%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS254+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:13:38 AM UTC 2025
% Result : Theorem 4.23s 4.42s
% Output : Proof 4.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS254+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.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 19:18:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.23/4.42 % SZS status Theorem
% 4.23/4.42 % SZS output start Proof
% 4.23/4.42 tff(status_type, type, (
% 4.23/4.42 status: ( $i * $i * $i ) > $o)).
% 4.23/4.42 tff(unp_type, type, (
% 4.23/4.42 unp: $i)).
% 4.23/4.42 tff(tptp_fun_Ax_34_type, type, (
% 4.23/4.42 tptp_fun_Ax_34: $i)).
% 4.23/4.42 tff(model_type, type, (
% 4.23/4.42 model: ( $i * $i ) > $o)).
% 4.23/4.42 tff(tptp_fun_I2_1_type, type, (
% 4.23/4.42 tptp_fun_I2_1: $i > $i)).
% 4.23/4.42 tff(tptp_fun_I1_0_type, type, (
% 4.23/4.42 tptp_fun_I1_0: $i > $i)).
% 4.23/4.42 tff(tptp_fun_I1_35_type, type, (
% 4.23/4.42 tptp_fun_I1_35: $i)).
% 4.23/4.42 tff(tptp_fun_C_33_type, type, (
% 4.23/4.42 tptp_fun_C_33: $i)).
% 4.23/4.42 tff(tptp_fun_I2_36_type, type, (
% 4.23/4.42 tptp_fun_I2_36: $i)).
% 4.23/4.42 tff(thm_type, type, (
% 4.23/4.42 thm: $i)).
% 4.23/4.42 tff(tptp_fun_I1_3_type, type, (
% 4.23/4.42 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 4.23/4.42 tff(mighta_type, type, (
% 4.23/4.42 mighta: ( $i * $i ) > $o)).
% 4.23/4.42 tff(tptp_fun_C_18_type, type, (
% 4.23/4.42 tptp_fun_C_18: ( $i * $i ) > $i)).
% 4.23/4.42 tff(tptp_fun_Ax_19_type, type, (
% 4.23/4.42 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 4.23/4.42 tff(1,assumption,(![I1: $i] : (~model(I1, Ax!34))), introduced(assumption)).
% 4.23/4.42 tff(2,plain,
% 4.23/4.42 (((model(I1!35, Ax!34) & model(I1!35, C!33)) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))) <=> (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33))))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(3,plain,
% 4.23/4.42 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C)))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(4,axiom,(?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+1.ax','sat_non_taut_pair')).
% 4.23/4.42 tff(5,plain,
% 4.23/4.42 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 4.23/4.42 tff(6,plain,
% 4.23/4.42 (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[5, 2])).
% 4.23/4.42 tff(7,plain,
% 4.23/4.42 (model(I1!35, Ax!34)),
% 4.23/4.42 inference(and_elim,[status(thm)],[6])).
% 4.23/4.42 tff(8,plain,
% 4.23/4.42 ((~![I1: $i] : (~model(I1, Ax!34))) | (~model(I1!35, Ax!34))),
% 4.23/4.42 inference(quant_inst,[status(thm)],[])).
% 4.23/4.42 tff(9,plain,
% 4.23/4.42 ($false),
% 4.23/4.42 inference(unit_resolution,[status(thm)],[8, 7, 1])).
% 4.23/4.42 tff(10,plain,(~![I1: $i] : (~model(I1, Ax!34))), inference(lemma,lemma(discharge,[]))).
% 4.23/4.42 tff(11,plain,
% 4.23/4.42 (((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34)))) | ![I1: $i] : (~model(I1, Ax!34))),
% 4.23/4.42 inference(tautology,[status(thm)],[])).
% 4.23/4.42 tff(12,plain,
% 4.23/4.42 ((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34)))),
% 4.23/4.42 inference(unit_resolution,[status(thm)],[11, 10])).
% 4.23/4.42 tff(13,assumption,(~status(Ax!34, Ax!34, thm)), introduced(assumption)).
% 4.23/4.42 tff(14,plain,
% 4.23/4.42 (^[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)))))))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(15,plain,
% 4.23/4.42 (![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))))))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[14])).
% 4.23/4.42 tff(16,plain,
% 4.23/4.42 (^[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)))))))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(17,plain,
% 4.23/4.42 (![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))))))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[16])).
% 4.23/4.42 tff(18,plain,
% 4.23/4.42 (^[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)))))))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(19,plain,
% 4.23/4.42 (![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))))))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[18])).
% 4.23/4.42 tff(20,plain,
% 4.23/4.42 (![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))))))),
% 4.23/4.42 inference(transitivity,[status(thm)],[19, 17])).
% 4.23/4.42 tff(21,plain,
% 4.23/4.42 (^[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))))))))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(22,plain,
% 4.23/4.42 (![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))))))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[21])).
% 4.23/4.42 tff(23,plain,
% 4.23/4.42 (![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))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(24,plain,
% 4.23/4.42 (^[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)))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(25,plain,
% 4.23/4.42 (![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))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[24])).
% 4.23/4.42 tff(26,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')).
% 4.23/4.42 tff(27,plain,
% 4.23/4.42 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 4.23/4.42 tff(28,plain,
% 4.23/4.42 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[27, 23])).
% 4.23/4.42 tff(29,plain,(
% 4.23/4.42 ![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))))),
% 4.23/4.42 inference(skolemize,[status(sab)],[28])).
% 4.23/4.42 tff(30,plain,
% 4.23/4.42 (![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))))))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[29, 22])).
% 4.23/4.42 tff(31,plain,
% 4.23/4.42 (![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))))))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[30, 20])).
% 4.23/4.42 tff(32,plain,
% 4.23/4.42 (![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))))))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[31, 15])).
% 4.23/4.42 tff(33,plain,
% 4.23/4.42 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(Ax!34, Ax!34, thm)) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(Ax!34, Ax!34, thm))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(34,plain,
% 4.23/4.42 ((~(~status(Ax!34, Ax!34, thm))) <=> status(Ax!34, Ax!34, thm)),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(35,plain,
% 4.23/4.42 (((~status(Ax!34, Ax!34, thm)) | $false) <=> (~status(Ax!34, Ax!34, thm))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(36,plain,
% 4.23/4.42 ((~$true) <=> $false),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(37,plain,
% 4.23/4.42 (((~status(Ax!34, Ax!34, thm)) | $true) <=> $true),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(38,plain,
% 4.23/4.42 (![I1: $i] : $true <=> $true),
% 4.23/4.42 inference(elim_unused_vars,[status(thm)],[])).
% 4.23/4.42 tff(39,plain,
% 4.23/4.42 (![I1: $i] : $true <=> ![I1: $i] : $true),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(40,plain,
% 4.23/4.42 (![I1: $i] : $true <=> $true),
% 4.23/4.42 inference(transitivity,[status(thm)],[39, 38])).
% 4.23/4.42 tff(41,plain,
% 4.23/4.42 (^[I1: $i] : rewrite(((~model(I1, Ax!34)) | model(I1, Ax!34)) <=> $true)),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(42,plain,
% 4.23/4.42 (![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)) <=> ![I1: $i] : $true),
% 4.23/4.42 inference(quant_intro,[status(thm)],[41])).
% 4.23/4.42 tff(43,plain,
% 4.23/4.42 (![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)) <=> $true),
% 4.23/4.42 inference(transitivity,[status(thm)],[42, 40])).
% 4.23/4.42 tff(44,plain,
% 4.23/4.42 (((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))) <=> ((~status(Ax!34, Ax!34, thm)) | $true)),
% 4.23/4.42 inference(monotonicity,[status(thm)],[43])).
% 4.23/4.42 tff(45,plain,
% 4.23/4.42 (((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))) <=> $true),
% 4.23/4.42 inference(transitivity,[status(thm)],[44, 37])).
% 4.23/4.42 tff(46,plain,
% 4.23/4.42 ((~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)))) <=> (~$true)),
% 4.23/4.42 inference(monotonicity,[status(thm)],[45])).
% 4.23/4.42 tff(47,plain,
% 4.23/4.42 ((~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)))) <=> $false),
% 4.23/4.42 inference(transitivity,[status(thm)],[46, 36])).
% 4.23/4.42 tff(48,plain,
% 4.23/4.42 ((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) <=> (~status(Ax!34, Ax!34, thm))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(49,plain,
% 4.23/4.42 (((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))) <=> ((~status(Ax!34, Ax!34, thm)) | $false)),
% 4.23/4.42 inference(monotonicity,[status(thm)],[48, 47])).
% 4.23/4.42 tff(50,plain,
% 4.23/4.42 (((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))) <=> (~status(Ax!34, Ax!34, thm))),
% 4.23/4.42 inference(transitivity,[status(thm)],[49, 35])).
% 4.23/4.42 tff(51,plain,
% 4.23/4.42 ((~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)))))) <=> (~(~status(Ax!34, Ax!34, thm)))),
% 4.23/4.42 inference(monotonicity,[status(thm)],[50])).
% 4.23/4.42 tff(52,plain,
% 4.23/4.42 ((~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34)))))) <=> status(Ax!34, Ax!34, thm)),
% 4.23/4.42 inference(transitivity,[status(thm)],[51, 34])).
% 4.23/4.42 tff(53,plain,
% 4.23/4.42 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(Ax!34, Ax!34, thm))),
% 4.23/4.42 inference(monotonicity,[status(thm)],[52])).
% 4.23/4.42 tff(54,plain,
% 4.23/4.42 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(Ax!34, Ax!34, thm))),
% 4.23/4.42 inference(transitivity,[status(thm)],[53, 33])).
% 4.23/4.42 tff(55,plain,
% 4.23/4.42 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34)) | model(tptp_fun_I1_3(Ax!34, Ax!34), Ax!34))) | status(Ax!34, Ax!34, thm))) | (~((~status(Ax!34, Ax!34, thm)) | ![I1: $i] : ((~model(I1, Ax!34)) | model(I1, Ax!34))))))),
% 4.23/4.42 inference(quant_inst,[status(thm)],[])).
% 4.23/4.42 tff(56,plain,
% 4.23/4.42 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | status(Ax!34, Ax!34, thm)),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 4.23/4.42 tff(57,plain,
% 4.23/4.42 ($false),
% 4.23/4.42 inference(unit_resolution,[status(thm)],[56, 32, 13])).
% 4.23/4.42 tff(58,plain,(status(Ax!34, Ax!34, thm)), inference(lemma,lemma(discharge,[]))).
% 4.23/4.42 tff(59,plain,
% 4.23/4.42 (^[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)))))))))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(60,plain,
% 4.23/4.42 (![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))))))))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[59])).
% 4.23/4.42 tff(61,plain,
% 4.23/4.42 (^[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)))))))))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(62,plain,
% 4.23/4.42 (![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))))))))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[61])).
% 4.23/4.42 tff(63,plain,
% 4.23/4.42 (![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))))))))),
% 4.23/4.42 inference(transitivity,[status(thm)],[62, 60])).
% 4.23/4.42 tff(64,plain,
% 4.23/4.42 (^[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))))))))))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(65,plain,
% 4.23/4.42 (![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))))))))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[64])).
% 4.23/4.42 tff(66,plain,
% 4.23/4.42 (^[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)))))),
% 4.23/4.42 inference(bind,[status(th)],[])).
% 4.23/4.42 tff(67,plain,
% 4.23/4.42 (![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))))),
% 4.23/4.42 inference(quant_intro,[status(thm)],[66])).
% 4.23/4.42 tff(68,plain,
% 4.23/4.42 (![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))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(69,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')).
% 4.23/4.42 tff(70,plain,
% 4.23/4.42 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 4.23/4.42 tff(71,plain,(
% 4.23/4.42 ![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))))),
% 4.23/4.42 inference(skolemize,[status(sab)],[70])).
% 4.23/4.42 tff(72,plain,
% 4.23/4.42 (![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))))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 4.23/4.42 tff(73,plain,
% 4.23/4.42 (![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))))))))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[72, 65])).
% 4.23/4.42 tff(74,plain,
% 4.23/4.42 (![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))))))))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[73, 63])).
% 4.23/4.42 tff(75,plain,
% 4.23/4.42 (((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp))))))))) <=> ((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp)))))))))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(76,plain,
% 4.23/4.42 ((~((~(mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)))))))) <=> (~((~(mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp))))))))),
% 4.23/4.42 inference(rewrite,[status(thm)],[])).
% 4.23/4.42 tff(77,plain,
% 4.23/4.42 (((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm))))))))) <=> ((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp)))))))))),
% 4.23/4.43 inference(monotonicity,[status(thm)],[76])).
% 4.23/4.43 tff(78,plain,
% 4.23/4.43 (((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm))))))))) <=> ((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp)))))))))),
% 4.23/4.43 inference(transitivity,[status(thm)],[77, 75])).
% 4.23/4.43 tff(79,plain,
% 4.23/4.43 ((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm))))))))),
% 4.23/4.43 inference(quant_inst,[status(thm)],[])).
% 4.23/4.43 tff(80,plain,
% 4.23/4.43 ((~![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(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp))))))))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 4.23/4.43 tff(81,plain,
% 4.23/4.43 (~((~(mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp)))))))),
% 4.23/4.43 inference(unit_resolution,[status(thm)],[80, 74])).
% 4.23/4.43 tff(82,plain,
% 4.23/4.43 (((~(mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | (~((~mighta(unp, thm)) | (~((~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), thm)) | (~status(tptp_fun_Ax_19(thm, unp), tptp_fun_C_18(thm, unp), unp))))))) | (mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))),
% 4.23/4.43 inference(tautology,[status(thm)],[])).
% 4.23/4.43 tff(83,plain,
% 4.23/4.43 (mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp)))),
% 4.23/4.43 inference(unit_resolution,[status(thm)],[82, 81])).
% 4.23/4.43 tff(84,plain,
% 4.23/4.43 ((~mighta(unp, thm)) <=> (~mighta(unp, thm))),
% 4.23/4.43 inference(rewrite,[status(thm)],[])).
% 4.23/4.43 tff(85,axiom,(~mighta(unp, thm)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mighta_unp_thm')).
% 4.23/4.43 tff(86,plain,
% 4.23/4.43 (~mighta(unp, thm)),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 4.23/4.43 tff(87,plain,
% 4.23/4.43 ((~(mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp)))),
% 4.23/4.43 inference(tautology,[status(thm)],[])).
% 4.23/4.43 tff(88,plain,
% 4.23/4.43 ((~(mighta(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp)))),
% 4.23/4.43 inference(unit_resolution,[status(thm)],[87, 86])).
% 4.23/4.43 tff(89,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp)))),
% 4.23/4.43 inference(unit_resolution,[status(thm)],[88, 83])).
% 4.23/4.43 tff(90,plain,
% 4.23/4.43 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp)))) | ((~status(Ax!34, Ax!34, thm)) | (~status(Ax!34, Ax!34, unp)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp)))) | (~status(Ax!34, Ax!34, thm)) | (~status(Ax!34, Ax!34, unp)))),
% 4.23/4.43 inference(rewrite,[status(thm)],[])).
% 4.23/4.43 tff(91,plain,
% 4.23/4.43 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp)))) | ((~status(Ax!34, Ax!34, thm)) | (~status(Ax!34, Ax!34, unp)))),
% 4.23/4.43 inference(quant_inst,[status(thm)],[])).
% 4.23/4.43 tff(92,plain,
% 4.23/4.43 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, unp)))) | (~status(Ax!34, Ax!34, thm)) | (~status(Ax!34, Ax!34, unp))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 4.23/4.43 tff(93,plain,
% 4.23/4.43 (~status(Ax!34, Ax!34, unp)),
% 4.23/4.43 inference(unit_resolution,[status(thm)],[92, 89, 58])).
% 4.23/4.43 tff(94,plain,
% 4.23/4.43 ((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))) | (~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp)),
% 4.23/4.43 inference(tautology,[status(thm)],[])).
% 4.23/4.43 tff(95,plain,
% 4.23/4.43 (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))),
% 4.23/4.43 inference(unit_resolution,[status(thm)],[94, 93, 12])).
% 4.23/4.43 tff(96,plain,
% 4.23/4.43 (((~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)))) | (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp)))) | ((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))),
% 4.23/4.43 inference(tautology,[status(thm)],[])).
% 4.23/4.43 tff(97,plain,
% 4.23/4.43 ((~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)))) | (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp)))),
% 4.23/4.43 inference(unit_resolution,[status(thm)],[96, 95])).
% 4.23/4.43 tff(98,plain,
% 4.23/4.43 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C)))))))),
% 4.23/4.43 inference(bind,[status(th)],[])).
% 4.23/4.43 tff(99,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 4.23/4.43 inference(quant_intro,[status(thm)],[98])).
% 4.23/4.43 tff(100,plain,
% 4.23/4.43 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 4.23/4.43 inference(bind,[status(th)],[])).
% 4.23/4.43 tff(101,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 4.23/4.43 inference(quant_intro,[status(thm)],[100])).
% 4.23/4.43 tff(102,plain,
% 4.23/4.43 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 4.23/4.43 inference(bind,[status(th)],[])).
% 4.23/4.43 tff(103,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 4.23/4.43 inference(quant_intro,[status(thm)],[102])).
% 4.23/4.43 tff(104,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 4.23/4.43 inference(transitivity,[status(thm)],[103, 101])).
% 4.23/4.43 tff(105,plain,
% 4.23/4.43 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite(((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) <=> ((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))), rewrite((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))) <=> (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))), rewrite((((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))))),
% 4.23/4.43 inference(bind,[status(th)],[])).
% 4.23/4.43 tff(106,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 4.23/4.43 inference(quant_intro,[status(thm)],[105])).
% 4.23/4.43 tff(107,plain,
% 4.23/4.43 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))),
% 4.23/4.43 inference(bind,[status(th)],[])).
% 4.23/4.43 tff(108,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 4.23/4.43 inference(quant_intro,[status(thm)],[107])).
% 4.23/4.43 tff(109,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 4.23/4.43 inference(rewrite,[status(thm)],[])).
% 4.23/4.43 tff(110,plain,
% 4.23/4.43 (^[Ax: $i, C: $i] : rewrite((((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)))),
% 4.23/4.43 inference(bind,[status(th)],[])).
% 4.23/4.43 tff(111,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 4.23/4.43 inference(quant_intro,[status(thm)],[110])).
% 4.23/4.43 tff(112,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp))), file('/export/starexec/sandbox2/benchmark/Axioms/KRS001+0.ax','unp')).
% 4.23/4.43 tff(113,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 4.23/4.43 tff(114,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[113, 109])).
% 4.23/4.43 tff(115,plain,(
% 4.23/4.43 ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp))))),
% 4.23/4.43 inference(skolemize,[status(sab)],[114])).
% 4.23/4.43 tff(116,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[115, 108])).
% 4.23/4.43 tff(117,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[116, 106])).
% 4.23/4.43 tff(118,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[117, 104])).
% 4.23/4.43 tff(119,plain,
% 4.23/4.43 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[118, 99])).
% 4.23/4.43 tff(120,plain,
% 4.23/4.43 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)))) | (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)))) | (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))))))),
% 4.23/4.43 inference(rewrite,[status(thm)],[])).
% 4.23/4.43 tff(121,plain,
% 4.23/4.43 ((~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)) | ![I2: $i] : (~model(I2, Ax!34)))))) <=> (~((~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)))) | (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp)))))),
% 4.23/4.43 inference(rewrite,[status(thm)],[])).
% 4.23/4.43 tff(122,plain,
% 4.23/4.43 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)) | ![I2: $i] : (~model(I2, Ax!34))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)))) | (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))))))),
% 4.23/4.43 inference(monotonicity,[status(thm)],[121])).
% 4.23/4.43 tff(123,plain,
% 4.23/4.43 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)) | ![I2: $i] : (~model(I2, Ax!34))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)))) | (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))))))),
% 4.23/4.43 inference(transitivity,[status(thm)],[122, 120])).
% 4.23/4.43 tff(124,plain,
% 4.23/4.43 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp))) | (~(model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)) | ![I2: $i] : (~model(I2, Ax!34))))))),
% 4.23/4.43 inference(quant_inst,[status(thm)],[])).
% 4.23/4.43 tff(125,plain,
% 4.23/4.43 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~(![I2: $i] : (~model(I2, Ax!34)) | model(tptp_fun_I1_0(Ax!34), Ax!34) | (~status(Ax!34, Ax!34, unp)))) | (~((~((~model(tptp_fun_I2_1(Ax!34), Ax!34)) | (~![I1: $i] : (~model(I1, Ax!34))))) | status(Ax!34, Ax!34, unp)))))),
% 4.23/4.43 inference(modus_ponens,[status(thm)],[124, 123])).
% 4.23/4.43 tff(126,plain,
% 4.23/4.43 ($false),
% 4.23/4.43 inference(unit_resolution,[status(thm)],[125, 119, 97])).
% 4.23/4.43 % SZS output end Proof
% 4.28/4.44 % E exiting
%------------------------------------------------------------------------------