%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS266+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 05:13:39 AM UTC 2025
% Result : Theorem 5.92s 6.16s
% Output : Proof 6.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KRS266+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 19:21:09 EDT 2025
% 0.13/0.35 % CPUTime :
% 5.92/6.16 % SZS status Theorem
% 5.92/6.16 % SZS output start Proof
% 5.92/6.16 tff(model_type, type, (
% 5.92/6.16 model: ( $i * $i ) > $o)).
% 5.92/6.16 tff(tptp_fun_C_18_type, type, (
% 5.92/6.16 tptp_fun_C_18: ( $i * $i ) > $i)).
% 5.92/6.16 tff(tac_type, type, (
% 5.92/6.16 tac: $i)).
% 5.92/6.16 tff(wec_type, type, (
% 5.92/6.16 wec: $i)).
% 5.92/6.16 tff(tptp_fun_I1_0_type, type, (
% 5.92/6.16 tptp_fun_I1_0: $i > $i)).
% 5.92/6.16 tff(not_type, type, (
% 5.92/6.16 not: $i > $i)).
% 5.92/6.16 tff(tptp_fun_Ax_43_type, type, (
% 5.92/6.16 tptp_fun_Ax_43: $i)).
% 5.92/6.16 tff(tptp_fun_I1_44_type, type, (
% 5.92/6.16 tptp_fun_I1_44: $i)).
% 5.92/6.16 tff(tptp_fun_C_42_type, type, (
% 5.92/6.16 tptp_fun_C_42: $i)).
% 5.92/6.16 tff(tptp_fun_I2_45_type, type, (
% 5.92/6.16 tptp_fun_I2_45: $i)).
% 5.92/6.16 tff(status_type, type, (
% 5.92/6.16 status: ( $i * $i * $i ) > $o)).
% 5.92/6.16 tff(sca_type, type, (
% 5.92/6.16 sca: $i)).
% 5.92/6.16 tff(nevera_type, type, (
% 5.92/6.16 nevera: ( $i * $i ) > $o)).
% 5.92/6.16 tff(tptp_fun_C_24_type, type, (
% 5.92/6.16 tptp_fun_C_24: ( $i * $i ) > $i)).
% 5.92/6.16 tff(tptp_fun_Ax_25_type, type, (
% 5.92/6.16 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 5.92/6.16 tff(tptp_fun_I1_3_type, type, (
% 5.92/6.16 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 5.92/6.16 tff(thm_type, type, (
% 5.92/6.16 thm: $i)).
% 5.92/6.16 tff(mighta_type, type, (
% 5.92/6.16 mighta: ( $i * $i ) > $o)).
% 5.92/6.16 tff(tptp_fun_Ax_19_type, type, (
% 5.92/6.16 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 5.92/6.16 tff(tptp_fun_I2_1_type, type, (
% 5.92/6.16 tptp_fun_I2_1: $i > $i)).
% 5.92/6.16 tff(tptp_fun_I2_5_type, type, (
% 5.92/6.16 tptp_fun_I2_5: $i > $i)).
% 5.92/6.16 tff(tptp_fun_F_28_type, type, (
% 5.92/6.16 tptp_fun_F_28: $i)).
% 5.92/6.16 tff(tptp_fun_I2_7_type, type, (
% 5.92/6.16 tptp_fun_I2_7: ( $i * $i ) > $i)).
% 5.92/6.16 tff(tptp_fun_I3_6_type, type, (
% 5.92/6.16 tptp_fun_I3_6: ( $i * $i ) > $i)).
% 5.92/6.16 tff(1,plain,
% 5.92/6.16 (^[I: $i, F: $i] : refl((~(model(I, F) <=> model(I, not(F)))) <=> (~(model(I, F) <=> model(I, not(F)))))),
% 5.92/6.16 inference(bind,[status(th)],[])).
% 5.92/6.16 tff(2,plain,
% 5.92/6.16 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.92/6.16 inference(quant_intro,[status(thm)],[1])).
% 5.92/6.16 tff(3,plain,
% 5.92/6.16 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(4,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','completeness')).
% 5.92/6.16 tff(5,plain,
% 5.92/6.16 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[4, 3])).
% 5.92/6.16 tff(6,plain,(
% 5.92/6.16 ![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.92/6.16 inference(skolemize,[status(sab)],[5])).
% 5.92/6.16 tff(7,plain,
% 5.92/6.16 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[6, 2])).
% 5.92/6.16 tff(8,plain,
% 5.92/6.16 ((~![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))) | (~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), tptp_fun_C_18(wec, tac)) <=> model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac)))))),
% 5.92/6.16 inference(quant_inst,[status(thm)],[])).
% 5.92/6.16 tff(9,plain,
% 5.92/6.16 (~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), tptp_fun_C_18(wec, tac)) <=> model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))))),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[8, 7])).
% 5.92/6.16 tff(10,assumption,(![I2: $i] : (~model(I2, Ax!43))), introduced(assumption)).
% 5.92/6.16 tff(11,plain,
% 5.92/6.16 (?[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))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(12,plain,
% 5.92/6.16 (^[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)))),
% 5.92/6.16 inference(bind,[status(th)],[])).
% 5.92/6.16 tff(13,plain,
% 5.92/6.16 (?[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))),
% 5.92/6.16 inference(quant_intro,[status(thm)],[12])).
% 5.92/6.16 tff(14,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')).
% 5.92/6.16 tff(15,plain,
% 5.92/6.16 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[14, 13])).
% 5.92/6.16 tff(16,plain,
% 5.92/6.16 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[15, 11])).
% 5.92/6.16 tff(17,plain,
% 5.92/6.16 (model(I1!44, Ax!43)),
% 5.92/6.16 inference(and_elim,[status(thm)],[16])).
% 5.92/6.16 tff(18,plain,
% 5.92/6.16 ((~![I2: $i] : (~model(I2, Ax!43))) | (~model(I1!44, Ax!43))),
% 5.92/6.16 inference(quant_inst,[status(thm)],[])).
% 5.92/6.16 tff(19,plain,
% 5.92/6.16 ($false),
% 5.92/6.16 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 5.92/6.16 tff(20,plain,(~![I2: $i] : (~model(I2, Ax!43))), inference(lemma,lemma(discharge,[]))).
% 5.92/6.16 tff(21,assumption,(status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)), introduced(assumption)).
% 5.92/6.16 tff(22,plain,
% 5.92/6.16 (^[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)))))))),
% 5.92/6.16 inference(bind,[status(th)],[])).
% 5.92/6.16 tff(23,plain,
% 5.92/6.16 (![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))))))),
% 5.92/6.16 inference(quant_intro,[status(thm)],[22])).
% 5.92/6.16 tff(24,plain,
% 5.92/6.16 (^[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)))))))),
% 5.92/6.16 inference(bind,[status(th)],[])).
% 5.92/6.16 tff(25,plain,
% 5.92/6.16 (![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))))))),
% 5.92/6.16 inference(quant_intro,[status(thm)],[24])).
% 5.92/6.16 tff(26,plain,
% 5.92/6.16 (^[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)))))))),
% 5.92/6.16 inference(bind,[status(th)],[])).
% 5.92/6.16 tff(27,plain,
% 5.92/6.16 (![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))))))),
% 5.92/6.16 inference(quant_intro,[status(thm)],[26])).
% 5.92/6.16 tff(28,plain,
% 5.92/6.16 (![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))))))),
% 5.92/6.16 inference(transitivity,[status(thm)],[27, 25])).
% 5.92/6.16 tff(29,plain,
% 5.92/6.16 (^[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))))))))),
% 5.92/6.16 inference(bind,[status(th)],[])).
% 5.92/6.16 tff(30,plain,
% 5.92/6.16 (![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))))))),
% 5.92/6.16 inference(quant_intro,[status(thm)],[29])).
% 5.92/6.16 tff(31,plain,
% 5.92/6.16 (![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))),
% 5.92/6.16 inference(rewrite,[status(thm)],[])).
% 5.92/6.16 tff(32,plain,
% 5.92/6.16 (^[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)))),
% 5.92/6.16 inference(bind,[status(th)],[])).
% 5.92/6.16 tff(33,plain,
% 5.92/6.16 (![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))),
% 5.92/6.16 inference(quant_intro,[status(thm)],[32])).
% 5.92/6.16 tff(34,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')).
% 5.92/6.16 tff(35,plain,
% 5.92/6.16 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[34, 33])).
% 5.92/6.16 tff(36,plain,
% 5.92/6.16 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[35, 31])).
% 5.92/6.16 tff(37,plain,(
% 5.92/6.16 ![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))))),
% 5.92/6.16 inference(skolemize,[status(sab)],[36])).
% 5.92/6.16 tff(38,plain,
% 5.92/6.16 (![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))))))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[37, 30])).
% 5.92/6.16 tff(39,plain,
% 5.92/6.16 (![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))))))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[38, 28])).
% 5.92/6.16 tff(40,plain,
% 5.92/6.16 (![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))))))),
% 5.92/6.16 inference(modus_ponens,[status(thm)],[39, 23])).
% 5.92/6.16 tff(41,plain,
% 5.92/6.16 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))))))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(42,plain,
% 5.92/6.17 ((~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))) | (~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))))) <=> (~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)))))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(43,plain,
% 5.92/6.17 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))) | (~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))))))),
% 5.92/6.17 inference(monotonicity,[status(thm)],[42])).
% 5.92/6.17 tff(44,plain,
% 5.92/6.17 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))) | (~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))))))),
% 5.92/6.17 inference(transitivity,[status(thm)],[43, 41])).
% 5.92/6.17 tff(45,plain,
% 5.92/6.17 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))) | (~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca)))))))),
% 5.92/6.17 inference(quant_inst,[status(thm)],[])).
% 5.92/6.17 tff(46,plain,
% 5.92/6.17 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[45, 44])).
% 5.92/6.17 tff(47,plain,
% 5.92/6.17 (~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[46, 40])).
% 5.92/6.17 tff(48,plain,
% 5.92/6.17 (((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sca, sca))) | model(I1, tptp_fun_C_24(sca, sca))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)))) | ((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))),
% 5.92/6.17 inference(tautology,[status(thm)],[])).
% 5.92/6.17 tff(49,plain,
% 5.92/6.17 ((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[48, 47])).
% 5.92/6.17 tff(50,assumption,(status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)), introduced(assumption)).
% 5.92/6.17 tff(51,plain,
% 5.92/6.17 (^[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)))))))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(52,plain,
% 5.92/6.17 (![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))))))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[51])).
% 5.92/6.17 tff(53,plain,
% 5.92/6.17 (^[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)))))))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(54,plain,
% 5.92/6.17 (![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))))))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[53])).
% 5.92/6.17 tff(55,plain,
% 5.92/6.17 (![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))))))))),
% 5.92/6.17 inference(transitivity,[status(thm)],[54, 52])).
% 5.92/6.17 tff(56,plain,
% 5.92/6.17 (^[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))))))))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(57,plain,
% 5.92/6.17 (![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))))))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[56])).
% 5.92/6.17 tff(58,plain,
% 5.92/6.17 (^[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)))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(59,plain,
% 5.92/6.17 (![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))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[58])).
% 5.92/6.17 tff(60,plain,
% 5.92/6.17 (![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))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(61,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')).
% 5.92/6.17 tff(62,plain,
% 5.92/6.17 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[61, 60])).
% 5.92/6.17 tff(63,plain,(
% 5.92/6.17 ![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))))),
% 5.92/6.17 inference(skolemize,[status(sab)],[62])).
% 5.92/6.17 tff(64,plain,
% 5.92/6.17 (![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))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[63, 59])).
% 5.92/6.17 tff(65,plain,
% 5.92/6.17 (![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))))))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[64, 57])).
% 5.92/6.17 tff(66,plain,
% 5.92/6.17 (![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))))))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[65, 55])).
% 5.92/6.17 tff(67,plain,
% 5.92/6.17 ((~![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(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca))))) | (~((~mighta(sca, thm)) | (~((~status(tptp_fun_Ax_19(thm, sca), tptp_fun_C_18(thm, sca), sca)) | (~status(tptp_fun_Ax_19(thm, sca), tptp_fun_C_18(thm, sca), thm))))))))),
% 5.92/6.17 inference(quant_inst,[status(thm)],[])).
% 5.92/6.17 tff(68,plain,
% 5.92/6.17 (~((~(mighta(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca))))) | (~((~mighta(sca, thm)) | (~((~status(tptp_fun_Ax_19(thm, sca), tptp_fun_C_18(thm, sca), sca)) | (~status(tptp_fun_Ax_19(thm, sca), tptp_fun_C_18(thm, sca), thm)))))))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[67, 66])).
% 5.92/6.17 tff(69,plain,
% 5.92/6.17 (((~(mighta(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca))))) | (~((~mighta(sca, thm)) | (~((~status(tptp_fun_Ax_19(thm, sca), tptp_fun_C_18(thm, sca), sca)) | (~status(tptp_fun_Ax_19(thm, sca), tptp_fun_C_18(thm, sca), thm))))))) | (mighta(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca))))),
% 5.92/6.17 inference(tautology,[status(thm)],[])).
% 5.92/6.17 tff(70,plain,
% 5.92/6.17 (mighta(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[69, 68])).
% 5.92/6.17 tff(71,plain,
% 5.92/6.17 ((~mighta(sca, thm)) <=> (~mighta(sca, thm))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(72,axiom,(~mighta(sca, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_sca_thm')).
% 5.92/6.17 tff(73,plain,
% 5.92/6.17 (~mighta(sca, thm)),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[72, 71])).
% 5.92/6.17 tff(74,plain,
% 5.92/6.17 ((~(mighta(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca))))) | mighta(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))),
% 5.92/6.17 inference(tautology,[status(thm)],[])).
% 5.92/6.17 tff(75,plain,
% 5.92/6.17 ((~(mighta(sca, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[74, 73])).
% 5.92/6.17 tff(76,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[75, 70])).
% 5.92/6.17 tff(77,plain,
% 5.92/6.17 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))) | ((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(78,plain,
% 5.92/6.17 (((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) <=> ((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(79,plain,
% 5.92/6.17 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))) | ((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))) | ((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))))),
% 5.92/6.17 inference(monotonicity,[status(thm)],[78])).
% 5.92/6.17 tff(80,plain,
% 5.92/6.17 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))) | ((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)))),
% 5.92/6.17 inference(transitivity,[status(thm)],[79, 77])).
% 5.92/6.17 tff(81,plain,
% 5.92/6.17 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))) | ((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)))),
% 5.92/6.17 inference(quant_inst,[status(thm)],[])).
% 5.92/6.17 tff(82,plain,
% 5.92/6.17 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, sca)))) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[81, 80])).
% 5.92/6.17 tff(83,plain,
% 5.92/6.17 (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[82, 76, 50])).
% 5.92/6.17 tff(84,plain,
% 5.92/6.17 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm)),
% 5.92/6.17 inference(tautology,[status(thm)],[])).
% 5.92/6.17 tff(85,plain,
% 5.92/6.17 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca))))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[84, 83])).
% 5.92/6.17 tff(86,plain,
% 5.92/6.17 (~((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca)))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[85, 49])).
% 5.92/6.17 tff(87,plain,
% 5.92/6.17 (((~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_C_24(sca, sca))) | model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))),
% 5.92/6.17 inference(tautology,[status(thm)],[])).
% 5.92/6.17 tff(88,plain,
% 5.92/6.17 (model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca))),
% 5.92/6.17 inference(unit_resolution,[status(thm)],[87, 86])).
% 5.92/6.17 tff(89,plain,
% 5.92/6.17 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(90,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[89])).
% 5.92/6.17 tff(91,plain,
% 5.92/6.17 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(92,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[91])).
% 5.92/6.17 tff(93,plain,
% 5.92/6.17 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(94,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[93])).
% 5.92/6.17 tff(95,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 5.92/6.17 inference(transitivity,[status(thm)],[94, 92])).
% 5.92/6.17 tff(96,plain,
% 5.92/6.17 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) <=> (status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))), trans(monotonicity(rewrite((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) <=> (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))) <=> ((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, sca))))), rewrite(((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | (~status(Ax, C, sca))) <=> ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))), (((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))) <=> ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))), (((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))))), rewrite(((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))), (((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(97,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[96])).
% 5.92/6.17 tff(98,plain,
% 5.92/6.17 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))))),
% 5.92/6.17 inference(bind,[status(th)],[])).
% 5.92/6.17 tff(99,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 5.92/6.17 inference(quant_intro,[status(thm)],[98])).
% 5.92/6.17 tff(100,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca)) <=> ![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))),
% 5.92/6.17 inference(rewrite,[status(thm)],[])).
% 5.92/6.17 tff(101,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','sca')).
% 5.92/6.17 tff(102,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) & ?[I2: $i] : model(I2, C)) <=> status(Ax, C, sca))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[101, 100])).
% 5.92/6.17 tff(103,plain,(
% 5.92/6.17 ![Ax: $i, C: $i] : (((model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))) | status(Ax, C, sca)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 5.92/6.17 inference(skolemize,[status(sab)],[102])).
% 5.92/6.17 tff(104,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : ((status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) & ((![I1: $i] : (~model(I1, Ax)) & model(tptp_fun_I2_1(C), C)) | (~status(Ax, C, sca))))),
% 5.92/6.17 inference(modus_ponens,[status(thm)],[103, 99])).
% 5.92/6.17 tff(105,plain,
% 5.92/6.17 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[104, 97])).
% 6.01/6.18 tff(106,plain,
% 6.01/6.18 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | ![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[105, 95])).
% 6.01/6.18 tff(107,plain,
% 6.01/6.18 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[106, 90])).
% 6.01/6.18 tff(108,plain,
% 6.01/6.18 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca) | model(tptp_fun_I1_0(tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca)) | ![I2: $i] : (~model(I2, tptp_fun_C_24(sca, sca))))) | (~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca))))))))))),
% 6.01/6.18 inference(quant_inst,[status(thm)],[])).
% 6.01/6.18 tff(109,plain,
% 6.01/6.18 (~((~(status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca) | model(tptp_fun_I1_0(tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca)) | ![I2: $i] : (~model(I2, tptp_fun_C_24(sca, sca))))) | (~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca)))))))))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[108, 107])).
% 6.01/6.18 tff(110,plain,
% 6.01/6.18 (((~(status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca) | model(tptp_fun_I1_0(tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca)) | ![I2: $i] : (~model(I2, tptp_fun_C_24(sca, sca))))) | (~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca))))))))) | ((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca)))))))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(111,plain,
% 6.01/6.18 ((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca))))))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[110, 109])).
% 6.01/6.18 tff(112,plain,
% 6.01/6.18 ((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca)))))))) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca))))))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(113,plain,
% 6.01/6.18 ((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca)))))))) | (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca))))))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[112, 50])).
% 6.01/6.18 tff(114,plain,
% 6.01/6.18 (~((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca)))))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[113, 111])).
% 6.01/6.18 tff(115,plain,
% 6.01/6.18 (((~model(tptp_fun_I2_1(tptp_fun_C_24(sca, sca)), tptp_fun_C_24(sca, sca))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca))))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca)))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(116,plain,
% 6.01/6.18 (![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca)))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[115, 114])).
% 6.01/6.18 tff(117,plain,
% 6.01/6.18 ((~![I1: $i] : (~model(I1, tptp_fun_Ax_25(sca, sca)))) | (~model(tptp_fun_I1_3(tptp_fun_C_24(sca, sca), tptp_fun_Ax_25(sca, sca)), tptp_fun_Ax_25(sca, sca)))),
% 6.01/6.18 inference(quant_inst,[status(thm)],[])).
% 6.01/6.18 tff(118,plain,
% 6.01/6.18 ($false),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[117, 116, 88])).
% 6.01/6.18 tff(119,plain,(~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)), inference(lemma,lemma(discharge,[]))).
% 6.01/6.18 tff(120,plain,
% 6.01/6.18 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))))))),
% 6.01/6.18 inference(bind,[status(th)],[])).
% 6.01/6.18 tff(121,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 6.01/6.18 inference(quant_intro,[status(thm)],[120])).
% 6.01/6.18 tff(122,plain,
% 6.01/6.18 (^[S1: $i, S2: $i] : refl((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 6.01/6.18 inference(bind,[status(th)],[])).
% 6.01/6.18 tff(123,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 6.01/6.18 inference(quant_intro,[status(thm)],[122])).
% 6.01/6.18 tff(124,plain,
% 6.01/6.18 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 6.01/6.18 inference(bind,[status(th)],[])).
% 6.01/6.18 tff(125,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 6.01/6.18 inference(quant_intro,[status(thm)],[124])).
% 6.01/6.18 tff(126,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 6.01/6.18 inference(transitivity,[status(thm)],[125, 123])).
% 6.01/6.18 tff(127,plain,
% 6.01/6.18 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))), rewrite((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))))),
% 6.01/6.18 inference(bind,[status(th)],[])).
% 6.01/6.18 tff(128,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 6.01/6.18 inference(quant_intro,[status(thm)],[127])).
% 6.01/6.18 tff(129,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 6.01/6.18 inference(rewrite,[status(thm)],[])).
% 6.01/6.18 tff(130,plain,
% 6.01/6.18 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)))),
% 6.01/6.18 inference(bind,[status(th)],[])).
% 6.01/6.18 tff(131,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 6.01/6.18 inference(quant_intro,[status(thm)],[130])).
% 6.01/6.18 tff(132,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','nevera')).
% 6.01/6.18 tff(133,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[132, 131])).
% 6.01/6.18 tff(134,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[133, 129])).
% 6.01/6.18 tff(135,plain,(
% 6.01/6.18 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))),
% 6.01/6.18 inference(skolemize,[status(sab)],[134])).
% 6.01/6.18 tff(136,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[135, 128])).
% 6.01/6.18 tff(137,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[136, 126])).
% 6.01/6.18 tff(138,plain,
% 6.01/6.18 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[137, 121])).
% 6.01/6.18 tff(139,plain,
% 6.01/6.18 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca)))))))),
% 6.01/6.18 inference(rewrite,[status(thm)],[])).
% 6.01/6.18 tff(140,plain,
% 6.01/6.18 ((~((~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)))) | nevera(sca, sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | (~status(Ax, C, sca))))))) <=> (~((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca))))))),
% 6.01/6.18 inference(rewrite,[status(thm)],[])).
% 6.01/6.18 tff(141,plain,
% 6.01/6.18 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)))) | nevera(sca, sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | (~status(Ax, C, sca)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca)))))))),
% 6.01/6.18 inference(monotonicity,[status(thm)],[140])).
% 6.01/6.18 tff(142,plain,
% 6.01/6.18 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)))) | nevera(sca, sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | (~status(Ax, C, sca)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca)))))))),
% 6.01/6.18 inference(transitivity,[status(thm)],[141, 139])).
% 6.01/6.18 tff(143,plain,
% 6.01/6.18 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)) | (~status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)))) | nevera(sca, sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sca)) | (~status(Ax, C, sca)))))))),
% 6.01/6.18 inference(quant_inst,[status(thm)],[])).
% 6.01/6.18 tff(144,plain,
% 6.01/6.18 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca))))))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[143, 142])).
% 6.01/6.18 tff(145,plain,
% 6.01/6.18 (~((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca)))))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[144, 138])).
% 6.01/6.18 tff(146,plain,
% 6.01/6.18 (((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca))))) | (nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(147,plain,
% 6.01/6.18 (nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[146, 145])).
% 6.01/6.18 tff(148,plain,
% 6.01/6.18 ((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(149,plain,
% 6.01/6.18 (nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca)),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[148, 147])).
% 6.01/6.18 tff(150,plain,
% 6.01/6.18 (nevera(sca, sca)),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[149, 119])).
% 6.01/6.18 tff(151,plain,
% 6.01/6.18 (((~(nevera(sca, sca) | status(tptp_fun_Ax_25(sca, sca), tptp_fun_C_24(sca, sca), sca))) | (~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca))))) | ((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca)))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(152,plain,
% 6.01/6.18 ((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[151, 145])).
% 6.01/6.18 tff(153,plain,
% 6.01/6.18 ((~((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca)))) | (~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(154,plain,
% 6.01/6.18 ((~nevera(sca, sca)) | ![Ax: $i, C: $i] : (~status(Ax, C, sca))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[153, 152])).
% 6.01/6.18 tff(155,plain,
% 6.01/6.18 (![Ax: $i, C: $i] : (~status(Ax, C, sca))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[154, 150])).
% 6.01/6.18 tff(156,plain,
% 6.01/6.18 ((~![Ax: $i, C: $i] : (~status(Ax, C, sca))) | (~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca))),
% 6.01/6.18 inference(quant_inst,[status(thm)],[])).
% 6.01/6.18 tff(157,plain,
% 6.01/6.18 ($false),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[156, 155, 21])).
% 6.01/6.18 tff(158,plain,(~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)), inference(lemma,lemma(discharge,[]))).
% 6.01/6.18 tff(159,plain,
% 6.01/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac)))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac))))))))))))),
% 6.01/6.18 inference(rewrite,[status(thm)],[])).
% 6.01/6.18 tff(160,plain,
% 6.01/6.18 ((~((~(status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac))))))))))) <=> (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac)))))))))))),
% 6.01/6.18 inference(rewrite,[status(thm)],[])).
% 6.01/6.18 tff(161,plain,
% 6.01/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac)))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac))))))))))))),
% 6.01/6.18 inference(monotonicity,[status(thm)],[160])).
% 6.01/6.18 tff(162,plain,
% 6.01/6.18 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac)))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac))))))))))))),
% 6.01/6.18 inference(transitivity,[status(thm)],[161, 159])).
% 6.01/6.18 tff(163,plain,
% 6.01/6.18 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac)))))))))))),
% 6.01/6.18 inference(quant_inst,[status(thm)],[])).
% 6.01/6.18 tff(164,plain,
% 6.01/6.18 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sca) | model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~((~status(Ax, C, sca)) | (~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax)))))))))) | (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac)))))))))))),
% 6.01/6.18 inference(modus_ponens,[status(thm)],[163, 162])).
% 6.01/6.18 tff(165,plain,
% 6.01/6.18 (~((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac))))))))))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[164, 107])).
% 6.01/6.18 tff(166,plain,
% 6.01/6.18 (((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | (~((~status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca)) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, not(tptp_fun_C_18(wec, tac)))))))))) | (model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(167,plain,
% 6.01/6.18 (model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[166, 165])).
% 6.01/6.18 tff(168,plain,
% 6.01/6.18 ((~(model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43)))) | model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(169,plain,
% 6.01/6.18 (model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))) | status(not(tptp_fun_C_18(wec, tac)), Ax!43, sca) | ![I2: $i] : (~model(I2, Ax!43))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[168, 167])).
% 6.01/6.18 tff(170,plain,
% 6.01/6.18 (model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac)))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[169, 158, 20])).
% 6.01/6.18 tff(171,plain,
% 6.01/6.18 ((model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), tptp_fun_C_18(wec, tac)) <=> model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac)))) | (~model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), tptp_fun_C_18(wec, tac))) | (~model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac))))),
% 6.01/6.18 inference(tautology,[status(thm)],[])).
% 6.01/6.18 tff(172,plain,
% 6.01/6.18 ((model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), tptp_fun_C_18(wec, tac)) <=> model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), not(tptp_fun_C_18(wec, tac)))) | (~model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), tptp_fun_C_18(wec, tac)))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[171, 170])).
% 6.01/6.18 tff(173,plain,
% 6.01/6.18 (~model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), tptp_fun_C_18(wec, tac))),
% 6.01/6.18 inference(unit_resolution,[status(thm)],[172, 9])).
% 6.01/6.18 tff(174,plain,
% 6.01/6.18 (^[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)))))))))),
% 6.01/6.18 inference(bind,[status(th)],[])).
% 6.01/6.18 tff(175,plain,
% 6.01/6.18 (![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)))))))) <=> ![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))))))))),
% 6.01/6.18 inference(quant_intro,[status(thm)],[174])).
% 6.01/6.18 tff(176,plain,
% 6.01/6.18 (^[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)))))))))),
% 6.01/6.18 inference(bind,[status(th)],[])).
% 6.01/6.18 tff(177,plain,
% 6.01/6.18 (![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)))))))) <=> ![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))))))))),
% 6.01/6.18 inference(quant_intro,[status(thm)],[176])).
% 6.01/6.18 tff(178,plain,
% 6.01/6.18 (^[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)))))))))),
% 6.01/6.18 inference(bind,[status(th)],[])).
% 6.01/6.18 tff(179,plain,
% 6.01/6.18 (![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)))))))) <=> ![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))))))))),
% 6.01/6.18 inference(quant_intro,[status(thm)],[178])).
% 6.01/6.18 tff(180,plain,
% 6.01/6.19 (![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))))))))),
% 6.01/6.19 inference(transitivity,[status(thm)],[179, 177])).
% 6.01/6.19 tff(181,plain,
% 6.01/6.19 (^[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))))))))))),
% 6.01/6.19 inference(bind,[status(th)],[])).
% 6.01/6.19 tff(182,plain,
% 6.01/6.19 (![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))))))))),
% 6.01/6.19 inference(quant_intro,[status(thm)],[181])).
% 6.01/6.19 tff(183,plain,
% 6.01/6.19 (^[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)))))),
% 6.01/6.19 inference(bind,[status(th)],[])).
% 6.01/6.19 tff(184,plain,
% 6.01/6.19 (![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))))),
% 6.01/6.19 inference(quant_intro,[status(thm)],[183])).
% 6.01/6.19 tff(185,plain,
% 6.01/6.19 (![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))),
% 6.01/6.19 inference(rewrite,[status(thm)],[])).
% 6.01/6.19 tff(186,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')).
% 6.01/6.19 tff(187,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : model(I2, C)) <=> status(Ax, C, tac))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[186, 185])).
% 6.01/6.19 tff(188,plain,(
% 6.01/6.19 ![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))))),
% 6.01/6.19 inference(skolemize,[status(sab)],[187])).
% 6.01/6.19 tff(189,plain,
% 6.01/6.19 (![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))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[188, 184])).
% 6.01/6.19 tff(190,plain,
% 6.01/6.19 (![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))))))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[189, 182])).
% 6.01/6.19 tff(191,plain,
% 6.01/6.19 (![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))))))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[190, 180])).
% 6.01/6.19 tff(192,plain,
% 6.01/6.19 (![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))))))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[191, 175])).
% 6.01/6.19 tff(193,plain,
% 6.01/6.19 (((~![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, tptp_fun_Ax_19(wec, tac))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))))))) <=> ((~![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, tptp_fun_Ax_19(wec, tac))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))))))))),
% 6.01/6.19 inference(rewrite,[status(thm)],[])).
% 6.01/6.19 tff(194,plain,
% 6.01/6.19 ((~((~(status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))))))) <=> (~((~(![I1: $i] : (~model(I1, tptp_fun_Ax_19(wec, tac))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))))))),
% 6.01/6.19 inference(rewrite,[status(thm)],[])).
% 6.01/6.19 tff(195,plain,
% 6.01/6.19 (((~![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(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))))))) <=> ((~![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, tptp_fun_Ax_19(wec, tac))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))))))))),
% 6.01/6.19 inference(monotonicity,[status(thm)],[194])).
% 6.01/6.19 tff(196,plain,
% 6.01/6.19 (((~![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(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))))))) <=> ((~![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, tptp_fun_Ax_19(wec, tac))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))))))))),
% 6.01/6.19 inference(transitivity,[status(thm)],[195, 193])).
% 6.01/6.19 tff(197,plain,
% 6.01/6.19 ((~![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(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_19(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))))))),
% 6.01/6.19 inference(quant_inst,[status(thm)],[])).
% 6.01/6.19 tff(198,plain,
% 6.01/6.19 ((~![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, tptp_fun_Ax_19(wec, tac))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[197, 196])).
% 6.01/6.19 tff(199,plain,
% 6.01/6.19 (~((~(![I1: $i] : (~model(I1, tptp_fun_Ax_19(wec, tac))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))))))),
% 6.01/6.19 inference(unit_resolution,[status(thm)],[198, 192])).
% 6.01/6.19 tff(200,plain,
% 6.01/6.19 (((~(![I1: $i] : (~model(I1, tptp_fun_Ax_19(wec, tac))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac) | (~model(tptp_fun_I2_5(tptp_fun_C_18(wec, tac)), tptp_fun_C_18(wec, tac))))) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))))) | ((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))))),
% 6.01/6.19 inference(tautology,[status(thm)],[])).
% 6.01/6.19 tff(201,plain,
% 6.01/6.19 ((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))),
% 6.01/6.19 inference(unit_resolution,[status(thm)],[200, 199])).
% 6.01/6.19 tff(202,assumption,((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28)))))))), introduced(assumption)).
% 6.01/6.19 tff(203,plain,
% 6.01/6.19 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))))))))))),
% 6.01/6.19 inference(bind,[status(th)],[])).
% 6.01/6.19 tff(204,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))),
% 6.01/6.19 inference(quant_intro,[status(thm)],[203])).
% 6.01/6.19 tff(205,plain,
% 6.01/6.19 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))))),
% 6.01/6.19 inference(bind,[status(th)],[])).
% 6.01/6.19 tff(206,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 6.01/6.19 inference(quant_intro,[status(thm)],[205])).
% 6.01/6.19 tff(207,plain,
% 6.01/6.19 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))))),
% 6.01/6.19 inference(bind,[status(th)],[])).
% 6.01/6.19 tff(208,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 6.01/6.19 inference(quant_intro,[status(thm)],[207])).
% 6.01/6.19 tff(209,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 6.01/6.19 inference(transitivity,[status(thm)],[208, 206])).
% 6.01/6.19 tff(210,plain,
% 6.01/6.19 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[I3: $i] : trans(monotonicity(rewrite((model(I3, C) & (~model(I3, Ax))) <=> (~((~model(I3, C)) | model(I3, Ax)))), ((~(model(I3, C) & (~model(I3, Ax)))) <=> (~(~((~model(I3, C)) | model(I3, Ax)))))), rewrite((~(~((~model(I3, C)) | model(I3, Ax)))) <=> ((~model(I3, C)) | model(I3, Ax))), ((~(model(I3, C) & (~model(I3, Ax)))) <=> ((~model(I3, C)) | model(I3, Ax))))), (![I3: $i] : (~(model(I3, C) & (~model(I3, Ax)))) <=> ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))), ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) <=> (status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))))), rewrite((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))) <=> (status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))), ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) <=> (status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))))), rewrite(((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))) <=> ((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))), (((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax))))) <=> ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))) & ((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))))), rewrite(((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax))) & ((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)))))) <=> (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))), (((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax))))) <=> (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))))),
% 6.01/6.19 inference(bind,[status(th)],[])).
% 6.01/6.19 tff(211,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 6.01/6.19 inference(quant_intro,[status(thm)],[210])).
% 6.01/6.19 tff(212,plain,
% 6.01/6.19 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) | status(Ax, C, wec)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & (model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))) | (~status(Ax, C, wec)))) <=> ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax))))))),
% 6.01/6.19 inference(bind,[status(th)],[])).
% 6.01/6.19 tff(213,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) | status(Ax, C, wec)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & (model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))) | (~status(Ax, C, wec)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))))),
% 6.01/6.19 inference(quant_intro,[status(thm)],[212])).
% 6.01/6.19 tff(214,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))),
% 6.01/6.19 inference(rewrite,[status(thm)],[])).
% 6.01/6.19 tff(215,plain,
% 6.01/6.19 (^[Ax: $i, C: $i] : rewrite((((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec)) <=> ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec)))),
% 6.01/6.19 inference(bind,[status(th)],[])).
% 6.01/6.19 tff(216,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))),
% 6.01/6.19 inference(quant_intro,[status(thm)],[215])).
% 6.01/6.19 tff(217,axiom,(![Ax: $i, C: $i] : (((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) => model(I2, C))) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','wec')).
% 6.01/6.19 tff(218,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[217, 216])).
% 6.01/6.19 tff(219,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & ?[I3: $i] : (model(I3, C) & (~model(I3, Ax)))) <=> status(Ax, C, wec))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[218, 214])).
% 6.01/6.19 tff(220,plain,(
% 6.01/6.19 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) | status(Ax, C, wec)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & (model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))) | (~status(Ax, C, wec))))),
% 6.01/6.19 inference(skolemize,[status(sab)],[219])).
% 6.01/6.19 tff(221,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : ((status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : (~(model(I3, C) & (~model(I3, Ax))))) & ((~status(Ax, C, wec)) | (model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : ((~model(I2, Ax)) | model(I2, C)) & model(tptp_fun_I3_6(C, Ax), C) & (~model(tptp_fun_I3_6(C, Ax), Ax)))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[220, 213])).
% 6.01/6.19 tff(222,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[221, 211])).
% 6.01/6.19 tff(223,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | ![I1: $i] : (~model(I1, Ax)) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C))) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C))))))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[222, 209])).
% 6.01/6.19 tff(224,plain,
% 6.01/6.19 (![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))),
% 6.01/6.19 inference(modus_ponens,[status(thm)],[223, 204])).
% 6.01/6.19 tff(225,plain,
% 6.01/6.19 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28))))))))))),
% 6.01/6.20 inference(rewrite,[status(thm)],[])).
% 6.01/6.20 tff(226,plain,
% 6.01/6.20 ((~((~(status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))) | ![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)))) | (~((~status(C!42, F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28))))))))) <=> (~((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28)))))))))),
% 6.01/6.20 inference(rewrite,[status(thm)],[])).
% 6.01/6.20 tff(227,plain,
% 6.01/6.20 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))) | ![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)))) | (~((~status(C!42, F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28))))))))))),
% 6.01/6.20 inference(monotonicity,[status(thm)],[226])).
% 6.01/6.20 tff(228,plain,
% 6.01/6.20 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))) | ![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)))) | (~((~status(C!42, F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28))))))))))),
% 6.03/6.20 inference(transitivity,[status(thm)],[227, 225])).
% 6.03/6.20 tff(229,plain,
% 6.03/6.20 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))) | ![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)))) | (~((~status(C!42, F!28, wec)) | (~(model(tptp_fun_I3_6(F!28, C!42), C!42) | (~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28)))))))))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(230,plain,
% 6.03/6.20 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, wec) | (~((~model(tptp_fun_I2_7(C, Ax), Ax)) | model(tptp_fun_I2_7(C, Ax), C))) | ![I1: $i] : (~model(I1, Ax)) | ![I3: $i] : ((~model(I3, C)) | model(I3, Ax)))) | (~((~status(Ax, C, wec)) | (~(model(tptp_fun_I3_6(C, Ax), Ax) | (~model(tptp_fun_I1_0(Ax), Ax)) | (~model(tptp_fun_I3_6(C, Ax), C)) | (~![I2: $i] : ((~model(I2, Ax)) | model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28)))))))))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[229, 228])).
% 6.03/6.20 tff(231,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[230, 224, 202])).
% 6.03/6.20 tff(232,plain,(~((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28))))))))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(233,plain,
% 6.03/6.20 (((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | (~((~status(C!42, F!28, wec)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~model(tptp_fun_I3_6(F!28, C!42), F!28)) | model(tptp_fun_I3_6(F!28, C!42), C!42) | (~![I2: $i] : ((~model(I2, C!42)) | model(I2, F!28)))))))) | (![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(234,plain,
% 6.03/6.20 (![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28)))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[233, 232])).
% 6.03/6.20 tff(235,assumption,(~model(tptp_fun_I2_7(F!28, C!42), F!28)), introduced(assumption)).
% 6.03/6.20 tff(236,plain,
% 6.03/6.20 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 6.03/6.20 inference(bind,[status(th)],[])).
% 6.03/6.20 tff(237,plain,
% 6.03/6.20 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 6.03/6.20 inference(quant_intro,[status(thm)],[236])).
% 6.03/6.20 tff(238,plain,
% 6.03/6.20 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(239,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','tautology')).
% 6.03/6.20 tff(240,plain,
% 6.03/6.20 (?[F: $i] : ![I: $i] : model(I, F)),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[239, 238])).
% 6.03/6.20 tff(241,plain,(
% 6.03/6.20 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 6.03/6.20 inference(transitivity,[status(sab)],[240])).
% 6.03/6.20 tff(242,plain,
% 6.03/6.20 (![I: $i] : model(I, F!28)),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[241, 237])).
% 6.03/6.20 tff(243,plain,
% 6.03/6.20 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I2_7(F!28, C!42), F!28)),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(244,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[243, 242, 235])).
% 6.03/6.20 tff(245,plain,(model(tptp_fun_I2_7(F!28, C!42), F!28)), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(246,plain,
% 6.03/6.20 (((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28)) | (~model(tptp_fun_I2_7(F!28, C!42), F!28))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(247,plain,
% 6.03/6.20 ((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[246, 245])).
% 6.03/6.20 tff(248,assumption,(![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42))), introduced(assumption)).
% 6.03/6.20 tff(249,assumption,(~model(I1!44, F!28)), introduced(assumption)).
% 6.03/6.20 tff(250,plain,
% 6.03/6.20 ((~![I: $i] : model(I, F!28)) | model(I1!44, F!28)),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(251,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[250, 242, 249])).
% 6.03/6.20 tff(252,plain,(model(I1!44, F!28)), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(253,plain,
% 6.03/6.20 (~model(I1!44, C!42)),
% 6.03/6.20 inference(and_elim,[status(thm)],[16])).
% 6.03/6.20 tff(254,plain,
% 6.03/6.20 (((~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42))) | ((~model(I1!44, F!28)) | model(I1!44, C!42))) <=> ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42))) | (~model(I1!44, F!28)) | model(I1!44, C!42))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(255,plain,
% 6.03/6.20 ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42))) | ((~model(I1!44, F!28)) | model(I1!44, C!42))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(256,plain,
% 6.03/6.20 ((~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42))) | (~model(I1!44, F!28)) | model(I1!44, C!42)),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[255, 254])).
% 6.03/6.20 tff(257,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[256, 253, 252, 248])).
% 6.03/6.20 tff(258,plain,(~![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(259,assumption,(![I1: $i] : (~model(I1, C!42))), introduced(assumption)).
% 6.03/6.20 tff(260,plain,
% 6.03/6.20 (model(I2!45, C!42)),
% 6.03/6.20 inference(and_elim,[status(thm)],[16])).
% 6.03/6.20 tff(261,plain,
% 6.03/6.20 ((~![I1: $i] : (~model(I1, C!42))) | (~model(I2!45, C!42))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(262,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[261, 260, 259])).
% 6.03/6.20 tff(263,plain,(~![I1: $i] : (~model(I1, C!42))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(264,plain,
% 6.03/6.20 ((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | ![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28)))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(265,plain,
% 6.03/6.20 ((~(![I1: $i] : (~model(I1, C!42)) | ![I3: $i] : ((~model(I3, F!28)) | model(I3, C!42)) | status(C!42, F!28, wec) | (~((~model(tptp_fun_I2_7(F!28, C!42), C!42)) | model(tptp_fun_I2_7(F!28, C!42), F!28))))) | status(C!42, F!28, wec)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[264, 263, 258, 247])).
% 6.03/6.20 tff(266,plain,
% 6.03/6.20 (status(C!42, F!28, wec)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[265, 234])).
% 6.03/6.20 tff(267,assumption,(![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))), introduced(assumption)).
% 6.03/6.20 tff(268,assumption,(~model(tptp_fun_I2_5(F!28), F!28)), introduced(assumption)).
% 6.03/6.20 tff(269,plain,
% 6.03/6.20 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I2_5(F!28), F!28)),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(270,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[269, 242, 268])).
% 6.03/6.20 tff(271,plain,(model(tptp_fun_I2_5(F!28), F!28)), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(272,plain,
% 6.03/6.20 (((~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))) <=> ((~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(273,plain,
% 6.03/6.20 ((~((~(status(C!42, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))) <=> (~((~(![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(274,plain,
% 6.03/6.20 (((~![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(C!42, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))) <=> ((~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 6.03/6.20 inference(monotonicity,[status(thm)],[273])).
% 6.03/6.20 tff(275,plain,
% 6.03/6.20 (((~![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(C!42, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))) <=> ((~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))))),
% 6.03/6.20 inference(transitivity,[status(thm)],[274, 272])).
% 6.03/6.20 tff(276,plain,
% 6.03/6.20 ((~![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(C!42, F!28, tac) | (~model(tptp_fun_I2_5(F!28), F!28)) | ![I1: $i] : (~model(I1, C!42)))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(277,plain,
% 6.03/6.20 ((~![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, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[276, 275])).
% 6.03/6.20 tff(278,plain,
% 6.03/6.20 (~((~(![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28)))))))),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[277, 192])).
% 6.03/6.20 tff(279,plain,
% 6.03/6.20 (((~(![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | (~((~status(C!42, F!28, tac)) | (~((~model(tptp_fun_I1_0(C!42), C!42)) | (~![I2: $i] : model(I2, F!28))))))) | (![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(280,plain,
% 6.03/6.20 (![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[279, 278])).
% 6.03/6.20 tff(281,plain,
% 6.03/6.20 ((~(![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac))) | ![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac)),
% 6.03/6.20 inference(tautology,[status(thm)],[])).
% 6.03/6.20 tff(282,plain,
% 6.03/6.20 (![I1: $i] : (~model(I1, C!42)) | (~model(tptp_fun_I2_5(F!28), F!28)) | status(C!42, F!28, tac)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[281, 280])).
% 6.03/6.20 tff(283,plain,
% 6.03/6.20 (![I1: $i] : (~model(I1, C!42)) | status(C!42, F!28, tac)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[282, 271])).
% 6.03/6.20 tff(284,plain,
% 6.03/6.20 (status(C!42, F!28, tac)),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[283, 263])).
% 6.03/6.20 tff(285,plain,
% 6.03/6.20 (((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))) | ((~status(C!42, F!28, tac)) | (~status(C!42, F!28, wec)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))) | (~status(C!42, F!28, tac)) | (~status(C!42, F!28, wec)))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(286,plain,
% 6.03/6.20 ((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))) | ((~status(C!42, F!28, tac)) | (~status(C!42, F!28, wec)))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(287,plain,
% 6.03/6.20 ((~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))) | (~status(C!42, F!28, tac)) | (~status(C!42, F!28, wec))),
% 6.03/6.20 inference(modus_ponens,[status(thm)],[286, 285])).
% 6.03/6.20 tff(288,plain,
% 6.03/6.20 ($false),
% 6.03/6.20 inference(unit_resolution,[status(thm)],[287, 284, 267, 266])).
% 6.03/6.20 tff(289,plain,(~![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))), inference(lemma,lemma(discharge,[]))).
% 6.03/6.20 tff(290,plain,
% 6.03/6.20 (((~![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(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec)))))))))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(291,plain,
% 6.03/6.20 ((~((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec)))))))) <=> (~((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))))))),
% 6.03/6.20 inference(rewrite,[status(thm)],[])).
% 6.03/6.20 tff(292,plain,
% 6.03/6.20 (((~![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(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec)))))))))),
% 6.03/6.20 inference(monotonicity,[status(thm)],[291])).
% 6.03/6.20 tff(293,plain,
% 6.03/6.20 (((~![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(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))))))) <=> ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec)))))))))),
% 6.03/6.20 inference(transitivity,[status(thm)],[292, 290])).
% 6.03/6.20 tff(294,plain,
% 6.03/6.20 ((~![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(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, wec)) | (~status(Ax, C, tac))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))))))),
% 6.03/6.20 inference(quant_inst,[status(thm)],[])).
% 6.03/6.20 tff(295,plain,
% 6.03/6.20 ((~![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(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))))))),
% 6.03/6.21 inference(modus_ponens,[status(thm)],[294, 293])).
% 6.03/6.21 tff(296,plain,
% 6.03/6.21 (~((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec)))))))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[295, 66])).
% 6.03/6.21 tff(297,plain,
% 6.03/6.21 (((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))))) | (mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(298,plain,
% 6.03/6.21 (mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[297, 296])).
% 6.03/6.21 tff(299,plain,
% 6.03/6.21 ((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(300,plain,
% 6.03/6.21 (mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec)))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[299, 298])).
% 6.03/6.21 tff(301,plain,
% 6.03/6.21 (mighta(tac, wec)),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[300, 289])).
% 6.03/6.21 tff(302,plain,
% 6.03/6.21 (((~(mighta(tac, wec) | ![Ax: $i, C: $i] : ((~status(Ax, C, tac)) | (~status(Ax, C, wec))))) | (~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))))) | ((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec)))))),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(303,plain,
% 6.03/6.21 ((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[302, 296])).
% 6.03/6.21 tff(304,plain,
% 6.03/6.21 ((~((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec)))))) | (~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(305,plain,
% 6.03/6.21 ((~mighta(tac, wec)) | (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[304, 303])).
% 6.03/6.21 tff(306,plain,
% 6.03/6.21 (~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec)))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[305, 301])).
% 6.03/6.21 tff(307,plain,
% 6.03/6.21 (((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), wec))) | status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(308,plain,
% 6.03/6.21 (status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[307, 306])).
% 6.03/6.21 tff(309,plain,
% 6.03/6.21 ((~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))))) | (~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(310,plain,
% 6.03/6.21 ((~((~status(tptp_fun_Ax_19(wec, tac), tptp_fun_C_18(wec, tac), tac)) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))))) | (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[309, 308])).
% 6.03/6.21 tff(311,plain,
% 6.03/6.21 (~((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[310, 201])).
% 6.03/6.21 tff(312,plain,
% 6.03/6.21 (((~model(tptp_fun_I1_0(tptp_fun_Ax_19(wec, tac)), tptp_fun_Ax_19(wec, tac))) | (~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac)))) | ![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))),
% 6.03/6.21 inference(tautology,[status(thm)],[])).
% 6.03/6.21 tff(313,plain,
% 6.03/6.21 (![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[312, 311])).
% 6.03/6.21 tff(314,plain,
% 6.03/6.21 ((~![I2: $i] : model(I2, tptp_fun_C_18(wec, tac))) | model(tptp_fun_I1_0(not(tptp_fun_C_18(wec, tac))), tptp_fun_C_18(wec, tac))),
% 6.03/6.21 inference(quant_inst,[status(thm)],[])).
% 6.03/6.21 tff(315,plain,
% 6.03/6.21 ($false),
% 6.03/6.21 inference(unit_resolution,[status(thm)],[314, 313, 173])).
% 6.03/6.21 % SZS output end Proof
% 6.03/6.21 % E exiting
%------------------------------------------------------------------------------