[status(thm)],[40, 38])).
% 5.94/6.10 tff(42,plain,
% 5.94/6.10 (^[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))))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(43,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[42])).
% 5.94/6.10 tff(44,plain,
% 5.94/6.10 (![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))),
% 5.94/6.10 inference(rewrite,[status(thm)],[])).
% 5.94/6.10 tff(45,plain,
% 5.94/6.10 (^[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)))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(46,plain,
% 5.94/6.10 (![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))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[45])).
% 5.94/6.10 tff(47,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')).
% 5.94/6.10 tff(48,plain,
% 5.94/6.10 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[47, 46])).
% 5.94/6.10 tff(49,plain,
% 5.94/6.10 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[48, 44])).
% 5.94/6.10 tff(50,plain,(
% 5.94/6.10 ![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))))),
% 5.94/6.10 inference(skolemize,[status(sab)],[49])).
% 5.94/6.10 tff(51,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[50, 43])).
% 5.94/6.10 tff(52,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[51, 41])).
% 5.94/6.10 tff(53,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[52, 36])).
% 5.94/6.10 tff(54,plain,
% 5.94/6.10 ((~![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_18(noc, noc), Ax!34), Ax!34)) | model(tptp_fun_I1_3(tptp_fun_C_18(noc, noc), Ax!34), tptp_fun_C_18(noc, noc)))) | status(Ax!34, tptp_fun_C_18(noc, noc), thm))) | (~((~status(Ax!34, tptp_fun_C_18(noc, noc), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))))))),
% 5.94/6.10 inference(quant_inst,[status(thm)],[])).
% 5.94/6.10 tff(55,plain,
% 5.94/6.10 (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_18(noc, noc), Ax!34), Ax!34)) | model(tptp_fun_I1_3(tptp_fun_C_18(noc, noc), Ax!34), tptp_fun_C_18(noc, noc)))) | status(Ax!34, tptp_fun_C_18(noc, noc), thm))) | (~((~status(Ax!34, tptp_fun_C_18(noc, noc), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc))))))),
% 5.94/6.10 inference(unit_resolution,[status(thm)],[54, 53])).
% 5.94/6.10 tff(56,plain,
% 5.94/6.10 (((~((~((~model(tptp_fun_I1_3(tptp_fun_C_18(noc, noc), Ax!34), Ax!34)) | model(tptp_fun_I1_3(tptp_fun_C_18(noc, noc), Ax!34), tptp_fun_C_18(noc, noc)))) | status(Ax!34, tptp_fun_C_18(noc, noc), thm))) | (~((~status(Ax!34, tptp_fun_C_18(noc, noc), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))))) | ((~status(Ax!34, tptp_fun_C_18(noc, noc), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc))))),
% 5.94/6.10 inference(tautology,[status(thm)],[])).
% 5.94/6.10 tff(57,plain,
% 5.94/6.10 ((~status(Ax!34, tptp_fun_C_18(noc, noc), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))),
% 5.94/6.10 inference(unit_resolution,[status(thm)],[56, 55])).
% 5.94/6.10 tff(58,assumption,(~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))), introduced(assumption)).
% 5.94/6.10 tff(59,plain,
% 5.94/6.10 (((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc)))) | model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))),
% 5.94/6.10 inference(tautology,[status(thm)],[])).
% 5.94/6.10 tff(60,plain,
% 5.94/6.10 (model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))),
% 5.94/6.10 inference(unit_resolution,[status(thm)],[59, 58])).
% 5.94/6.10 tff(61,assumption,(![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))), introduced(assumption)).
% 5.94/6.10 tff(62,assumption,(model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))), introduced(assumption)).
% 5.94/6.10 tff(63,plain,
% 5.94/6.10 ((~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)))),
% 5.94/6.10 inference(quant_inst,[status(thm)],[])).
% 5.94/6.10 tff(64,plain,
% 5.94/6.10 ($false),
% 5.94/6.10 inference(unit_resolution,[status(thm)],[63, 62, 61])).
% 5.94/6.10 tff(65,plain,((~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.10 tff(66,plain,
% 5.94/6.10 (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))),
% 5.94/6.10 inference(unit_resolution,[status(thm)],[65, 60])).
% 5.94/6.10 tff(67,plain,
% 5.94/6.10 (((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc))))) | ![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))),
% 5.94/6.10 inference(tautology,[status(thm)],[])).
% 5.94/6.10 tff(68,plain,
% 5.94/6.10 ((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc))))),
% 5.94/6.10 inference(unit_resolution,[status(thm)],[67, 66])).
% 5.94/6.10 tff(69,plain,
% 5.94/6.10 (^[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)))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(70,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[69])).
% 5.94/6.10 tff(71,plain,
% 5.94/6.10 (^[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)))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(72,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[71])).
% 5.94/6.10 tff(73,plain,
% 5.94/6.10 (^[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)))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(74,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[73])).
% 5.94/6.10 tff(75,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(transitivity,[status(thm)],[74, 72])).
% 5.94/6.10 tff(76,plain,
% 5.94/6.10 (^[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))))))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(77,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[76])).
% 5.94/6.10 tff(78,plain,
% 5.94/6.10 (^[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)))))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(79,plain,
% 5.94/6.10 (![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))))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[78])).
% 5.94/6.10 tff(80,plain,
% 5.94/6.10 (![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))),
% 5.94/6.10 inference(rewrite,[status(thm)],[])).
% 5.94/6.10 tff(81,plain,
% 5.94/6.10 (^[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)))),
% 5.94/6.10 inference(bind,[status(th)],[])).
% 5.94/6.10 tff(82,plain,
% 5.94/6.10 (![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))),
% 5.94/6.10 inference(quant_intro,[status(thm)],[81])).
% 5.94/6.10 tff(83,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')).
% 5.94/6.10 tff(84,plain,
% 5.94/6.10 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[83, 82])).
% 5.94/6.10 tff(85,plain,
% 5.94/6.10 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) | ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sap))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[84, 80])).
% 5.94/6.10 tff(86,plain,(
% 5.94/6.10 ![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))))),
% 5.94/6.10 inference(skolemize,[status(sab)],[85])).
% 5.94/6.10 tff(87,plain,
% 5.94/6.10 (![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))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[86, 79])).
% 5.94/6.10 tff(88,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[87, 77])).
% 5.94/6.10 tff(89,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[88, 75])).
% 5.94/6.10 tff(90,plain,
% 5.94/6.10 (![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))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[89, 70])).
% 5.94/6.10 tff(91,plain,
% 5.94/6.10 (((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), 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))))))) | (~((~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)))))))),
% 5.94/6.10 inference(rewrite,[status(thm)],[])).
% 5.94/6.10 tff(92,plain,
% 5.94/6.10 ((~((~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)) | ![I1: $i] : (~model(I1, Ax!34)))))) <=> (~((~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap))))))),
% 5.94/6.10 inference(rewrite,[status(thm)],[])).
% 5.94/6.10 tff(93,plain,
% 5.94/6.10 (((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)) | ![I1: $i] : (~model(I1, Ax!34))))))) <=> ((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)))))))),
% 5.94/6.10 inference(monotonicity,[status(thm)],[92])).
% 5.94/6.10 tff(94,plain,
% 5.94/6.10 (((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)) | ![I1: $i] : (~model(I1, Ax!34))))))) <=> ((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)))))))),
% 5.94/6.10 inference(transitivity,[status(thm)],[93, 91])).
% 5.94/6.10 tff(95,plain,
% 5.94/6.10 ((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)) | ![I1: $i] : (~model(I1, Ax!34))))))),
% 5.94/6.10 inference(quant_inst,[status(thm)],[])).
% 5.94/6.10 tff(96,plain,
% 5.94/6.10 ((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap))))))),
% 5.94/6.10 inference(modus_ponens,[status(thm)],[95, 94])).
% 5.94/6.10 tff(97,plain,
% 5.94/6.10 (~((~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)))))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[96, 90])).
% 5.94/6.11 tff(98,plain,
% 5.94/6.11 (((~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~(model(tptp_fun_I2_1(tptp_fun_C_18(noc, noc)), tptp_fun_C_18(noc, noc)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap))))) | ((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(99,plain,
% 5.94/6.11 ((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap)),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[98, 97])).
% 5.94/6.11 tff(100,plain,
% 5.94/6.11 ((~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap))) | (~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap)),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(101,plain,
% 5.94/6.11 ((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, tptp_fun_C_18(noc, noc)))))) | status(Ax!34, tptp_fun_C_18(noc, noc), sap)),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[100, 99])).
% 5.94/6.11 tff(102,plain,
% 5.94/6.11 (status(Ax!34, tptp_fun_C_18(noc, noc), sap)),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[101, 68])).
% 5.94/6.11 tff(103,plain,
% 5.94/6.11 (^[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))))))))),
% 5.94/6.11 inference(bind,[status(th)],[])).
% 5.94/6.11 tff(104,plain,
% 5.94/6.11 (![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)))))))),
% 5.94/6.11 inference(quant_intro,[status(thm)],[103])).
% 5.94/6.11 tff(105,plain,
% 5.94/6.11 (^[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))))))))),
% 5.94/6.11 inference(bind,[status(th)],[])).
% 5.94/6.11 tff(106,plain,
% 5.94/6.11 (![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)))))))),
% 5.94/6.11 inference(quant_intro,[status(thm)],[105])).
% 5.94/6.11 tff(107,plain,
% 5.94/6.11 (![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)))))))),
% 5.94/6.11 inference(transitivity,[status(thm)],[106, 104])).
% 5.94/6.11 tff(108,plain,
% 5.94/6.11 (^[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)))))))))),
% 5.94/6.11 inference(bind,[status(th)],[])).
% 5.94/6.11 tff(109,plain,
% 5.94/6.11 (![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)))))))),
% 5.94/6.11 inference(quant_intro,[status(thm)],[108])).
% 5.94/6.11 tff(110,plain,
% 5.94/6.11 (^[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)))))),
% 5.94/6.11 inference(bind,[status(th)],[])).
% 5.94/6.11 tff(111,plain,
% 5.94/6.11 (![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))))),
% 5.94/6.11 inference(quant_intro,[status(thm)],[110])).
% 5.94/6.11 tff(112,plain,
% 5.94/6.11 (![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))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(113,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')).
% 5.94/6.11 tff(114,plain,
% 5.94/6.11 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[113, 112])).
% 5.94/6.11 tff(115,plain,(
% 5.94/6.11 ![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))))),
% 5.94/6.11 inference(skolemize,[status(sab)],[114])).
% 5.94/6.11 tff(116,plain,
% 5.94/6.11 (![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))))),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[115, 111])).
% 5.94/6.11 tff(117,plain,
% 5.94/6.11 (![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)))))))),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[116, 109])).
% 5.94/6.11 tff(118,plain,
% 5.94/6.11 (![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)))))))),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[117, 107])).
% 5.94/6.11 tff(119,plain,
% 5.94/6.11 ((~![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(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm)))) | (~((~nota(sap, thm)) | (~((~status(tptp_fun_Ax_23(thm, sap), tptp_fun_C_22(thm, sap), sap)) | status(tptp_fun_Ax_23(thm, sap), tptp_fun_C_22(thm, sap), thm)))))))),
% 5.94/6.11 inference(quant_inst,[status(thm)],[])).
% 5.94/6.11 tff(120,plain,
% 5.94/6.11 (~((~(nota(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm)))) | (~((~nota(sap, thm)) | (~((~status(tptp_fun_Ax_23(thm, sap), tptp_fun_C_22(thm, sap), sap)) | status(tptp_fun_Ax_23(thm, sap), tptp_fun_C_22(thm, sap), thm))))))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[119, 118])).
% 5.94/6.11 tff(121,plain,
% 5.94/6.11 (((~(nota(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm)))) | (~((~nota(sap, thm)) | (~((~status(tptp_fun_Ax_23(thm, sap), tptp_fun_C_22(thm, sap), sap)) | status(tptp_fun_Ax_23(thm, sap), tptp_fun_C_22(thm, sap), thm)))))) | (nota(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm)))),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(122,plain,
% 5.94/6.11 (nota(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[121, 120])).
% 5.94/6.11 tff(123,plain,
% 5.94/6.11 ((~nota(sap, thm)) <=> (~nota(sap, thm))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(124,axiom,(~nota(sap, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nota_sap_thm')).
% 5.94/6.11 tff(125,plain,
% 5.94/6.11 (~nota(sap, thm)),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[124, 123])).
% 5.94/6.11 tff(126,plain,
% 5.94/6.11 ((~(nota(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm)))) | nota(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(127,plain,
% 5.94/6.11 ((~(nota(sap, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[126, 125])).
% 5.94/6.11 tff(128,plain,
% 5.94/6.11 (![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[127, 122])).
% 5.94/6.11 tff(129,plain,
% 5.94/6.11 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(Ax!34, tptp_fun_C_18(noc, noc), sap)) | status(Ax!34, tptp_fun_C_18(noc, noc), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)) | status(Ax!34, tptp_fun_C_18(noc, noc), thm))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(130,plain,
% 5.94/6.11 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(Ax!34, tptp_fun_C_18(noc, noc), sap)) | status(Ax!34, tptp_fun_C_18(noc, noc), thm))),
% 5.94/6.11 inference(quant_inst,[status(thm)],[])).
% 5.94/6.11 tff(131,plain,
% 5.94/6.11 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(Ax!34, tptp_fun_C_18(noc, noc), sap)) | status(Ax!34, tptp_fun_C_18(noc, noc), thm)),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[130, 129])).
% 5.94/6.11 tff(132,plain,
% 5.94/6.11 (status(Ax!34, tptp_fun_C_18(noc, noc), thm)),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[131, 128, 102])).
% 5.94/6.11 tff(133,plain,
% 5.94/6.11 ((~((~status(Ax!34, tptp_fun_C_18(noc, noc), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc))))) | (~status(Ax!34, tptp_fun_C_18(noc, noc), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(134,plain,
% 5.94/6.11 ((~((~status(Ax!34, tptp_fun_C_18(noc, noc), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc))))) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[133, 132])).
% 5.94/6.11 tff(135,plain,
% 5.94/6.11 (![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[134, 57])).
% 5.94/6.11 tff(136,assumption,(model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))), introduced(assumption)).
% 5.94/6.11 tff(137,plain,
% 5.94/6.11 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))))),
% 5.94/6.11 inference(quant_inst,[status(thm)],[])).
% 5.94/6.11 tff(138,plain,
% 5.94/6.11 ($false),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[137, 8, 136])).
% 5.94/6.11 tff(139,plain,(~(model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.11 tff(140,assumption,(~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34)), introduced(assumption)).
% 5.94/6.11 tff(141,assumption,((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap)))), introduced(assumption)).
% 5.94/6.11 tff(142,plain,
% 5.94/6.11 (((~![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_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, 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))))))) | (~((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))))))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(143,plain,
% 5.94/6.11 ((~((~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | (~status(not(F!29), Ax!34, sap)) | ![I1: $i] : (~model(I1, not(F!29))))))) <=> (~((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap)))))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(144,plain,
% 5.94/6.11 (((~![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(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | (~status(not(F!29), Ax!34, sap)) | ![I1: $i] : (~model(I1, not(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_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))))))),
% 5.94/6.11 inference(monotonicity,[status(thm)],[143])).
% 5.94/6.11 tff(145,plain,
% 5.94/6.11 (((~![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(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | (~status(not(F!29), Ax!34, sap)) | ![I1: $i] : (~model(I1, not(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_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))))))),
% 5.94/6.11 inference(transitivity,[status(thm)],[144, 142])).
% 5.94/6.11 tff(146,plain,
% 5.94/6.11 ((~![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(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | (~status(not(F!29), Ax!34, sap)) | ![I1: $i] : (~model(I1, not(F!29)))))))),
% 5.94/6.11 inference(quant_inst,[status(thm)],[])).
% 5.94/6.11 tff(147,plain,
% 5.94/6.11 ((~![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_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap)))))),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[146, 145])).
% 5.94/6.11 tff(148,plain,
% 5.94/6.11 ($false),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[147, 90, 141])).
% 5.94/6.11 tff(149,plain,(~((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.11 tff(150,plain,
% 5.94/6.11 (((~(model(tptp_fun_I2_1(Ax!34), Ax!34) | ![I1: $i] : (~model(I1, not(F!29))) | (~status(not(F!29), Ax!34, sap)))) | (~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap)))) | ((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(151,plain,
% 5.94/6.11 ((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap)),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[150, 149])).
% 5.94/6.11 tff(152,assumption,(![I2: $i] : (~model(I2, Ax!34))), introduced(assumption)).
% 5.94/6.11 tff(153,plain,
% 5.94/6.11 (((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))))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(154,plain,
% 5.94/6.11 (?[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))))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(155,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')).
% 5.94/6.11 tff(156,plain,
% 5.94/6.11 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[155, 154])).
% 5.94/6.11 tff(157,plain,
% 5.94/6.11 (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[156, 153])).
% 5.94/6.11 tff(158,plain,
% 5.94/6.11 (model(I1!35, Ax!34)),
% 5.94/6.11 inference(and_elim,[status(thm)],[157])).
% 5.94/6.11 tff(159,plain,
% 5.94/6.11 ((~![I2: $i] : (~model(I2, Ax!34))) | (~model(I1!35, Ax!34))),
% 5.94/6.11 inference(quant_inst,[status(thm)],[])).
% 5.94/6.11 tff(160,plain,
% 5.94/6.11 ($false),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[159, 158, 152])).
% 5.94/6.11 tff(161,plain,(~![I2: $i] : (~model(I2, Ax!34))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.11 tff(162,plain,
% 5.94/6.11 (((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34)))) | ![I2: $i] : (~model(I2, Ax!34))),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(163,plain,
% 5.94/6.11 ((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34)))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[162, 161])).
% 5.94/6.11 tff(164,plain,
% 5.94/6.11 ((~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))) | (~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap)),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(165,plain,
% 5.94/6.11 ((~((~((~model(tptp_fun_I1_0(not(F!29)), not(F!29))) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(not(F!29), Ax!34, sap))) | status(not(F!29), Ax!34, sap)),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[164, 163])).
% 5.94/6.11 tff(166,plain,
% 5.94/6.11 (status(not(F!29), Ax!34, sap)),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[165, 151])).
% 5.94/6.11 tff(167,assumption,(~status(not(F!29), Ax!34, thm)), introduced(assumption)).
% 5.94/6.11 tff(168,plain,
% 5.94/6.11 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(not(F!29), Ax!34, sap)) | status(not(F!29), Ax!34, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(not(F!29), Ax!34, sap)) | status(not(F!29), Ax!34, thm))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(169,plain,
% 5.94/6.11 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(not(F!29), Ax!34, sap)) | status(not(F!29), Ax!34, thm))),
% 5.94/6.11 inference(quant_inst,[status(thm)],[])).
% 5.94/6.11 tff(170,plain,
% 5.94/6.11 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(not(F!29), Ax!34, sap)) | status(not(F!29), Ax!34, thm)),
% 5.94/6.11 inference(modus_ponens,[status(thm)],[169, 168])).
% 5.94/6.11 tff(171,plain,
% 5.94/6.11 ($false),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[170, 128, 167, 166])).
% 5.94/6.11 tff(172,plain,(status(not(F!29), Ax!34, thm)), inference(lemma,lemma(discharge,[]))).
% 5.94/6.11 tff(173,plain,
% 5.94/6.11 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!34, not(F!29)), not(F!29))) | model(tptp_fun_I1_3(Ax!34, not(F!29)), Ax!34))) | status(not(F!29), Ax!34, thm))) | (~((~status(not(F!29), Ax!34, thm)) | ![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))))))),
% 5.94/6.11 inference(quant_inst,[status(thm)],[])).
% 5.94/6.11 tff(174,plain,
% 5.94/6.11 (~((~((~((~model(tptp_fun_I1_3(Ax!34, not(F!29)), not(F!29))) | model(tptp_fun_I1_3(Ax!34, not(F!29)), Ax!34))) | status(not(F!29), Ax!34, thm))) | (~((~status(not(F!29), Ax!34, thm)) | ![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34)))))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[173, 53])).
% 5.94/6.11 tff(175,plain,
% 5.94/6.11 (((~((~((~model(tptp_fun_I1_3(Ax!34, not(F!29)), not(F!29))) | model(tptp_fun_I1_3(Ax!34, not(F!29)), Ax!34))) | status(not(F!29), Ax!34, thm))) | (~((~status(not(F!29), Ax!34, thm)) | ![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))))) | ((~status(not(F!29), Ax!34, thm)) | ![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34)))),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(176,plain,
% 5.94/6.11 ((~status(not(F!29), Ax!34, thm)) | ![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[175, 174])).
% 5.94/6.11 tff(177,plain,
% 5.94/6.11 ((~((~status(not(F!29), Ax!34, thm)) | ![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34)))) | (~status(not(F!29), Ax!34, thm)) | ![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))),
% 5.94/6.11 inference(tautology,[status(thm)],[])).
% 5.94/6.11 tff(178,plain,
% 5.94/6.11 ((~status(not(F!29), Ax!34, thm)) | ![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[177, 176])).
% 5.94/6.11 tff(179,plain,
% 5.94/6.11 (![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))),
% 5.94/6.11 inference(unit_resolution,[status(thm)],[178, 172])).
% 5.94/6.11 tff(180,plain,
% 5.94/6.11 (((~![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))) | ((~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34))) <=> ((~![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34))),
% 5.94/6.11 inference(rewrite,[status(thm)],[])).
% 5.94/6.11 tff(181,plain,
% 5.94/6.11 ((~![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))) | ((~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34))),
% 5.94/6.11 inference(quant_inst,[status(thm)],[])).
% 5.94/6.11 tff(182,plain,
% 5.94/6.11 ((~![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34)),
% 5.94/6.12 inference(modus_ponens,[status(thm)],[181, 180])).
% 5.94/6.12 tff(183,plain,
% 5.94/6.12 (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[182, 179, 140])).
% 5.94/6.12 tff(184,assumption,((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34)))), introduced(assumption)).
% 5.94/6.12 tff(185,plain,
% 5.94/6.12 (((~![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, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34)))))) <=> ((~![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, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34))))))),
% 5.94/6.12 inference(rewrite,[status(thm)],[])).
% 5.94/6.12 tff(186,plain,
% 5.94/6.12 ((~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | (~status(F!29, Ax!34, sap)) | ![I1: $i] : (~model(I1, F!29)))))) <=> (~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34)))))),
% 5.94/6.12 inference(rewrite,[status(thm)],[])).
% 5.94/6.12 tff(187,plain,
% 5.94/6.12 (((~![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, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | (~status(F!29, Ax!34, 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, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34))))))),
% 5.94/6.12 inference(monotonicity,[status(thm)],[186])).
% 5.94/6.12 tff(188,plain,
% 5.94/6.12 (((~![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, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | (~status(F!29, Ax!34, 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, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34))))))),
% 5.94/6.12 inference(transitivity,[status(thm)],[187, 185])).
% 5.94/6.12 tff(189,plain,
% 5.94/6.12 ((~![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, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(model(tptp_fun_I2_1(Ax!34), Ax!34) | (~status(F!29, Ax!34, sap)) | ![I1: $i] : (~model(I1, F!29))))))),
% 5.94/6.12 inference(quant_inst,[status(thm)],[])).
% 5.94/6.12 tff(190,plain,
% 5.94/6.12 ((~![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, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34)))))),
% 5.94/6.12 inference(modus_ponens,[status(thm)],[189, 188])).
% 5.94/6.12 tff(191,plain,
% 5.94/6.12 ($false),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[190, 90, 184])).
% 5.94/6.12 tff(192,plain,(~((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34))))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.12 tff(193,plain,
% 5.94/6.12 (((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap))) | (~(![I1: $i] : (~model(I1, F!29)) | (~status(F!29, Ax!34, sap)) | model(tptp_fun_I2_1(Ax!34), Ax!34)))) | ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap))),
% 5.94/6.12 inference(tautology,[status(thm)],[])).
% 5.94/6.12 tff(194,plain,
% 5.94/6.12 ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap)),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[193, 192])).
% 5.94/6.12 tff(195,plain,
% 5.94/6.12 (((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34)))) | ![I2: $i] : (~model(I2, Ax!34))),
% 5.94/6.12 inference(tautology,[status(thm)],[])).
% 5.94/6.12 tff(196,plain,
% 5.94/6.12 ((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34)))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[195, 161])).
% 5.94/6.12 tff(197,plain,
% 5.94/6.12 ((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap))) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap)),
% 5.94/6.12 inference(tautology,[status(thm)],[])).
% 5.94/6.12 tff(198,plain,
% 5.94/6.12 ((~((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, Ax!34))))) | status(F!29, Ax!34, sap))) | status(F!29, Ax!34, sap)),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[197, 196])).
% 5.94/6.12 tff(199,plain,
% 5.94/6.12 (status(F!29, Ax!34, sap)),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[198, 194])).
% 5.94/6.12 tff(200,assumption,(~status(F!29, Ax!34, thm)), introduced(assumption)).
% 5.94/6.12 tff(201,plain,
% 5.94/6.12 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(F!29, Ax!34, sap)) | status(F!29, Ax!34, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(F!29, Ax!34, sap)) | status(F!29, Ax!34, thm))),
% 5.94/6.12 inference(rewrite,[status(thm)],[])).
% 5.94/6.12 tff(202,plain,
% 5.94/6.12 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(F!29, Ax!34, sap)) | status(F!29, Ax!34, thm))),
% 5.94/6.12 inference(quant_inst,[status(thm)],[])).
% 5.94/6.12 tff(203,plain,
% 5.94/6.12 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(F!29, Ax!34, sap)) | status(F!29, Ax!34, thm)),
% 5.94/6.12 inference(modus_ponens,[status(thm)],[202, 201])).
% 5.94/6.12 tff(204,plain,
% 5.94/6.12 ($false),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[203, 128, 200, 199])).
% 5.94/6.12 tff(205,plain,(status(F!29, Ax!34, thm)), inference(lemma,lemma(discharge,[]))).
% 5.94/6.12 tff(206,plain,
% 5.94/6.12 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))) | (~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))))))),
% 5.94/6.12 inference(quant_inst,[status(thm)],[])).
% 5.94/6.12 tff(207,plain,
% 5.94/6.12 (~((~((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))) | (~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34)))))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[206, 53])).
% 5.94/6.12 tff(208,plain,
% 5.94/6.12 (((~((~((~model(tptp_fun_I1_3(Ax!34, F!29), F!29)) | model(tptp_fun_I1_3(Ax!34, F!29), Ax!34))) | status(F!29, Ax!34, thm))) | (~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))))) | ((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34)))),
% 5.94/6.12 inference(tautology,[status(thm)],[])).
% 5.94/6.12 tff(209,plain,
% 5.94/6.12 ((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[208, 207])).
% 5.94/6.12 tff(210,plain,
% 5.94/6.12 ((~((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34)))) | (~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))),
% 5.94/6.12 inference(tautology,[status(thm)],[])).
% 5.94/6.12 tff(211,plain,
% 5.94/6.12 ((~status(F!29, Ax!34, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[210, 209])).
% 5.94/6.12 tff(212,plain,
% 5.94/6.12 (![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[211, 205])).
% 5.94/6.12 tff(213,plain,
% 5.94/6.12 (((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | ((~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29)) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29)) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34))),
% 5.94/6.12 inference(rewrite,[status(thm)],[])).
% 5.94/6.12 tff(214,plain,
% 5.94/6.12 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | ((~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29)) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34))),
% 5.94/6.12 inference(quant_inst,[status(thm)],[])).
% 5.94/6.12 tff(215,plain,
% 5.94/6.12 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29)) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34)),
% 5.94/6.12 inference(modus_ponens,[status(thm)],[214, 213])).
% 5.94/6.12 tff(216,plain,
% 5.94/6.12 (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29)),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[215, 212, 140])).
% 5.94/6.12 tff(217,plain,
% 5.94/6.12 ((model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), F!29) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(F!29))),
% 5.94/6.12 inference(tautology,[status(thm)],[])).
% 5.94/6.12 tff(218,plain,
% 5.94/6.12 ($false),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[217, 216, 183, 139])).
% 5.94/6.12 tff(219,plain,(model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34)), inference(lemma,lemma(discharge,[]))).
% 5.94/6.12 tff(220,plain,
% 5.94/6.12 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))))),
% 5.94/6.12 inference(quant_inst,[status(thm)],[])).
% 5.94/6.12 tff(221,plain,
% 5.94/6.12 (~(model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc))))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[220, 8])).
% 5.94/6.12 tff(222,plain,
% 5.94/6.12 (((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc)))) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))),
% 5.94/6.12 inference(tautology,[status(thm)],[])).
% 5.94/6.12 tff(223,plain,
% 5.94/6.12 (model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[222, 58])).
% 5.94/6.12 tff(224,plain,
% 5.94/6.12 ((model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc))))),
% 5.94/6.12 inference(tautology,[status(thm)],[])).
% 5.94/6.12 tff(225,plain,
% 5.94/6.12 ((model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)) <=> model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[224, 223])).
% 5.94/6.12 tff(226,plain,
% 5.94/6.12 (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[225, 221])).
% 5.94/6.12 tff(227,plain,
% 5.94/6.12 (((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))) | ((~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34)) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)))) <=> ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34)) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)))),
% 5.94/6.12 inference(rewrite,[status(thm)],[])).
% 5.94/6.12 tff(228,plain,
% 5.94/6.12 ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))) | ((~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34)) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc)))),
% 5.94/6.12 inference(quant_inst,[status(thm)],[])).
% 5.94/6.12 tff(229,plain,
% 5.94/6.12 ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), Ax!34)) | model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))),
% 5.94/6.12 inference(modus_ponens,[status(thm)],[228, 227])).
% 5.94/6.12 tff(230,plain,
% 5.94/6.12 ($false),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[229, 226, 219, 135])).
% 5.94/6.12 tff(231,plain,((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.12 tff(232,assumption,((~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc)))))))), introduced(assumption)).
% 5.94/6.12 tff(233,plain,
% 5.94/6.12 (((~![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_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(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_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc))))))))))),
% 5.94/6.12 inference(rewrite,[status(thm)],[])).
% 5.94/6.12 tff(234,plain,
% 5.94/6.12 ((~((~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc))))))))) <=> (~((~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc)))))))))),
% 5.94/6.12 inference(rewrite,[status(thm)],[])).
% 5.94/6.12 tff(235,plain,
% 5.94/6.12 (((~![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_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(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_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc))))))))))),
% 5.94/6.12 inference(monotonicity,[status(thm)],[234])).
% 5.94/6.12 tff(236,plain,
% 5.94/6.12 (((~![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_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(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_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc))))))))))),
% 5.94/6.12 inference(transitivity,[status(thm)],[235, 233])).
% 5.94/6.12 tff(237,plain,
% 5.94/6.12 ((~![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_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc)))))))))),
% 5.94/6.12 inference(quant_inst,[status(thm)],[])).
% 5.94/6.12 tff(238,plain,
% 5.94/6.12 ((~![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_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc)))))))))),
% 5.94/6.12 inference(modus_ponens,[status(thm)],[237, 236])).
% 5.94/6.12 tff(239,plain,
% 5.94/6.12 ($false),
% 5.94/6.12 inference(unit_resolution,[status(thm)],[238, 30, 232])).
% 5.94/6.12 tff(240,plain,(~((~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc))))))))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.12 tff(241,plain,
% 5.94/6.12 (((~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~(status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_19(noc, noc))) | (~model(I1, tptp_fun_C_18(noc, noc)))) | ![I2: $i] : ((~model(I2, tptp_fun_Ax_19(noc, noc))) | (~model(I2, not(tptp_fun_C_18(noc, noc)))))))) | ((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(242,plain,
% 5.94/6.13 ((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc)))))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[241, 240])).
% 5.94/6.13 tff(243,plain,
% 5.94/6.13 ((~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))))))) | (~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc)))))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(244,plain,
% 5.94/6.13 ((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~((~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc))) | (~model(tptp_fun_I1_2(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_C_18(noc, noc))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), not(tptp_fun_C_18(noc, noc)))) | (~model(tptp_fun_I2_17(tptp_fun_C_18(noc, noc), tptp_fun_Ax_19(noc, noc)), tptp_fun_Ax_19(noc, noc)))))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[243, 242])).
% 5.94/6.13 tff(245,plain,
% 5.94/6.13 (~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[244, 231])).
% 5.94/6.13 tff(246,plain,
% 5.94/6.13 (^[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)))))))))),
% 5.94/6.13 inference(bind,[status(th)],[])).
% 5.94/6.13 tff(247,plain,
% 5.94/6.13 (![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))))))))),
% 5.94/6.13 inference(quant_intro,[status(thm)],[246])).
% 5.94/6.13 tff(248,plain,
% 5.94/6.13 (^[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)))))))))),
% 5.94/6.13 inference(bind,[status(th)],[])).
% 5.94/6.13 tff(249,plain,
% 5.94/6.13 (![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))))))))),
% 5.94/6.13 inference(quant_intro,[status(thm)],[248])).
% 5.94/6.13 tff(250,plain,
% 5.94/6.13 (![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))))))))),
% 5.94/6.13 inference(transitivity,[status(thm)],[249, 247])).
% 5.94/6.13 tff(251,plain,
% 5.94/6.13 (^[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))))))))))),
% 5.94/6.13 inference(bind,[status(th)],[])).
% 5.94/6.13 tff(252,plain,
% 5.94/6.13 (![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))))))))),
% 5.94/6.13 inference(quant_intro,[status(thm)],[251])).
% 5.94/6.13 tff(253,plain,
% 5.94/6.13 (^[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)))))),
% 5.94/6.13 inference(bind,[status(th)],[])).
% 5.94/6.13 tff(254,plain,
% 5.94/6.13 (![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))))),
% 5.94/6.13 inference(quant_intro,[status(thm)],[253])).
% 5.94/6.13 tff(255,plain,
% 5.94/6.13 (![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))),
% 5.94/6.13 inference(rewrite,[status(thm)],[])).
% 5.94/6.13 tff(256,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')).
% 5.94/6.13 tff(257,plain,
% 5.94/6.13 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 5.94/6.13 inference(modus_ponens,[status(thm)],[256, 255])).
% 5.94/6.13 tff(258,plain,(
% 5.94/6.13 ![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))))),
% 5.94/6.13 inference(skolemize,[status(sab)],[257])).
% 5.94/6.13 tff(259,plain,
% 5.94/6.13 (![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))))),
% 5.94/6.13 inference(modus_ponens,[status(thm)],[258, 254])).
% 5.94/6.13 tff(260,plain,
% 5.94/6.13 (![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))))))))),
% 5.94/6.13 inference(modus_ponens,[status(thm)],[259, 252])).
% 5.94/6.13 tff(261,plain,
% 5.94/6.13 (![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))))))))),
% 5.94/6.13 inference(modus_ponens,[status(thm)],[260, 250])).
% 5.94/6.13 tff(262,plain,
% 5.94/6.13 (((~![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, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)))))) <=> ((~![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, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))))))),
% 5.94/6.13 inference(rewrite,[status(thm)],[])).
% 5.94/6.13 tff(263,plain,
% 5.94/6.13 ((~((~(mighta(noc, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, noc)) | (~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)))))))) <=> (~((~(mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)))))),
% 5.94/6.13 inference(rewrite,[status(thm)],[])).
% 5.94/6.13 tff(264,plain,
% 5.94/6.13 (((~![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, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, noc)) | (~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))))))))) <=> ((~![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, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))))))),
% 5.94/6.13 inference(monotonicity,[status(thm)],[263])).
% 5.94/6.13 tff(265,plain,
% 5.94/6.13 (((~![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, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, noc)) | (~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))))))))) <=> ((~![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, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))))))),
% 5.94/6.13 inference(transitivity,[status(thm)],[264, 262])).
% 5.94/6.13 tff(266,plain,
% 5.94/6.13 ((~![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, noc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | (~status(Ax, C, noc))))) | (~((~mighta(noc, noc)) | (~((~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)) | (~status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))))))))),
% 5.94/6.13 inference(quant_inst,[status(thm)],[])).
% 5.94/6.13 tff(267,plain,
% 5.94/6.13 ((~![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, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)))))),
% 5.94/6.13 inference(modus_ponens,[status(thm)],[266, 265])).
% 5.94/6.13 tff(268,plain,
% 5.94/6.13 (~((~(mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[267, 261])).
% 5.94/6.13 tff(269,plain,
% 5.94/6.13 (((~(mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)))) | ((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(270,plain,
% 5.94/6.13 ((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[269, 268])).
% 5.94/6.13 tff(271,plain,
% 5.94/6.13 ((~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc))) | (~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(272,plain,
% 5.94/6.13 ((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[271, 270])).
% 5.94/6.13 tff(273,plain,
% 5.94/6.13 (~mighta(noc, noc)),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[272, 245])).
% 5.94/6.13 tff(274,plain,
% 5.94/6.13 (((~(mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | (~((~mighta(noc, noc)) | status(tptp_fun_Ax_19(noc, noc), tptp_fun_C_18(noc, noc), noc)))) | (mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(275,plain,
% 5.94/6.13 (mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[274, 268])).
% 5.94/6.13 tff(276,plain,
% 5.94/6.13 ((~(mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc)))) | mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(277,plain,
% 5.94/6.13 (mighta(noc, noc) | ![Ax: $i, C: $i] : (~status(Ax, C, noc))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[276, 275])).
% 5.94/6.13 tff(278,plain,
% 5.94/6.13 (![Ax: $i, C: $i] : (~status(Ax, C, noc))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[277, 273])).
% 5.94/6.13 tff(279,assumption,(status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)), introduced(assumption)).
% 5.94/6.13 tff(280,assumption,(![Ax: $i, C: $i] : (~status(Ax, C, noc))), introduced(assumption)).
% 5.94/6.13 tff(281,plain,
% 5.94/6.13 ((~![Ax: $i, C: $i] : (~status(Ax, C, noc))) | (~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc))),
% 5.94/6.13 inference(quant_inst,[status(thm)],[])).
% 5.94/6.13 tff(282,plain,
% 5.94/6.13 ($false),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[281, 280, 279])).
% 5.94/6.13 tff(283,plain,((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | (~![Ax: $i, C: $i] : (~status(Ax, C, noc)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.13 tff(284,plain,
% 5.94/6.13 (~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[283, 278])).
% 5.94/6.13 tff(285,plain,
% 5.94/6.13 (((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(286,plain,
% 5.94/6.13 ((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc)),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[285, 284])).
% 5.94/6.13 tff(287,plain,
% 5.94/6.13 ((~![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, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc)))) | (~((~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc)))))))),
% 5.94/6.13 inference(quant_inst,[status(thm)],[])).
% 5.94/6.13 tff(288,plain,
% 5.94/6.13 (~((~(nota(noc, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc)))) | (~((~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc))))))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[287, 118])).
% 5.94/6.13 tff(289,plain,
% 5.94/6.13 (((~(nota(noc, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc)))) | (~((~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc)))))) | ((~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc))))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(290,plain,
% 5.94/6.13 ((~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc)))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[289, 288])).
% 5.94/6.13 tff(291,plain,
% 5.94/6.13 ((~((~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc))))) | (~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc)))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(292,plain,
% 5.94/6.13 ((~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc)))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[291, 290])).
% 5.94/6.13 tff(293,plain,
% 5.94/6.13 (~nota(noc, wtc)),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[292, 286])).
% 5.94/6.13 tff(294,plain,
% 5.94/6.13 (((~(nota(noc, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc)))) | (~((~nota(noc, wtc)) | (~((~status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), noc)) | status(tptp_fun_Ax_23(wtc, noc), tptp_fun_C_22(wtc, noc), wtc)))))) | (nota(noc, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc)))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(295,plain,
% 5.94/6.13 (nota(noc, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[294, 288])).
% 5.94/6.13 tff(296,plain,
% 5.94/6.13 ((~(nota(noc, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc)))) | nota(noc, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(297,plain,
% 5.94/6.13 (nota(noc, wtc) | ![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[296, 295])).
% 5.94/6.13 tff(298,plain,
% 5.94/6.13 (![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[297, 293])).
% 5.94/6.13 tff(299,assumption,(![I3: $i] : model(I3, F!29)), introduced(assumption)).
% 5.94/6.13 tff(300,plain,
% 5.94/6.13 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 5.94/6.13 inference(rewrite,[status(thm)],[])).
% 5.94/6.13 tff(301,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 5.94/6.13 tff(302,plain,
% 5.94/6.13 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 5.94/6.13 inference(modus_ponens,[status(thm)],[301, 300])).
% 5.94/6.13 tff(303,plain,
% 5.94/6.13 (~model(I2!31, F!29)),
% 5.94/6.13 inference(and_elim,[status(thm)],[302])).
% 5.94/6.13 tff(304,plain,
% 5.94/6.13 ((~![I3: $i] : model(I3, F!29)) | model(I2!31, F!29)),
% 5.94/6.13 inference(quant_inst,[status(thm)],[])).
% 5.94/6.13 tff(305,plain,
% 5.94/6.13 ($false),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[304, 303, 299])).
% 5.94/6.13 tff(306,plain,(~![I3: $i] : model(I3, F!29)), inference(lemma,lemma(discharge,[]))).
% 5.94/6.13 tff(307,plain,
% 5.94/6.13 (((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))) | ![I3: $i] : model(I3, F!29)),
% 5.94/6.13 inference(tautology,[status(thm)],[])).
% 5.94/6.13 tff(308,plain,
% 5.94/6.13 ((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))),
% 5.94/6.13 inference(unit_resolution,[status(thm)],[307, 306])).
% 5.94/6.13 tff(309,plain,
% 5.94/6.13 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C)))))))))),
% 5.94/6.13 inference(bind,[status(th)],[])).
% 5.94/6.13 tff(310,plain,
% 5.94/6.13 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))),
% 5.94/6.13 inference(quant_intro,[status(thm)],[309])).
% 5.94/6.13 tff(311,plain,
% 5.94/6.13 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 5.94/6.13 inference(bind,[status(th)],[])).
% 5.94/6.13 tff(312,plain,
% 5.94/6.13 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.13 inference(quant_intro,[status(thm)],[311])).
% 5.94/6.13 tff(313,plain,
% 5.94/6.13 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 5.94/6.13 inference(bind,[status(th)],[])).
% 5.94/6.13 tff(314,plain,
% 5.94/6.13 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.13 inference(quant_intro,[status(thm)],[313])).
% 5.94/6.13 tff(315,plain,
% 5.94/6.13 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.13 inference(transitivity,[status(thm)],[314, 312])).
% 5.94/6.13 tff(316,plain,
% 5.94/6.13 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) <=> (status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) <=> (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))) <=> ((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, wtc))))), rewrite(((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, wtc))) <=> ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))) <=> ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))), (((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))))), rewrite(((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax)))))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))), (((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))))),
% 5.94/6.14 inference(bind,[status(th)],[])).
% 5.94/6.14 tff(317,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.14 inference(quant_intro,[status(thm)],[316])).
% 5.94/6.14 tff(318,plain,
% 5.94/6.14 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))))),
% 5.94/6.14 inference(bind,[status(th)],[])).
% 5.94/6.14 tff(319,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 5.94/6.14 inference(quant_intro,[status(thm)],[318])).
% 5.94/6.14 tff(320,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(321,plain,
% 5.94/6.14 (^[Ax: $i, C: $i] : rewrite((((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)))),
% 5.94/6.14 inference(bind,[status(th)],[])).
% 5.94/6.14 tff(322,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 5.94/6.14 inference(quant_intro,[status(thm)],[321])).
% 5.94/6.14 tff(323,axiom,(![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','wtc')).
% 5.94/6.14 tff(324,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[323, 322])).
% 5.94/6.14 tff(325,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : model(I3, C)) <=> status(Ax, C, wtc))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[324, 320])).
% 5.94/6.14 tff(326,plain,(
% 5.94/6.14 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) | status(Ax, C, wtc)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 5.94/6.14 inference(skolemize,[status(sab)],[325])).
% 5.94/6.14 tff(327,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : ((status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : model(I3, C)) | (~status(Ax, C, wtc))))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[326, 319])).
% 5.94/6.14 tff(328,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[327, 317])).
% 5.94/6.14 tff(329,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~model(tptp_fun_I3_11(C), C)))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : model(I3, C)) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[328, 315])).
% 5.94/6.14 tff(330,plain,
% 5.94/6.14 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[329, 310])).
% 5.94/6.14 tff(331,plain,
% 5.94/6.14 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)))) | (~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)))) | (~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29)))))))))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(332,plain,
% 5.94/6.14 ((~((~(status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!29, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, F!29)))))))) <=> (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)))) | (~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))))))))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(333,plain,
% 5.94/6.14 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!29, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, F!29))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)))) | (~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29)))))))))),
% 5.94/6.14 inference(monotonicity,[status(thm)],[332])).
% 5.94/6.14 tff(334,plain,
% 5.94/6.14 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!29, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, F!29))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)))) | (~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29)))))))))),
% 5.94/6.14 inference(transitivity,[status(thm)],[333, 331])).
% 5.94/6.14 tff(335,plain,
% 5.94/6.14 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!29, wtc)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : model(I3, F!29))))))))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(336,plain,
% 5.94/6.14 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)))) | (~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))))))))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[335, 334])).
% 5.94/6.14 tff(337,plain,
% 5.94/6.14 (~((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)))) | (~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29)))))))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[336, 330])).
% 5.94/6.14 tff(338,plain,
% 5.94/6.14 (((~(![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42) | status(C!42, F!29, wtc) | (~model(tptp_fun_I3_11(F!29), F!29)))) | (~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))))))) | ((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29)))))),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(339,plain,
% 5.94/6.14 ((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[338, 337])).
% 5.94/6.14 tff(340,plain,
% 5.94/6.14 ((~((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29)))))) | (~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))))),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(341,plain,
% 5.94/6.14 ((~status(C!42, F!29, wtc)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | model(tptp_fun_I2_8(C!42), C!42) | (~![I3: $i] : model(I3, F!29))))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[340, 339])).
% 5.94/6.14 tff(342,plain,
% 5.94/6.14 (~status(C!42, F!29, wtc)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[341, 308])).
% 5.94/6.14 tff(343,plain,
% 5.94/6.14 (((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | ((~status(C!42, F!29, noc)) | status(C!42, F!29, wtc))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | (~status(C!42, F!29, noc)) | status(C!42, F!29, wtc))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(344,plain,
% 5.94/6.14 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | ((~status(C!42, F!29, noc)) | status(C!42, F!29, wtc))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(345,plain,
% 5.94/6.14 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | (~status(C!42, F!29, noc)) | status(C!42, F!29, wtc)),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[344, 343])).
% 5.94/6.14 tff(346,plain,
% 5.94/6.14 (~status(C!42, F!29, noc)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[345, 342, 298])).
% 5.94/6.14 tff(347,assumption,(![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29)))), introduced(assumption)).
% 5.94/6.14 tff(348,plain,
% 5.94/6.14 ((~![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(C!42, F!29), F!29)) | model(tptp_fun_I1_3(C!42, F!29), C!42))) | status(F!29, C!42, thm))) | (~((~status(F!29, C!42, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))))))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(349,plain,
% 5.94/6.14 (~((~((~((~model(tptp_fun_I1_3(C!42, F!29), F!29)) | model(tptp_fun_I1_3(C!42, F!29), C!42))) | status(F!29, C!42, thm))) | (~((~status(F!29, C!42, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42)))))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[348, 53])).
% 5.94/6.14 tff(350,plain,
% 5.94/6.14 (((~((~((~model(tptp_fun_I1_3(C!42, F!29), F!29)) | model(tptp_fun_I1_3(C!42, F!29), C!42))) | status(F!29, C!42, thm))) | (~((~status(F!29, C!42, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))))) | ((~status(F!29, C!42, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42)))),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(351,plain,
% 5.94/6.14 ((~status(F!29, C!42, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[350, 349])).
% 5.94/6.14 tff(352,assumption,(![I2: $i] : (~model(I2, C!42))), introduced(assumption)).
% 5.94/6.14 tff(353,plain,
% 5.94/6.14 (?[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))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(354,plain,
% 5.94/6.14 (^[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)))),
% 5.94/6.14 inference(bind,[status(th)],[])).
% 5.94/6.14 tff(355,plain,
% 5.94/6.14 (?[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))),
% 5.94/6.14 inference(quant_intro,[status(thm)],[354])).
% 5.94/6.14 tff(356,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')).
% 5.94/6.14 tff(357,plain,
% 5.94/6.14 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[356, 355])).
% 5.94/6.14 tff(358,plain,
% 5.94/6.14 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[357, 353])).
% 5.94/6.14 tff(359,plain,
% 5.94/6.14 (model(I2!45, C!42)),
% 5.94/6.14 inference(and_elim,[status(thm)],[358])).
% 5.94/6.14 tff(360,plain,
% 5.94/6.14 ((~![I2: $i] : (~model(I2, C!42))) | (~model(I2!45, C!42))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(361,plain,
% 5.94/6.14 ($false),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[360, 359, 352])).
% 5.94/6.14 tff(362,plain,(~![I2: $i] : (~model(I2, C!42))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.14 tff(363,plain,
% 5.94/6.14 (((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42)))) | ![I2: $i] : (~model(I2, C!42))),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(364,plain,
% 5.94/6.14 ((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42)))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[363, 362])).
% 5.94/6.14 tff(365,plain,
% 5.94/6.14 (((~![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))))))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(366,plain,
% 5.94/6.14 ((~((~((~((~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)))))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(367,plain,
% 5.94/6.14 (((~![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))))))),
% 5.94/6.14 inference(monotonicity,[status(thm)],[366])).
% 5.94/6.14 tff(368,plain,
% 5.94/6.14 (((~![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))))))),
% 5.94/6.14 inference(transitivity,[status(thm)],[367, 365])).
% 5.94/6.14 tff(369,plain,
% 5.94/6.14 ((~![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))))))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(370,plain,
% 5.94/6.14 ((~![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)))))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[369, 368])).
% 5.94/6.14 tff(371,plain,
% 5.94/6.14 (~((~((~((~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))))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[370, 90])).
% 5.94/6.14 tff(372,plain,
% 5.94/6.14 (((~((~((~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))),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(373,plain,
% 5.94/6.14 ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[372, 371])).
% 5.94/6.14 tff(374,plain,
% 5.94/6.14 ((~((~((~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)),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(375,plain,
% 5.94/6.14 ((~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : (~model(I2, C!42))))) | status(F!29, C!42, sap)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[374, 373])).
% 5.94/6.14 tff(376,plain,
% 5.94/6.14 (status(F!29, C!42, sap)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[375, 364])).
% 5.94/6.14 tff(377,plain,
% 5.94/6.14 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(F!29, C!42, sap)) | status(F!29, C!42, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(F!29, C!42, sap)) | status(F!29, C!42, thm))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(378,plain,
% 5.94/6.14 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(F!29, C!42, sap)) | status(F!29, C!42, thm))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(379,plain,
% 5.94/6.14 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(F!29, C!42, sap)) | status(F!29, C!42, thm)),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[378, 377])).
% 5.94/6.14 tff(380,plain,
% 5.94/6.14 (status(F!29, C!42, thm)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[379, 128, 376])).
% 5.94/6.14 tff(381,plain,
% 5.94/6.14 ((~((~status(F!29, C!42, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42)))) | (~status(F!29, C!42, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(382,plain,
% 5.94/6.14 ((~((~status(F!29, C!42, thm)) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42)))) | ![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[381, 380])).
% 5.94/6.14 tff(383,plain,
% 5.94/6.14 (![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[382, 351])).
% 5.94/6.14 tff(384,plain,
% 5.94/6.14 (model(I1!30, F!29)),
% 5.94/6.14 inference(and_elim,[status(thm)],[302])).
% 5.94/6.14 tff(385,plain,
% 5.94/6.14 (((~![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))) | ((~model(I1!30, F!29)) | model(I1!30, C!42))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))) | (~model(I1!30, F!29)) | model(I1!30, C!42))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(386,plain,
% 5.94/6.14 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))) | ((~model(I1!30, F!29)) | model(I1!30, C!42))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(387,plain,
% 5.94/6.14 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))) | (~model(I1!30, F!29)) | model(I1!30, C!42)),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[386, 385])).
% 5.94/6.14 tff(388,plain,
% 5.94/6.14 (model(I1!30, C!42)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[387, 384, 383])).
% 5.94/6.14 tff(389,plain,
% 5.94/6.14 (((~![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29)))) | ((~model(I1!30, C!42)) | (~model(I1!30, F!29)))) <=> ((~![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29)))) | (~model(I1!30, C!42)) | (~model(I1!30, F!29)))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(390,plain,
% 5.94/6.14 ((~![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29)))) | ((~model(I1!30, C!42)) | (~model(I1!30, F!29)))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(391,plain,
% 5.94/6.14 ((~![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29)))) | (~model(I1!30, C!42)) | (~model(I1!30, F!29))),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[390, 389])).
% 5.94/6.14 tff(392,plain,
% 5.94/6.14 ($false),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[391, 384, 388, 347])).
% 5.94/6.14 tff(393,plain,(~![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.14 tff(394,plain,
% 5.94/6.14 ((~(status(C!42, F!29, noc) | ![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29)))))) | status(C!42, F!29, noc) | ![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(395,plain,
% 5.94/6.14 ((~(status(C!42, F!29, noc) | ![I1: $i] : ((~model(I1, C!42)) | (~model(I1, F!29))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29)))))) | ![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[394, 393, 346])).
% 5.94/6.14 tff(396,plain,
% 5.94/6.14 (![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[395, 34])).
% 5.94/6.14 tff(397,assumption,(![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))), introduced(assumption)).
% 5.94/6.14 tff(398,assumption,(model(tptp_fun_I3_9(F!29, C!42), F!29) <=> model(tptp_fun_I3_9(F!29, C!42), not(F!29))), introduced(assumption)).
% 5.94/6.14 tff(399,plain,
% 5.94/6.14 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I3_9(F!29, C!42), F!29) <=> model(tptp_fun_I3_9(F!29, C!42), not(F!29))))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(400,plain,
% 5.94/6.14 ($false),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[399, 8, 398])).
% 5.94/6.14 tff(401,plain,(~(model(tptp_fun_I3_9(F!29, C!42), F!29) <=> model(tptp_fun_I3_9(F!29, C!42), not(F!29)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.14 tff(402,assumption,(~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))), introduced(assumption)).
% 5.94/6.14 tff(403,assumption,(~model(tptp_fun_I3_9(F!29, C!42), C!42)), introduced(assumption)).
% 5.94/6.14 tff(404,plain,
% 5.94/6.14 ((model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)) | model(tptp_fun_I3_9(F!29, C!42), C!42) | model(tptp_fun_I3_9(F!29, C!42), F!29)),
% 5.94/6.14 inference(tautology,[status(thm)],[])).
% 5.94/6.14 tff(405,plain,
% 5.94/6.14 (model(tptp_fun_I3_9(F!29, C!42), F!29)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[404, 403, 402])).
% 5.94/6.14 tff(406,plain,
% 5.94/6.14 (((~![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))) | ((~model(tptp_fun_I3_9(F!29, C!42), F!29)) | model(tptp_fun_I3_9(F!29, C!42), C!42))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))) | (~model(tptp_fun_I3_9(F!29, C!42), F!29)) | model(tptp_fun_I3_9(F!29, C!42), C!42))),
% 5.94/6.14 inference(rewrite,[status(thm)],[])).
% 5.94/6.14 tff(407,plain,
% 5.94/6.14 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))) | ((~model(tptp_fun_I3_9(F!29, C!42), F!29)) | model(tptp_fun_I3_9(F!29, C!42), C!42))),
% 5.94/6.14 inference(quant_inst,[status(thm)],[])).
% 5.94/6.14 tff(408,plain,
% 5.94/6.14 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, C!42))) | (~model(tptp_fun_I3_9(F!29, C!42), F!29)) | model(tptp_fun_I3_9(F!29, C!42), C!42)),
% 5.94/6.14 inference(modus_ponens,[status(thm)],[407, 406])).
% 5.94/6.14 tff(409,plain,
% 5.94/6.14 ((~model(tptp_fun_I3_9(F!29, C!42), F!29)) | model(tptp_fun_I3_9(F!29, C!42), C!42)),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[408, 383])).
% 5.94/6.14 tff(410,plain,
% 5.94/6.14 ($false),
% 5.94/6.14 inference(unit_resolution,[status(thm)],[409, 405, 403])).
% 5.94/6.14 tff(411,plain,(model(tptp_fun_I3_9(F!29, C!42), C!42) | (model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.15 tff(412,plain,
% 5.94/6.15 (model(tptp_fun_I3_9(F!29, C!42), C!42)),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[411, 402])).
% 5.94/6.15 tff(413,plain,
% 5.94/6.15 ((model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)) | (~model(tptp_fun_I3_9(F!29, C!42), C!42)) | (~model(tptp_fun_I3_9(F!29, C!42), F!29))),
% 5.94/6.15 inference(tautology,[status(thm)],[])).
% 5.94/6.15 tff(414,plain,
% 5.94/6.15 (~model(tptp_fun_I3_9(F!29, C!42), F!29)),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[413, 412, 402])).
% 5.94/6.15 tff(415,plain,
% 5.94/6.15 ((model(tptp_fun_I3_9(F!29, C!42), F!29) <=> model(tptp_fun_I3_9(F!29, C!42), not(F!29))) | model(tptp_fun_I3_9(F!29, C!42), F!29) | model(tptp_fun_I3_9(F!29, C!42), not(F!29))),
% 5.94/6.15 inference(tautology,[status(thm)],[])).
% 5.94/6.15 tff(416,plain,
% 5.94/6.15 (model(tptp_fun_I3_9(F!29, C!42), not(F!29))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[415, 414, 401])).
% 5.94/6.15 tff(417,plain,
% 5.94/6.15 (((~![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))) | ((~model(tptp_fun_I3_9(F!29, C!42), C!42)) | (~model(tptp_fun_I3_9(F!29, C!42), not(F!29))))) <=> ((~![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))) | (~model(tptp_fun_I3_9(F!29, C!42), C!42)) | (~model(tptp_fun_I3_9(F!29, C!42), not(F!29))))),
% 5.94/6.15 inference(rewrite,[status(thm)],[])).
% 5.94/6.15 tff(418,plain,
% 5.94/6.15 ((~![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))) | ((~model(tptp_fun_I3_9(F!29, C!42), C!42)) | (~model(tptp_fun_I3_9(F!29, C!42), not(F!29))))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(419,plain,
% 5.94/6.15 ((~![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29))))) | (~model(tptp_fun_I3_9(F!29, C!42), C!42)) | (~model(tptp_fun_I3_9(F!29, C!42), not(F!29)))),
% 5.94/6.15 inference(modus_ponens,[status(thm)],[418, 417])).
% 5.94/6.15 tff(420,plain,
% 5.94/6.15 ($false),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[419, 412, 416, 397])).
% 5.94/6.15 tff(421,plain,((model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)) | (~![I2: $i] : ((~model(I2, C!42)) | (~model(I2, not(F!29)))))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.15 tff(422,plain,
% 5.94/6.15 (model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[421, 396])).
% 5.94/6.15 tff(423,assumption,(![I2: $i] : model(I2, C!42)), introduced(assumption)).
% 5.94/6.15 tff(424,plain,
% 5.94/6.15 (~model(I1!44, C!42)),
% 5.94/6.15 inference(and_elim,[status(thm)],[358])).
% 5.94/6.15 tff(425,plain,
% 5.94/6.15 ((~![I2: $i] : model(I2, C!42)) | model(I1!44, C!42)),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(426,plain,
% 5.94/6.15 ($false),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[425, 424, 423])).
% 5.94/6.15 tff(427,plain,(~![I2: $i] : model(I2, C!42)), inference(lemma,lemma(discharge,[]))).
% 5.94/6.15 tff(428,assumption,(![I1: $i] : (~model(I1, C!42))), introduced(assumption)).
% 5.94/6.15 tff(429,plain,
% 5.94/6.15 ((~![I1: $i] : (~model(I1, C!42))) | (~model(I2!45, C!42))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(430,plain,
% 5.94/6.15 ($false),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[429, 359, 428])).
% 5.94/6.15 tff(431,plain,(~![I1: $i] : (~model(I1, C!42))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.15 tff(432,plain,
% 5.94/6.15 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))))))))))),
% 5.94/6.15 inference(bind,[status(th)],[])).
% 5.94/6.15 tff(433,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))),
% 5.94/6.15 inference(quant_intro,[status(thm)],[432])).
% 5.94/6.15 tff(434,plain,
% 5.94/6.15 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 5.94/6.15 inference(bind,[status(th)],[])).
% 5.94/6.15 tff(435,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.15 inference(quant_intro,[status(thm)],[434])).
% 5.94/6.15 tff(436,plain,
% 5.94/6.15 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))))),
% 5.94/6.15 inference(bind,[status(th)],[])).
% 5.94/6.15 tff(437,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.15 inference(quant_intro,[status(thm)],[436])).
% 5.94/6.15 tff(438,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.15 inference(transitivity,[status(thm)],[437, 435])).
% 5.94/6.15 tff(439,plain,
% 5.94/6.15 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) <=> (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))), ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) <=> (status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))))), rewrite((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) <=> (status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))), ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) <=> (status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))) <=> ((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, eth))))), rewrite(((~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))) | (~status(Ax, C, eth))) <=> ((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))), (((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))) <=> ((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))), (((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))))), rewrite(((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax)))))) <=> (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))), (((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))))),
% 5.94/6.15 inference(bind,[status(th)],[])).
% 5.94/6.15 tff(440,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.15 inference(quant_intro,[status(thm)],[439])).
% 5.94/6.15 tff(441,plain,
% 5.94/6.15 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) | status(Ax, C, eth)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))))),
% 5.94/6.15 inference(bind,[status(th)],[])).
% 5.94/6.15 tff(442,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) | status(Ax, C, eth)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))))),
% 5.94/6.15 inference(quant_intro,[status(thm)],[441])).
% 5.94/6.15 tff(443,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))),
% 5.94/6.15 inference(rewrite,[status(thm)],[])).
% 5.94/6.15 tff(444,plain,
% 5.94/6.15 (^[Ax: $i, C: $i] : rewrite((((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth)) <=> ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth)))),
% 5.94/6.15 inference(bind,[status(th)],[])).
% 5.94/6.15 tff(445,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))),
% 5.94/6.15 inference(quant_intro,[status(thm)],[444])).
% 5.94/6.15 tff(446,axiom,(![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax))) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','eth')).
% 5.94/6.15 tff(447,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))),
% 5.94/6.15 inference(modus_ponens,[status(thm)],[446, 445])).
% 5.94/6.15 tff(448,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ?[I2: $i] : (~model(I2, Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) <=> status(Ax, C, eth))),
% 5.94/6.15 inference(modus_ponens,[status(thm)],[447, 443])).
% 5.94/6.15 tff(449,plain,(
% 5.94/6.15 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) | status(Ax, C, eth)) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))))),
% 5.94/6.15 inference(skolemize,[status(sab)],[448])).
% 5.94/6.15 tff(450,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : ((status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C)))) & ((model(tptp_fun_I1_0(Ax), Ax) & (~model(tptp_fun_I2_8(Ax), Ax)) & ![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~status(Ax, C, eth))))),
% 5.94/6.15 inference(modus_ponens,[status(thm)],[449, 442])).
% 5.94/6.15 tff(451,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.15 inference(modus_ponens,[status(thm)],[450, 440])).
% 5.94/6.15 tff(452,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C))) | (~model(tptp_fun_I1_0(Ax), Ax))))))))),
% 5.94/6.15 inference(modus_ponens,[status(thm)],[451, 438])).
% 5.94/6.15 tff(453,plain,
% 5.94/6.15 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))),
% 5.94/6.15 inference(modus_ponens,[status(thm)],[452, 433])).
% 5.94/6.15 tff(454,plain,
% 5.94/6.15 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42))))))))),
% 5.94/6.15 inference(rewrite,[status(thm)],[])).
% 5.94/6.15 tff(455,plain,
% 5.94/6.15 ((~((~(status(C!42, F!29, eth) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!29, eth)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))))))))) <=> (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)))))))),
% 5.94/6.15 inference(rewrite,[status(thm)],[])).
% 5.94/6.15 tff(456,plain,
% 5.94/6.15 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(status(C!42, F!29, eth) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!29, eth)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42))))))))),
% 5.94/6.15 inference(monotonicity,[status(thm)],[455])).
% 5.94/6.15 tff(457,plain,
% 5.94/6.15 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(status(C!42, F!29, eth) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!29, eth)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42))))))))),
% 5.94/6.15 inference(transitivity,[status(thm)],[456, 454])).
% 5.94/6.15 tff(458,plain,
% 5.94/6.15 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(status(C!42, F!29, eth) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))) | ![I1: $i] : (~model(I1, C!42)) | ![I2: $i] : model(I2, C!42))) | (~((~status(C!42, F!29, eth)) | (~(model(tptp_fun_I2_8(C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29)))))))))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(459,plain,
% 5.94/6.15 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eth) | (~(model(tptp_fun_I3_9(C, Ax), Ax) <=> model(tptp_fun_I3_9(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, eth)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : (model(I3, Ax) <=> model(I3, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)))))))),
% 5.94/6.15 inference(modus_ponens,[status(thm)],[458, 457])).
% 5.94/6.15 tff(460,plain,
% 5.94/6.15 (~((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42))))))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[459, 453])).
% 5.94/6.15 tff(461,plain,
% 5.94/6.15 (((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)))))) | (![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))),
% 5.94/6.15 inference(tautology,[status(thm)],[])).
% 5.94/6.15 tff(462,plain,
% 5.94/6.15 (![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[461, 460])).
% 5.94/6.15 tff(463,plain,
% 5.94/6.15 ((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | ![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)))),
% 5.94/6.15 inference(tautology,[status(thm)],[])).
% 5.94/6.15 tff(464,plain,
% 5.94/6.15 (![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[463, 462])).
% 5.94/6.15 tff(465,plain,
% 5.94/6.15 (status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[464, 431])).
% 5.94/6.15 tff(466,plain,
% 5.94/6.15 (status(C!42, F!29, eth) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29)))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[465, 427])).
% 5.94/6.15 tff(467,plain,
% 5.94/6.15 (status(C!42, F!29, eth)),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[466, 422])).
% 5.94/6.15 tff(468,plain,
% 5.94/6.15 (((~(![I1: $i] : (~model(I1, C!42)) | status(C!42, F!29, eth) | ![I2: $i] : model(I2, C!42) | (~(model(tptp_fun_I3_9(F!29, C!42), C!42) <=> model(tptp_fun_I3_9(F!29, C!42), F!29))))) | (~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)))))) | ((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42))))),
% 5.94/6.15 inference(tautology,[status(thm)],[])).
% 5.94/6.15 tff(469,plain,
% 5.94/6.15 ((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[468, 460])).
% 5.94/6.15 tff(470,plain,
% 5.94/6.15 ((~((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42))))) | (~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)))),
% 5.94/6.15 inference(tautology,[status(thm)],[])).
% 5.94/6.15 tff(471,plain,
% 5.94/6.15 ((~status(C!42, F!29, eth)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[470, 469])).
% 5.94/6.15 tff(472,plain,
% 5.94/6.15 (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[471, 467])).
% 5.94/6.15 tff(473,plain,
% 5.94/6.15 (((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | model(tptp_fun_I2_8(C!42), C!42)) | ![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))),
% 5.94/6.15 inference(tautology,[status(thm)],[])).
% 5.94/6.15 tff(474,plain,
% 5.94/6.15 (![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[473, 472])).
% 5.94/6.15 tff(475,plain,
% 5.94/6.15 ((~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | (model(tptp_fun_I1_0(C!33), C!42) <=> model(tptp_fun_I1_0(C!33), F!29))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(476,plain,
% 5.94/6.15 (model(tptp_fun_I1_0(C!33), C!42) <=> model(tptp_fun_I1_0(C!33), F!29)),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[475, 474])).
% 5.94/6.15 tff(477,assumption,(model(tptp_fun_I1_0(C!33), Ax!38) <=> model(tptp_fun_I1_0(C!33), not(Ax!38))), introduced(assumption)).
% 5.94/6.15 tff(478,plain,
% 5.94/6.15 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I1_0(C!33), Ax!38) <=> model(tptp_fun_I1_0(C!33), not(Ax!38))))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(479,plain,
% 5.94/6.15 ($false),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[478, 8, 477])).
% 5.94/6.15 tff(480,plain,(~(model(tptp_fun_I1_0(C!33), Ax!38) <=> model(tptp_fun_I1_0(C!33), not(Ax!38)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.15 tff(481,assumption,(status(C!37, C!33, noc)), introduced(assumption)).
% 5.94/6.15 tff(482,plain,
% 5.94/6.15 ((~![Ax: $i, C: $i] : (~status(Ax, C, noc))) | (~status(C!37, C!33, noc))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(483,plain,
% 5.94/6.15 ($false),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[482, 481, 280])).
% 5.94/6.15 tff(484,plain,((~![Ax: $i, C: $i] : (~status(Ax, C, noc))) | (~status(C!37, C!33, noc))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.15 tff(485,plain,
% 5.94/6.15 (~status(C!37, C!33, noc)),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[484, 278])).
% 5.94/6.15 tff(486,plain,
% 5.94/6.15 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38) <=> model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38))))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(487,plain,
% 5.94/6.15 (~(model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38) <=> model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38)))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[486, 8])).
% 5.94/6.15 tff(488,plain,
% 5.94/6.15 ((~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | (model(tptp_fun_I1_2(F!28, not(C!33)), C!42) <=> model(tptp_fun_I1_2(F!28, not(C!33)), F!29))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(489,plain,
% 5.94/6.15 (model(tptp_fun_I1_2(F!28, not(C!33)), C!42) <=> model(tptp_fun_I1_2(F!28, not(C!33)), F!29)),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[488, 474])).
% 5.94/6.15 tff(490,plain,
% 5.94/6.15 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I1_2(F!28, not(C!33)), C!42) <=> model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42))))),
% 5.94/6.15 inference(quant_inst,[status(thm)],[])).
% 5.94/6.15 tff(491,plain,
% 5.94/6.15 (~(model(tptp_fun_I1_2(F!28, not(C!33)), C!42) <=> model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42)))),
% 5.94/6.15 inference(unit_resolution,[status(thm)],[490, 8])).
% 5.94/6.15 tff(492,assumption,((~((~((~model(tptp_fun_I1_3(not(C!42), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!42), Ax!34), not(C!42)))) | status(Ax!34, not(C!42), thm))) | (~((~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))))), introduced(assumption)).
% 5.94/6.15 tff(493,plain,
% 5.94/6.15 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(not(C!42), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!42), Ax!34), not(C!42)))) | status(Ax!34, not(C!42), thm))) | (~((~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))))))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(494,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[493, 53, 492])).
% 5.94/6.16 tff(495,plain,(~((~((~((~model(tptp_fun_I1_3(not(C!42), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!42), Ax!34), not(C!42)))) | status(Ax!34, not(C!42), thm))) | (~((~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42))))))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(496,plain,
% 5.94/6.16 (((~((~((~model(tptp_fun_I1_3(not(C!42), Ax!34), Ax!34)) | model(tptp_fun_I1_3(not(C!42), Ax!34), not(C!42)))) | status(Ax!34, not(C!42), thm))) | (~((~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))))) | ((~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42))))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(497,plain,
% 5.94/6.16 ((~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[496, 495])).
% 5.94/6.16 tff(498,assumption,(![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))), introduced(assumption)).
% 5.94/6.16 tff(499,assumption,(model(I1!30, C!42) <=> model(I1!30, not(C!42))), introduced(assumption)).
% 5.94/6.16 tff(500,plain,
% 5.94/6.16 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I1!30, C!42) <=> model(I1!30, not(C!42))))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(501,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[500, 8, 499])).
% 5.94/6.16 tff(502,plain,(~(model(I1!30, C!42) <=> model(I1!30, not(C!42)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(503,plain,
% 5.94/6.16 ((model(I1!30, C!42) <=> model(I1!30, not(C!42))) | (~model(I1!30, C!42)) | (~model(I1!30, not(C!42)))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(504,plain,
% 5.94/6.16 ((model(I1!30, C!42) <=> model(I1!30, not(C!42))) | (~model(I1!30, not(C!42)))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[503, 388])).
% 5.94/6.16 tff(505,plain,
% 5.94/6.16 (~model(I1!30, not(C!42))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[504, 502])).
% 5.94/6.16 tff(506,plain,
% 5.94/6.16 (((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | ((~model(I1!30, F!29)) | model(I1!30, Ax!34))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | (~model(I1!30, F!29)) | model(I1!30, Ax!34))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(507,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | ((~model(I1!30, F!29)) | model(I1!30, Ax!34))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(508,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | (~model(I1!30, F!29)) | model(I1!30, Ax!34)),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[507, 506])).
% 5.94/6.16 tff(509,plain,
% 5.94/6.16 (model(I1!30, Ax!34)),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[508, 384, 212])).
% 5.94/6.16 tff(510,plain,
% 5.94/6.16 (((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))) | ((~model(I1!30, Ax!34)) | model(I1!30, not(C!42)))) <=> ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))) | (~model(I1!30, Ax!34)) | model(I1!30, not(C!42)))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(511,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))) | ((~model(I1!30, Ax!34)) | model(I1!30, not(C!42)))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(512,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))) | (~model(I1!30, Ax!34)) | model(I1!30, not(C!42))),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[511, 510])).
% 5.94/6.16 tff(513,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[512, 509, 505, 498])).
% 5.94/6.16 tff(514,plain,(~![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(515,plain,
% 5.94/6.16 ((~((~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42))))) | (~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42)))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(516,plain,
% 5.94/6.16 ((~((~status(Ax!34, not(C!42), thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, not(C!42))))) | (~status(Ax!34, not(C!42), thm))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[515, 514])).
% 5.94/6.16 tff(517,plain,
% 5.94/6.16 (~status(Ax!34, not(C!42), thm)),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[516, 497])).
% 5.94/6.16 tff(518,assumption,(status(Ax!34, not(C!42), sap)), introduced(assumption)).
% 5.94/6.16 tff(519,plain,
% 5.94/6.16 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(Ax!34, not(C!42), sap)) | status(Ax!34, not(C!42), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(Ax!34, not(C!42), sap)) | status(Ax!34, not(C!42), thm))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(520,plain,
% 5.94/6.16 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | ((~status(Ax!34, not(C!42), sap)) | status(Ax!34, not(C!42), thm))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(521,plain,
% 5.94/6.16 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sap)) | status(Ax, C, thm))) | (~status(Ax!34, not(C!42), sap)) | status(Ax!34, not(C!42), thm)),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[520, 519])).
% 5.94/6.16 tff(522,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[521, 128, 518, 517])).
% 5.94/6.16 tff(523,plain,(~status(Ax!34, not(C!42), sap)), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(524,plain,
% 5.94/6.16 (((~![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_I2_1(not(C!42)), not(C!42)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, not(C!42), sap)))) | (~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), 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))))))) | (~((~(model(tptp_fun_I2_1(not(C!42)), not(C!42)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, not(C!42), sap)))) | (~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))))))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(525,plain,
% 5.94/6.16 ((~((~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))) | (~(model(tptp_fun_I2_1(not(C!42)), not(C!42)) | (~status(Ax!34, not(C!42), sap)) | ![I1: $i] : (~model(I1, Ax!34)))))) <=> (~((~(model(tptp_fun_I2_1(not(C!42)), not(C!42)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, not(C!42), sap)))) | (~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap)))))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(526,plain,
% 5.94/6.16 (((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))) | (~(model(tptp_fun_I2_1(not(C!42)), not(C!42)) | (~status(Ax!34, not(C!42), sap)) | ![I1: $i] : (~model(I1, Ax!34))))))) <=> ((~![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_I2_1(not(C!42)), not(C!42)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, not(C!42), sap)))) | (~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))))))),
% 5.94/6.16 inference(monotonicity,[status(thm)],[525])).
% 5.94/6.16 tff(527,plain,
% 5.94/6.16 (((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))) | (~(model(tptp_fun_I2_1(not(C!42)), not(C!42)) | (~status(Ax!34, not(C!42), sap)) | ![I1: $i] : (~model(I1, Ax!34))))))) <=> ((~![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_I2_1(not(C!42)), not(C!42)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, not(C!42), sap)))) | (~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))))))),
% 5.94/6.16 inference(transitivity,[status(thm)],[526, 524])).
% 5.94/6.16 tff(528,plain,
% 5.94/6.16 ((~![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(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))) | (~(model(tptp_fun_I2_1(not(C!42)), not(C!42)) | (~status(Ax!34, not(C!42), sap)) | ![I1: $i] : (~model(I1, Ax!34))))))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(529,plain,
% 5.94/6.16 ((~![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_I2_1(not(C!42)), not(C!42)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, not(C!42), sap)))) | (~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap)))))),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[528, 527])).
% 5.94/6.16 tff(530,plain,
% 5.94/6.16 (~((~(model(tptp_fun_I2_1(not(C!42)), not(C!42)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, not(C!42), sap)))) | (~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[529, 90])).
% 5.94/6.16 tff(531,plain,
% 5.94/6.16 (((~(model(tptp_fun_I2_1(not(C!42)), not(C!42)) | ![I1: $i] : (~model(I1, Ax!34)) | (~status(Ax!34, not(C!42), sap)))) | (~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap)))) | ((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(532,plain,
% 5.94/6.16 ((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap)),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[531, 530])).
% 5.94/6.16 tff(533,plain,
% 5.94/6.16 ((~((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap))) | (~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap)),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(534,plain,
% 5.94/6.16 ((~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))) | status(Ax!34, not(C!42), sap)),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[533, 532])).
% 5.94/6.16 tff(535,plain,
% 5.94/6.16 (~((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42)))))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[534, 523])).
% 5.94/6.16 tff(536,plain,
% 5.94/6.16 (((~model(tptp_fun_I1_0(Ax!34), Ax!34)) | (~![I2: $i] : (~model(I2, not(C!42))))) | ![I2: $i] : (~model(I2, not(C!42)))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(537,plain,
% 5.94/6.16 (![I2: $i] : (~model(I2, not(C!42)))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[536, 535])).
% 5.94/6.16 tff(538,assumption,(![I2: $i] : (~model(I2, not(C!42)))), introduced(assumption)).
% 5.94/6.16 tff(539,assumption,(model(tptp_fun_I1_14(C!42, F!28), not(C!42))), introduced(assumption)).
% 5.94/6.16 tff(540,plain,
% 5.94/6.16 ((~![I2: $i] : (~model(I2, not(C!42)))) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42)))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(541,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[540, 539, 538])).
% 5.94/6.16 tff(542,plain,((~![I2: $i] : (~model(I2, not(C!42)))) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(543,plain,
% 5.94/6.16 (~model(tptp_fun_I1_14(C!42, F!28), not(C!42))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[542, 537])).
% 5.94/6.16 tff(544,plain,
% 5.94/6.16 (((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42)))) | model(tptp_fun_I1_14(C!42, F!28), not(C!42))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(545,plain,
% 5.94/6.16 ((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42)))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[544, 543])).
% 5.94/6.16 tff(546,plain,
% 5.94/6.16 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))))))),
% 5.94/6.16 inference(bind,[status(th)],[])).
% 5.94/6.16 tff(547,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))),
% 5.94/6.16 inference(quant_intro,[status(thm)],[546])).
% 5.94/6.16 tff(548,plain,
% 5.94/6.16 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))))),
% 5.94/6.16 inference(bind,[status(th)],[])).
% 5.94/6.16 tff(549,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 5.94/6.16 inference(quant_intro,[status(thm)],[548])).
% 5.94/6.16 tff(550,plain,
% 5.94/6.16 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))))),
% 5.94/6.16 inference(bind,[status(th)],[])).
% 5.94/6.16 tff(551,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 5.94/6.16 inference(quant_intro,[status(thm)],[550])).
% 5.94/6.16 tff(552,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 5.94/6.16 inference(transitivity,[status(thm)],[551, 549])).
% 5.94/6.16 tff(553,plain,
% 5.94/6.16 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) <=> (status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))), trans(monotonicity(rewrite((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) <=> (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))), (((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))) <=> ((~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))) | (~status(Ax, C, csa))))), rewrite(((~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))) | (~status(Ax, C, csa))) <=> ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))), (((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))) <=> ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))), (((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ((status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))) & ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))), rewrite(((status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))) & ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))), (((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))))),
% 5.94/6.16 inference(bind,[status(th)],[])).
% 5.94/6.16 tff(554,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 5.94/6.16 inference(quant_intro,[status(thm)],[553])).
% 5.94/6.16 tff(555,plain,
% 5.94/6.16 (^[Ax: $i, C: $i] : rewrite(((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))))),
% 5.94/6.16 inference(bind,[status(th)],[])).
% 5.94/6.16 tff(556,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 5.94/6.16 inference(quant_intro,[status(thm)],[555])).
% 5.94/6.16 tff(557,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa)) <=> ![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(558,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','csa')).
% 5.94/6.16 tff(559,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[558, 557])).
% 5.94/6.16 tff(560,plain,(
% 5.94/6.16 ![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 5.94/6.16 inference(skolemize,[status(sab)],[559])).
% 5.94/6.16 tff(561,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[560, 556])).
% 5.94/6.16 tff(562,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[561, 554])).
% 5.94/6.16 tff(563,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[562, 552])).
% 5.94/6.16 tff(564,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[563, 547])).
% 5.94/6.16 tff(565,plain,
% 5.94/6.16 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42))))))) | (~(status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))))))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(566,plain,
% 5.94/6.16 (~((~((~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42))))))) | (~(status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42)))))))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[565, 564])).
% 5.94/6.16 tff(567,plain,
% 5.94/6.16 (((~((~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42))))))) | (~(status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))))) | ((~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42))))))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(568,plain,
% 5.94/6.16 ((~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42)))))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[567, 566])).
% 5.94/6.16 tff(569,plain,
% 5.94/6.16 ((~((~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42))))))) | (~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42)))))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(570,plain,
% 5.94/6.16 ((~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42)))))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[569, 568])).
% 5.94/6.16 tff(571,plain,
% 5.94/6.16 (~status(F!28, C!42, csa)),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[570, 545])).
% 5.94/6.16 tff(572,plain,
% 5.94/6.16 (((~((~status(F!28, C!42, csa)) | (~((~model(tptp_fun_I1_14(C!42, F!28), F!28)) | (~model(tptp_fun_I1_14(C!42, F!28), not(C!42))))))) | (~(status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))))) | (status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42)))))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(573,plain,
% 5.94/6.16 (status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[572, 566])).
% 5.94/6.16 tff(574,plain,
% 5.94/6.16 ((~(status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42)))))) | status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(575,plain,
% 5.94/6.16 (status(F!28, C!42, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[574, 573])).
% 5.94/6.16 tff(576,plain,
% 5.94/6.16 (![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[575, 571])).
% 5.94/6.16 tff(577,assumption,(model(I2!36, F!29) <=> model(I2!36, not(F!29))), introduced(assumption)).
% 5.94/6.16 tff(578,plain,
% 5.94/6.16 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I2!36, F!29) <=> model(I2!36, not(F!29))))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(579,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[578, 8, 577])).
% 5.94/6.16 tff(580,plain,(~(model(I2!36, F!29) <=> model(I2!36, not(F!29)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(581,assumption,(~model(I2!36, Ax!34)), introduced(assumption)).
% 5.94/6.16 tff(582,plain,
% 5.94/6.16 (((~![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))) | ((~model(I2!36, not(F!29))) | model(I2!36, Ax!34))) <=> ((~![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))) | (~model(I2!36, not(F!29))) | model(I2!36, Ax!34))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(583,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))) | ((~model(I2!36, not(F!29))) | model(I2!36, Ax!34))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(584,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, not(F!29))) | model(I1, Ax!34))) | (~model(I2!36, not(F!29))) | model(I2!36, Ax!34)),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[583, 582])).
% 5.94/6.16 tff(585,plain,
% 5.94/6.16 (~model(I2!36, not(F!29))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[584, 581, 179])).
% 5.94/6.16 tff(586,plain,
% 5.94/6.16 (((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | ((~model(I2!36, F!29)) | model(I2!36, Ax!34))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | (~model(I2!36, F!29)) | model(I2!36, Ax!34))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(587,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | ((~model(I2!36, F!29)) | model(I2!36, Ax!34))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(588,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, F!29)) | model(I1, Ax!34))) | (~model(I2!36, F!29)) | model(I2!36, Ax!34)),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[587, 586])).
% 5.94/6.16 tff(589,plain,
% 5.94/6.16 (~model(I2!36, F!29)),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[588, 581, 212])).
% 5.94/6.16 tff(590,plain,
% 5.94/6.16 ((model(I2!36, F!29) <=> model(I2!36, not(F!29))) | model(I2!36, F!29) | model(I2!36, not(F!29))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(591,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[590, 589, 585, 580])).
% 5.94/6.16 tff(592,plain,(model(I2!36, Ax!34)), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(593,plain,
% 5.94/6.16 ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33))),
% 5.94/6.16 inference(and_elim,[status(thm)],[157])).
% 5.94/6.16 tff(594,plain,
% 5.94/6.16 (~model(I2!36, C!33)),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[593, 592])).
% 5.94/6.16 tff(595,assumption,(model(I2!36, C!33) <=> model(I2!36, not(C!33))), introduced(assumption)).
% 5.94/6.16 tff(596,plain,
% 5.94/6.16 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I2!36, C!33) <=> model(I2!36, not(C!33))))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(597,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[596, 8, 595])).
% 5.94/6.16 tff(598,plain,(~(model(I2!36, C!33) <=> model(I2!36, not(C!33)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(599,plain,
% 5.94/6.16 ((model(I2!36, C!33) <=> model(I2!36, not(C!33))) | model(I2!36, C!33) | model(I2!36, not(C!33))),
% 5.94/6.16 inference(tautology,[status(thm)],[])).
% 5.94/6.16 tff(600,plain,
% 5.94/6.16 (model(I2!36, C!33) | model(I2!36, not(C!33))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[599, 598])).
% 5.94/6.16 tff(601,plain,
% 5.94/6.16 (model(I2!36, not(C!33))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[600, 594])).
% 5.94/6.16 tff(602,assumption,(model(I2!36, not(C!33))), introduced(assumption)).
% 5.94/6.16 tff(603,assumption,(![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))), introduced(assumption)).
% 5.94/6.16 tff(604,plain,
% 5.94/6.16 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 5.94/6.16 inference(bind,[status(th)],[])).
% 5.94/6.16 tff(605,plain,
% 5.94/6.16 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 5.94/6.16 inference(quant_intro,[status(thm)],[604])).
% 5.94/6.16 tff(606,plain,
% 5.94/6.16 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(607,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','tautology')).
% 5.94/6.16 tff(608,plain,
% 5.94/6.16 (?[F: $i] : ![I: $i] : model(I, F)),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[607, 606])).
% 5.94/6.16 tff(609,plain,(
% 5.94/6.16 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 5.94/6.16 inference(transitivity,[status(sab)],[608])).
% 5.94/6.16 tff(610,plain,
% 5.94/6.16 (![I: $i] : model(I, F!28)),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[609, 605])).
% 5.94/6.16 tff(611,plain,
% 5.94/6.16 ((~![I: $i] : model(I, F!28)) | model(I2!36, F!28)),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(612,plain,
% 5.94/6.16 (model(I2!36, F!28)),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[611, 610])).
% 5.94/6.16 tff(613,plain,
% 5.94/6.16 (((~![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))) | ((~model(I2!36, not(C!33))) | (~model(I2!36, F!28)))) <=> ((~![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))) | (~model(I2!36, not(C!33))) | (~model(I2!36, F!28)))),
% 5.94/6.16 inference(rewrite,[status(thm)],[])).
% 5.94/6.16 tff(614,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))) | ((~model(I2!36, not(C!33))) | (~model(I2!36, F!28)))),
% 5.94/6.16 inference(quant_inst,[status(thm)],[])).
% 5.94/6.16 tff(615,plain,
% 5.94/6.16 ((~![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))) | (~model(I2!36, not(C!33))) | (~model(I2!36, F!28))),
% 5.94/6.16 inference(modus_ponens,[status(thm)],[614, 613])).
% 5.94/6.16 tff(616,plain,
% 5.94/6.16 ($false),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[615, 612, 603, 602])).
% 5.94/6.16 tff(617,plain,((~![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))) | (~model(I2!36, not(C!33)))), inference(lemma,lemma(discharge,[]))).
% 5.94/6.16 tff(618,plain,
% 5.94/6.16 (~![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))),
% 5.94/6.16 inference(unit_resolution,[status(thm)],[617, 601])).
% 5.94/6.16 tff(619,plain,
% 5.94/6.16 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))))),
% 5.94/6.16 inference(bind,[status(th)],[])).
% 5.94/6.16 tff(620,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 5.94/6.16 inference(quant_intro,[status(thm)],[619])).
% 5.94/6.16 tff(621,plain,
% 5.94/6.16 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))))),
% 5.94/6.16 inference(bind,[status(th)],[])).
% 5.94/6.16 tff(622,plain,
% 5.94/6.16 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 5.94/6.17 inference(quant_intro,[status(thm)],[621])).
% 5.94/6.17 tff(623,plain,
% 5.94/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 5.94/6.17 inference(transitivity,[status(thm)],[622, 620])).
% 5.94/6.17 tff(624,plain,
% 5.94/6.17 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) <=> (status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))), trans(monotonicity(rewrite((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) <=> (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))), (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))) <=> ((~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))) | (~status(Ax, C, sat))))), rewrite(((~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))) | (~status(Ax, C, sat))) <=> ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))), (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))) <=> ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))), (((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ((status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C)))) & ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))), rewrite(((status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C)))) & ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))), (((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))))),
% 5.94/6.17 inference(bind,[status(th)],[])).
% 5.94/6.17 tff(625,plain,
% 5.94/6.17 (![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 5.94/6.17 inference(quant_intro,[status(thm)],[624])).
% 5.94/6.17 tff(626,plain,
% 5.94/6.17 (^[Ax: $i, C: $i] : rewrite(((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))))),
% 5.94/6.17 inference(bind,[status(th)],[])).
% 5.94/6.17 tff(627,plain,
% 5.94/6.17 (![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 5.94/6.17 inference(quant_intro,[status(thm)],[626])).
% 5.94/6.17 tff(628,plain,
% 5.94/6.17 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat)) <=> ![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))),
% 5.94/6.17 inference(rewrite,[status(thm)],[])).
% 5.94/6.17 tff(629,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','sat')).
% 5.94/6.17 tff(630,plain,
% 5.94/6.17 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))),
% 5.94/6.17 inference(modus_ponens,[status(thm)],[629, 628])).
% 5.94/6.17 tff(631,plain,(
% 5.94/6.17 ![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 5.94/6.17 inference(skolemize,[status(sab)],[630])).
% 5.94/6.17 tff(632,plain,
% 5.94/6.17 (![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 5.94/6.17 inference(modus_ponens,[status(thm)],[631, 627])).
% 5.94/6.17 tff(633,plain,
% 5.94/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 5.94/6.17 inference(modus_ponens,[status(thm)],[632, 625])).
% 5.94/6.17 tff(634,plain,
% 5.94/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 5.94/6.17 inference(modus_ponens,[status(thm)],[633, 623])).
% 5.94/6.17 tff(635,plain,
% 5.94/6.17 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))))))))),
% 5.94/6.17 inference(rewrite,[status(thm)],[])).
% 5.94/6.17 tff(636,plain,
% 5.94/6.17 ((~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)))))))) <=> (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))))))))),
% 5.94/6.17 inference(rewrite,[status(thm)],[])).
% 5.94/6.17 tff(637,plain,
% 5.94/6.17 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))))))))),
% 5.94/6.17 inference(monotonicity,[status(thm)],[636])).
% 5.94/6.17 tff(638,plain,
% 5.94/6.17 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))))))))),
% 5.94/6.17 inference(transitivity,[status(thm)],[637, 635])).
% 5.94/6.17 tff(639,plain,
% 5.94/6.17 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), F!28))))))))),
% 5.94/6.17 inference(quant_inst,[status(thm)],[])).
% 5.94/6.17 tff(640,plain,
% 5.94/6.17 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))))))))),
% 5.94/6.17 inference(modus_ponens,[status(thm)],[639, 638])).
% 5.94/6.17 tff(641,plain,
% 5.94/6.17 (~((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))))))),
% 5.94/6.17 inference(unit_resolution,[status(thm)],[640, 634])).
% 5.94/6.17 tff(642,plain,
% 5.94/6.17 (((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))))))) | (status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))),
% 5.94/6.17 inference(tautology,[status(thm)],[])).
% 5.94/6.17 tff(643,plain,
% 5.94/6.17 (status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))),
% 5.94/6.17 inference(unit_resolution,[status(thm)],[642, 641])).
% 5.94/6.17 tff(644,plain,
% 5.94/6.17 ((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))),
% 5.94/6.17 inference(tautology,[status(thm)],[])).
% 5.94/6.17 tff(645,plain,
% 5.94/6.17 (status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28)))),
% 5.94/6.17 inference(unit_resolution,[status(thm)],[644, 643])).
% 5.94/6.17 tff(646,plain,
% 5.94/6.17 (status(not(C!33), F!28, sat)),
% 5.94/6.17 inference(unit_resolution,[status(thm)],[645, 618])).
% 5.94/6.17 tff(647,plain,
% 5.94/6.17 (((~(status(not(C!33), F!28, sat) | ![I1: $i] : ((~model(I1, not(C!33))) | (~model(I1, F!28))))) | (~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))))))) | ((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))))),
% 5.94/6.17 inference(tautology,[status(thm)],[])).
% 6.02/6.17 tff(648,plain,
% 6.02/6.17 ((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))))),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[647, 641])).
% 6.02/6.17 tff(649,plain,
% 6.02/6.17 ((~((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))))) | (~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))))),
% 6.02/6.17 inference(tautology,[status(thm)],[])).
% 6.02/6.17 tff(650,plain,
% 6.02/6.17 ((~status(not(C!33), F!28, sat)) | (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))))),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[649, 648])).
% 6.02/6.17 tff(651,plain,
% 6.02/6.17 (~((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[650, 646])).
% 6.02/6.17 tff(652,plain,
% 6.02/6.17 (((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))) | model(tptp_fun_I1_2(F!28, not(C!33)), F!28)),
% 6.02/6.17 inference(tautology,[status(thm)],[])).
% 6.02/6.17 tff(653,plain,
% 6.02/6.17 (model(tptp_fun_I1_2(F!28, not(C!33)), F!28)),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[652, 651])).
% 6.02/6.17 tff(654,plain,
% 6.02/6.17 (((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))) | ((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42))))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42))))),
% 6.02/6.17 inference(rewrite,[status(thm)],[])).
% 6.02/6.17 tff(655,plain,
% 6.02/6.17 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))) | ((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42))))),
% 6.02/6.17 inference(quant_inst,[status(thm)],[])).
% 6.02/6.17 tff(656,plain,
% 6.02/6.17 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42)))),
% 6.02/6.17 inference(modus_ponens,[status(thm)],[655, 654])).
% 6.02/6.17 tff(657,plain,
% 6.02/6.17 (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42))),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[656, 653, 576])).
% 6.02/6.17 tff(658,plain,
% 6.02/6.17 ((model(tptp_fun_I1_2(F!28, not(C!33)), C!42) <=> model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42))) | model(tptp_fun_I1_2(F!28, not(C!33)), C!42) | model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42))),
% 6.02/6.17 inference(tautology,[status(thm)],[])).
% 6.02/6.17 tff(659,plain,
% 6.02/6.17 ((model(tptp_fun_I1_2(F!28, not(C!33)), C!42) <=> model(tptp_fun_I1_2(F!28, not(C!33)), not(C!42))) | model(tptp_fun_I1_2(F!28, not(C!33)), C!42)),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[658, 657])).
% 6.02/6.17 tff(660,plain,
% 6.02/6.17 (model(tptp_fun_I1_2(F!28, not(C!33)), C!42)),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[659, 491])).
% 6.02/6.17 tff(661,plain,
% 6.02/6.17 ((~(model(tptp_fun_I1_2(F!28, not(C!33)), C!42) <=> model(tptp_fun_I1_2(F!28, not(C!33)), F!29))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), C!42)) | model(tptp_fun_I1_2(F!28, not(C!33)), F!29)),
% 6.02/6.17 inference(tautology,[status(thm)],[])).
% 6.02/6.17 tff(662,plain,
% 6.02/6.17 ((~(model(tptp_fun_I1_2(F!28, not(C!33)), C!42) <=> model(tptp_fun_I1_2(F!28, not(C!33)), F!29))) | model(tptp_fun_I1_2(F!28, not(C!33)), F!29)),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[661, 660])).
% 6.02/6.17 tff(663,plain,
% 6.02/6.17 (model(tptp_fun_I1_2(F!28, not(C!33)), F!29)),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[662, 489])).
% 6.02/6.17 tff(664,assumption,(![I3: $i] : model(I3, not(Ax!38))), introduced(assumption)).
% 6.02/6.17 tff(665,plain,
% 6.02/6.17 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(I1!39, Ax!38) <=> model(I1!39, not(Ax!38))))),
% 6.02/6.17 inference(quant_inst,[status(thm)],[])).
% 6.02/6.17 tff(666,plain,
% 6.02/6.17 (~(model(I1!39, Ax!38) <=> model(I1!39, not(Ax!38)))),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[665, 8])).
% 6.02/6.17 tff(667,plain,
% 6.02/6.17 ((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)))),
% 6.02/6.17 inference(rewrite,[status(thm)],[])).
% 6.02/6.17 tff(668,plain,
% 6.02/6.17 (?[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)))),
% 6.02/6.17 inference(rewrite,[status(thm)],[])).
% 6.02/6.17 tff(669,plain,
% 6.02/6.17 (^[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)))))),
% 6.02/6.17 inference(bind,[status(th)],[])).
% 6.02/6.17 tff(670,plain,
% 6.02/6.17 (?[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)))),
% 6.02/6.17 inference(quant_intro,[status(thm)],[669])).
% 6.02/6.17 tff(671,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')).
% 6.02/6.17 tff(672,plain,
% 6.02/6.17 (?[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)))),
% 6.02/6.17 inference(modus_ponens,[status(thm)],[671, 670])).
% 6.02/6.17 tff(673,plain,
% 6.02/6.17 (?[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)))),
% 6.02/6.17 inference(modus_ponens,[status(thm)],[672, 668])).
% 6.02/6.17 tff(674,plain,
% 6.02/6.17 (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))),
% 6.02/6.17 inference(modus_ponens,[status(thm)],[673, 667])).
% 6.02/6.17 tff(675,plain,
% 6.02/6.17 (model(I1!39, Ax!38)),
% 6.02/6.17 inference(and_elim,[status(thm)],[674])).
% 6.02/6.17 tff(676,plain,
% 6.02/6.17 ((model(I1!39, Ax!38) <=> model(I1!39, not(Ax!38))) | (~model(I1!39, Ax!38)) | (~model(I1!39, not(Ax!38)))),
% 6.02/6.17 inference(tautology,[status(thm)],[])).
% 6.02/6.17 tff(677,plain,
% 6.02/6.17 ((model(I1!39, Ax!38) <=> model(I1!39, not(Ax!38))) | (~model(I1!39, not(Ax!38)))),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[676, 675])).
% 6.02/6.17 tff(678,plain,
% 6.02/6.17 (~model(I1!39, not(Ax!38))),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[677, 666])).
% 6.02/6.17 tff(679,assumption,(![I2: $i] : model(I2, not(Ax!38))), introduced(assumption)).
% 6.02/6.17 tff(680,plain,
% 6.02/6.17 ((~![I2: $i] : model(I2, not(Ax!38))) | model(I1!39, not(Ax!38))),
% 6.02/6.17 inference(quant_inst,[status(thm)],[])).
% 6.02/6.17 tff(681,plain,
% 6.02/6.17 ($false),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[680, 679, 678])).
% 6.02/6.17 tff(682,plain,(~![I2: $i] : model(I2, not(Ax!38))), inference(lemma,lemma(discharge,[]))).
% 6.02/6.17 tff(683,plain,
% 6.02/6.17 (((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))) | ![I2: $i] : model(I2, not(Ax!38))),
% 6.02/6.17 inference(tautology,[status(thm)],[])).
% 6.02/6.17 tff(684,plain,
% 6.02/6.17 ((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))),
% 6.02/6.17 inference(unit_resolution,[status(thm)],[683, 682])).
% 6.02/6.17 tff(685,plain,
% 6.02/6.17 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))))),
% 6.02/6.17 inference(bind,[status(th)],[])).
% 6.02/6.17 tff(686,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 6.02/6.17 inference(quant_intro,[status(thm)],[685])).
% 6.02/6.17 tff(687,plain,
% 6.02/6.17 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))))),
% 6.02/6.17 inference(bind,[status(th)],[])).
% 6.02/6.17 tff(688,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 6.02/6.17 inference(quant_intro,[status(thm)],[687])).
% 6.02/6.17 tff(689,plain,
% 6.02/6.17 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))))),
% 6.02/6.17 inference(bind,[status(th)],[])).
% 6.02/6.17 tff(690,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 6.02/6.17 inference(quant_intro,[status(thm)],[689])).
% 6.02/6.17 tff(691,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 6.02/6.17 inference(transitivity,[status(thm)],[690, 688])).
% 6.02/6.17 tff(692,plain,
% 6.02/6.17 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) <=> (status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) <=> (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))) <=> ((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))) | (~status(Ax, C, tac))))), rewrite(((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))) | (~status(Ax, C, tac))) <=> ((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))) <=> ((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))), (((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))))), rewrite(((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C)))))) <=> (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))), (((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))))),
% 6.02/6.17 inference(bind,[status(th)],[])).
% 6.02/6.17 tff(693,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 6.02/6.17 inference(quant_intro,[status(thm)],[692])).
% 6.02/6.17 tff(694,plain,
% 6.02/6.17 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tac)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))))),
% 6.02/6.17 inference(bind,[status(th)],[])).
% 6.02/6.17 tff(695,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tac)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))))),
% 6.02/6.17 inference(quant_intro,[status(thm)],[694])).
% 6.02/6.17 tff(696,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac))),
% 6.02/6.17 inference(rewrite,[status(thm)],[])).
% 6.02/6.17 tff(697,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','tac')).
% 6.02/6.17 tff(698,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac))),
% 6.02/6.17 inference(modus_ponens,[status(thm)],[697, 696])).
% 6.02/6.17 tff(699,plain,(
% 6.02/6.17 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) | status(Ax, C, tac)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))))),
% 6.02/6.17 inference(skolemize,[status(sab)],[698])).
% 6.02/6.17 tff(700,plain,
% 6.02/6.17 (![Ax: $i, C: $i] : ((status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : model(I2, C)) | (~status(Ax, C, tac))))),
% 6.02/6.18 inference(modus_ponens,[status(thm)],[699, 695])).
% 6.02/6.18 tff(701,plain,
% 6.02/6.18 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 6.02/6.18 inference(modus_ponens,[status(thm)],[700, 693])).
% 6.02/6.18 tff(702,plain,
% 6.02/6.18 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | ![I1: $i] : (~model(I1, Ax)) | (~model(tptp_fun_I2_5(C), C)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 6.02/6.18 inference(modus_ponens,[status(thm)],[701, 691])).
% 6.02/6.18 tff(703,plain,
% 6.02/6.18 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))),
% 6.02/6.18 inference(modus_ponens,[status(thm)],[702, 686])).
% 6.02/6.18 tff(704,plain,
% 6.02/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38))))))))))),
% 6.02/6.18 inference(rewrite,[status(thm)],[])).
% 6.02/6.18 tff(705,plain,
% 6.02/6.18 ((~((~(status(F!29, not(Ax!38), tac) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38))))))))) <=> (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))))))),
% 6.02/6.18 inference(rewrite,[status(thm)],[])).
% 6.02/6.18 tff(706,plain,
% 6.02/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(F!29, not(Ax!38), tac) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38))))))))))),
% 6.02/6.18 inference(monotonicity,[status(thm)],[705])).
% 6.02/6.18 tff(707,plain,
% 6.02/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(F!29, not(Ax!38), tac) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38))))))))))),
% 6.02/6.18 inference(transitivity,[status(thm)],[706, 704])).
% 6.02/6.18 tff(708,plain,
% 6.02/6.18 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(status(F!29, not(Ax!38), tac) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | ![I1: $i] : (~model(I1, F!29)))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))))))),
% 6.02/6.18 inference(quant_inst,[status(thm)],[])).
% 6.02/6.18 tff(709,plain,
% 6.02/6.18 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tac) | (~model(tptp_fun_I2_5(C), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, tac)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : model(I2, C))))))))) | (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))))))),
% 6.02/6.18 inference(modus_ponens,[status(thm)],[708, 707])).
% 6.02/6.18 tff(710,plain,
% 6.02/6.18 (~((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38))))))))),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[709, 703])).
% 6.02/6.18 tff(711,plain,
% 6.02/6.18 (((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))))) | ((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38))))))),
% 6.02/6.18 inference(tautology,[status(thm)],[])).
% 6.02/6.18 tff(712,plain,
% 6.02/6.18 ((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[711, 710])).
% 6.02/6.18 tff(713,plain,
% 6.02/6.18 ((~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38))))))) | (~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))),
% 6.02/6.18 inference(tautology,[status(thm)],[])).
% 6.02/6.18 tff(714,plain,
% 6.02/6.18 ((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[713, 712])).
% 6.02/6.18 tff(715,plain,
% 6.02/6.18 (~status(F!29, not(Ax!38), tac)),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[714, 684])).
% 6.02/6.18 tff(716,plain,
% 6.02/6.18 (((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~((~status(F!29, not(Ax!38), tac)) | (~((~model(tptp_fun_I1_0(F!29), F!29)) | (~![I2: $i] : model(I2, not(Ax!38)))))))) | (![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))),
% 6.02/6.18 inference(tautology,[status(thm)],[])).
% 6.02/6.18 tff(717,plain,
% 6.02/6.18 (![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac)),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[716, 710])).
% 6.02/6.18 tff(718,assumption,(![I1: $i] : (~model(I1, F!29))), introduced(assumption)).
% 6.02/6.18 tff(719,plain,
% 6.02/6.18 ((~![I1: $i] : (~model(I1, F!29))) | (~model(I1!30, F!29))),
% 6.02/6.18 inference(quant_inst,[status(thm)],[])).
% 6.02/6.18 tff(720,plain,
% 6.02/6.18 ($false),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[719, 384, 718])).
% 6.02/6.18 tff(721,plain,(~![I1: $i] : (~model(I1, F!29))), inference(lemma,lemma(discharge,[]))).
% 6.02/6.18 tff(722,plain,
% 6.02/6.18 ((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac)),
% 6.02/6.18 inference(tautology,[status(thm)],[])).
% 6.02/6.18 tff(723,plain,
% 6.02/6.18 ((~(![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac))) | (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac)),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[722, 721])).
% 6.02/6.18 tff(724,plain,
% 6.02/6.18 ((~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), tac)),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[723, 717])).
% 6.02/6.18 tff(725,plain,
% 6.02/6.18 (~model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[724, 715])).
% 6.02/6.18 tff(726,plain,
% 6.02/6.18 ((~![I3: $i] : model(I3, not(Ax!38))) | model(tptp_fun_I2_5(not(Ax!38)), not(Ax!38))),
% 6.02/6.18 inference(quant_inst,[status(thm)],[])).
% 6.02/6.18 tff(727,plain,
% 6.02/6.18 ($false),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[726, 725, 664])).
% 6.02/6.18 tff(728,plain,(~![I3: $i] : model(I3, not(Ax!38))), inference(lemma,lemma(discharge,[]))).
% 6.02/6.18 tff(729,plain,
% 6.02/6.18 ((model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))) | ![I3: $i] : model(I3, not(Ax!38))),
% 6.02/6.18 inference(tautology,[status(thm)],[])).
% 6.02/6.18 tff(730,plain,
% 6.02/6.18 (model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))),
% 6.02/6.18 inference(unit_resolution,[status(thm)],[729, 728])).
% 6.02/6.18 tff(731,plain,
% 6.02/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), wtc))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), wtc))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38))))))))))),
% 6.02/6.18 inference(rewrite,[status(thm)],[])).
% 6.02/6.18 tff(732,plain,
% 6.02/6.18 ((~((~(status(F!29, not(Ax!38), wtc) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38))))))))) <=> (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), wtc))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))))))),
% 6.03/6.18 inference(rewrite,[status(thm)],[])).
% 6.03/6.18 tff(733,plain,
% 6.03/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(F!29, not(Ax!38), wtc) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), wtc))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38))))))))))),
% 6.03/6.18 inference(monotonicity,[status(thm)],[732])).
% 6.03/6.18 tff(734,plain,
% 6.03/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(F!29, not(Ax!38), wtc) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), wtc))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38))))))))))),
% 6.03/6.18 inference(transitivity,[status(thm)],[733, 731])).
% 6.03/6.18 tff(735,plain,
% 6.03/6.18 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(status(F!29, not(Ax!38), wtc) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : model(I2, F!29))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))))))),
% 6.03/6.18 inference(quant_inst,[status(thm)],[])).
% 6.03/6.18 tff(736,plain,
% 6.03/6.18 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wtc) | (~model(tptp_fun_I3_11(C), C)) | ![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : model(I2, Ax))) | (~((~status(Ax, C, wtc)) | (~(model(tptp_fun_I2_8(Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~![I3: $i] : model(I3, C))))))))) | (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), wtc))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))))))),
% 6.03/6.18 inference(modus_ponens,[status(thm)],[735, 734])).
% 6.03/6.18 tff(737,plain,
% 6.03/6.18 (~((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), wtc))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38))))))))),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[736, 330])).
% 6.03/6.18 tff(738,plain,
% 6.03/6.18 (((~(![I2: $i] : model(I2, F!29) | ![I1: $i] : (~model(I1, F!29)) | (~model(tptp_fun_I3_11(not(Ax!38)), not(Ax!38))) | status(F!29, not(Ax!38), wtc))) | (~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))))) | ((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38))))))),
% 6.03/6.18 inference(tautology,[status(thm)],[])).
% 6.03/6.18 tff(739,plain,
% 6.03/6.18 ((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[738, 737])).
% 6.03/6.18 tff(740,plain,
% 6.03/6.18 ((~((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38))))))) | (~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))),
% 6.03/6.18 inference(tautology,[status(thm)],[])).
% 6.03/6.18 tff(741,plain,
% 6.03/6.18 ((~status(F!29, not(Ax!38), wtc)) | (~(model(tptp_fun_I2_8(F!29), F!29) | (~model(tptp_fun_I1_0(F!29), F!29)) | (~![I3: $i] : model(I3, not(Ax!38)))))),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[740, 739])).
% 6.03/6.18 tff(742,plain,
% 6.03/6.18 (~status(F!29, not(Ax!38), wtc)),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[741, 730])).
% 6.03/6.18 tff(743,assumption,(status(F!29, not(Ax!38), noc)), introduced(assumption)).
% 6.03/6.18 tff(744,assumption,(~status(F!29, not(Ax!38), wtc)), introduced(assumption)).
% 6.03/6.18 tff(745,assumption,(![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))), introduced(assumption)).
% 6.03/6.18 tff(746,plain,
% 6.03/6.18 (((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | ((~status(F!29, not(Ax!38), noc)) | status(F!29, not(Ax!38), wtc))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | (~status(F!29, not(Ax!38), noc)) | status(F!29, not(Ax!38), wtc))),
% 6.03/6.18 inference(rewrite,[status(thm)],[])).
% 6.03/6.18 tff(747,plain,
% 6.03/6.18 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | ((~status(F!29, not(Ax!38), noc)) | status(F!29, not(Ax!38), wtc))),
% 6.03/6.18 inference(quant_inst,[status(thm)],[])).
% 6.03/6.18 tff(748,plain,
% 6.03/6.18 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | (~status(F!29, not(Ax!38), noc)) | status(F!29, not(Ax!38), wtc)),
% 6.03/6.18 inference(modus_ponens,[status(thm)],[747, 746])).
% 6.03/6.18 tff(749,plain,
% 6.03/6.18 ($false),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[748, 745, 744, 743])).
% 6.03/6.18 tff(750,plain,(status(F!29, not(Ax!38), wtc) | (~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | (~status(F!29, not(Ax!38), noc))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.18 tff(751,plain,
% 6.03/6.18 ((~![Ax: $i, C: $i] : ((~status(Ax, C, noc)) | status(Ax, C, wtc))) | (~status(F!29, not(Ax!38), noc))),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[750, 742])).
% 6.03/6.18 tff(752,plain,
% 6.03/6.18 (~status(F!29, not(Ax!38), noc)),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[751, 298])).
% 6.03/6.18 tff(753,plain,
% 6.03/6.18 ((~![I3: $i] : (model(I3, C!42) <=> model(I3, F!29))) | (model(tptp_fun_I2_1(Ax!38), C!42) <=> model(tptp_fun_I2_1(Ax!38), F!29))),
% 6.03/6.18 inference(quant_inst,[status(thm)],[])).
% 6.03/6.18 tff(754,plain,
% 6.03/6.18 (model(tptp_fun_I2_1(Ax!38), C!42) <=> model(tptp_fun_I2_1(Ax!38), F!29)),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[753, 474])).
% 6.03/6.18 tff(755,plain,
% 6.03/6.18 ((~![I2: $i] : (~model(I2, not(C!42)))) | (~model(tptp_fun_I2_1(Ax!38), not(C!42)))),
% 6.03/6.18 inference(quant_inst,[status(thm)],[])).
% 6.03/6.18 tff(756,plain,
% 6.03/6.18 (~model(tptp_fun_I2_1(Ax!38), not(C!42))),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[755, 537])).
% 6.03/6.18 tff(757,plain,
% 6.03/6.18 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_1(Ax!38), C!42) <=> model(tptp_fun_I2_1(Ax!38), not(C!42))))),
% 6.03/6.18 inference(quant_inst,[status(thm)],[])).
% 6.03/6.18 tff(758,plain,
% 6.03/6.18 (~(model(tptp_fun_I2_1(Ax!38), C!42) <=> model(tptp_fun_I2_1(Ax!38), not(C!42)))),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[757, 8])).
% 6.03/6.18 tff(759,plain,
% 6.03/6.18 ((model(tptp_fun_I2_1(Ax!38), C!42) <=> model(tptp_fun_I2_1(Ax!38), not(C!42))) | model(tptp_fun_I2_1(Ax!38), C!42) | model(tptp_fun_I2_1(Ax!38), not(C!42))),
% 6.03/6.18 inference(tautology,[status(thm)],[])).
% 6.03/6.18 tff(760,plain,
% 6.03/6.18 (model(tptp_fun_I2_1(Ax!38), C!42) | model(tptp_fun_I2_1(Ax!38), not(C!42))),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[759, 758])).
% 6.03/6.18 tff(761,plain,
% 6.03/6.18 (model(tptp_fun_I2_1(Ax!38), C!42)),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[760, 756])).
% 6.03/6.18 tff(762,plain,
% 6.03/6.18 ((~(model(tptp_fun_I2_1(Ax!38), C!42) <=> model(tptp_fun_I2_1(Ax!38), F!29))) | (~model(tptp_fun_I2_1(Ax!38), C!42)) | model(tptp_fun_I2_1(Ax!38), F!29)),
% 6.03/6.18 inference(tautology,[status(thm)],[])).
% 6.03/6.18 tff(763,plain,
% 6.03/6.18 (model(tptp_fun_I2_1(Ax!38), F!29)),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[762, 761, 754])).
% 6.03/6.18 tff(764,assumption,(![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))), introduced(assumption)).
% 6.03/6.18 tff(765,assumption,(model(tptp_fun_I2_1(Ax!38), not(Ax!38)) <=> model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))), introduced(assumption)).
% 6.03/6.18 tff(766,plain,
% 6.03/6.18 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_1(Ax!38), not(Ax!38)) <=> model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))))),
% 6.03/6.18 inference(quant_inst,[status(thm)],[])).
% 6.03/6.18 tff(767,plain,
% 6.03/6.18 ($false),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[766, 8, 765])).
% 6.03/6.18 tff(768,plain,(~(model(tptp_fun_I2_1(Ax!38), not(Ax!38)) <=> model(tptp_fun_I2_1(Ax!38), not(not(Ax!38))))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.18 tff(769,assumption,(model(tptp_fun_I2_1(Ax!38), Ax!38) <=> model(tptp_fun_I2_1(Ax!38), not(Ax!38))), introduced(assumption)).
% 6.03/6.18 tff(770,plain,
% 6.03/6.18 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) <=> model(tptp_fun_I2_1(Ax!38), not(Ax!38))))),
% 6.03/6.18 inference(quant_inst,[status(thm)],[])).
% 6.03/6.18 tff(771,plain,
% 6.03/6.18 ($false),
% 6.03/6.18 inference(unit_resolution,[status(thm)],[770, 8, 769])).
% 6.03/6.18 tff(772,plain,(~(model(tptp_fun_I2_1(Ax!38), Ax!38) <=> model(tptp_fun_I2_1(Ax!38), not(Ax!38)))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.18 tff(773,plain,
% 6.03/6.18 (^[Ax: $i, C: $i] : refl((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 6.03/6.18 inference(bind,[status(th)],[])).
% 6.03/6.18 tff(774,plain,
% 6.03/6.18 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 6.03/6.18 inference(quant_intro,[status(thm)],[773])).
% 6.03/6.18 tff(775,plain,
% 6.03/6.18 (^[Ax: $i, C: $i] : rewrite((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 6.03/6.18 inference(bind,[status(th)],[])).
% 6.03/6.18 tff(776,plain,
% 6.03/6.18 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 6.03/6.18 inference(quant_intro,[status(thm)],[775])).
% 6.03/6.18 tff(777,plain,
% 6.03/6.18 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 6.03/6.18 inference(transitivity,[status(thm)],[776, 774])).
% 6.03/6.18 tff(778,plain,
% 6.03/6.18 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) <=> ((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))), rewrite(((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))) <=> ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))), rewrite((((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))))),
% 6.03/6.18 inference(bind,[status(th)],[])).
% 6.03/6.18 tff(779,plain,
% 6.03/6.18 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 6.03/6.18 inference(quant_intro,[status(thm)],[778])).
% 6.03/6.18 tff(780,plain,
% 6.03/6.18 (^[Ax: $i, C: $i] : rewrite(((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))),
% 6.03/6.18 inference(bind,[status(th)],[])).
% 6.03/6.18 tff(781,plain,
% 6.03/6.18 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 6.03/6.18 inference(quant_intro,[status(thm)],[780])).
% 6.03/6.18 tff(782,plain,
% 6.03/6.18 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 6.03/6.18 inference(rewrite,[status(thm)],[])).
% 6.03/6.18 tff(783,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','esa')).
% 6.03/6.18 tff(784,plain,
% 6.03/6.18 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 6.03/6.18 inference(modus_ponens,[status(thm)],[783, 782])).
% 6.03/6.18 tff(785,plain,(
% 6.03/6.18 ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa))))),
% 6.03/6.18 inference(skolemize,[status(sab)],[784])).
% 6.03/6.18 tff(786,plain,
% 6.03/6.18 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[785, 781])).
% 6.03/6.19 tff(787,plain,
% 6.03/6.19 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[786, 779])).
% 6.03/6.19 tff(788,plain,
% 6.03/6.19 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[787, 777])).
% 6.03/6.19 tff(789,plain,
% 6.03/6.19 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))))))))))),
% 6.03/6.19 inference(rewrite,[status(thm)],[])).
% 6.03/6.19 tff(790,plain,
% 6.03/6.19 ((~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))) | (~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))))))))))),
% 6.03/6.19 inference(rewrite,[status(thm)],[])).
% 6.03/6.19 tff(791,plain,
% 6.03/6.19 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))) | (~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))))))))))),
% 6.03/6.19 inference(monotonicity,[status(thm)],[790])).
% 6.03/6.19 tff(792,plain,
% 6.03/6.19 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))) | (~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))))))))))),
% 6.03/6.19 inference(transitivity,[status(thm)],[791, 789])).
% 6.03/6.19 tff(793,plain,
% 6.03/6.19 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))) | (~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38))))))))))),
% 6.03/6.19 inference(quant_inst,[status(thm)],[])).
% 6.03/6.19 tff(794,plain,
% 6.03/6.19 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))))))))))),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[793, 792])).
% 6.03/6.19 tff(795,plain,
% 6.03/6.19 (~((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))))))))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[794, 788])).
% 6.03/6.19 tff(796,plain,
% 6.03/6.19 (((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))))))))) | ((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))))))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(797,plain,
% 6.03/6.19 ((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))))))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[796, 795])).
% 6.03/6.19 tff(798,plain,
% 6.03/6.19 (((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))))))))) | ((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(799,plain,
% 6.03/6.19 ((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa)),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[798, 795])).
% 6.03/6.19 tff(800,assumption,(![I2: $i] : (~model(I2, Ax!38))), introduced(assumption)).
% 6.03/6.19 tff(801,plain,
% 6.03/6.19 ((~![I2: $i] : (~model(I2, Ax!38))) | (~model(I1!39, Ax!38))),
% 6.03/6.19 inference(quant_inst,[status(thm)],[])).
% 6.03/6.19 tff(802,plain,
% 6.03/6.19 ($false),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[801, 675, 800])).
% 6.03/6.19 tff(803,plain,(~![I2: $i] : (~model(I2, Ax!38))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.19 tff(804,plain,
% 6.03/6.19 ((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))) | ![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(805,plain,
% 6.03/6.19 ((~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))) | ![I2: $i] : (~model(I2, Ax!38))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[804, 721])).
% 6.03/6.19 tff(806,plain,
% 6.03/6.19 (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[805, 803])).
% 6.03/6.19 tff(807,plain,
% 6.03/6.19 (((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38))))) | (![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(808,plain,
% 6.03/6.19 ((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38))))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[807, 806])).
% 6.03/6.19 tff(809,plain,
% 6.03/6.19 ((~((~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa))) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | model(tptp_fun_I2_1(Ax!38), Ax!38))) | (~(![I1: $i] : (~model(I1, F!29)) | ![I2: $i] : (~model(I2, Ax!38)))))) | status(F!29, Ax!38, esa)),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(810,plain,
% 6.03/6.19 (status(F!29, Ax!38, esa)),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[809, 808, 799])).
% 6.03/6.19 tff(811,plain,
% 6.03/6.19 ((~((~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))))))) | (~status(F!29, Ax!38, esa)) | (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))))))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(812,plain,
% 6.03/6.19 (~((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[811, 810, 797])).
% 6.03/6.19 tff(813,plain,
% 6.03/6.19 (((~(model(tptp_fun_I1_0(F!29), F!29) | ![I2: $i] : (~model(I2, Ax!38)))) | (~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))))) | (model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(814,plain,
% 6.03/6.19 (model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[813, 812])).
% 6.03/6.19 tff(815,plain,
% 6.03/6.19 ((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))) | model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(816,plain,
% 6.03/6.19 ((~(model(tptp_fun_I2_1(Ax!38), Ax!38) | ![I1: $i] : (~model(I1, F!29)))) | model(tptp_fun_I2_1(Ax!38), Ax!38)),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[815, 721])).
% 6.03/6.19 tff(817,plain,
% 6.03/6.19 (model(tptp_fun_I2_1(Ax!38), Ax!38)),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[816, 814])).
% 6.03/6.19 tff(818,plain,
% 6.03/6.19 ((model(tptp_fun_I2_1(Ax!38), Ax!38) <=> model(tptp_fun_I2_1(Ax!38), not(Ax!38))) | (~model(tptp_fun_I2_1(Ax!38), Ax!38)) | (~model(tptp_fun_I2_1(Ax!38), not(Ax!38)))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(819,plain,
% 6.03/6.19 ((model(tptp_fun_I2_1(Ax!38), Ax!38) <=> model(tptp_fun_I2_1(Ax!38), not(Ax!38))) | (~model(tptp_fun_I2_1(Ax!38), not(Ax!38)))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[818, 817])).
% 6.03/6.19 tff(820,plain,
% 6.03/6.19 (~model(tptp_fun_I2_1(Ax!38), not(Ax!38))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[819, 772])).
% 6.03/6.19 tff(821,plain,
% 6.03/6.19 ((model(tptp_fun_I2_1(Ax!38), not(Ax!38)) <=> model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))) | model(tptp_fun_I2_1(Ax!38), not(Ax!38)) | model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(822,plain,
% 6.03/6.19 ((model(tptp_fun_I2_1(Ax!38), not(Ax!38)) <=> model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))) | model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[821, 820])).
% 6.03/6.19 tff(823,plain,
% 6.03/6.19 (model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[822, 768])).
% 6.03/6.19 tff(824,assumption,(model(tptp_fun_I2_1(Ax!38), F!29)), introduced(assumption)).
% 6.03/6.19 tff(825,plain,
% 6.03/6.19 (((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))) | ((~model(tptp_fun_I2_1(Ax!38), F!29)) | (~model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))))) <=> ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))) | (~model(tptp_fun_I2_1(Ax!38), F!29)) | (~model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))))),
% 6.03/6.19 inference(rewrite,[status(thm)],[])).
% 6.03/6.19 tff(826,plain,
% 6.03/6.19 ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))) | ((~model(tptp_fun_I2_1(Ax!38), F!29)) | (~model(tptp_fun_I2_1(Ax!38), not(not(Ax!38)))))),
% 6.03/6.19 inference(quant_inst,[status(thm)],[])).
% 6.03/6.19 tff(827,plain,
% 6.03/6.19 ((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))) | (~model(tptp_fun_I2_1(Ax!38), F!29)) | (~model(tptp_fun_I2_1(Ax!38), not(not(Ax!38))))),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[826, 825])).
% 6.03/6.19 tff(828,plain,
% 6.03/6.19 ($false),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[827, 824, 823, 764])).
% 6.03/6.19 tff(829,plain,((~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))) | (~model(tptp_fun_I2_1(Ax!38), F!29))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.19 tff(830,plain,
% 6.03/6.19 (~![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[829, 763])).
% 6.03/6.19 tff(831,assumption,((~((~status(F!29, not(Ax!38), noc)) | (~((~model(tptp_fun_I1_2(not(Ax!38), F!29), F!29)) | (~model(tptp_fun_I1_2(not(Ax!38), F!29), not(Ax!38))) | (~model(tptp_fun_I2_17(not(Ax!38), F!29), F!29)) | (~model(tptp_fun_I2_17(not(Ax!38), F!29), not(not(Ax!38)))))))) | (~(status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))))), introduced(assumption)).
% 6.03/6.19 tff(832,plain,
% 6.03/6.19 ((~![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, not(Ax!38), noc)) | (~((~model(tptp_fun_I1_2(not(Ax!38), F!29), F!29)) | (~model(tptp_fun_I1_2(not(Ax!38), F!29), not(Ax!38))) | (~model(tptp_fun_I2_17(not(Ax!38), F!29), F!29)) | (~model(tptp_fun_I2_17(not(Ax!38), F!29), not(not(Ax!38)))))))) | (~(status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))))))),
% 6.03/6.19 inference(quant_inst,[status(thm)],[])).
% 6.03/6.19 tff(833,plain,
% 6.03/6.19 ($false),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[832, 30, 831])).
% 6.03/6.19 tff(834,plain,(~((~((~status(F!29, not(Ax!38), noc)) | (~((~model(tptp_fun_I1_2(not(Ax!38), F!29), F!29)) | (~model(tptp_fun_I1_2(not(Ax!38), F!29), not(Ax!38))) | (~model(tptp_fun_I2_17(not(Ax!38), F!29), F!29)) | (~model(tptp_fun_I2_17(not(Ax!38), F!29), not(not(Ax!38)))))))) | (~(status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38))))))))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.19 tff(835,plain,
% 6.03/6.19 (((~((~status(F!29, not(Ax!38), noc)) | (~((~model(tptp_fun_I1_2(not(Ax!38), F!29), F!29)) | (~model(tptp_fun_I1_2(not(Ax!38), F!29), not(Ax!38))) | (~model(tptp_fun_I2_17(not(Ax!38), F!29), F!29)) | (~model(tptp_fun_I2_17(not(Ax!38), F!29), not(not(Ax!38)))))))) | (~(status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))))) | (status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38))))))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(836,plain,
% 6.03/6.19 (status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[835, 834])).
% 6.03/6.19 tff(837,plain,
% 6.03/6.19 ((~(status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38))))))) | status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(838,plain,
% 6.03/6.19 (status(F!29, not(Ax!38), noc) | ![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38)))) | ![I2: $i] : ((~model(I2, F!29)) | (~model(I2, not(not(Ax!38)))))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[837, 836])).
% 6.03/6.19 tff(839,plain,
% 6.03/6.19 (![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[838, 830, 752])).
% 6.03/6.19 tff(840,plain,
% 6.03/6.19 (((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))) | ((~model(tptp_fun_I1_2(F!28, not(C!33)), F!29)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38))))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), F!29)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38))))),
% 6.03/6.19 inference(rewrite,[status(thm)],[])).
% 6.03/6.19 tff(841,plain,
% 6.03/6.19 ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))) | ((~model(tptp_fun_I1_2(F!28, not(C!33)), F!29)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38))))),
% 6.03/6.19 inference(quant_inst,[status(thm)],[])).
% 6.03/6.19 tff(842,plain,
% 6.03/6.19 ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), F!29)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38)))),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[841, 840])).
% 6.03/6.19 tff(843,plain,
% 6.03/6.19 (~model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[842, 839, 663])).
% 6.03/6.19 tff(844,plain,
% 6.03/6.19 ((model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38) <=> model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38))) | model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38) | model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(845,plain,
% 6.03/6.19 ((model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38) <=> model(tptp_fun_I1_2(F!28, not(C!33)), not(Ax!38))) | model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38)),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[844, 843])).
% 6.03/6.19 tff(846,plain,
% 6.03/6.19 (model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38)),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[845, 487])).
% 6.03/6.19 tff(847,plain,
% 6.03/6.19 (^[I2: $i] : refl(((~model(I2, Ax!38)) | model(I2, C!37)) <=> ((~model(I2, Ax!38)) | model(I2, C!37)))),
% 6.03/6.19 inference(bind,[status(th)],[])).
% 6.03/6.19 tff(848,plain,
% 6.03/6.19 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37)) <=> ![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 6.03/6.19 inference(quant_intro,[status(thm)],[847])).
% 6.03/6.19 tff(849,plain,
% 6.03/6.19 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 6.03/6.19 inference(and_elim,[status(thm)],[674])).
% 6.03/6.19 tff(850,plain,
% 6.03/6.19 (![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[849, 848])).
% 6.03/6.19 tff(851,plain,
% 6.03/6.19 (((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38)) | model(tptp_fun_I1_2(F!28, not(C!33)), C!37))) <=> ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38)) | model(tptp_fun_I1_2(F!28, not(C!33)), C!37))),
% 6.03/6.19 inference(rewrite,[status(thm)],[])).
% 6.03/6.19 tff(852,plain,
% 6.03/6.19 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38)) | model(tptp_fun_I1_2(F!28, not(C!33)), C!37))),
% 6.03/6.19 inference(quant_inst,[status(thm)],[])).
% 6.03/6.19 tff(853,plain,
% 6.03/6.19 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), Ax!38)) | model(tptp_fun_I1_2(F!28, not(C!33)), C!37)),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[852, 851])).
% 6.03/6.19 tff(854,plain,
% 6.03/6.19 (model(tptp_fun_I1_2(F!28, not(C!33)), C!37)),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[853, 850, 846])).
% 6.03/6.19 tff(855,plain,
% 6.03/6.19 (((~model(tptp_fun_I1_2(F!28, not(C!33)), F!28)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))) | model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))),
% 6.03/6.19 inference(tautology,[status(thm)],[])).
% 6.03/6.19 tff(856,plain,
% 6.03/6.19 (model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[855, 651])).
% 6.03/6.19 tff(857,assumption,(![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))), introduced(assumption)).
% 6.03/6.19 tff(858,plain,
% 6.03/6.19 (((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | ((~model(tptp_fun_I1_2(F!28, not(C!33)), C!37)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))) <=> ((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), C!37)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))),
% 6.03/6.19 inference(rewrite,[status(thm)],[])).
% 6.03/6.19 tff(859,plain,
% 6.03/6.19 ((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | ((~model(tptp_fun_I1_2(F!28, not(C!33)), C!37)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33))))),
% 6.03/6.19 inference(quant_inst,[status(thm)],[])).
% 6.03/6.19 tff(860,plain,
% 6.03/6.19 ((~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))) | (~model(tptp_fun_I1_2(F!28, not(C!33)), C!37)) | (~model(tptp_fun_I1_2(F!28, not(C!33)), not(C!33)))),
% 6.03/6.19 inference(modus_ponens,[status(thm)],[859, 858])).
% 6.03/6.19 tff(861,plain,
% 6.03/6.19 ($false),
% 6.03/6.19 inference(unit_resolution,[status(thm)],[860, 857, 856, 854])).
% 6.03/6.19 tff(862,plain,(~![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.19 tff(863,plain,
% 6.03/6.19 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))))),
% 6.03/6.19 inference(rewrite,[status(thm)],[])).
% 6.03/6.19 tff(864,plain,
% 6.03/6.19 ((~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I1_2(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33))))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, C!33))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))) <=> (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))),
% 6.03/6.19 inference(rewrite,[status(thm)],[])).
% 6.03/6.19 tff(865,plain,
% 6.03/6.19 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I1_2(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33))))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, C!33))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))))),
% 6.03/6.20 inference(monotonicity,[status(thm)],[864])).
% 6.03/6.20 tff(866,plain,
% 6.03/6.20 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I1_2(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33))))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, C!33))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))))),
% 6.03/6.20 inference(transitivity,[status(thm)],[865, 863])).
% 6.03/6.20 tff(867,plain,
% 6.03/6.20 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I1_2(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I2_17(C!33, C!37), not(C!33))))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!37)) | (~model(I1, C!33))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(868,plain,
% 6.03/6.20 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, noc)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)) | (~model(tptp_fun_I2_17(C, Ax), Ax)) | (~model(tptp_fun_I2_17(C, Ax), not(C))))))) | (~(status(Ax, C, noc) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))) | ![I2: $i] : ((~model(I2, Ax)) | (~model(I2, not(C))))))))) | (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[867, 866])).
% 6.03/6.20 tff(869,plain,
% 6.03/6.20 (~((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[868, 30])).
% 6.03/6.20 tff(870,plain,
% 6.03/6.20 (((~((~status(C!37, C!33, noc)) | (~((~model(tptp_fun_I2_17(C!33, C!37), not(C!33))) | (~model(tptp_fun_I2_17(C!33, C!37), C!37)) | (~model(tptp_fun_I1_2(C!33, C!37), C!33)) | (~model(tptp_fun_I1_2(C!33, C!37), C!37)))))) | (~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))))) | (status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(871,plain,
% 6.03/6.20 (status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[870, 869])).
% 6.03/6.20 tff(872,plain,
% 6.03/6.20 ((~(status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33)))))) | status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(873,plain,
% 6.03/6.20 (status(C!37, C!33, noc) | ![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37))) | ![I2: $i] : ((~model(I2, C!37)) | (~model(I2, not(C!33))))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[872, 871])).
% 6.03/6.20 tff(874,plain,
% 6.03/6.20 (![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[873, 862, 485])).
% 6.03/6.20 tff(875,assumption,(model(tptp_fun_I1_0(C!33), C!37)), introduced(assumption)).
% 6.03/6.20 tff(876,assumption,(![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))), introduced(assumption)).
% 6.03/6.20 tff(877,assumption,(![I1: $i] : (~model(I1, C!33))), introduced(assumption)).
% 6.03/6.20 tff(878,plain,
% 6.03/6.20 (model(I1!35, C!33)),
% 6.03/6.20 inference(and_elim,[status(thm)],[157])).
% 6.03/6.20 tff(879,plain,
% 6.03/6.20 ((~![I1: $i] : (~model(I1, C!33))) | (~model(I1!35, C!33))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(880,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[879, 878, 877])).
% 6.03/6.20 tff(881,plain,(~![I1: $i] : (~model(I1, C!33))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(882,plain,
% 6.03/6.20 (((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33)))) | ![I1: $i] : (~model(I1, C!33))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(883,plain,
% 6.03/6.20 ((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33)))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[882, 881])).
% 6.03/6.20 tff(884,plain,
% 6.03/6.20 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C)))))))),
% 6.03/6.20 inference(bind,[status(th)],[])).
% 6.03/6.20 tff(885,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 6.03/6.20 inference(quant_intro,[status(thm)],[884])).
% 6.03/6.20 tff(886,plain,
% 6.03/6.20 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 6.03/6.20 inference(bind,[status(th)],[])).
% 6.03/6.20 tff(887,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 6.03/6.20 inference(quant_intro,[status(thm)],[886])).
% 6.03/6.20 tff(888,plain,
% 6.03/6.20 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 6.03/6.20 inference(bind,[status(th)],[])).
% 6.03/6.20 tff(889,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 6.03/6.20 inference(quant_intro,[status(thm)],[888])).
% 6.03/6.20 tff(890,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 6.03/6.20 inference(transitivity,[status(thm)],[889, 887])).
% 6.03/6.20 tff(891,plain,
% 6.03/6.20 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite(((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) <=> ((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))), rewrite((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))) <=> (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))), rewrite((((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))))),
% 6.03/6.20 inference(bind,[status(th)],[])).
% 6.03/6.20 tff(892,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 6.03/6.20 inference(quant_intro,[status(thm)],[891])).
% 6.03/6.20 tff(893,plain,
% 6.03/6.20 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))),
% 6.03/6.20 inference(bind,[status(th)],[])).
% 6.03/6.20 tff(894,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 6.03/6.20 inference(quant_intro,[status(thm)],[893])).
% 6.03/6.20 tff(895,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(896,plain,
% 6.03/6.20 (^[Ax: $i, C: $i] : rewrite((((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)))),
% 6.03/6.20 inference(bind,[status(th)],[])).
% 6.03/6.20 tff(897,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 6.03/6.20 inference(quant_intro,[status(thm)],[896])).
% 6.03/6.20 tff(898,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','unp')).
% 6.03/6.20 tff(899,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[898, 897])).
% 6.03/6.20 tff(900,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[899, 895])).
% 6.03/6.20 tff(901,plain,(
% 6.03/6.20 ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp))))),
% 6.03/6.20 inference(skolemize,[status(sab)],[900])).
% 6.03/6.20 tff(902,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[901, 894])).
% 6.03/6.20 tff(903,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[902, 892])).
% 6.03/6.20 tff(904,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[903, 890])).
% 6.03/6.20 tff(905,plain,
% 6.03/6.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[904, 885])).
% 6.03/6.20 tff(906,plain,
% 6.03/6.20 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp)))))))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(907,plain,
% 6.03/6.20 ((~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, F!29, unp)) | ![I2: $i] : (~model(I2, F!29)))))) <=> (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp))))))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(908,plain,
% 6.03/6.20 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, F!29, unp)) | ![I2: $i] : (~model(I2, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp)))))))),
% 6.03/6.20 inference(monotonicity,[status(thm)],[907])).
% 6.03/6.20 tff(909,plain,
% 6.03/6.20 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, F!29, unp)) | ![I2: $i] : (~model(I2, F!29))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp)))))))),
% 6.03/6.20 inference(transitivity,[status(thm)],[908, 906])).
% 6.03/6.20 tff(910,plain,
% 6.03/6.20 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, F!29, unp)) | ![I2: $i] : (~model(I2, F!29))))))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(911,plain,
% 6.03/6.20 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp))))))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[910, 909])).
% 6.03/6.20 tff(912,plain,
% 6.03/6.20 (~((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp)))))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[911, 905])).
% 6.03/6.20 tff(913,plain,
% 6.03/6.20 (((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp))))) | ((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(914,plain,
% 6.03/6.20 ((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[913, 912])).
% 6.03/6.20 tff(915,plain,
% 6.03/6.20 ((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp)),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(916,plain,
% 6.03/6.20 ((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[915, 914])).
% 6.03/6.20 tff(917,plain,
% 6.03/6.20 (status(C!33, F!29, unp)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[916, 883])).
% 6.03/6.20 tff(918,assumption,(![I2: $i] : (~model(I2, F!29))), introduced(assumption)).
% 6.03/6.20 tff(919,plain,
% 6.03/6.20 ((~![I2: $i] : (~model(I2, F!29))) | (~model(I1!30, F!29))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(920,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[919, 384, 918])).
% 6.03/6.20 tff(921,plain,(~![I2: $i] : (~model(I2, F!29))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(922,plain,
% 6.03/6.20 (((~((~((~model(tptp_fun_I2_1(F!29), F!29)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, F!29, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp))))) | (model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp)))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(923,plain,
% 6.03/6.20 (model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[922, 912])).
% 6.03/6.20 tff(924,plain,
% 6.03/6.20 ((~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp)))) | model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(925,plain,
% 6.03/6.20 (model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, F!29)) | (~status(C!33, F!29, unp))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[924, 923])).
% 6.03/6.20 tff(926,plain,
% 6.03/6.20 (model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, F!29, unp))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[925, 921])).
% 6.03/6.20 tff(927,plain,
% 6.03/6.20 (model(tptp_fun_I1_0(C!33), C!33)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[926, 917])).
% 6.03/6.20 tff(928,plain,
% 6.03/6.20 (((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | ((~model(tptp_fun_I1_0(C!33), C!33)) | (~model(tptp_fun_I1_0(C!33), C!37)))) <=> ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | (~model(tptp_fun_I1_0(C!33), C!33)) | (~model(tptp_fun_I1_0(C!33), C!37)))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(929,plain,
% 6.03/6.20 ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | ((~model(tptp_fun_I1_0(C!33), C!33)) | (~model(tptp_fun_I1_0(C!33), C!37)))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(930,plain,
% 6.03/6.20 ((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | (~model(tptp_fun_I1_0(C!33), C!33)) | (~model(tptp_fun_I1_0(C!33), C!37))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[929, 928])).
% 6.03/6.20 tff(931,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[930, 927, 876, 875])).
% 6.03/6.20 tff(932,plain,((~![I1: $i] : ((~model(I1, C!33)) | (~model(I1, C!37)))) | (~model(tptp_fun_I1_0(C!33), C!37))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(933,plain,
% 6.03/6.20 (~model(tptp_fun_I1_0(C!33), C!37)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[932, 874])).
% 6.03/6.20 tff(934,plain,
% 6.03/6.20 (((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(tptp_fun_I1_0(C!33), Ax!38)) | model(tptp_fun_I1_0(C!33), C!37))) <=> ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(tptp_fun_I1_0(C!33), Ax!38)) | model(tptp_fun_I1_0(C!33), C!37))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(935,plain,
% 6.03/6.20 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | ((~model(tptp_fun_I1_0(C!33), Ax!38)) | model(tptp_fun_I1_0(C!33), C!37))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(936,plain,
% 6.03/6.20 ((~![I2: $i] : ((~model(I2, Ax!38)) | model(I2, C!37))) | (~model(tptp_fun_I1_0(C!33), Ax!38)) | model(tptp_fun_I1_0(C!33), C!37)),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[935, 934])).
% 6.03/6.20 tff(937,plain,
% 6.03/6.20 (~model(tptp_fun_I1_0(C!33), Ax!38)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[936, 850, 933])).
% 6.03/6.20 tff(938,plain,
% 6.03/6.20 ((model(tptp_fun_I1_0(C!33), Ax!38) <=> model(tptp_fun_I1_0(C!33), not(Ax!38))) | model(tptp_fun_I1_0(C!33), Ax!38) | model(tptp_fun_I1_0(C!33), not(Ax!38))),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(939,plain,
% 6.03/6.21 ((model(tptp_fun_I1_0(C!33), Ax!38) <=> model(tptp_fun_I1_0(C!33), not(Ax!38))) | model(tptp_fun_I1_0(C!33), not(Ax!38))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[938, 937])).
% 6.03/6.21 tff(940,plain,
% 6.03/6.21 (model(tptp_fun_I1_0(C!33), not(Ax!38))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[939, 480])).
% 6.03/6.21 tff(941,plain,
% 6.03/6.21 (((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))) | ((~model(tptp_fun_I1_0(C!33), F!29)) | (~model(tptp_fun_I1_0(C!33), not(Ax!38))))) <=> ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))) | (~model(tptp_fun_I1_0(C!33), F!29)) | (~model(tptp_fun_I1_0(C!33), not(Ax!38))))),
% 6.03/6.21 inference(rewrite,[status(thm)],[])).
% 6.03/6.21 tff(942,plain,
% 6.03/6.21 ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))) | ((~model(tptp_fun_I1_0(C!33), F!29)) | (~model(tptp_fun_I1_0(C!33), not(Ax!38))))),
% 6.03/6.21 inference(quant_inst,[status(thm)],[])).
% 6.03/6.21 tff(943,plain,
% 6.03/6.21 ((~![I1: $i] : ((~model(I1, F!29)) | (~model(I1, not(Ax!38))))) | (~model(tptp_fun_I1_0(C!33), F!29)) | (~model(tptp_fun_I1_0(C!33), not(Ax!38)))),
% 6.03/6.21 inference(modus_ponens,[status(thm)],[942, 941])).
% 6.03/6.21 tff(944,plain,
% 6.03/6.21 ((~model(tptp_fun_I1_0(C!33), F!29)) | (~model(tptp_fun_I1_0(C!33), not(Ax!38)))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[943, 839])).
% 6.03/6.21 tff(945,plain,
% 6.03/6.21 (~model(tptp_fun_I1_0(C!33), F!29)),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[944, 940])).
% 6.03/6.21 tff(946,plain,
% 6.03/6.21 ((~(model(tptp_fun_I1_0(C!33), C!42) <=> model(tptp_fun_I1_0(C!33), F!29))) | (~model(tptp_fun_I1_0(C!33), C!42)) | model(tptp_fun_I1_0(C!33), F!29)),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(947,plain,
% 6.03/6.21 (~model(tptp_fun_I1_0(C!33), C!42)),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[946, 945, 476])).
% 6.03/6.21 tff(948,plain,
% 6.03/6.21 ((model(tptp_fun_I1_0(C!33), C!42) <=> model(tptp_fun_I1_0(C!33), not(C!42))) | model(tptp_fun_I1_0(C!33), C!42) | model(tptp_fun_I1_0(C!33), not(C!42))),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(949,plain,
% 6.03/6.21 ((model(tptp_fun_I1_0(C!33), C!42) <=> model(tptp_fun_I1_0(C!33), not(C!42))) | model(tptp_fun_I1_0(C!33), not(C!42))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[948, 947])).
% 6.03/6.21 tff(950,plain,
% 6.03/6.21 (model(tptp_fun_I1_0(C!33), not(C!42))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[949, 11])).
% 6.03/6.21 tff(951,assumption,(model(tptp_fun_I1_0(C!33), F!28)), introduced(assumption)).
% 6.03/6.21 tff(952,plain,
% 6.03/6.21 (((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))) | ((~model(tptp_fun_I1_0(C!33), F!28)) | (~model(tptp_fun_I1_0(C!33), not(C!42))))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))) | (~model(tptp_fun_I1_0(C!33), F!28)) | (~model(tptp_fun_I1_0(C!33), not(C!42))))),
% 6.03/6.21 inference(rewrite,[status(thm)],[])).
% 6.03/6.21 tff(953,plain,
% 6.03/6.21 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))) | ((~model(tptp_fun_I1_0(C!33), F!28)) | (~model(tptp_fun_I1_0(C!33), not(C!42))))),
% 6.03/6.21 inference(quant_inst,[status(thm)],[])).
% 6.03/6.21 tff(954,plain,
% 6.03/6.21 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(C!42))))) | (~model(tptp_fun_I1_0(C!33), F!28)) | (~model(tptp_fun_I1_0(C!33), not(C!42)))),
% 6.03/6.21 inference(modus_ponens,[status(thm)],[953, 952])).
% 6.03/6.21 tff(955,plain,
% 6.03/6.21 ($false),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[954, 576, 951, 950])).
% 6.03/6.21 tff(956,plain,(~model(tptp_fun_I1_0(C!33), F!28)), inference(lemma,lemma(discharge,[]))).
% 6.03/6.21 tff(957,plain,
% 6.03/6.21 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I1_0(C!33), F!28)),
% 6.03/6.21 inference(quant_inst,[status(thm)],[])).
% 6.03/6.21 tff(958,plain,
% 6.03/6.21 ($false),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[957, 610, 956])).
% 6.03/6.21 % SZS output end Proof
% 6.03/6.21 % E exiting
%------------------------------------------------------------------------------