TSTP Solution File: KRS200+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS200+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 Sep 17 17:45:11 EDT 2022
% Result : Theorem 1.49s 1.20s
% Output : Proof 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KRS200+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n016.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Sep 1 10:10:04 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.33 Usage: tptp [options] [-file:]file
% 0.10/0.33 -h, -? prints this message.
% 0.10/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.33 -m, -model generate model.
% 0.10/0.33 -p, -proof generate proof.
% 0.10/0.33 -c, -core generate unsat core of named formulas.
% 0.10/0.33 -st, -statistics display statistics.
% 0.10/0.33 -t:timeout set timeout (in second).
% 0.10/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.33 -<param>:<value> configuration parameter and value.
% 0.10/0.33 -o:<output-file> file to place output in.
% 1.49/1.20 % SZS status Theorem
% 1.49/1.20 % SZS output start Proof
% 1.49/1.20 tff(model_type, type, (
% 1.49/1.20 model: ( $i * $i ) > $o)).
% 1.49/1.20 tff(not_type, type, (
% 1.49/1.20 not: $i > $i)).
% 1.49/1.20 tff(tptp_fun_C_33_type, type, (
% 1.49/1.20 tptp_fun_C_33: $i)).
% 1.49/1.20 tff(tptp_fun_I1_0_type, type, (
% 1.49/1.20 tptp_fun_I1_0: $i > $i)).
% 1.49/1.20 tff(tptp_fun_Ax_25_type, type, (
% 1.49/1.20 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 1.49/1.20 tff(unp_type, type, (
% 1.49/1.20 unp: $i)).
% 1.49/1.20 tff(status_type, type, (
% 1.49/1.20 status: ( $i * $i * $i ) > $o)).
% 1.49/1.20 tff(thm_type, type, (
% 1.49/1.20 thm: $i)).
% 1.49/1.20 tff(tptp_fun_I1_3_type, type, (
% 1.49/1.20 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 1.49/1.20 tff(tptp_fun_I2_1_type, type, (
% 1.49/1.20 tptp_fun_I2_1: $i > $i)).
% 1.49/1.20 tff(tptp_fun_F_28_type, type, (
% 1.49/1.20 tptp_fun_F_28: $i)).
% 1.49/1.20 tff(tptp_fun_I2_31_type, type, (
% 1.49/1.20 tptp_fun_I2_31: $i)).
% 1.49/1.20 tff(nota_type, type, (
% 1.49/1.20 nota: ( $i * $i ) > $o)).
% 1.49/1.20 tff(tptp_fun_C_22_type, type, (
% 1.49/1.20 tptp_fun_C_22: ( $i * $i ) > $i)).
% 1.49/1.20 tff(tptp_fun_Ax_23_type, type, (
% 1.49/1.20 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 1.49/1.20 tff(tptp_fun_Ax_43_type, type, (
% 1.49/1.20 tptp_fun_Ax_43: $i)).
% 1.49/1.20 tff(tptp_fun_I1_35_type, type, (
% 1.49/1.20 tptp_fun_I1_35: $i)).
% 1.49/1.20 tff(tptp_fun_I2_36_type, type, (
% 1.49/1.20 tptp_fun_I2_36: $i)).
% 1.49/1.20 tff(tptp_fun_Ax_34_type, type, (
% 1.49/1.20 tptp_fun_Ax_34: $i)).
% 1.49/1.20 tff(tptp_fun_I1_44_type, type, (
% 1.49/1.20 tptp_fun_I1_44: $i)).
% 1.49/1.20 tff(tptp_fun_C_42_type, type, (
% 1.49/1.20 tptp_fun_C_42: $i)).
% 1.49/1.20 tff(tptp_fun_I2_45_type, type, (
% 1.49/1.20 tptp_fun_I2_45: $i)).
% 1.49/1.20 tff(1,plain,
% 1.49/1.20 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C)))))))),
% 1.49/1.20 inference(bind,[status(th)],[])).
% 1.49/1.20 tff(2,plain,
% 1.49/1.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 1.49/1.20 inference(quant_intro,[status(thm)],[1])).
% 1.49/1.20 tff(3,plain,
% 1.49/1.20 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 1.49/1.20 inference(bind,[status(th)],[])).
% 1.49/1.20 tff(4,plain,
% 1.49/1.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.49/1.20 inference(quant_intro,[status(thm)],[3])).
% 1.49/1.20 tff(5,plain,
% 1.49/1.20 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))))),
% 1.49/1.20 inference(bind,[status(th)],[])).
% 1.49/1.20 tff(6,plain,
% 1.49/1.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.49/1.20 inference(quant_intro,[status(thm)],[5])).
% 1.49/1.20 tff(7,plain,
% 1.49/1.20 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.49/1.21 inference(transitivity,[status(thm)],[6, 4])).
% 1.49/1.21 tff(8,plain,
% 1.49/1.21 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))))), rewrite((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))), ((((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))))),
% 1.49/1.21 inference(bind,[status(th)],[])).
% 1.49/1.21 tff(9,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.49/1.21 inference(quant_intro,[status(thm)],[8])).
% 1.49/1.21 tff(10,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.49/1.21 inference(rewrite,[status(thm)],[])).
% 1.49/1.21 tff(11,plain,
% 1.49/1.21 (^[Ax: $i, C: $i] : rewrite((![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm)))),
% 1.49/1.21 inference(bind,[status(th)],[])).
% 1.49/1.21 tff(12,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm)) <=> ![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.49/1.21 inference(quant_intro,[status(thm)],[11])).
% 1.49/1.21 tff(13,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','thm')).
% 1.49/1.21 tff(14,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.49/1.21 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.49/1.21 tff(15,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.49/1.21 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.49/1.21 tff(16,plain,(
% 1.49/1.21 ![Ax: $i, C: $i] : (((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm)) & (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))),
% 1.49/1.21 inference(skolemize,[status(sab)],[15])).
% 1.49/1.21 tff(17,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.49/1.21 inference(modus_ponens,[status(thm)],[16, 9])).
% 1.49/1.21 tff(18,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~(![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) | (~status(Ax, C, thm))))))),
% 1.49/1.21 inference(modus_ponens,[status(thm)],[17, 7])).
% 1.49/1.21 tff(19,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))),
% 1.49/1.21 inference(modus_ponens,[status(thm)],[18, 2])).
% 1.49/1.21 tff(20,plain,
% 1.49/1.21 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(not(C!33), tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_3(not(C!33), tptp_fun_Ax_25(unp, unp)), not(C!33)))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), thm))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))))))),
% 1.49/1.21 inference(quant_inst,[status(thm)],[])).
% 1.49/1.21 tff(21,plain,
% 1.49/1.21 (~((~((~((~model(tptp_fun_I1_3(not(C!33), tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_3(not(C!33), tptp_fun_Ax_25(unp, unp)), not(C!33)))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), thm))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33))))))),
% 1.49/1.21 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.49/1.21 tff(22,plain,
% 1.49/1.21 (((~((~((~model(tptp_fun_I1_3(not(C!33), tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_3(not(C!33), tptp_fun_Ax_25(unp, unp)), not(C!33)))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), thm))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))))) | ((~status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33))))),
% 1.49/1.21 inference(tautology,[status(thm)],[])).
% 1.49/1.21 tff(23,plain,
% 1.49/1.21 ((~status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))),
% 1.49/1.21 inference(unit_resolution,[status(thm)],[22, 21])).
% 1.49/1.21 tff(24,plain,
% 1.49/1.21 ((~![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_Ax_25(unp, unp), F!28), F!28)) | model(tptp_fun_I1_3(tptp_fun_Ax_25(unp, unp), F!28), tptp_fun_Ax_25(unp, unp)))) | status(F!28, tptp_fun_Ax_25(unp, unp), thm))) | (~((~status(F!28, tptp_fun_Ax_25(unp, unp), thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))))))),
% 1.49/1.21 inference(quant_inst,[status(thm)],[])).
% 1.49/1.21 tff(25,plain,
% 1.49/1.21 (~((~((~((~model(tptp_fun_I1_3(tptp_fun_Ax_25(unp, unp), F!28), F!28)) | model(tptp_fun_I1_3(tptp_fun_Ax_25(unp, unp), F!28), tptp_fun_Ax_25(unp, unp)))) | status(F!28, tptp_fun_Ax_25(unp, unp), thm))) | (~((~status(F!28, tptp_fun_Ax_25(unp, unp), thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp))))))),
% 1.49/1.21 inference(unit_resolution,[status(thm)],[24, 19])).
% 1.49/1.21 tff(26,plain,
% 1.49/1.21 (((~((~((~model(tptp_fun_I1_3(tptp_fun_Ax_25(unp, unp), F!28), F!28)) | model(tptp_fun_I1_3(tptp_fun_Ax_25(unp, unp), F!28), tptp_fun_Ax_25(unp, unp)))) | status(F!28, tptp_fun_Ax_25(unp, unp), thm))) | (~((~status(F!28, tptp_fun_Ax_25(unp, unp), thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))))) | ((~status(F!28, tptp_fun_Ax_25(unp, unp), thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp))))),
% 1.49/1.21 inference(tautology,[status(thm)],[])).
% 1.49/1.21 tff(27,plain,
% 1.49/1.21 ((~status(F!28, tptp_fun_Ax_25(unp, unp), thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))),
% 1.49/1.21 inference(unit_resolution,[status(thm)],[26, 25])).
% 1.49/1.21 tff(28,assumption,(~status(F!28, tptp_fun_Ax_25(unp, unp), thm)), introduced(assumption)).
% 1.49/1.21 tff(29,assumption,((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp)))), introduced(assumption)).
% 1.49/1.21 tff(30,plain,
% 1.49/1.21 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C)))))))),
% 1.49/1.21 inference(bind,[status(th)],[])).
% 1.49/1.21 tff(31,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 1.49/1.21 inference(quant_intro,[status(thm)],[30])).
% 1.49/1.21 tff(32,plain,
% 1.49/1.21 (^[Ax: $i, C: $i] : refl((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 1.49/1.21 inference(bind,[status(th)],[])).
% 1.49/1.21 tff(33,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.49/1.21 inference(quant_intro,[status(thm)],[32])).
% 1.49/1.21 tff(34,plain,
% 1.49/1.21 (^[Ax: $i, C: $i] : rewrite((~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))))),
% 1.49/1.21 inference(bind,[status(th)],[])).
% 1.49/1.21 tff(35,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.49/1.21 inference(quant_intro,[status(thm)],[34])).
% 1.49/1.21 tff(36,plain,
% 1.49/1.21 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.49/1.21 inference(transitivity,[status(thm)],[35, 33])).
% 1.49/1.21 tff(37,plain,
% 1.49/1.21 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite(((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) <=> ((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))), rewrite((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))) <=> (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))), rewrite((((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))), ((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))))),
% 1.49/1.22 inference(bind,[status(th)],[])).
% 1.49/1.22 tff(38,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.49/1.22 inference(quant_intro,[status(thm)],[37])).
% 1.49/1.22 tff(39,plain,
% 1.49/1.22 (^[Ax: $i, C: $i] : rewrite((((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)))))),
% 1.49/1.22 inference(bind,[status(th)],[])).
% 1.49/1.22 tff(40,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp)))) <=> ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 1.49/1.22 inference(quant_intro,[status(thm)],[39])).
% 1.49/1.22 tff(41,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 1.49/1.22 inference(rewrite,[status(thm)],[])).
% 1.49/1.22 tff(42,plain,
% 1.49/1.22 (^[Ax: $i, C: $i] : rewrite((((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp)))),
% 1.49/1.22 inference(bind,[status(th)],[])).
% 1.49/1.22 tff(43,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp)) <=> ![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 1.49/1.22 inference(quant_intro,[status(thm)],[42])).
% 1.49/1.22 tff(44,axiom,(![Ax: $i, C: $i] : (((~?[I1: $i] : model(I1, Ax)) => (~?[I2: $i] : model(I2, C))) <=> status(Ax, C, unp))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','unp')).
% 1.49/1.22 tff(45,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 1.49/1.22 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.49/1.22 tff(46,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (((~?[I2: $i] : model(I2, C)) | ?[I1: $i] : model(I1, Ax)) <=> status(Ax, C, unp))),
% 1.49/1.22 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.49/1.22 tff(47,plain,(
% 1.49/1.22 ![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & ((![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax)) | (~status(Ax, C, unp))))),
% 1.49/1.22 inference(skolemize,[status(sab)],[46])).
% 1.49/1.22 tff(48,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (((model(tptp_fun_I2_1(C), C) & ![I1: $i] : (~model(I1, Ax))) | status(Ax, C, unp)) & (![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))),
% 1.49/1.22 inference(modus_ponens,[status(thm)],[47, 40])).
% 1.49/1.22 tff(49,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.49/1.22 inference(modus_ponens,[status(thm)],[48, 38])).
% 1.49/1.22 tff(50,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(![I2: $i] : (~model(I2, C)) | model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp))))))),
% 1.49/1.22 inference(modus_ponens,[status(thm)],[49, 36])).
% 1.49/1.22 tff(51,plain,
% 1.49/1.22 (![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))),
% 1.49/1.22 inference(modus_ponens,[status(thm)],[50, 31])).
% 1.49/1.22 tff(52,plain,
% 1.49/1.22 (((~![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))))))) | (~((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), 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))))))) | (~((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))))))),
% 1.49/1.22 inference(rewrite,[status(thm)],[])).
% 1.49/1.22 tff(53,plain,
% 1.49/1.22 ((~((~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))) | (~(model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))))))) <=> (~((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp)))))),
% 1.49/1.22 inference(rewrite,[status(thm)],[])).
% 1.49/1.22 tff(54,plain,
% 1.49/1.22 (((~![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(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))) | (~(model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, 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))))))) | (~((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))))))),
% 1.49/1.22 inference(monotonicity,[status(thm)],[53])).
% 1.49/1.22 tff(55,plain,
% 1.49/1.22 (((~![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(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))) | (~(model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, 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))))))) | (~((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))))))),
% 1.49/1.22 inference(transitivity,[status(thm)],[54, 52])).
% 1.49/1.22 tff(56,plain,
% 1.49/1.22 ((~![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(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))) | (~(model(tptp_fun_I1_0(F!28), F!28) | (~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp)))))))),
% 1.49/1.22 inference(quant_inst,[status(thm)],[])).
% 1.49/1.22 tff(57,plain,
% 1.49/1.22 ((~![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))))))) | (~((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp)))))),
% 1.49/1.22 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.49/1.22 tff(58,plain,
% 1.49/1.22 ($false),
% 1.49/1.22 inference(unit_resolution,[status(thm)],[57, 51, 29])).
% 1.49/1.22 tff(59,plain,(~((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.22 tff(60,plain,
% 1.49/1.22 (((~((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | ![I2: $i] : (~model(I2, tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(F!28), F!28))) | (~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp)))) | ((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))),
% 1.49/1.22 inference(tautology,[status(thm)],[])).
% 1.49/1.22 tff(61,plain,
% 1.49/1.22 ((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp)),
% 1.49/1.22 inference(unit_resolution,[status(thm)],[60, 59])).
% 1.49/1.22 tff(62,assumption,(![I1: $i] : (~model(I1, F!28))), introduced(assumption)).
% 1.49/1.22 tff(63,plain,
% 1.49/1.22 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 1.49/1.22 inference(bind,[status(th)],[])).
% 1.49/1.22 tff(64,plain,
% 1.49/1.22 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 1.49/1.22 inference(quant_intro,[status(thm)],[63])).
% 1.49/1.22 tff(65,plain,
% 1.49/1.22 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 1.49/1.22 inference(rewrite,[status(thm)],[])).
% 1.49/1.23 tff(66,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','tautology')).
% 1.49/1.23 tff(67,plain,
% 1.49/1.23 (?[F: $i] : ![I: $i] : model(I, F)),
% 1.49/1.23 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.49/1.23 tff(68,plain,(
% 1.49/1.23 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 1.49/1.23 inference(transitivity,[status(sab)],[67])).
% 1.49/1.23 tff(69,plain,
% 1.49/1.23 (![I: $i] : model(I, F!28)),
% 1.49/1.23 inference(modus_ponens,[status(thm)],[68, 64])).
% 1.49/1.23 tff(70,plain,
% 1.49/1.23 ((~![I: $i] : model(I, F!28)) | model(I2!31, F!28)),
% 1.49/1.23 inference(quant_inst,[status(thm)],[])).
% 1.49/1.23 tff(71,plain,
% 1.49/1.23 (model(I2!31, F!28)),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.49/1.23 tff(72,plain,
% 1.49/1.23 ((~![I1: $i] : (~model(I1, F!28))) | (~model(I2!31, F!28))),
% 1.49/1.23 inference(quant_inst,[status(thm)],[])).
% 1.49/1.23 tff(73,plain,
% 1.49/1.23 ($false),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[72, 71, 62])).
% 1.49/1.23 tff(74,plain,(~![I1: $i] : (~model(I1, F!28))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.23 tff(75,plain,
% 1.49/1.23 (((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28)))) | ![I1: $i] : (~model(I1, F!28))),
% 1.49/1.23 inference(tautology,[status(thm)],[])).
% 1.49/1.23 tff(76,plain,
% 1.49/1.23 ((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28)))),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.49/1.23 tff(77,plain,
% 1.49/1.23 ((~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))) | (~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp)),
% 1.49/1.23 inference(tautology,[status(thm)],[])).
% 1.49/1.23 tff(78,plain,
% 1.49/1.23 ((~((~((~model(tptp_fun_I2_1(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))) | (~![I1: $i] : (~model(I1, F!28))))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp))) | status(F!28, tptp_fun_Ax_25(unp, unp), unp)),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[77, 76])).
% 1.49/1.23 tff(79,plain,
% 1.49/1.23 (status(F!28, tptp_fun_Ax_25(unp, unp), unp)),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[78, 61])).
% 1.49/1.23 tff(80,plain,
% 1.49/1.23 (^[S1: $i, S2: $i] : refl((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 1.49/1.23 inference(bind,[status(th)],[])).
% 1.49/1.23 tff(81,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.49/1.23 inference(quant_intro,[status(thm)],[80])).
% 1.49/1.23 tff(82,plain,
% 1.49/1.23 (^[S1: $i, S2: $i] : rewrite((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 1.49/1.23 inference(bind,[status(th)],[])).
% 1.49/1.23 tff(83,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.49/1.23 inference(quant_intro,[status(thm)],[82])).
% 1.49/1.23 tff(84,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.49/1.23 inference(transitivity,[status(thm)],[83, 81])).
% 1.49/1.23 tff(85,plain,
% 1.49/1.23 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) <=> (nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))), trans(monotonicity(rewrite((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) <=> (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))), rewrite(((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))))),
% 1.49/1.23 inference(bind,[status(th)],[])).
% 1.49/1.23 tff(86,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.49/1.23 inference(quant_intro,[status(thm)],[85])).
% 1.49/1.23 tff(87,plain,
% 1.49/1.23 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))))),
% 1.49/1.23 inference(bind,[status(th)],[])).
% 1.49/1.23 tff(88,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 1.49/1.23 inference(quant_intro,[status(thm)],[87])).
% 1.49/1.23 tff(89,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 1.49/1.23 inference(rewrite,[status(thm)],[])).
% 1.49/1.23 tff(90,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','nota')).
% 1.49/1.23 tff(91,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 1.49/1.23 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.49/1.23 tff(92,plain,(
% 1.49/1.23 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 1.49/1.23 inference(skolemize,[status(sab)],[91])).
% 1.49/1.23 tff(93,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 1.49/1.23 inference(modus_ponens,[status(thm)],[92, 88])).
% 1.49/1.23 tff(94,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.49/1.23 inference(modus_ponens,[status(thm)],[93, 86])).
% 1.49/1.23 tff(95,plain,
% 1.49/1.23 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 1.49/1.23 inference(modus_ponens,[status(thm)],[94, 84])).
% 1.49/1.23 tff(96,plain,
% 1.49/1.23 ((~![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))) | (~((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | (~((~nota(unp, thm)) | (~((~status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), unp)) | status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), thm)))))))),
% 1.49/1.23 inference(quant_inst,[status(thm)],[])).
% 1.49/1.23 tff(97,plain,
% 1.49/1.23 (~((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | (~((~nota(unp, thm)) | (~((~status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), unp)) | status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), thm))))))),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[96, 95])).
% 1.49/1.23 tff(98,plain,
% 1.49/1.23 (((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | (~((~nota(unp, thm)) | (~((~status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), unp)) | status(tptp_fun_Ax_23(thm, unp), tptp_fun_C_22(thm, unp), thm)))))) | (nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))),
% 1.49/1.23 inference(tautology,[status(thm)],[])).
% 1.49/1.23 tff(99,plain,
% 1.49/1.23 (nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[98, 97])).
% 1.49/1.23 tff(100,plain,
% 1.49/1.23 ((~nota(unp, thm)) <=> (~nota(unp, thm))),
% 1.49/1.23 inference(rewrite,[status(thm)],[])).
% 1.49/1.23 tff(101,axiom,(~nota(unp, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nota_unp_thm')).
% 1.49/1.23 tff(102,plain,
% 1.49/1.23 (~nota(unp, thm)),
% 1.49/1.23 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.49/1.23 tff(103,plain,
% 1.49/1.23 ((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))),
% 1.49/1.23 inference(tautology,[status(thm)],[])).
% 1.49/1.23 tff(104,plain,
% 1.49/1.23 ((~(nota(unp, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[103, 102])).
% 1.49/1.23 tff(105,plain,
% 1.49/1.23 (![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[104, 99])).
% 1.49/1.23 tff(106,plain,
% 1.49/1.23 (((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | ((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | status(F!28, tptp_fun_Ax_25(unp, unp), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | (~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | status(F!28, tptp_fun_Ax_25(unp, unp), thm))),
% 1.49/1.23 inference(rewrite,[status(thm)],[])).
% 1.49/1.23 tff(107,plain,
% 1.49/1.23 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | ((~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | status(F!28, tptp_fun_Ax_25(unp, unp), thm))),
% 1.49/1.23 inference(quant_inst,[status(thm)],[])).
% 1.49/1.23 tff(108,plain,
% 1.49/1.23 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | (~status(F!28, tptp_fun_Ax_25(unp, unp), unp)) | status(F!28, tptp_fun_Ax_25(unp, unp), thm)),
% 1.49/1.23 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.49/1.23 tff(109,plain,
% 1.49/1.23 ($false),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[108, 105, 79, 28])).
% 1.49/1.23 tff(110,plain,(status(F!28, tptp_fun_Ax_25(unp, unp), thm)), inference(lemma,lemma(discharge,[]))).
% 1.49/1.23 tff(111,plain,
% 1.49/1.23 ((~((~status(F!28, tptp_fun_Ax_25(unp, unp), thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp))))) | (~status(F!28, tptp_fun_Ax_25(unp, unp), thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))),
% 1.49/1.23 inference(tautology,[status(thm)],[])).
% 1.49/1.23 tff(112,plain,
% 1.49/1.23 ((~((~status(F!28, tptp_fun_Ax_25(unp, unp), thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp))))) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[111, 110])).
% 1.49/1.23 tff(113,plain,
% 1.49/1.23 (![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[112, 27])).
% 1.49/1.23 tff(114,plain,
% 1.49/1.23 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I1_0(C!33), F!28)),
% 1.49/1.23 inference(quant_inst,[status(thm)],[])).
% 1.49/1.23 tff(115,plain,
% 1.49/1.23 (model(tptp_fun_I1_0(C!33), F!28)),
% 1.49/1.23 inference(unit_resolution,[status(thm)],[114, 69])).
% 1.49/1.23 tff(116,plain,
% 1.49/1.23 (((~![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))) | ((~model(tptp_fun_I1_0(C!33), F!28)) | model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp)))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))) | (~model(tptp_fun_I1_0(C!33), F!28)) | model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp)))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(117,plain,
% 1.59/1.24 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))) | ((~model(tptp_fun_I1_0(C!33), F!28)) | model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp)))),
% 1.59/1.24 inference(quant_inst,[status(thm)],[])).
% 1.59/1.24 tff(118,plain,
% 1.59/1.24 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, tptp_fun_Ax_25(unp, unp)))) | (~model(tptp_fun_I1_0(C!33), F!28)) | model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp))),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.59/1.24 tff(119,plain,
% 1.59/1.24 (model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[118, 115, 113])).
% 1.59/1.24 tff(120,assumption,(![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))), introduced(assumption)).
% 1.59/1.24 tff(121,plain,
% 1.59/1.24 ((~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))) | (~model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp)))),
% 1.59/1.24 inference(quant_inst,[status(thm)],[])).
% 1.59/1.24 tff(122,plain,
% 1.59/1.24 ($false),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[121, 120, 119])).
% 1.59/1.24 tff(123,plain,(~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.24 tff(124,plain,
% 1.59/1.24 (((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp))))) | ![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(125,plain,
% 1.59/1.24 ((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp))))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[124, 123])).
% 1.59/1.24 tff(126,plain,
% 1.59/1.24 (((~![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(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))) | model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))) | model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp)))))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(127,plain,
% 1.59/1.24 ((~((~((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~(model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp)) | (~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))))))) <=> (~((~((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))) | model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(128,plain,
% 1.59/1.24 (((~![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(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~(model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp)) | (~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33)))))))) <=> ((~![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(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))) | model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp)))))))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[127])).
% 1.59/1.24 tff(129,plain,
% 1.59/1.24 (((~![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(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~(model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp)) | (~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33)))))))) <=> ((~![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(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))) | model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp)))))))),
% 1.59/1.24 inference(transitivity,[status(thm)],[128, 126])).
% 1.59/1.24 tff(130,plain,
% 1.59/1.24 ((~![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(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~(model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp)) | (~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33)))))))),
% 1.59/1.24 inference(quant_inst,[status(thm)],[])).
% 1.59/1.24 tff(131,plain,
% 1.59/1.24 ((~![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(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))) | model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))))))),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[130, 129])).
% 1.59/1.24 tff(132,plain,
% 1.59/1.24 (~((~((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))) | model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp)))))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[131, 51])).
% 1.59/1.24 tff(133,plain,
% 1.59/1.24 (((~((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | ![I2: $i] : (~model(I2, not(C!33))) | model(tptp_fun_I1_0(tptp_fun_Ax_25(unp, unp)), tptp_fun_Ax_25(unp, unp))))) | ((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(134,plain,
% 1.59/1.24 ((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[133, 132])).
% 1.59/1.24 tff(135,plain,
% 1.59/1.24 ((~((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp))) | (~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(136,plain,
% 1.59/1.24 ((~((~model(tptp_fun_I2_1(not(C!33)), not(C!33))) | (~![I1: $i] : (~model(I1, tptp_fun_Ax_25(unp, unp)))))) | status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[135, 134])).
% 1.59/1.24 tff(137,plain,
% 1.59/1.24 (status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[136, 125])).
% 1.59/1.24 tff(138,plain,
% 1.59/1.24 (((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | status(tptp_fun_Ax_25(unp, unp), not(C!33), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | status(tptp_fun_Ax_25(unp, unp), not(C!33), thm))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(139,plain,
% 1.59/1.24 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | status(tptp_fun_Ax_25(unp, unp), not(C!33), thm))),
% 1.59/1.24 inference(quant_inst,[status(thm)],[])).
% 1.59/1.24 tff(140,plain,
% 1.59/1.24 ((~![Ax: $i, C: $i] : ((~status(Ax, C, unp)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(unp, unp), not(C!33), unp)) | status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.59/1.24 tff(141,plain,
% 1.59/1.24 (status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[140, 105, 137])).
% 1.59/1.24 tff(142,plain,
% 1.59/1.24 ((~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33))))) | (~status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(143,plain,
% 1.59/1.24 ((~((~status(tptp_fun_Ax_25(unp, unp), not(C!33), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33))))) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[142, 141])).
% 1.59/1.24 tff(144,plain,
% 1.59/1.24 (![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[143, 23])).
% 1.59/1.24 tff(145,plain,
% 1.59/1.24 (((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))) | ((~model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(C!33), not(C!33)))) <=> ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))) | (~model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(C!33), not(C!33)))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(146,plain,
% 1.59/1.24 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))) | ((~model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(C!33), not(C!33)))),
% 1.59/1.24 inference(quant_inst,[status(thm)],[])).
% 1.59/1.24 tff(147,plain,
% 1.59/1.24 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(unp, unp))) | model(I1, not(C!33)))) | (~model(tptp_fun_I1_0(C!33), tptp_fun_Ax_25(unp, unp))) | model(tptp_fun_I1_0(C!33), not(C!33))),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[146, 145])).
% 1.59/1.24 tff(148,plain,
% 1.59/1.24 (model(tptp_fun_I1_0(C!33), not(C!33))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[147, 119, 144])).
% 1.59/1.24 tff(149,assumption,((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp))))), introduced(assumption)).
% 1.59/1.24 tff(150,plain,
% 1.59/1.24 (((~![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!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I2_1(C), C)) | (~![I1: $i] : (~model(I1, Ax))))) | status(Ax, C, unp))) | (~(model(tptp_fun_I1_0(Ax), Ax) | (~status(Ax, C, unp)) | ![I2: $i] : (~model(I2, C))))))) | (~((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp)))))))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(151,plain,
% 1.59/1.25 ((~((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, Ax!43, unp)) | ![I2: $i] : (~model(I2, Ax!43)))))) <=> (~((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp))))))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(152,plain,
% 1.59/1.25 (((~![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!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, Ax!43, unp)) | ![I2: $i] : (~model(I2, Ax!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!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp)))))))),
% 1.59/1.25 inference(monotonicity,[status(thm)],[151])).
% 1.59/1.25 tff(153,plain,
% 1.59/1.25 (((~![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!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, Ax!43, unp)) | ![I2: $i] : (~model(I2, Ax!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!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp)))))))),
% 1.59/1.25 inference(transitivity,[status(thm)],[152, 150])).
% 1.59/1.25 tff(154,plain,
% 1.59/1.25 ((~![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!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, Ax!43, unp)) | ![I2: $i] : (~model(I2, Ax!43))))))),
% 1.59/1.25 inference(quant_inst,[status(thm)],[])).
% 1.59/1.25 tff(155,plain,
% 1.59/1.25 ((~![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!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp))))))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.59/1.25 tff(156,plain,
% 1.59/1.25 ($false),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[155, 51, 149])).
% 1.59/1.25 tff(157,plain,(~((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp)))))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.25 tff(158,plain,
% 1.59/1.25 (((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp))))) | (model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp)))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(159,plain,
% 1.59/1.25 (model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[158, 157])).
% 1.59/1.25 tff(160,plain,
% 1.59/1.25 (((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp))))) | ((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(161,plain,
% 1.59/1.25 ((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[160, 157])).
% 1.59/1.25 tff(162,assumption,(![I1: $i] : (~model(I1, C!33))), introduced(assumption)).
% 1.59/1.25 tff(163,plain,
% 1.59/1.25 (((model(I1!35, Ax!34) & model(I1!35, C!33)) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))) <=> (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33))))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(164,plain,
% 1.59/1.25 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C)))) <=> ?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(165,axiom,(?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','sat_non_taut_pair')).
% 1.59/1.25 tff(166,plain,
% 1.59/1.25 (?[Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) & ?[I2: $i] : ((~model(I2, Ax)) | (~model(I2, C))))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.59/1.25 tff(167,plain,
% 1.59/1.25 (model(I1!35, Ax!34) & model(I1!35, C!33) & ((~model(I2!36, Ax!34)) | (~model(I2!36, C!33)))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[166, 163])).
% 1.59/1.25 tff(168,plain,
% 1.59/1.25 (model(I1!35, C!33)),
% 1.59/1.25 inference(and_elim,[status(thm)],[167])).
% 1.59/1.25 tff(169,plain,
% 1.59/1.25 ((~![I1: $i] : (~model(I1, C!33))) | (~model(I1!35, C!33))),
% 1.59/1.25 inference(quant_inst,[status(thm)],[])).
% 1.59/1.25 tff(170,plain,
% 1.59/1.25 ($false),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[169, 168, 162])).
% 1.59/1.25 tff(171,plain,(~![I1: $i] : (~model(I1, C!33))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.25 tff(172,plain,
% 1.59/1.25 (((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33)))) | ![I1: $i] : (~model(I1, C!33))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(173,plain,
% 1.59/1.25 ((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33)))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[172, 171])).
% 1.59/1.25 tff(174,plain,
% 1.59/1.25 ((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | (~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp)),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(175,plain,
% 1.59/1.25 ((~((~((~model(tptp_fun_I2_1(Ax!43), Ax!43)) | (~![I1: $i] : (~model(I1, C!33))))) | status(C!33, Ax!43, unp))) | status(C!33, Ax!43, unp)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[174, 173])).
% 1.59/1.25 tff(176,plain,
% 1.59/1.25 (status(C!33, Ax!43, unp)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[175, 161])).
% 1.59/1.25 tff(177,assumption,(![I2: $i] : (~model(I2, Ax!43))), introduced(assumption)).
% 1.59/1.25 tff(178,plain,
% 1.59/1.25 (?[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))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(179,plain,
% 1.59/1.25 (^[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)))),
% 1.59/1.25 inference(bind,[status(th)],[])).
% 1.59/1.25 tff(180,plain,
% 1.59/1.25 (?[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))),
% 1.59/1.25 inference(quant_intro,[status(thm)],[179])).
% 1.59/1.25 tff(181,axiom,(?[I1: $i, Ax: $i, C: $i] : ((model(I1, Ax) & (~model(I1, C))) & ?[I2: $i] : model(I2, C))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','non_thm_spt')).
% 1.59/1.25 tff(182,plain,
% 1.59/1.25 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.59/1.25 tff(183,plain,
% 1.59/1.25 (?[I1: $i, Ax: $i, C: $i] : (model(I1, Ax) & (~model(I1, C)) & ?[I2: $i] : model(I2, C))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[182, 178])).
% 1.59/1.25 tff(184,plain,
% 1.59/1.25 (model(I1!44, Ax!43)),
% 1.59/1.25 inference(and_elim,[status(thm)],[183])).
% 1.59/1.25 tff(185,plain,
% 1.59/1.25 ((~![I2: $i] : (~model(I2, Ax!43))) | (~model(I1!44, Ax!43))),
% 1.59/1.25 inference(quant_inst,[status(thm)],[])).
% 1.59/1.25 tff(186,plain,
% 1.59/1.25 ($false),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[185, 184, 177])).
% 1.59/1.25 tff(187,plain,(~![I2: $i] : (~model(I2, Ax!43))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.25 tff(188,plain,
% 1.59/1.25 ((~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp)))) | model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(189,plain,
% 1.59/1.25 ((~(model(tptp_fun_I1_0(C!33), C!33) | ![I2: $i] : (~model(I2, Ax!43)) | (~status(C!33, Ax!43, unp)))) | model(tptp_fun_I1_0(C!33), C!33) | (~status(C!33, Ax!43, unp))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[188, 187])).
% 1.59/1.25 tff(190,plain,
% 1.59/1.25 (model(tptp_fun_I1_0(C!33), C!33)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[189, 176, 159])).
% 1.59/1.25 tff(191,plain,
% 1.59/1.25 ((~((~model(tptp_fun_I1_0(C!33), C!33)) <=> model(tptp_fun_I1_0(C!33), not(C!33)))) | (~model(tptp_fun_I1_0(C!33), C!33)) | (~model(tptp_fun_I1_0(C!33), not(C!33)))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(192,plain,
% 1.59/1.25 (~((~model(tptp_fun_I1_0(C!33), C!33)) <=> model(tptp_fun_I1_0(C!33), not(C!33)))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[191, 190, 148])).
% 1.59/1.25 tff(193,plain,
% 1.59/1.25 (^[I: $i, F: $i] : refl(((~model(I, F)) <=> model(I, not(F))) <=> ((~model(I, F)) <=> model(I, not(F))))),
% 1.59/1.25 inference(bind,[status(th)],[])).
% 1.59/1.25 tff(194,plain,
% 1.59/1.25 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 1.59/1.25 inference(quant_intro,[status(thm)],[193])).
% 1.59/1.25 tff(195,plain,
% 1.59/1.25 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(196,plain,
% 1.59/1.25 (^[I: $i, F: $i] : rewrite((~(model(I, F) <=> model(I, not(F)))) <=> ((~model(I, F)) <=> model(I, not(F))))),
% 1.59/1.25 inference(bind,[status(th)],[])).
% 1.59/1.25 tff(197,plain,
% 1.59/1.25 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 1.59/1.25 inference(quant_intro,[status(thm)],[196])).
% 1.59/1.25 tff(198,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','completeness')).
% 1.59/1.25 tff(199,plain,
% 1.59/1.25 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.59/1.25 tff(200,plain,
% 1.59/1.26 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[199, 195])).
% 1.59/1.26 tff(201,plain,(
% 1.59/1.26 ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 1.59/1.26 inference(skolemize,[status(sab)],[200])).
% 1.59/1.26 tff(202,plain,
% 1.59/1.26 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[201, 194])).
% 1.59/1.26 tff(203,plain,
% 1.59/1.26 ((~![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))) | ((~model(tptp_fun_I1_0(C!33), C!33)) <=> model(tptp_fun_I1_0(C!33), not(C!33)))),
% 1.59/1.26 inference(quant_inst,[status(thm)],[])).
% 1.59/1.26 tff(204,plain,
% 1.59/1.26 ($false),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[203, 202, 192])).
% 1.59/1.26 % SZS output end Proof
%------------------------------------------------------------------------------