TSTP Solution File: KRS202+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS202+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 7.79s 5.51s
% Output : Proof 7.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : KRS202+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n018.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Sep 1 09:52:42 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 7.79/5.51 % SZS status Theorem
% 7.79/5.51 % SZS output start Proof
% 7.79/5.51 tff(status_type, type, (
% 7.79/5.51 status: ( $i * $i * $i ) > $o)).
% 7.79/5.51 tff(esa_type, type, (
% 7.79/5.51 esa: $i)).
% 7.79/5.51 tff(tptp_fun_F_29_type, type, (
% 7.79/5.51 tptp_fun_F_29: $i)).
% 7.79/5.51 tff(tptp_fun_F_28_type, type, (
% 7.79/5.51 tptp_fun_F_28: $i)).
% 7.79/5.51 tff(model_type, type, (
% 7.79/5.51 model: ( $i * $i ) > $o)).
% 7.79/5.51 tff(tptp_fun_I2_1_type, type, (
% 7.79/5.51 tptp_fun_I2_1: $i > $i)).
% 7.79/5.51 tff(tptp_fun_I1_0_type, type, (
% 7.79/5.51 tptp_fun_I1_0: $i > $i)).
% 7.79/5.51 tff(tptp_fun_I2_31_type, type, (
% 7.79/5.51 tptp_fun_I2_31: $i)).
% 7.79/5.51 tff(tptp_fun_I1_30_type, type, (
% 7.79/5.51 tptp_fun_I1_30: $i)).
% 7.79/5.51 tff(thm_type, type, (
% 7.79/5.51 thm: $i)).
% 7.79/5.51 tff(tptp_fun_I1_3_type, type, (
% 7.79/5.51 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 7.79/5.51 tff(nota_type, type, (
% 7.79/5.51 nota: ( $i * $i ) > $o)).
% 7.79/5.51 tff(tptp_fun_C_22_type, type, (
% 7.79/5.51 tptp_fun_C_22: ( $i * $i ) > $i)).
% 7.79/5.51 tff(tptp_fun_Ax_23_type, type, (
% 7.79/5.51 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 7.79/5.51 tff(1,assumption,(![I1: $i] : (~model(I1, F!28))), introduced(assumption)).
% 7.79/5.51 tff(2,plain,
% 7.79/5.51 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 7.79/5.51 inference(bind,[status(th)],[])).
% 7.79/5.51 tff(3,plain,
% 7.79/5.51 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 7.79/5.51 inference(quant_intro,[status(thm)],[2])).
% 7.79/5.51 tff(4,plain,
% 7.79/5.51 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 7.79/5.51 inference(rewrite,[status(thm)],[])).
% 7.79/5.51 tff(5,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','tautology')).
% 7.79/5.51 tff(6,plain,
% 7.79/5.51 (?[F: $i] : ![I: $i] : model(I, F)),
% 7.79/5.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 7.79/5.51 tff(7,plain,(
% 7.79/5.51 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 7.79/5.51 inference(transitivity,[status(sab)],[6])).
% 7.79/5.51 tff(8,plain,
% 7.79/5.51 (![I: $i] : model(I, F!28)),
% 7.79/5.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 7.79/5.51 tff(9,plain,
% 7.79/5.51 ((~![I: $i] : model(I, F!28)) | model(I2!31, F!28)),
% 7.79/5.51 inference(quant_inst,[status(thm)],[])).
% 7.79/5.51 tff(10,plain,
% 7.79/5.51 (model(I2!31, F!28)),
% 7.79/5.51 inference(unit_resolution,[status(thm)],[9, 8])).
% 7.79/5.51 tff(11,plain,
% 7.79/5.51 ((~![I1: $i] : (~model(I1, F!28))) | (~model(I2!31, F!28))),
% 7.79/5.51 inference(quant_inst,[status(thm)],[])).
% 7.79/5.51 tff(12,plain,
% 7.79/5.51 ($false),
% 7.79/5.51 inference(unit_resolution,[status(thm)],[11, 10, 1])).
% 7.79/5.51 tff(13,plain,(~![I1: $i] : (~model(I1, F!28))), inference(lemma,lemma(discharge,[]))).
% 7.79/5.51 tff(14,assumption,(![I2: $i] : (~model(I2, F!29))), introduced(assumption)).
% 7.79/5.51 tff(15,plain,
% 7.79/5.51 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 7.79/5.51 inference(rewrite,[status(thm)],[])).
% 7.79/5.51 tff(16,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 7.79/5.51 tff(17,plain,
% 7.79/5.51 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 7.79/5.51 inference(modus_ponens,[status(thm)],[16, 15])).
% 7.79/5.51 tff(18,plain,
% 7.79/5.51 (model(I1!30, F!29)),
% 7.79/5.51 inference(and_elim,[status(thm)],[17])).
% 7.79/5.51 tff(19,plain,
% 7.79/5.51 ((~![I2: $i] : (~model(I2, F!29))) | (~model(I1!30, F!29))),
% 7.79/5.51 inference(quant_inst,[status(thm)],[])).
% 7.79/5.51 tff(20,plain,
% 7.79/5.51 ($false),
% 7.79/5.51 inference(unit_resolution,[status(thm)],[19, 18, 14])).
% 7.79/5.51 tff(21,plain,(~![I2: $i] : (~model(I2, F!29))), inference(lemma,lemma(discharge,[]))).
% 7.79/5.51 tff(22,plain,
% 7.79/5.51 ((~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))) | ![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29))),
% 7.79/5.51 inference(tautology,[status(thm)],[])).
% 7.79/5.51 tff(23,plain,
% 7.79/5.51 (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))),
% 7.79/5.51 inference(unit_resolution,[status(thm)],[22, 21, 13])).
% 7.79/5.51 tff(24,plain,
% 7.79/5.51 (((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29))))) | (![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))),
% 7.79/5.51 inference(tautology,[status(thm)],[])).
% 7.79/5.51 tff(25,plain,
% 7.79/5.51 ((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29))))),
% 7.79/5.51 inference(unit_resolution,[status(thm)],[24, 23])).
% 7.79/5.51 tff(26,assumption,(![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))), introduced(assumption)).
% 7.79/5.51 tff(27,plain,
% 7.79/5.51 (~model(I2!31, F!29)),
% 7.79/5.51 inference(and_elim,[status(thm)],[17])).
% 7.79/5.51 tff(28,plain,
% 7.79/5.51 (((~![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))) | ((~model(I2!31, F!28)) | model(I2!31, F!29))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))) | (~model(I2!31, F!28)) | model(I2!31, F!29))),
% 7.79/5.51 inference(rewrite,[status(thm)],[])).
% 7.79/5.51 tff(29,plain,
% 7.79/5.51 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))) | ((~model(I2!31, F!28)) | model(I2!31, F!29))),
% 7.79/5.51 inference(quant_inst,[status(thm)],[])).
% 7.79/5.51 tff(30,plain,
% 7.79/5.51 ((~![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))) | (~model(I2!31, F!28)) | model(I2!31, F!29)),
% 7.79/5.51 inference(modus_ponens,[status(thm)],[29, 28])).
% 7.79/5.51 tff(31,plain,
% 7.79/5.51 ($false),
% 7.79/5.51 inference(unit_resolution,[status(thm)],[30, 27, 10, 26])).
% 7.79/5.51 tff(32,plain,(~![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))), inference(lemma,lemma(discharge,[]))).
% 7.79/5.51 tff(33,plain,
% 7.79/5.51 (^[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)))))))),
% 7.79/5.51 inference(bind,[status(th)],[])).
% 7.79/5.51 tff(34,plain,
% 7.79/5.51 (![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))))))),
% 7.79/5.51 inference(quant_intro,[status(thm)],[33])).
% 7.79/5.51 tff(35,plain,
% 7.79/5.51 (^[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)))))))),
% 7.79/5.51 inference(bind,[status(th)],[])).
% 7.79/5.51 tff(36,plain,
% 7.79/5.51 (![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))))))),
% 7.79/5.51 inference(quant_intro,[status(thm)],[35])).
% 7.79/5.51 tff(37,plain,
% 7.79/5.51 (^[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)))))))),
% 7.79/5.51 inference(bind,[status(th)],[])).
% 7.79/5.51 tff(38,plain,
% 7.79/5.51 (![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))))))),
% 7.79/5.51 inference(quant_intro,[status(thm)],[37])).
% 7.79/5.51 tff(39,plain,
% 7.79/5.51 (![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))))))),
% 7.79/5.51 inference(transitivity,[status(thm)],[38, 36])).
% 7.79/5.51 tff(40,plain,
% 7.79/5.51 (^[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))))))))),
% 7.79/5.51 inference(bind,[status(th)],[])).
% 7.79/5.51 tff(41,plain,
% 7.79/5.51 (![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))))))),
% 7.79/5.51 inference(quant_intro,[status(thm)],[40])).
% 7.79/5.51 tff(42,plain,
% 7.79/5.51 (![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))),
% 7.79/5.51 inference(rewrite,[status(thm)],[])).
% 7.79/5.51 tff(43,plain,
% 7.79/5.51 (^[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)))),
% 7.79/5.51 inference(bind,[status(th)],[])).
% 7.79/5.51 tff(44,plain,
% 7.79/5.51 (![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))),
% 7.79/5.51 inference(quant_intro,[status(thm)],[43])).
% 7.79/5.51 tff(45,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')).
% 7.79/5.51 tff(46,plain,
% 7.79/5.51 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 7.79/5.51 inference(modus_ponens,[status(thm)],[45, 44])).
% 7.79/5.51 tff(47,plain,
% 7.79/5.51 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 7.79/5.51 inference(modus_ponens,[status(thm)],[46, 42])).
% 7.79/5.51 tff(48,plain,(
% 7.79/5.51 ![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))))),
% 7.79/5.51 inference(skolemize,[status(sab)],[47])).
% 7.79/5.51 tff(49,plain,
% 7.79/5.51 (![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))))))),
% 7.79/5.51 inference(modus_ponens,[status(thm)],[48, 41])).
% 7.79/5.51 tff(50,plain,
% 7.79/5.51 (![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))))))),
% 7.79/5.51 inference(modus_ponens,[status(thm)],[49, 39])).
% 7.79/5.51 tff(51,plain,
% 7.79/5.51 (![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))))))),
% 7.79/5.52 inference(modus_ponens,[status(thm)],[50, 34])).
% 7.79/5.52 tff(52,plain,
% 7.79/5.52 (((~![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(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, 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(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm))))))),
% 7.79/5.52 inference(rewrite,[status(thm)],[])).
% 7.79/5.52 tff(53,plain,
% 7.79/5.52 ((~((~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm))) | (~((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))))) <=> (~((~((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm)))))),
% 7.79/5.52 inference(rewrite,[status(thm)],[])).
% 7.79/5.52 tff(54,plain,
% 7.79/5.52 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm))) | (~((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))))))) <=> ((~![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(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm))))))),
% 7.79/5.52 inference(monotonicity,[status(thm)],[53])).
% 7.79/5.52 tff(55,plain,
% 7.79/5.52 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm))) | (~((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))))))) <=> ((~![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(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm))))))),
% 7.79/5.52 inference(transitivity,[status(thm)],[54, 52])).
% 7.79/5.52 tff(56,plain,
% 7.79/5.52 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm))) | (~((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))))))),
% 7.79/5.52 inference(quant_inst,[status(thm)],[])).
% 7.79/5.52 tff(57,plain,
% 7.79/5.52 ((~![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(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm)))))),
% 7.79/5.52 inference(modus_ponens,[status(thm)],[56, 55])).
% 7.79/5.52 tff(58,plain,
% 7.79/5.52 (~((~((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm))))),
% 7.79/5.52 inference(unit_resolution,[status(thm)],[57, 51])).
% 7.79/5.52 tff(59,plain,
% 7.79/5.52 (((~((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~((~((~model(tptp_fun_I1_3(F!29, F!28), F!28)) | model(tptp_fun_I1_3(F!29, F!28), F!29))) | status(F!28, F!29, thm)))) | ((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))),
% 7.79/5.52 inference(tautology,[status(thm)],[])).
% 7.79/5.52 tff(60,plain,
% 7.79/5.52 ((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))),
% 7.79/5.52 inference(unit_resolution,[status(thm)],[59, 58])).
% 7.79/5.52 tff(61,plain,
% 7.79/5.52 ((~((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29)))) | (~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))),
% 7.79/5.52 inference(tautology,[status(thm)],[])).
% 7.79/5.52 tff(62,plain,
% 7.79/5.52 ((~status(F!28, F!29, thm)) | ![I1: $i] : ((~model(I1, F!28)) | model(I1, F!29))),
% 7.79/5.52 inference(unit_resolution,[status(thm)],[61, 60])).
% 7.79/5.52 tff(63,plain,
% 7.79/5.52 (~status(F!28, F!29, thm)),
% 7.79/5.52 inference(unit_resolution,[status(thm)],[62, 32])).
% 7.79/5.52 tff(64,plain,
% 7.79/5.52 (^[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))))))))),
% 7.79/5.52 inference(bind,[status(th)],[])).
% 7.79/5.52 tff(65,plain,
% 7.79/5.52 (![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)))))))),
% 7.79/5.52 inference(quant_intro,[status(thm)],[64])).
% 7.79/5.52 tff(66,plain,
% 7.79/5.52 (^[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))))))))),
% 7.79/5.52 inference(bind,[status(th)],[])).
% 7.79/5.52 tff(67,plain,
% 7.79/5.52 (![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)))))))),
% 7.79/5.52 inference(quant_intro,[status(thm)],[66])).
% 7.79/5.52 tff(68,plain,
% 7.79/5.52 (![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)))))))),
% 7.79/5.52 inference(transitivity,[status(thm)],[67, 65])).
% 7.79/5.52 tff(69,plain,
% 7.79/5.52 (^[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)))))))))),
% 7.79/5.52 inference(bind,[status(th)],[])).
% 7.79/5.52 tff(70,plain,
% 7.79/5.52 (![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)))))))),
% 7.79/5.52 inference(quant_intro,[status(thm)],[69])).
% 7.79/5.52 tff(71,plain,
% 7.79/5.52 (^[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)))))),
% 7.79/5.52 inference(bind,[status(th)],[])).
% 7.79/5.52 tff(72,plain,
% 7.79/5.52 (![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))))),
% 7.79/5.52 inference(quant_intro,[status(thm)],[71])).
% 7.79/5.52 tff(73,plain,
% 7.79/5.52 (![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))),
% 7.79/5.52 inference(rewrite,[status(thm)],[])).
% 7.79/5.52 tff(74,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')).
% 7.79/5.52 tff(75,plain,
% 7.79/5.52 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 7.79/5.52 inference(modus_ponens,[status(thm)],[74, 73])).
% 7.79/5.52 tff(76,plain,(
% 7.79/5.52 ![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))))),
% 7.79/5.52 inference(skolemize,[status(sab)],[75])).
% 7.79/5.52 tff(77,plain,
% 7.79/5.52 (![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))))),
% 7.79/5.52 inference(modus_ponens,[status(thm)],[76, 72])).
% 7.79/5.52 tff(78,plain,
% 7.79/5.52 (![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)))))))),
% 7.79/5.52 inference(modus_ponens,[status(thm)],[77, 70])).
% 7.79/5.52 tff(79,plain,
% 7.79/5.52 (![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)))))))),
% 7.79/5.52 inference(modus_ponens,[status(thm)],[78, 68])).
% 7.79/5.52 tff(80,plain,
% 7.79/5.52 ((~![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(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | (~((~nota(esa, thm)) | (~((~status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), esa)) | status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), thm)))))))),
% 7.79/5.52 inference(quant_inst,[status(thm)],[])).
% 7.79/5.52 tff(81,plain,
% 7.79/5.52 (~((~(nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | (~((~nota(esa, thm)) | (~((~status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), esa)) | status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), thm))))))),
% 7.79/5.52 inference(unit_resolution,[status(thm)],[80, 79])).
% 7.79/5.52 tff(82,plain,
% 7.79/5.52 (((~(nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | (~((~nota(esa, thm)) | (~((~status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), esa)) | status(tptp_fun_Ax_23(thm, esa), tptp_fun_C_22(thm, esa), thm)))))) | (nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))),
% 7.79/5.52 inference(tautology,[status(thm)],[])).
% 7.79/5.52 tff(83,plain,
% 7.79/5.52 (nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))),
% 7.88/5.53 inference(unit_resolution,[status(thm)],[82, 81])).
% 7.88/5.53 tff(84,plain,
% 7.88/5.53 ((~nota(esa, thm)) <=> (~nota(esa, thm))),
% 7.88/5.53 inference(rewrite,[status(thm)],[])).
% 7.88/5.53 tff(85,axiom,(~nota(esa, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nota_esa_thm')).
% 7.88/5.53 tff(86,plain,
% 7.88/5.53 (~nota(esa, thm)),
% 7.88/5.53 inference(modus_ponens,[status(thm)],[85, 84])).
% 7.88/5.53 tff(87,plain,
% 7.88/5.53 ((~(nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))),
% 7.88/5.53 inference(tautology,[status(thm)],[])).
% 7.88/5.53 tff(88,plain,
% 7.88/5.53 ((~(nota(esa, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))),
% 7.88/5.53 inference(unit_resolution,[status(thm)],[87, 86])).
% 7.88/5.53 tff(89,plain,
% 7.88/5.53 (![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))),
% 7.88/5.53 inference(unit_resolution,[status(thm)],[88, 83])).
% 7.88/5.53 tff(90,plain,
% 7.88/5.53 (((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(F!28, F!29, esa)) | status(F!28, F!29, thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(F!28, F!29, esa)) | status(F!28, F!29, thm))),
% 7.88/5.53 inference(rewrite,[status(thm)],[])).
% 7.88/5.53 tff(91,plain,
% 7.88/5.53 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | ((~status(F!28, F!29, esa)) | status(F!28, F!29, thm))),
% 7.88/5.53 inference(quant_inst,[status(thm)],[])).
% 7.88/5.53 tff(92,plain,
% 7.88/5.53 ((~![Ax: $i, C: $i] : ((~status(Ax, C, esa)) | status(Ax, C, thm))) | (~status(F!28, F!29, esa)) | status(F!28, F!29, thm)),
% 7.88/5.53 inference(modus_ponens,[status(thm)],[91, 90])).
% 7.88/5.53 tff(93,plain,
% 7.88/5.53 (~status(F!28, F!29, esa)),
% 7.88/5.53 inference(unit_resolution,[status(thm)],[92, 89, 63])).
% 7.88/5.53 tff(94,plain,
% 7.88/5.53 ((~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))) | (~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa)),
% 7.88/5.53 inference(tautology,[status(thm)],[])).
% 7.88/5.53 tff(95,plain,
% 7.88/5.53 (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))),
% 7.88/5.53 inference(unit_resolution,[status(thm)],[94, 93, 25])).
% 7.88/5.53 tff(96,plain,
% 7.88/5.53 (((~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa)))) | ((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))),
% 7.88/5.53 inference(tautology,[status(thm)],[])).
% 7.88/5.53 tff(97,plain,
% 7.88/5.53 ((~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa)))),
% 7.88/5.53 inference(unit_resolution,[status(thm)],[96, 95])).
% 7.88/5.53 tff(98,plain,
% 7.88/5.53 (^[Ax: $i, C: $i] : refl((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 7.88/5.53 inference(bind,[status(th)],[])).
% 7.88/5.53 tff(99,plain,
% 7.88/5.53 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.88/5.53 inference(quant_intro,[status(thm)],[98])).
% 7.88/5.53 tff(100,plain,
% 7.88/5.53 (^[Ax: $i, C: $i] : rewrite((~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))))),
% 7.88/5.53 inference(bind,[status(th)],[])).
% 7.88/5.53 tff(101,plain,
% 7.88/5.53 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.88/5.53 inference(quant_intro,[status(thm)],[100])).
% 7.88/5.53 tff(102,plain,
% 7.88/5.53 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.88/5.53 inference(transitivity,[status(thm)],[101, 99])).
% 7.88/5.53 tff(103,plain,
% 7.88/5.53 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) <=> ((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))), rewrite(((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))) <=> ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))))), rewrite((((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))), (((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))))),
% 7.88/5.53 inference(bind,[status(th)],[])).
% 7.88/5.53 tff(104,plain,
% 7.88/5.53 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))) <=> ![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.88/5.53 inference(quant_intro,[status(thm)],[103])).
% 7.88/5.53 tff(105,plain,
% 7.88/5.53 (^[Ax: $i, C: $i] : rewrite(((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))))))),
% 7.88/5.53 inference(bind,[status(th)],[])).
% 7.88/5.53 tff(106,plain,
% 7.88/5.53 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa)))) <=> ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 7.88/5.53 inference(quant_intro,[status(thm)],[105])).
% 7.88/5.53 tff(107,plain,
% 7.88/5.53 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 7.88/5.54 inference(rewrite,[status(thm)],[])).
% 7.88/5.54 tff(108,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','esa')).
% 7.88/5.54 tff(109,plain,
% 7.88/5.54 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) <=> ?[I2: $i] : model(I2, C)) <=> status(Ax, C, esa))),
% 7.88/5.54 inference(modus_ponens,[status(thm)],[108, 107])).
% 7.88/5.54 tff(110,plain,(
% 7.88/5.54 ![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & (((![I1: $i] : (~model(I1, Ax)) | model(tptp_fun_I2_1(C), C)) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C)))) | (~status(Ax, C, esa))))),
% 7.88/5.54 inference(skolemize,[status(sab)],[109])).
% 7.88/5.54 tff(111,plain,
% 7.88/5.54 (![Ax: $i, C: $i] : ((((model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C)) & (![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))) | status(Ax, C, esa)) & ((~status(Ax, C, esa)) | ((model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax))) & (model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))),
% 7.88/5.54 inference(modus_ponens,[status(thm)],[110, 106])).
% 7.88/5.54 tff(112,plain,
% 7.88/5.54 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.88/5.54 inference(modus_ponens,[status(thm)],[111, 104])).
% 7.88/5.54 tff(113,plain,
% 7.88/5.54 (![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))),
% 7.88/5.54 inference(modus_ponens,[status(thm)],[112, 102])).
% 7.88/5.54 tff(114,plain,
% 7.88/5.54 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))))))),
% 7.88/5.54 inference(rewrite,[status(thm)],[])).
% 7.88/5.54 tff(115,plain,
% 7.88/5.54 ((~((~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))) | (~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))))) <=> (~((~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa)))))),
% 7.88/5.54 inference(rewrite,[status(thm)],[])).
% 7.88/5.54 tff(116,plain,
% 7.88/5.54 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))) | (~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))))))),
% 7.88/5.54 inference(monotonicity,[status(thm)],[115])).
% 7.88/5.54 tff(117,plain,
% 7.88/5.54 (((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))) | (~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29))))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))))))),
% 7.88/5.54 inference(transitivity,[status(thm)],[116, 114])).
% 7.88/5.54 tff(118,plain,
% 7.88/5.54 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa))) | (~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29))))))))))),
% 7.88/5.55 inference(quant_inst,[status(thm)],[])).
% 7.88/5.55 tff(119,plain,
% 7.88/5.55 ((~![Ax: $i, C: $i] : (~((~((~((~(model(tptp_fun_I1_0(Ax), Ax) | model(tptp_fun_I2_1(C), C))) | (~(![I1: $i] : (~model(I1, Ax)) | ![I2: $i] : (~model(I2, C)))))) | status(Ax, C, esa))) | (~((~status(Ax, C, esa)) | (~((~(model(tptp_fun_I2_1(C), C) | ![I1: $i] : (~model(I1, Ax)))) | (~(model(tptp_fun_I1_0(Ax), Ax) | ![I2: $i] : (~model(I2, C))))))))))) | (~((~((~status(F!28, F!29, esa)) | (~((~(model(tptp_fun_I2_1(F!29), F!29) | ![I1: $i] : (~model(I1, F!28)))) | (~(model(tptp_fun_I1_0(F!28), F!28) | ![I2: $i] : (~model(I2, F!29)))))))) | (~((~((~(model(tptp_fun_I1_0(F!28), F!28) | model(tptp_fun_I2_1(F!29), F!29))) | (~(![I1: $i] : (~model(I1, F!28)) | ![I2: $i] : (~model(I2, F!29)))))) | status(F!28, F!29, esa)))))),
% 7.88/5.55 inference(modus_ponens,[status(thm)],[118, 117])).
% 7.88/5.55 tff(120,plain,
% 7.88/5.55 ($false),
% 7.88/5.55 inference(unit_resolution,[status(thm)],[119, 113, 97])).
% 7.88/5.55 % SZS output end Proof
%------------------------------------------------------------------------------