TSTP Solution File: KRS262+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS262+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 17:45:21 EDT 2022
% Result : Theorem 1.01s 0.87s
% Output : Proof 1.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS262+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 10:15:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.01/0.87 % SZS status Theorem
% 1.01/0.87 % SZS output start Proof
% 1.01/0.87 tff(status_type, type, (
% 1.01/0.87 status: ( $i * $i * $i ) > $o)).
% 1.01/0.87 tff(tau_type, type, (
% 1.01/0.87 tau: $i)).
% 1.01/0.87 tff(tptp_fun_C_24_type, type, (
% 1.01/0.87 tptp_fun_C_24: ( $i * $i ) > $i)).
% 1.01/0.87 tff(eqv_type, type, (
% 1.01/0.87 eqv: $i)).
% 1.01/0.87 tff(tptp_fun_Ax_25_type, type, (
% 1.01/0.87 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 1.01/0.87 tff(nevera_type, type, (
% 1.01/0.87 nevera: ( $i * $i ) > $o)).
% 1.01/0.87 tff(tptp_fun_F_28_type, type, (
% 1.01/0.87 tptp_fun_F_28: $i)).
% 1.01/0.87 tff(model_type, type, (
% 1.01/0.87 model: ( $i * $i ) > $o)).
% 1.01/0.87 tff(tptp_fun_I2_31_type, type, (
% 1.01/0.87 tptp_fun_I2_31: $i)).
% 1.01/0.87 tff(tptp_fun_I1_0_type, type, (
% 1.01/0.87 tptp_fun_I1_0: $i > $i)).
% 1.01/0.87 tff(tptp_fun_I2_4_type, type, (
% 1.01/0.87 tptp_fun_I2_4: ( $i * $i ) > $i)).
% 1.01/0.87 tff(tptp_fun_I1_10_type, type, (
% 1.01/0.87 tptp_fun_I1_10: ( $i * $i ) > $i)).
% 1.01/0.87 tff(tptp_fun_I1_3_type, type, (
% 1.01/0.87 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 1.01/0.87 tff(thm_type, type, (
% 1.01/0.87 thm: $i)).
% 1.01/0.87 tff(mighta_type, type, (
% 1.01/0.87 mighta: ( $i * $i ) > $o)).
% 1.01/0.87 tff(tptp_fun_C_18_type, type, (
% 1.01/0.87 tptp_fun_C_18: ( $i * $i ) > $i)).
% 1.01/0.87 tff(tptp_fun_Ax_19_type, type, (
% 1.01/0.87 tptp_fun_Ax_19: ( $i * $i ) > $i)).
% 1.01/0.87 tff(1,assumption,(![I1: $i] : (~model(I1, F!28))), introduced(assumption)).
% 1.01/0.87 tff(2,plain,
% 1.01/0.87 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 1.01/0.87 inference(bind,[status(th)],[])).
% 1.01/0.87 tff(3,plain,
% 1.01/0.87 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 1.01/0.87 inference(quant_intro,[status(thm)],[2])).
% 1.01/0.87 tff(4,plain,
% 1.01/0.87 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 1.01/0.87 inference(rewrite,[status(thm)],[])).
% 1.01/0.87 tff(5,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','tautology')).
% 1.01/0.87 tff(6,plain,
% 1.01/0.87 (?[F: $i] : ![I: $i] : model(I, F)),
% 1.01/0.87 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.01/0.87 tff(7,plain,(
% 1.01/0.87 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 1.01/0.87 inference(transitivity,[status(sab)],[6])).
% 1.01/0.87 tff(8,plain,
% 1.01/0.87 (![I: $i] : model(I, F!28)),
% 1.01/0.87 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.01/0.87 tff(9,plain,
% 1.01/0.87 ((~![I: $i] : model(I, F!28)) | model(I2!31, F!28)),
% 1.01/0.87 inference(quant_inst,[status(thm)],[])).
% 1.01/0.87 tff(10,plain,
% 1.01/0.87 (model(I2!31, F!28)),
% 1.01/0.87 inference(unit_resolution,[status(thm)],[9, 8])).
% 1.01/0.87 tff(11,plain,
% 1.01/0.87 ((~![I1: $i] : (~model(I1, F!28))) | (~model(I2!31, F!28))),
% 1.01/0.87 inference(quant_inst,[status(thm)],[])).
% 1.01/0.87 tff(12,plain,
% 1.01/0.87 ($false),
% 1.01/0.87 inference(unit_resolution,[status(thm)],[11, 10, 1])).
% 1.01/0.87 tff(13,plain,(~![I1: $i] : (~model(I1, F!28))), inference(lemma,lemma(discharge,[]))).
% 1.01/0.87 tff(14,plain,
% 1.01/0.87 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 1.01/0.87 inference(bind,[status(th)],[])).
% 1.01/0.87 tff(15,plain,
% 1.01/0.87 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 1.01/0.87 inference(quant_intro,[status(thm)],[14])).
% 1.01/0.87 tff(16,plain,
% 1.01/0.87 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(17,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[16])).
% 1.01/0.88 tff(18,plain,
% 1.01/0.88 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(19,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[18])).
% 1.01/0.88 tff(20,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 1.01/0.88 inference(transitivity,[status(thm)],[19, 17])).
% 1.01/0.88 tff(21,plain,
% 1.01/0.88 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) <=> (status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))), trans(monotonicity(rewrite((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))) <=> ((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))) | (~status(Ax, C, eqv))))), rewrite(((~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))) | (~status(Ax, C, eqv))) <=> ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))), (((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))) <=> ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))), (((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) & ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))))), rewrite(((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) & ((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C))))))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))), (((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(22,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[21])).
% 1.01/0.88 tff(23,plain,
% 1.01/0.88 (^[Ax: $i, C: $i] : rewrite((((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(24,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[23])).
% 1.01/0.88 tff(25,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv)) <=> ![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(26,axiom,(![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','eqv')).
% 1.01/0.88 tff(27,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : ((?[I1: $i] : model(I1, Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) <=> status(Ax, C, eqv))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.01/0.88 tff(28,plain,(
% 1.01/0.88 ![Ax: $i, C: $i] : (((![I1: $i] : (~model(I1, Ax)) | (~(model(tptp_fun_I2_4(C, Ax), Ax) <=> model(tptp_fun_I2_4(C, Ax), C)))) | status(Ax, C, eqv)) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 1.01/0.88 inference(skolemize,[status(sab)],[27])).
% 1.01/0.88 tff(29,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : ((status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C))) & ((model(tptp_fun_I1_0(Ax), Ax) & ![I2: $i] : (model(I2, Ax) <=> model(I2, C))) | (~status(Ax, C, eqv))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.01/0.88 tff(30,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[29, 22])).
% 1.01/0.88 tff(31,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ![I1: $i] : (~model(I1, Ax)) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[30, 20])).
% 1.01/0.88 tff(32,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[31, 15])).
% 1.01/0.88 tff(33,plain,
% 1.01/0.88 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | (~((~status(F!28, F!28, eqv)) | model(tptp_fun_I1_0(F!28), F!28)))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | (~((~status(F!28, F!28, eqv)) | model(tptp_fun_I1_0(F!28), F!28))))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(34,plain,
% 1.01/0.88 ((~((~(status(F!28, F!28, eqv) | ((~model(tptp_fun_I2_4(F!28, F!28), F!28)) <=> model(tptp_fun_I2_4(F!28, F!28), F!28)) | ![I1: $i] : (~model(I1, F!28)))) | (~((~status(F!28, F!28, eqv)) | (~((~model(tptp_fun_I1_0(F!28), F!28)) | (~![I2: $i] : (model(I2, F!28) <=> model(I2, F!28))))))))) <=> (~((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | (~((~status(F!28, F!28, eqv)) | model(tptp_fun_I1_0(F!28), F!28)))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(35,plain,
% 1.01/0.88 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!28, F!28, eqv) | ((~model(tptp_fun_I2_4(F!28, F!28), F!28)) <=> model(tptp_fun_I2_4(F!28, F!28), F!28)) | ![I1: $i] : (~model(I1, F!28)))) | (~((~status(F!28, F!28, eqv)) | (~((~model(tptp_fun_I1_0(F!28), F!28)) | (~![I2: $i] : (model(I2, F!28) <=> model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | (~((~status(F!28, F!28, eqv)) | model(tptp_fun_I1_0(F!28), F!28))))))),
% 1.01/0.88 inference(monotonicity,[status(thm)],[34])).
% 1.01/0.88 tff(36,plain,
% 1.01/0.88 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!28, F!28, eqv) | ((~model(tptp_fun_I2_4(F!28, F!28), F!28)) <=> model(tptp_fun_I2_4(F!28, F!28), F!28)) | ![I1: $i] : (~model(I1, F!28)))) | (~((~status(F!28, F!28, eqv)) | (~((~model(tptp_fun_I1_0(F!28), F!28)) | (~![I2: $i] : (model(I2, F!28) <=> model(I2, F!28)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | (~((~status(F!28, F!28, eqv)) | model(tptp_fun_I1_0(F!28), F!28))))))),
% 1.01/0.88 inference(transitivity,[status(thm)],[35, 33])).
% 1.01/0.88 tff(37,plain,
% 1.01/0.88 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(status(F!28, F!28, eqv) | ((~model(tptp_fun_I2_4(F!28, F!28), F!28)) <=> model(tptp_fun_I2_4(F!28, F!28), F!28)) | ![I1: $i] : (~model(I1, F!28)))) | (~((~status(F!28, F!28, eqv)) | (~((~model(tptp_fun_I1_0(F!28), F!28)) | (~![I2: $i] : (model(I2, F!28) <=> model(I2, F!28)))))))))),
% 1.01/0.88 inference(quant_inst,[status(thm)],[])).
% 1.01/0.88 tff(38,plain,
% 1.01/0.88 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, eqv) | ((~model(tptp_fun_I2_4(C, Ax), Ax)) <=> model(tptp_fun_I2_4(C, Ax), C)) | ![I1: $i] : (~model(I1, Ax)))) | (~((~status(Ax, C, eqv)) | (~((~model(tptp_fun_I1_0(Ax), Ax)) | (~![I2: $i] : (model(I2, Ax) <=> model(I2, C)))))))))) | (~((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | (~((~status(F!28, F!28, eqv)) | model(tptp_fun_I1_0(F!28), F!28)))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.01/0.88 tff(39,plain,
% 1.01/0.88 (~((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | (~((~status(F!28, F!28, eqv)) | model(tptp_fun_I1_0(F!28), F!28))))),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[38, 32])).
% 1.01/0.88 tff(40,plain,
% 1.01/0.88 (((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | (~((~status(F!28, F!28, eqv)) | model(tptp_fun_I1_0(F!28), F!28)))) | (![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))),
% 1.01/0.88 inference(tautology,[status(thm)],[])).
% 1.01/0.88 tff(41,plain,
% 1.01/0.88 (![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv)),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[40, 39])).
% 1.01/0.88 tff(42,plain,
% 1.01/0.88 ((~(![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv))) | ![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv)),
% 1.01/0.88 inference(tautology,[status(thm)],[])).
% 1.01/0.88 tff(43,plain,
% 1.01/0.88 (![I1: $i] : (~model(I1, F!28)) | status(F!28, F!28, eqv)),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[42, 41])).
% 1.01/0.88 tff(44,plain,
% 1.01/0.88 (status(F!28, F!28, eqv)),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[43, 13])).
% 1.01/0.88 tff(45,assumption,((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau)))), introduced(assumption)).
% 1.01/0.88 tff(46,plain,
% 1.01/0.88 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(47,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[46])).
% 1.01/0.88 tff(48,plain,
% 1.01/0.88 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(49,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[48])).
% 1.01/0.88 tff(50,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.01/0.88 inference(transitivity,[status(thm)],[49, 47])).
% 1.01/0.88 tff(51,plain,
% 1.01/0.88 (^[Ax: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C)) <=> (~((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))), ((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) <=> (~(~((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))))), rewrite((~(~((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))) <=> ((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))), ((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) <=> ((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))), (((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) <=> (((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)))), rewrite((((~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) <=> (status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))), (((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) <=> (status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))))), trans(monotonicity(quant_intro(proof_bind(^[I1: $i] : rewrite((model(I1, Ax) & model(I1, C)) <=> (~((~model(I1, Ax)) | (~model(I1, C)))))), (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))), ((![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau))) <=> (![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))) | (~status(Ax, C, tau))))), rewrite((![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))) | (~status(Ax, C, tau))) <=> ((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))), ((![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau))) <=> ((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))), ((((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) & (![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau)))) <=> ((status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))) & ((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))))), rewrite(((status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C))) & ((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C)))))) <=> (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))), ((((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) & (![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau)))) <=> (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(52,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) & (![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[51])).
% 1.01/0.88 tff(53,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, tau)) <=> ![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, tau))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(54,axiom,(![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, tau))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','tau')).
% 1.01/0.88 tff(55,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (![I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, tau))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.01/0.88 tff(56,plain,(
% 1.01/0.88 ![Ax: $i, C: $i] : (((~(model(tptp_fun_I1_10(C, Ax), Ax) & model(tptp_fun_I1_10(C, Ax), C))) | status(Ax, C, tau)) & (![I1: $i] : (model(I1, Ax) & model(I1, C)) | (~status(Ax, C, tau))))),
% 1.01/0.88 inference(skolemize,[status(sab)],[55])).
% 1.01/0.88 tff(57,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.01/0.88 tff(58,plain,
% 1.01/0.88 (![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[57, 50])).
% 1.01/0.88 tff(59,plain,
% 1.01/0.88 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau)))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau))))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(60,plain,
% 1.01/0.88 ((~((~(status(F!28, F!28, tau) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)))) | (~((~status(F!28, F!28, tau)) | ![I1: $i] : (~((~model(I1, F!28)) | (~model(I1, F!28)))))))) <=> (~((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau)))))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(61,plain,
% 1.01/0.88 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(F!28, F!28, tau) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)))) | (~((~status(F!28, F!28, tau)) | ![I1: $i] : (~((~model(I1, F!28)) | (~model(I1, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau))))))),
% 1.01/0.88 inference(monotonicity,[status(thm)],[60])).
% 1.01/0.88 tff(62,plain,
% 1.01/0.88 (((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(F!28, F!28, tau) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)))) | (~((~status(F!28, F!28, tau)) | ![I1: $i] : (~((~model(I1, F!28)) | (~model(I1, F!28))))))))) <=> ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau))))))),
% 1.01/0.88 inference(transitivity,[status(thm)],[61, 59])).
% 1.01/0.88 tff(63,plain,
% 1.01/0.88 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(F!28, F!28, tau) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)))) | (~((~status(F!28, F!28, tau)) | ![I1: $i] : (~((~model(I1, F!28)) | (~model(I1, F!28))))))))),
% 1.01/0.88 inference(quant_inst,[status(thm)],[])).
% 1.01/0.88 tff(64,plain,
% 1.01/0.88 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau)))))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.01/0.88 tff(65,plain,
% 1.01/0.88 ($false),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[64, 58, 45])).
% 1.01/0.88 tff(66,plain,(~((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau))))), inference(lemma,lemma(discharge,[]))).
% 1.01/0.88 tff(67,plain,
% 1.01/0.88 (((~((~status(F!28, F!28, tau)) | ![I1: $i] : model(I1, F!28))) | (~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau)))) | ((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau))),
% 1.01/0.88 inference(tautology,[status(thm)],[])).
% 1.01/0.88 tff(68,plain,
% 1.01/0.88 ((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau)),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[67, 66])).
% 1.01/0.88 tff(69,assumption,(~model(tptp_fun_I1_10(F!28, F!28), F!28)), introduced(assumption)).
% 1.01/0.88 tff(70,plain,
% 1.01/0.88 ((~![I: $i] : model(I, F!28)) | model(tptp_fun_I1_10(F!28, F!28), F!28)),
% 1.01/0.88 inference(quant_inst,[status(thm)],[])).
% 1.01/0.88 tff(71,plain,
% 1.01/0.88 ($false),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[70, 8, 69])).
% 1.01/0.88 tff(72,plain,(model(tptp_fun_I1_10(F!28, F!28), F!28)), inference(lemma,lemma(discharge,[]))).
% 1.01/0.88 tff(73,plain,
% 1.01/0.88 ((~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau))) | (~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau)),
% 1.01/0.88 inference(tautology,[status(thm)],[])).
% 1.01/0.88 tff(74,plain,
% 1.01/0.88 ((~((~model(tptp_fun_I1_10(F!28, F!28), F!28)) | status(F!28, F!28, tau))) | status(F!28, F!28, tau)),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[73, 72])).
% 1.01/0.88 tff(75,plain,
% 1.01/0.88 (status(F!28, F!28, tau)),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[74, 68])).
% 1.01/0.88 tff(76,assumption,(![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))), introduced(assumption)).
% 1.01/0.88 tff(77,assumption,(status(F!28, F!28, eqv)), introduced(assumption)).
% 1.01/0.88 tff(78,plain,
% 1.01/0.88 (((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))) | ((~status(F!28, F!28, eqv)) | (~status(F!28, F!28, tau)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))) | (~status(F!28, F!28, eqv)) | (~status(F!28, F!28, tau)))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(79,plain,
% 1.01/0.88 ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))) | ((~status(F!28, F!28, eqv)) | (~status(F!28, F!28, tau)))),
% 1.01/0.88 inference(quant_inst,[status(thm)],[])).
% 1.01/0.88 tff(80,plain,
% 1.01/0.88 ((~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))) | (~status(F!28, F!28, eqv)) | (~status(F!28, F!28, tau))),
% 1.01/0.88 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.01/0.88 tff(81,plain,
% 1.01/0.88 ($false),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[80, 77, 76, 75])).
% 1.01/0.88 tff(82,plain,((~status(F!28, F!28, eqv)) | (~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau))))), inference(lemma,lemma(discharge,[]))).
% 1.01/0.88 tff(83,plain,
% 1.01/0.88 (~![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))),
% 1.01/0.88 inference(unit_resolution,[status(thm)],[82, 44])).
% 1.01/0.88 tff(84,plain,
% 1.01/0.88 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(85,plain,
% 1.01/0.88 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[84])).
% 1.01/0.88 tff(86,plain,
% 1.01/0.88 (^[S1: $i, S2: $i] : refl((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(87,plain,
% 1.01/0.88 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[86])).
% 1.01/0.88 tff(88,plain,
% 1.01/0.88 (^[S1: $i, S2: $i] : rewrite((~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(89,plain,
% 1.01/0.88 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[88])).
% 1.01/0.88 tff(90,plain,
% 1.01/0.88 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.01/0.88 inference(transitivity,[status(thm)],[89, 87])).
% 1.01/0.88 tff(91,plain,
% 1.01/0.88 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))))), rewrite((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))), ((((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(92,plain,
% 1.01/0.88 (![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[91])).
% 1.01/0.88 tff(93,plain,
% 1.01/0.88 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.01/0.88 inference(rewrite,[status(thm)],[])).
% 1.01/0.88 tff(94,plain,
% 1.01/0.88 (^[S1: $i, S2: $i] : rewrite((![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2)))),
% 1.01/0.88 inference(bind,[status(th)],[])).
% 1.01/0.88 tff(95,plain,
% 1.01/0.88 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2)) <=> ![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.01/0.88 inference(quant_intro,[status(thm)],[94])).
% 1.01/0.89 tff(96,axiom,(![S1: $i, S2: $i] : (![Ax: $i, C: $i] : (status(Ax, C, S1) => (~status(Ax, C, S2))) <=> nevera(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','nevera')).
% 1.01/0.89 tff(97,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.01/0.89 tff(98,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[97, 93])).
% 1.01/0.89 tff(99,plain,(
% 1.01/0.89 ![S1: $i, S2: $i] : (((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2)) & (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))),
% 1.01/0.89 inference(skolemize,[status(sab)],[98])).
% 1.01/0.89 tff(100,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[99, 92])).
% 1.01/0.89 tff(101,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~(![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) | (~nevera(S1, S2))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[100, 90])).
% 1.01/0.89 tff(102,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[101, 85])).
% 1.01/0.89 tff(103,plain,
% 1.01/0.89 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv))) | (~((~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))))))),
% 1.01/0.89 inference(quant_inst,[status(thm)],[])).
% 1.01/0.89 tff(104,plain,
% 1.01/0.89 (~((~((~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv))) | (~((~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau))))))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[103, 102])).
% 1.01/0.89 tff(105,plain,
% 1.01/0.89 (((~((~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv))) | (~((~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))))) | ((~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau))))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(106,plain,
% 1.01/0.89 ((~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[105, 104])).
% 1.01/0.89 tff(107,plain,
% 1.01/0.89 ((~((~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau))))) | (~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(108,plain,
% 1.01/0.89 ((~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[107, 106])).
% 1.01/0.89 tff(109,plain,
% 1.01/0.89 (~nevera(tau, eqv)),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[108, 83])).
% 1.01/0.89 tff(110,plain,
% 1.01/0.89 (((~((~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv))) | (~((~nevera(tau, eqv)) | ![Ax: $i, C: $i] : ((~status(Ax, C, eqv)) | (~status(Ax, C, tau)))))) | ((~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(111,plain,
% 1.01/0.89 ((~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv)),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[110, 104])).
% 1.01/0.89 tff(112,plain,
% 1.01/0.89 ((~((~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv))) | (~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv)),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(113,plain,
% 1.01/0.89 ((~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))) | nevera(tau, eqv)),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[112, 111])).
% 1.01/0.89 tff(114,plain,
% 1.01/0.89 (~((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[113, 109])).
% 1.01/0.89 tff(115,plain,
% 1.01/0.89 (((~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), eqv)) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau))) | status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(116,plain,
% 1.01/0.89 (status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau)),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[115, 114])).
% 1.01/0.89 tff(117,plain,
% 1.01/0.89 (^[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)))))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(118,plain,
% 1.01/0.89 (![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))))))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[117])).
% 1.01/0.89 tff(119,plain,
% 1.01/0.89 (^[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)))))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(120,plain,
% 1.01/0.89 (![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))))))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[119])).
% 1.01/0.89 tff(121,plain,
% 1.01/0.89 (^[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)))))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(122,plain,
% 1.01/0.89 (![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))))))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[121])).
% 1.01/0.89 tff(123,plain,
% 1.01/0.89 (![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))))))),
% 1.01/0.89 inference(transitivity,[status(thm)],[122, 120])).
% 1.01/0.89 tff(124,plain,
% 1.01/0.89 (^[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))))))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(125,plain,
% 1.01/0.89 (![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))))))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[124])).
% 1.01/0.89 tff(126,plain,
% 1.01/0.89 (![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))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(127,plain,
% 1.01/0.89 (^[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)))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(128,plain,
% 1.01/0.89 (![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))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[127])).
% 1.01/0.89 tff(129,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')).
% 1.01/0.89 tff(130,plain,
% 1.01/0.89 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.01/0.89 tff(131,plain,
% 1.01/0.89 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[130, 126])).
% 1.01/0.89 tff(132,plain,(
% 1.01/0.89 ![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))))),
% 1.01/0.89 inference(skolemize,[status(sab)],[131])).
% 1.01/0.89 tff(133,plain,
% 1.01/0.89 (![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))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[132, 125])).
% 1.01/0.89 tff(134,plain,
% 1.01/0.89 (![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))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[133, 123])).
% 1.01/0.89 tff(135,plain,
% 1.01/0.89 (![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))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[134, 118])).
% 1.01/0.89 tff(136,plain,
% 1.01/0.89 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm))) | (~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(tau, tau))) | model(I1, tptp_fun_C_24(tau, tau)))))))),
% 1.01/0.89 inference(quant_inst,[status(thm)],[])).
% 1.01/0.89 tff(137,plain,
% 1.01/0.89 (~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm))) | (~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(tau, tau))) | model(I1, tptp_fun_C_24(tau, tau))))))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[136, 135])).
% 1.01/0.89 tff(138,plain,
% 1.01/0.89 (((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm))) | (~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(tau, tau))) | model(I1, tptp_fun_C_24(tau, tau)))))) | ((~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(139,plain,
% 1.01/0.89 ((~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[138, 137])).
% 1.01/0.89 tff(140,assumption,(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)), introduced(assumption)).
% 1.01/0.89 tff(141,plain,
% 1.01/0.89 (^[S1: $i, S2: $i] : refl((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(142,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[141])).
% 1.01/0.89 tff(143,plain,
% 1.01/0.89 (^[S1: $i, S2: $i] : rewrite((~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(144,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[143])).
% 1.01/0.89 tff(145,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.01/0.89 inference(transitivity,[status(thm)],[144, 142])).
% 1.01/0.89 tff(146,plain,
% 1.01/0.89 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) <=> (mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))), trans(monotonicity(rewrite((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) <=> (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))), (((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))) <=> ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))))), rewrite(((mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))) & ((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)))))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))), (((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(147,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[146])).
% 1.01/0.89 tff(148,plain,
% 1.01/0.89 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))))),
% 1.01/0.89 inference(bind,[status(th)],[])).
% 1.01/0.89 tff(149,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2)))) <=> ![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 1.01/0.89 inference(quant_intro,[status(thm)],[148])).
% 1.01/0.89 tff(150,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(151,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','mighta')).
% 1.01/0.89 tff(152,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.01/0.89 tff(153,plain,(
% 1.01/0.89 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2))) | mighta(S1, S2)) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 1.01/0.89 inference(skolemize,[status(sab)],[152])).
% 1.01/0.89 tff(154,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : ((mighta(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & status(Ax, C, S2)))) & ((status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1) & status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2)) | (~mighta(S1, S2))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[153, 149])).
% 1.01/0.89 tff(155,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[154, 147])).
% 1.01/0.89 tff(156,plain,
% 1.01/0.89 (![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[155, 145])).
% 1.01/0.89 tff(157,plain,
% 1.01/0.89 ((~![S1: $i, S2: $i] : (~((~(mighta(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))))) | (~((~mighta(S1, S2)) | (~((~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S1)) | (~status(tptp_fun_Ax_19(S2, S1), tptp_fun_C_18(S2, S1), S2))))))))) | (~((~(mighta(tau, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau))))) | (~((~mighta(tau, thm)) | (~((~status(tptp_fun_Ax_19(thm, tau), tptp_fun_C_18(thm, tau), tau)) | (~status(tptp_fun_Ax_19(thm, tau), tptp_fun_C_18(thm, tau), thm))))))))),
% 1.01/0.89 inference(quant_inst,[status(thm)],[])).
% 1.01/0.89 tff(158,plain,
% 1.01/0.89 (~((~(mighta(tau, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau))))) | (~((~mighta(tau, thm)) | (~((~status(tptp_fun_Ax_19(thm, tau), tptp_fun_C_18(thm, tau), tau)) | (~status(tptp_fun_Ax_19(thm, tau), tptp_fun_C_18(thm, tau), thm)))))))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[157, 156])).
% 1.01/0.89 tff(159,plain,
% 1.01/0.89 (((~(mighta(tau, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau))))) | (~((~mighta(tau, thm)) | (~((~status(tptp_fun_Ax_19(thm, tau), tptp_fun_C_18(thm, tau), tau)) | (~status(tptp_fun_Ax_19(thm, tau), tptp_fun_C_18(thm, tau), thm))))))) | (mighta(tau, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau))))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(160,plain,
% 1.01/0.89 (mighta(tau, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[159, 158])).
% 1.01/0.89 tff(161,plain,
% 1.01/0.89 ((~mighta(tau, thm)) <=> (~mighta(tau, thm))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(162,axiom,(~mighta(tau, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mighta_tau_thm')).
% 1.01/0.89 tff(163,plain,
% 1.01/0.89 (~mighta(tau, thm)),
% 1.01/0.89 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.01/0.89 tff(164,plain,
% 1.01/0.89 ((~(mighta(tau, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau))))) | mighta(tau, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))),
% 1.01/0.89 inference(tautology,[status(thm)],[])).
% 1.01/0.89 tff(165,plain,
% 1.01/0.89 ((~(mighta(tau, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau))))) | ![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[164, 163])).
% 1.01/0.89 tff(166,plain,
% 1.01/0.89 (![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))),
% 1.01/0.89 inference(unit_resolution,[status(thm)],[165, 160])).
% 1.01/0.89 tff(167,plain,
% 1.01/0.89 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))) | ((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)))),
% 1.01/0.89 inference(rewrite,[status(thm)],[])).
% 1.01/0.89 tff(168,plain,
% 1.01/0.89 (((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau))) <=> ((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)))),
% 1.05/0.89 inference(rewrite,[status(thm)],[])).
% 1.05/0.89 tff(169,plain,
% 1.05/0.89 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))) | ((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))) | ((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm))))),
% 1.05/0.89 inference(monotonicity,[status(thm)],[168])).
% 1.05/0.89 tff(170,plain,
% 1.05/0.89 (((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))) | ((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)))),
% 1.05/0.89 inference(transitivity,[status(thm)],[169, 167])).
% 1.05/0.89 tff(171,plain,
% 1.05/0.89 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))) | ((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)))),
% 1.05/0.89 inference(quant_inst,[status(thm)],[])).
% 1.05/0.89 tff(172,plain,
% 1.05/0.89 ((~![Ax: $i, C: $i] : ((~status(Ax, C, thm)) | (~status(Ax, C, tau)))) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm))),
% 1.05/0.89 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.05/0.89 tff(173,plain,
% 1.05/0.89 (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)),
% 1.05/0.89 inference(unit_resolution,[status(thm)],[172, 166, 140])).
% 1.05/0.89 tff(174,plain,
% 1.05/0.89 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm)),
% 1.05/0.89 inference(tautology,[status(thm)],[])).
% 1.05/0.89 tff(175,plain,
% 1.05/0.89 ((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), thm))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau))))),
% 1.05/0.89 inference(unit_resolution,[status(thm)],[174, 173])).
% 1.05/0.89 tff(176,plain,
% 1.05/0.89 (~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))),
% 1.05/0.89 inference(unit_resolution,[status(thm)],[175, 139])).
% 1.05/0.89 tff(177,plain,
% 1.05/0.89 (((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau))) | (~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))),
% 1.05/0.89 inference(tautology,[status(thm)],[])).
% 1.05/0.89 tff(178,plain,
% 1.05/0.89 (~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau))),
% 1.05/0.89 inference(unit_resolution,[status(thm)],[177, 176])).
% 1.05/0.89 tff(179,plain,
% 1.05/0.89 (((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | (~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))) | model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau))),
% 1.05/0.90 inference(tautology,[status(thm)],[])).
% 1.05/0.90 tff(180,plain,
% 1.05/0.90 ((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | (~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[179, 178])).
% 1.05/0.90 tff(181,plain,
% 1.05/0.90 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, tau) | (~model(tptp_fun_I1_10(C, Ax), Ax)) | (~model(tptp_fun_I1_10(C, Ax), C)))) | (~((~status(Ax, C, tau)) | ![I1: $i] : (~((~model(I1, Ax)) | (~model(I1, C))))))))) | (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | (~model(tptp_fun_I1_10(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | (~model(tptp_fun_I1_10(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau))))) | (~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau)))))))))),
% 1.05/0.90 inference(quant_inst,[status(thm)],[])).
% 1.05/0.90 tff(182,plain,
% 1.05/0.90 (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | (~model(tptp_fun_I1_10(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | (~model(tptp_fun_I1_10(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau))))) | (~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau))))))))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[181, 58])).
% 1.05/0.90 tff(183,plain,
% 1.05/0.90 (((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | (~model(tptp_fun_I1_10(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | (~model(tptp_fun_I1_10(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau))))) | (~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau)))))))) | ((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau))))))),
% 1.05/0.90 inference(tautology,[status(thm)],[])).
% 1.05/0.90 tff(184,plain,
% 1.05/0.90 ((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau)))))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[183, 182])).
% 1.05/0.90 tff(185,plain,
% 1.05/0.90 ((~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau))))))) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau)))))),
% 1.05/0.90 inference(tautology,[status(thm)],[])).
% 1.05/0.90 tff(186,plain,
% 1.05/0.90 ((~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau))))))) | ![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau)))))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[185, 140])).
% 1.05/0.90 tff(187,plain,
% 1.05/0.90 (![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau)))))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[186, 184])).
% 1.05/0.90 tff(188,plain,
% 1.05/0.90 ((~![I1: $i] : (~((~model(I1, tptp_fun_Ax_25(tau, tau))) | (~model(I1, tptp_fun_C_24(tau, tau)))))) | (~((~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_Ax_25(tau, tau))) | (~model(tptp_fun_I1_3(tptp_fun_C_24(tau, tau), tptp_fun_Ax_25(tau, tau)), tptp_fun_C_24(tau, tau)))))),
% 1.05/0.90 inference(quant_inst,[status(thm)],[])).
% 1.05/0.90 tff(189,plain,
% 1.05/0.90 ($false),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[188, 187, 180])).
% 1.05/0.90 tff(190,plain,(~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.90 tff(191,plain,
% 1.05/0.90 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau)))))))),
% 1.05/0.90 inference(rewrite,[status(thm)],[])).
% 1.05/0.90 tff(192,plain,
% 1.05/0.90 ((~((~((~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)))) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tau)) | (~status(Ax, C, tau))))))) <=> (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau))))))),
% 1.05/0.90 inference(rewrite,[status(thm)],[])).
% 1.05/0.90 tff(193,plain,
% 1.05/0.90 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)))) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tau)) | (~status(Ax, C, tau)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau)))))))),
% 1.05/0.90 inference(monotonicity,[status(thm)],[192])).
% 1.05/0.90 tff(194,plain,
% 1.05/0.90 (((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)))) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tau)) | (~status(Ax, C, tau)))))))) <=> ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau)))))))),
% 1.05/0.90 inference(transitivity,[status(thm)],[193, 191])).
% 1.05/0.90 tff(195,plain,
% 1.05/0.90 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~((~((~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)) | (~status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau)))) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : ((~status(Ax, C, tau)) | (~status(Ax, C, tau)))))))),
% 1.05/0.90 inference(quant_inst,[status(thm)],[])).
% 1.05/0.90 tff(196,plain,
% 1.05/0.90 ((~![S1: $i, S2: $i] : (~((~((~((~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S2)) | (~status(tptp_fun_Ax_25(S2, S1), tptp_fun_C_24(S2, S1), S1)))) | nevera(S1, S2))) | (~((~nevera(S1, S2)) | ![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1)))))))) | (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau))))))),
% 1.05/0.90 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.05/0.90 tff(197,plain,
% 1.05/0.90 (~((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau)))))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[196, 102])).
% 1.05/0.90 tff(198,plain,
% 1.05/0.90 (((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau))))) | (status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))),
% 1.05/0.90 inference(tautology,[status(thm)],[])).
% 1.05/0.90 tff(199,plain,
% 1.05/0.90 (status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau)),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[198, 197])).
% 1.05/0.90 tff(200,plain,
% 1.05/0.90 ((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau)),
% 1.05/0.90 inference(tautology,[status(thm)],[])).
% 1.05/0.90 tff(201,plain,
% 1.05/0.90 (status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau)),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[200, 199])).
% 1.05/0.90 tff(202,plain,
% 1.05/0.90 (nevera(tau, tau)),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[201, 190])).
% 1.05/0.90 tff(203,plain,
% 1.05/0.90 (((~(status(tptp_fun_Ax_25(tau, tau), tptp_fun_C_24(tau, tau), tau) | nevera(tau, tau))) | (~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau))))) | ((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau)))),
% 1.05/0.90 inference(tautology,[status(thm)],[])).
% 1.05/0.90 tff(204,plain,
% 1.05/0.90 ((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[203, 197])).
% 1.05/0.90 tff(205,plain,
% 1.05/0.90 ((~((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau)))) | (~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau))),
% 1.05/0.90 inference(tautology,[status(thm)],[])).
% 1.05/0.90 tff(206,plain,
% 1.05/0.90 ((~nevera(tau, tau)) | ![Ax: $i, C: $i] : (~status(Ax, C, tau))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[205, 204])).
% 1.05/0.90 tff(207,plain,
% 1.05/0.90 (![Ax: $i, C: $i] : (~status(Ax, C, tau))),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[206, 202])).
% 1.05/0.90 tff(208,plain,
% 1.05/0.90 ((~![Ax: $i, C: $i] : (~status(Ax, C, tau))) | (~status(tptp_fun_Ax_25(eqv, tau), tptp_fun_C_24(eqv, tau), tau))),
% 1.05/0.90 inference(quant_inst,[status(thm)],[])).
% 1.05/0.90 tff(209,plain,
% 1.05/0.90 ($false),
% 1.05/0.90 inference(unit_resolution,[status(thm)],[208, 207, 116])).
% 1.05/0.90 % SZS output end Proof
%------------------------------------------------------------------------------