TSTP Solution File: KRS203+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS203+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:45:11 EDT 2022
% Result : Theorem 19.57s 12.75s
% Output : Proof 19.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS203+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 09:51:40 EDT 2022
% 0.13/0.33 % 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.
% 19.57/12.75 % SZS status Theorem
% 19.57/12.75 % SZS output start Proof
% 19.57/12.75 tff(model_type, type, (
% 19.57/12.75 model: ( $i * $i ) > $o)).
% 19.57/12.75 tff(not_type, type, (
% 19.57/12.75 not: $i > $i)).
% 19.57/12.75 tff(tptp_fun_F_29_type, type, (
% 19.57/12.75 tptp_fun_F_29: $i)).
% 19.57/12.75 tff(tptp_fun_I2_31_type, type, (
% 19.57/12.75 tptp_fun_I2_31: $i)).
% 19.57/12.75 tff(tptp_fun_F_28_type, type, (
% 19.57/12.75 tptp_fun_F_28: $i)).
% 19.57/12.75 tff(status_type, type, (
% 19.57/12.75 status: ( $i * $i * $i ) > $o)).
% 19.57/12.75 tff(csa_type, type, (
% 19.57/12.75 csa: $i)).
% 19.57/12.75 tff(sat_type, type, (
% 19.57/12.75 sat: $i)).
% 19.57/12.75 tff(tptp_fun_I1_2_type, type, (
% 19.57/12.75 tptp_fun_I1_2: ( $i * $i ) > $i)).
% 19.57/12.75 tff(tptp_fun_I1_30_type, type, (
% 19.57/12.75 tptp_fun_I1_30: $i)).
% 19.57/12.75 tff(nevera_type, type, (
% 19.57/12.75 nevera: ( $i * $i ) > $o)).
% 19.57/12.75 tff(tptp_fun_C_24_type, type, (
% 19.57/12.75 tptp_fun_C_24: ( $i * $i ) > $i)).
% 19.57/12.75 tff(tptp_fun_Ax_25_type, type, (
% 19.57/12.75 tptp_fun_Ax_25: ( $i * $i ) > $i)).
% 19.57/12.75 tff(tptp_fun_I1_14_type, type, (
% 19.57/12.75 tptp_fun_I1_14: ( $i * $i ) > $i)).
% 19.57/12.75 tff(thm_type, type, (
% 19.57/12.75 thm: $i)).
% 19.57/12.75 tff(tptp_fun_I1_3_type, type, (
% 19.57/12.75 tptp_fun_I1_3: ( $i * $i ) > $i)).
% 19.57/12.75 tff(nota_type, type, (
% 19.57/12.75 nota: ( $i * $i ) > $o)).
% 19.57/12.75 tff(tptp_fun_C_22_type, type, (
% 19.57/12.75 tptp_fun_C_22: ( $i * $i ) > $i)).
% 19.57/12.75 tff(tptp_fun_Ax_23_type, type, (
% 19.57/12.75 tptp_fun_Ax_23: ( $i * $i ) > $i)).
% 19.57/12.75 tff(1,assumption,((~(status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))))) | (~((~status(F!28, F!29, sat)) | (~((~model(tptp_fun_I1_2(F!29, F!28), F!28)) | (~model(tptp_fun_I1_2(F!29, F!28), F!29))))))), introduced(assumption)).
% 19.57/12.75 tff(2,plain,
% 19.57/12.75 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))))),
% 19.57/12.75 inference(bind,[status(th)],[])).
% 19.57/12.75 tff(3,plain,
% 19.57/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 19.57/12.75 inference(quant_intro,[status(thm)],[2])).
% 19.57/12.75 tff(4,plain,
% 19.57/12.75 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))))),
% 19.57/12.75 inference(bind,[status(th)],[])).
% 19.57/12.75 tff(5,plain,
% 19.57/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 19.57/12.75 inference(quant_intro,[status(thm)],[4])).
% 19.57/12.75 tff(6,plain,
% 19.57/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 19.57/12.75 inference(transitivity,[status(thm)],[5, 3])).
% 19.57/12.75 tff(7,plain,
% 19.57/12.75 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) <=> (status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))), trans(monotonicity(rewrite((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) <=> (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))), (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))) <=> ((~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))) | (~status(Ax, C, sat))))), rewrite(((~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))) | (~status(Ax, C, sat))) <=> ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))), (((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))) <=> ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))), (((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ((status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C)))) & ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))))), rewrite(((status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C)))) & ((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C)))))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))), (((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))))),
% 19.57/12.75 inference(bind,[status(th)],[])).
% 19.57/12.75 tff(8,plain,
% 19.57/12.75 (![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 19.57/12.75 inference(quant_intro,[status(thm)],[7])).
% 19.57/12.75 tff(9,plain,
% 19.57/12.75 (^[Ax: $i, C: $i] : rewrite(((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))))),
% 19.57/12.75 inference(bind,[status(th)],[])).
% 19.57/12.75 tff(10,plain,
% 19.57/12.75 (![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 19.57/12.75 inference(quant_intro,[status(thm)],[9])).
% 19.57/12.75 tff(11,plain,
% 19.57/12.75 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat)) <=> ![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))),
% 19.57/12.75 inference(rewrite,[status(thm)],[])).
% 19.57/12.75 tff(12,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','sat')).
% 19.57/12.75 tff(13,plain,
% 19.57/12.75 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, C)) <=> status(Ax, C, sat))),
% 19.57/12.75 inference(modus_ponens,[status(thm)],[12, 11])).
% 19.57/12.75 tff(14,plain,(
% 19.57/12.75 ![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, C))) | status(Ax, C, sat)) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 19.57/12.75 inference(skolemize,[status(sab)],[13])).
% 19.57/12.75 tff(15,plain,
% 19.57/12.75 (![Ax: $i, C: $i] : ((status(Ax, C, sat) | ![I1: $i] : (~(model(I1, Ax) & model(I1, C)))) & ((model(tptp_fun_I1_2(C, Ax), Ax) & model(tptp_fun_I1_2(C, Ax), C)) | (~status(Ax, C, sat))))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[14, 10])).
% 19.61/12.75 tff(16,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[15, 8])).
% 19.61/12.75 tff(17,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[16, 6])).
% 19.61/12.75 tff(18,plain,
% 19.61/12.75 ((~![Ax: $i, C: $i] : (~((~(status(Ax, C, sat) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, C))))) | (~((~status(Ax, C, sat)) | (~((~model(tptp_fun_I1_2(C, Ax), Ax)) | (~model(tptp_fun_I1_2(C, Ax), C))))))))) | (~((~(status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))))) | (~((~status(F!28, F!29, sat)) | (~((~model(tptp_fun_I1_2(F!29, F!28), F!28)) | (~model(tptp_fun_I1_2(F!29, F!28), F!29))))))))),
% 19.61/12.75 inference(quant_inst,[status(thm)],[])).
% 19.61/12.75 tff(19,plain,
% 19.61/12.75 ($false),
% 19.61/12.75 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 19.61/12.75 tff(20,plain,(~((~(status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))))) | (~((~status(F!28, F!29, sat)) | (~((~model(tptp_fun_I1_2(F!29, F!28), F!28)) | (~model(tptp_fun_I1_2(F!29, F!28), F!29)))))))), inference(lemma,lemma(discharge,[]))).
% 19.61/12.75 tff(21,plain,
% 19.61/12.75 (((~(status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))))) | (~((~status(F!28, F!29, sat)) | (~((~model(tptp_fun_I1_2(F!29, F!28), F!28)) | (~model(tptp_fun_I1_2(F!29, F!28), F!29))))))) | (status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))))),
% 19.61/12.75 inference(tautology,[status(thm)],[])).
% 19.61/12.75 tff(22,plain,
% 19.61/12.75 (status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))),
% 19.61/12.75 inference(unit_resolution,[status(thm)],[21, 20])).
% 19.61/12.75 tff(23,assumption,(![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))), introduced(assumption)).
% 19.61/12.75 tff(24,plain,
% 19.61/12.75 (^[I: $i] : refl(model(I, F!28) <=> model(I, F!28))),
% 19.61/12.75 inference(bind,[status(th)],[])).
% 19.61/12.75 tff(25,plain,
% 19.61/12.75 (![I: $i] : model(I, F!28) <=> ![I: $i] : model(I, F!28)),
% 19.61/12.75 inference(quant_intro,[status(thm)],[24])).
% 19.61/12.75 tff(26,plain,
% 19.61/12.75 (?[F: $i] : ![I: $i] : model(I, F) <=> ?[F: $i] : ![I: $i] : model(I, F)),
% 19.61/12.75 inference(rewrite,[status(thm)],[])).
% 19.61/12.75 tff(27,axiom,(?[F: $i] : ![I: $i] : model(I, F)), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','tautology')).
% 19.61/12.75 tff(28,plain,
% 19.61/12.75 (?[F: $i] : ![I: $i] : model(I, F)),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[27, 26])).
% 19.61/12.75 tff(29,plain,(
% 19.61/12.75 $oeq(![I: $i] : model(I, F!28), ![I: $i] : model(I, F!28))),
% 19.61/12.75 inference(transitivity,[status(sab)],[28])).
% 19.61/12.75 tff(30,plain,
% 19.61/12.75 (![I: $i] : model(I, F!28)),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[29, 25])).
% 19.61/12.75 tff(31,plain,
% 19.61/12.75 ((~![I: $i] : model(I, F!28)) | model(I1!30, F!28)),
% 19.61/12.75 inference(quant_inst,[status(thm)],[])).
% 19.61/12.75 tff(32,plain,
% 19.61/12.75 (model(I1!30, F!28)),
% 19.61/12.75 inference(unit_resolution,[status(thm)],[31, 30])).
% 19.61/12.75 tff(33,plain,
% 19.61/12.75 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F))) <=> ?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 19.61/12.75 inference(rewrite,[status(thm)],[])).
% 19.61/12.75 tff(34,axiom,(?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','satisfiable')).
% 19.61/12.75 tff(35,plain,
% 19.61/12.75 (?[F: $i] : (?[I1: $i] : model(I1, F) & ?[I2: $i] : (~model(I2, F)))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[34, 33])).
% 19.61/12.75 tff(36,plain,
% 19.61/12.75 (model(I1!30, F!29)),
% 19.61/12.75 inference(and_elim,[status(thm)],[35])).
% 19.61/12.75 tff(37,plain,
% 19.61/12.75 (((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))) | ((~model(I1!30, F!28)) | (~model(I1!30, F!29)))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))) | (~model(I1!30, F!28)) | (~model(I1!30, F!29)))),
% 19.61/12.75 inference(rewrite,[status(thm)],[])).
% 19.61/12.75 tff(38,plain,
% 19.61/12.75 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))) | ((~model(I1!30, F!28)) | (~model(I1!30, F!29)))),
% 19.61/12.75 inference(quant_inst,[status(thm)],[])).
% 19.61/12.75 tff(39,plain,
% 19.61/12.75 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))) | (~model(I1!30, F!28)) | (~model(I1!30, F!29))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[38, 37])).
% 19.61/12.75 tff(40,plain,
% 19.61/12.75 ($false),
% 19.61/12.75 inference(unit_resolution,[status(thm)],[39, 36, 32, 23])).
% 19.61/12.75 tff(41,plain,(~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))), inference(lemma,lemma(discharge,[]))).
% 19.61/12.75 tff(42,plain,
% 19.61/12.75 ((~(status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))))) | status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29)))),
% 19.61/12.75 inference(tautology,[status(thm)],[])).
% 19.61/12.75 tff(43,plain,
% 19.61/12.75 ((~(status(F!28, F!29, sat) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, F!29))))) | status(F!28, F!29, sat)),
% 19.61/12.75 inference(unit_resolution,[status(thm)],[42, 41])).
% 19.61/12.75 tff(44,plain,
% 19.61/12.75 (status(F!28, F!29, sat)),
% 19.61/12.75 inference(unit_resolution,[status(thm)],[43, 22])).
% 19.61/12.75 tff(45,plain,
% 19.61/12.75 (^[I: $i, F: $i] : refl(((~model(I, F)) <=> model(I, not(F))) <=> ((~model(I, F)) <=> model(I, not(F))))),
% 19.61/12.75 inference(bind,[status(th)],[])).
% 19.61/12.75 tff(46,plain,
% 19.61/12.75 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 19.61/12.75 inference(quant_intro,[status(thm)],[45])).
% 19.61/12.75 tff(47,plain,
% 19.61/12.75 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 19.61/12.75 inference(rewrite,[status(thm)],[])).
% 19.61/12.75 tff(48,plain,
% 19.61/12.75 (^[I: $i, F: $i] : rewrite((~(model(I, F) <=> model(I, not(F)))) <=> ((~model(I, F)) <=> model(I, not(F))))),
% 19.61/12.75 inference(bind,[status(th)],[])).
% 19.61/12.75 tff(49,plain,
% 19.61/12.75 (![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F)))) <=> ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 19.61/12.75 inference(quant_intro,[status(thm)],[48])).
% 19.61/12.75 tff(50,axiom,(![I: $i, F: $i] : (~(model(I, F) <=> model(I, not(F))))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','completeness')).
% 19.61/12.75 tff(51,plain,
% 19.61/12.75 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[50, 49])).
% 19.61/12.75 tff(52,plain,
% 19.61/12.75 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[51, 47])).
% 19.61/12.75 tff(53,plain,(
% 19.61/12.75 ![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 19.61/12.75 inference(skolemize,[status(sab)],[52])).
% 19.61/12.75 tff(54,plain,
% 19.61/12.75 (![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[53, 46])).
% 19.61/12.75 tff(55,plain,
% 19.61/12.75 ((~![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa))))),
% 19.61/12.75 inference(quant_inst,[status(thm)],[])).
% 19.61/12.75 tff(56,plain,
% 19.61/12.75 ((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))),
% 19.61/12.75 inference(unit_resolution,[status(thm)],[55, 54])).
% 19.61/12.75 tff(57,plain,
% 19.61/12.75 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))))))),
% 19.61/12.75 inference(bind,[status(th)],[])).
% 19.61/12.75 tff(58,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))),
% 19.61/12.75 inference(quant_intro,[status(thm)],[57])).
% 19.61/12.75 tff(59,plain,
% 19.61/12.75 (^[Ax: $i, C: $i] : refl((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))))),
% 19.61/12.75 inference(bind,[status(th)],[])).
% 19.61/12.75 tff(60,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 19.61/12.75 inference(quant_intro,[status(thm)],[59])).
% 19.61/12.75 tff(61,plain,
% 19.61/12.75 (^[Ax: $i, C: $i] : rewrite((~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))))),
% 19.61/12.75 inference(bind,[status(th)],[])).
% 19.61/12.75 tff(62,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 19.61/12.75 inference(quant_intro,[status(thm)],[61])).
% 19.61/12.75 tff(63,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 19.61/12.75 inference(transitivity,[status(thm)],[62, 60])).
% 19.61/12.75 tff(64,plain,
% 19.61/12.75 (^[Ax: $i, C: $i] : trans(monotonicity(rewrite((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) <=> (status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))), trans(monotonicity(rewrite((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) <=> (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))), (((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))) <=> ((~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))) | (~status(Ax, C, csa))))), rewrite(((~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))) | (~status(Ax, C, csa))) <=> ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))), (((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))) <=> ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))), (((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ((status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))) & ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))))), rewrite(((status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))) & ((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))), (((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))))),
% 19.61/12.75 inference(bind,[status(th)],[])).
% 19.61/12.75 tff(65,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 19.61/12.75 inference(quant_intro,[status(thm)],[64])).
% 19.61/12.75 tff(66,plain,
% 19.61/12.75 (^[Ax: $i, C: $i] : rewrite(((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))))),
% 19.61/12.75 inference(bind,[status(th)],[])).
% 19.61/12.75 tff(67,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa)))) <=> ![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 19.61/12.75 inference(quant_intro,[status(thm)],[66])).
% 19.61/12.75 tff(68,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa)) <=> ![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 19.61/12.75 inference(rewrite,[status(thm)],[])).
% 19.61/12.75 tff(69,axiom,(![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax','csa')).
% 19.61/12.75 tff(70,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (?[I1: $i] : (model(I1, Ax) & model(I1, not(C))) <=> status(Ax, C, csa))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[69, 68])).
% 19.61/12.75 tff(71,plain,(
% 19.61/12.75 ![Ax: $i, C: $i] : ((![I1: $i] : (~(model(I1, Ax) & model(I1, not(C)))) | status(Ax, C, csa)) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 19.61/12.75 inference(skolemize,[status(sab)],[70])).
% 19.61/12.75 tff(72,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : ((status(Ax, C, csa) | ![I1: $i] : (~(model(I1, Ax) & model(I1, not(C))))) & ((model(tptp_fun_I1_14(C, Ax), Ax) & model(tptp_fun_I1_14(C, Ax), not(C))) | (~status(Ax, C, csa))))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[71, 67])).
% 19.61/12.75 tff(73,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[72, 65])).
% 19.61/12.75 tff(74,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C)))))) | (~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C)))))))))),
% 19.61/12.75 inference(modus_ponens,[status(thm)],[73, 63])).
% 19.61/12.75 tff(75,plain,
% 19.61/12.75 (![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))),
% 19.61/12.76 inference(modus_ponens,[status(thm)],[74, 58])).
% 19.61/12.76 tff(76,plain,
% 19.61/12.76 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa))))))))))),
% 19.61/12.76 inference(rewrite,[status(thm)],[])).
% 19.61/12.76 tff(77,plain,
% 19.61/12.76 ((~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa))))))))) <=> (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa)))))))))),
% 19.61/12.76 inference(rewrite,[status(thm)],[])).
% 19.61/12.76 tff(78,plain,
% 19.61/12.76 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa))))))))))),
% 19.61/12.76 inference(monotonicity,[status(thm)],[77])).
% 19.61/12.76 tff(79,plain,
% 19.61/12.76 (((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa)))))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa))))))))))),
% 19.61/12.76 inference(transitivity,[status(thm)],[78, 76])).
% 19.61/12.76 tff(80,plain,
% 19.61/12.76 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa)))))))))),
% 19.61/12.76 inference(quant_inst,[status(thm)],[])).
% 19.61/12.76 tff(81,plain,
% 19.61/12.76 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa)))))))))),
% 19.61/12.76 inference(modus_ponens,[status(thm)],[80, 79])).
% 19.61/12.76 tff(82,plain,
% 19.61/12.76 (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa))))))))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[81, 75])).
% 19.61/12.76 tff(83,plain,
% 19.61/12.76 (((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~(status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | (~model(I1, not(tptp_fun_C_24(sat, csa)))))))) | ((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))),
% 19.61/12.76 inference(tautology,[status(thm)],[])).
% 19.61/12.76 tff(84,plain,
% 19.61/12.76 ((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa)))))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[83, 82])).
% 19.61/12.76 tff(85,assumption,(~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))), introduced(assumption)).
% 19.61/12.76 tff(86,plain,
% 19.61/12.76 (((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)),
% 19.61/12.76 inference(tautology,[status(thm)],[])).
% 19.61/12.76 tff(87,plain,
% 19.61/12.76 (status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[86, 85])).
% 19.61/12.76 tff(88,plain,
% 19.61/12.76 ((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa)))))),
% 19.61/12.76 inference(tautology,[status(thm)],[])).
% 19.61/12.76 tff(89,plain,
% 19.61/12.76 ((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))))) | (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa)))))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[88, 87])).
% 19.61/12.76 tff(90,plain,
% 19.61/12.76 (~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[89, 84])).
% 19.61/12.76 tff(91,plain,
% 19.61/12.76 (((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa)))) | model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))),
% 19.61/12.76 inference(tautology,[status(thm)],[])).
% 19.61/12.76 tff(92,plain,
% 19.61/12.76 (model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[91, 90])).
% 19.61/12.76 tff(93,plain,
% 19.61/12.76 ((~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa))))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa))))),
% 19.61/12.76 inference(tautology,[status(thm)],[])).
% 19.61/12.76 tff(94,plain,
% 19.61/12.76 ((~((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa))) <=> model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa))))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[93, 92])).
% 19.61/12.76 tff(95,plain,
% 19.61/12.76 (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[94, 56])).
% 19.61/12.76 tff(96,plain,
% 19.61/12.76 (^[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)))))))),
% 19.61/12.76 inference(bind,[status(th)],[])).
% 19.61/12.76 tff(97,plain,
% 19.61/12.76 (![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))))))),
% 19.61/12.76 inference(quant_intro,[status(thm)],[96])).
% 19.61/12.76 tff(98,plain,
% 19.61/12.76 (^[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)))))))),
% 19.61/12.76 inference(bind,[status(th)],[])).
% 19.61/12.76 tff(99,plain,
% 19.61/12.76 (![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))))))),
% 19.61/12.76 inference(quant_intro,[status(thm)],[98])).
% 19.61/12.76 tff(100,plain,
% 19.61/12.76 (^[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)))))))),
% 19.61/12.76 inference(bind,[status(th)],[])).
% 19.61/12.76 tff(101,plain,
% 19.61/12.76 (![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))))))),
% 19.61/12.76 inference(quant_intro,[status(thm)],[100])).
% 19.61/12.76 tff(102,plain,
% 19.61/12.76 (![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))))))),
% 19.61/12.76 inference(transitivity,[status(thm)],[101, 99])).
% 19.61/12.76 tff(103,plain,
% 19.61/12.76 (^[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))))))))),
% 19.61/12.76 inference(bind,[status(th)],[])).
% 19.61/12.76 tff(104,plain,
% 19.61/12.76 (![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))))))),
% 19.61/12.76 inference(quant_intro,[status(thm)],[103])).
% 19.61/12.76 tff(105,plain,
% 19.61/12.76 (![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))),
% 19.61/12.76 inference(rewrite,[status(thm)],[])).
% 19.61/12.76 tff(106,plain,
% 19.61/12.76 (^[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)))),
% 19.61/12.76 inference(bind,[status(th)],[])).
% 19.61/12.76 tff(107,plain,
% 19.61/12.76 (![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))),
% 19.61/12.76 inference(quant_intro,[status(thm)],[106])).
% 19.61/12.76 tff(108,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')).
% 19.61/12.76 tff(109,plain,
% 19.61/12.76 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 19.61/12.76 inference(modus_ponens,[status(thm)],[108, 107])).
% 19.61/12.76 tff(110,plain,
% 19.61/12.76 (![Ax: $i, C: $i] : (![I1: $i] : ((~model(I1, Ax)) | model(I1, C)) <=> status(Ax, C, thm))),
% 19.61/12.76 inference(modus_ponens,[status(thm)],[109, 105])).
% 19.61/12.76 tff(111,plain,(
% 19.61/12.76 ![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))))),
% 19.61/12.76 inference(skolemize,[status(sab)],[110])).
% 19.61/12.76 tff(112,plain,
% 19.61/12.76 (![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))))))),
% 19.61/12.76 inference(modus_ponens,[status(thm)],[111, 104])).
% 19.61/12.76 tff(113,plain,
% 19.61/12.76 (![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))))))),
% 19.61/12.76 inference(modus_ponens,[status(thm)],[112, 102])).
% 19.61/12.76 tff(114,plain,
% 19.61/12.76 (![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))))))),
% 19.61/12.76 inference(modus_ponens,[status(thm)],[113, 97])).
% 19.61/12.76 tff(115,plain,
% 19.61/12.76 (((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))))))),
% 19.61/12.76 inference(rewrite,[status(thm)],[])).
% 19.61/12.76 tff(116,plain,
% 19.61/12.76 ((~((~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))) | (~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))))) <=> (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)))))),
% 19.61/12.76 inference(rewrite,[status(thm)],[])).
% 19.61/12.76 tff(117,plain,
% 19.61/12.76 (((~![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(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))) | (~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))))))),
% 19.61/12.76 inference(monotonicity,[status(thm)],[116])).
% 19.61/12.76 tff(118,plain,
% 19.61/12.76 (((~![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(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))) | (~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))))))) <=> ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))))))),
% 19.61/12.76 inference(transitivity,[status(thm)],[117, 115])).
% 19.61/12.76 tff(119,plain,
% 19.61/12.76 ((~![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(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))) | (~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))))))),
% 19.61/12.76 inference(quant_inst,[status(thm)],[])).
% 19.61/12.76 tff(120,plain,
% 19.61/12.76 ((~![Ax: $i, C: $i] : (~((~((~((~model(tptp_fun_I1_3(C, Ax), Ax)) | model(tptp_fun_I1_3(C, Ax), C))) | status(Ax, C, thm))) | (~((~status(Ax, C, thm)) | ![I1: $i] : ((~model(I1, Ax)) | model(I1, C))))))) | (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)))))),
% 19.61/12.76 inference(modus_ponens,[status(thm)],[119, 118])).
% 19.61/12.76 tff(121,plain,
% 19.61/12.76 (~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[120, 114])).
% 19.61/12.76 tff(122,plain,
% 19.61/12.76 (((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~((~((~model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_3(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)))) | ((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))),
% 19.61/12.76 inference(tautology,[status(thm)],[])).
% 19.61/12.76 tff(123,plain,
% 19.61/12.76 ((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[122, 121])).
% 19.61/12.76 tff(124,plain,
% 19.61/12.76 (((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa))) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)),
% 19.61/12.76 inference(tautology,[status(thm)],[])).
% 19.61/12.76 tff(125,plain,
% 19.61/12.76 (status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)),
% 19.61/12.76 inference(unit_resolution,[status(thm)],[124, 85])).
% 19.61/12.76 tff(126,plain,
% 19.61/12.76 (^[S1: $i, S2: $i] : refl((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(127,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[126])).
% 19.61/12.77 tff(128,plain,
% 19.61/12.77 (^[S1: $i, S2: $i] : rewrite((~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(129,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[128])).
% 19.61/12.77 tff(130,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 19.61/12.77 inference(transitivity,[status(thm)],[129, 127])).
% 19.61/12.77 tff(131,plain,
% 19.61/12.77 (^[S1: $i, S2: $i] : trans(monotonicity(rewrite((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) <=> (nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))), trans(monotonicity(rewrite((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) <=> (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))), rewrite(((~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))), (((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))) <=> ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))))), rewrite(((nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2))) & ((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))), (((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(132,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[131])).
% 19.61/12.77 tff(133,plain,
% 19.61/12.77 (^[S1: $i, S2: $i] : rewrite(((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(134,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2)))) <=> ![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[133])).
% 19.61/12.77 tff(135,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2)) <=> ![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 19.61/12.77 inference(rewrite,[status(thm)],[])).
% 19.61/12.77 tff(136,axiom,(![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))), file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax','nota')).
% 19.61/12.77 tff(137,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (?[Ax: $i, C: $i] : (status(Ax, C, S1) & (~status(Ax, C, S2))) <=> nota(S1, S2))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[136, 135])).
% 19.61/12.77 tff(138,plain,(
% 19.61/12.77 ![S1: $i, S2: $i] : ((![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2)))) | nota(S1, S2)) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 19.61/12.77 inference(skolemize,[status(sab)],[137])).
% 19.61/12.77 tff(139,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : ((nota(S1, S2) | ![Ax: $i, C: $i] : (~(status(Ax, C, S1) & (~status(Ax, C, S2))))) & ((status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1) & (~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2))) | (~nota(S1, S2))))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[138, 134])).
% 19.61/12.77 tff(140,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[139, 132])).
% 19.61/12.77 tff(141,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[140, 130])).
% 19.61/12.77 tff(142,plain,
% 19.61/12.77 ((~![S1: $i, S2: $i] : (~((~(nota(S1, S2) | ![Ax: $i, C: $i] : ((~status(Ax, C, S1)) | status(Ax, C, S2)))) | (~((~nota(S1, S2)) | (~((~status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S1)) | status(tptp_fun_Ax_23(S2, S1), tptp_fun_C_22(S2, S1), S2)))))))) | (~((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | (~((~nota(sat, thm)) | (~((~status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), sat)) | status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), thm)))))))),
% 19.61/12.77 inference(quant_inst,[status(thm)],[])).
% 19.61/12.77 tff(143,plain,
% 19.61/12.77 (~((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | (~((~nota(sat, thm)) | (~((~status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), sat)) | status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), thm))))))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[142, 141])).
% 19.61/12.77 tff(144,plain,
% 19.61/12.77 (((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | (~((~nota(sat, thm)) | (~((~status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), sat)) | status(tptp_fun_Ax_23(thm, sat), tptp_fun_C_22(thm, sat), thm)))))) | (nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(145,plain,
% 19.61/12.77 (nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[144, 143])).
% 19.61/12.77 tff(146,plain,
% 19.61/12.77 ((~nota(sat, thm)) <=> (~nota(sat, thm))),
% 19.61/12.77 inference(rewrite,[status(thm)],[])).
% 19.61/12.77 tff(147,axiom,(~nota(sat, thm)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nota_sat_thm')).
% 19.61/12.77 tff(148,plain,
% 19.61/12.77 (~nota(sat, thm)),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[147, 146])).
% 19.61/12.77 tff(149,plain,
% 19.61/12.77 ((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(150,plain,
% 19.61/12.77 ((~(nota(sat, thm) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm)))) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[149, 148])).
% 19.61/12.77 tff(151,plain,
% 19.61/12.77 (![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[150, 145])).
% 19.61/12.77 tff(152,plain,
% 19.61/12.77 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))),
% 19.61/12.77 inference(rewrite,[status(thm)],[])).
% 19.61/12.77 tff(153,plain,
% 19.61/12.77 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))) | ((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm))),
% 19.61/12.77 inference(quant_inst,[status(thm)],[])).
% 19.61/12.77 tff(154,plain,
% 19.61/12.77 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | status(Ax, C, thm))) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[153, 152])).
% 19.61/12.77 tff(155,plain,
% 19.61/12.77 (status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[154, 151, 125])).
% 19.61/12.77 tff(156,plain,
% 19.61/12.77 ((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(157,plain,
% 19.61/12.77 ((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), thm)) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa))))) | ![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[156, 155])).
% 19.61/12.77 tff(158,plain,
% 19.61/12.77 (![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[157, 123])).
% 19.61/12.77 tff(159,plain,
% 19.61/12.77 (((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), not(tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa)))) | model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(160,plain,
% 19.61/12.77 (model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[159, 90])).
% 19.61/12.77 tff(161,plain,
% 19.61/12.77 (((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))) <=> ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))),
% 19.61/12.77 inference(rewrite,[status(thm)],[])).
% 19.61/12.77 tff(162,plain,
% 19.61/12.77 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))) | ((~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa)))),
% 19.61/12.77 inference(quant_inst,[status(thm)],[])).
% 19.61/12.77 tff(163,plain,
% 19.61/12.77 ((~![I1: $i] : ((~model(I1, tptp_fun_Ax_25(sat, csa))) | model(I1, tptp_fun_C_24(sat, csa)))) | (~model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_Ax_25(sat, csa))) | model(tptp_fun_I1_14(tptp_fun_C_24(sat, csa), tptp_fun_Ax_25(sat, csa)), tptp_fun_C_24(sat, csa))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[162, 161])).
% 19.61/12.77 tff(164,plain,
% 19.61/12.77 ($false),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[163, 160, 158, 95])).
% 19.61/12.77 tff(165,plain,((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa))), inference(lemma,lemma(discharge,[]))).
% 19.61/12.77 tff(166,plain,
% 19.61/12.77 (^[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))))))))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(167,plain,
% 19.61/12.77 (![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)))))))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[166])).
% 19.61/12.77 tff(168,plain,
% 19.61/12.77 (^[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)))))))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(169,plain,
% 19.61/12.77 (![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))))))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[168])).
% 19.61/12.77 tff(170,plain,
% 19.61/12.77 (^[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)))))))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(171,plain,
% 19.61/12.77 (![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))))))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[170])).
% 19.61/12.77 tff(172,plain,
% 19.61/12.77 (![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))))))),
% 19.61/12.77 inference(transitivity,[status(thm)],[171, 169])).
% 19.61/12.77 tff(173,plain,
% 19.61/12.77 (^[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))))))))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(174,plain,
% 19.61/12.77 (![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))))))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[173])).
% 19.61/12.77 tff(175,plain,
% 19.61/12.77 (![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))),
% 19.61/12.77 inference(rewrite,[status(thm)],[])).
% 19.61/12.77 tff(176,plain,
% 19.61/12.77 (^[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)))),
% 19.61/12.77 inference(bind,[status(th)],[])).
% 19.61/12.77 tff(177,plain,
% 19.61/12.77 (![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))),
% 19.61/12.77 inference(quant_intro,[status(thm)],[176])).
% 19.61/12.77 tff(178,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')).
% 19.61/12.77 tff(179,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[178, 177])).
% 19.61/12.77 tff(180,plain,
% 19.61/12.77 (![S1: $i, S2: $i] : (![Ax: $i, C: $i] : ((~status(Ax, C, S2)) | (~status(Ax, C, S1))) <=> nevera(S1, S2))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[179, 175])).
% 19.61/12.77 tff(181,plain,(
% 19.61/12.77 ![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))))),
% 19.61/12.77 inference(skolemize,[status(sab)],[180])).
% 19.61/12.77 tff(182,plain,
% 19.61/12.77 (![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))))))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[181, 174])).
% 19.61/12.77 tff(183,plain,
% 19.61/12.77 (![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))))))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[182, 172])).
% 19.61/12.77 tff(184,plain,
% 19.61/12.77 (![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)))))))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[183, 167])).
% 19.61/12.77 tff(185,plain,
% 19.61/12.77 ((~![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(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat))) | (~((~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))))))),
% 19.61/12.77 inference(quant_inst,[status(thm)],[])).
% 19.61/12.77 tff(186,plain,
% 19.61/12.77 (~((~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat))) | (~((~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa))))))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[185, 184])).
% 19.61/12.77 tff(187,plain,
% 19.61/12.77 (((~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat))) | (~((~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))))) | ((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(188,plain,
% 19.61/12.77 ((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat)),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[187, 186])).
% 19.61/12.77 tff(189,plain,
% 19.61/12.77 ((~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat))) | (~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat)),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(190,plain,
% 19.61/12.77 ((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat)),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[189, 188])).
% 19.61/12.77 tff(191,plain,
% 19.61/12.77 (nevera(csa, sat)),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[190, 165])).
% 19.61/12.77 tff(192,plain,
% 19.61/12.77 (((~((~((~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), sat)) | (~status(tptp_fun_Ax_25(sat, csa), tptp_fun_C_24(sat, csa), csa)))) | nevera(csa, sat))) | (~((~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))))) | ((~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa))))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(193,plain,
% 19.61/12.77 ((~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[192, 186])).
% 19.61/12.77 tff(194,plain,
% 19.61/12.77 ((~((~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa))))) | (~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(195,plain,
% 19.61/12.77 ((~nevera(csa, sat)) | ![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[194, 193])).
% 19.61/12.77 tff(196,plain,
% 19.61/12.77 (![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[195, 191])).
% 19.61/12.77 tff(197,assumption,(status(F!28, F!29, csa)), introduced(assumption)).
% 19.61/12.77 tff(198,plain,
% 19.61/12.77 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))) | ((~status(F!28, F!29, csa)) | (~status(F!28, F!29, sat)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))) | (~status(F!28, F!29, csa)) | (~status(F!28, F!29, sat)))),
% 19.61/12.77 inference(rewrite,[status(thm)],[])).
% 19.61/12.77 tff(199,plain,
% 19.61/12.77 (((~status(F!28, F!29, sat)) | (~status(F!28, F!29, csa))) <=> ((~status(F!28, F!29, csa)) | (~status(F!28, F!29, sat)))),
% 19.61/12.77 inference(rewrite,[status(thm)],[])).
% 19.61/12.77 tff(200,plain,
% 19.61/12.77 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))) | ((~status(F!28, F!29, sat)) | (~status(F!28, F!29, csa)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))) | ((~status(F!28, F!29, csa)) | (~status(F!28, F!29, sat))))),
% 19.61/12.77 inference(monotonicity,[status(thm)],[199])).
% 19.61/12.77 tff(201,plain,
% 19.61/12.77 (((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))) | ((~status(F!28, F!29, sat)) | (~status(F!28, F!29, csa)))) <=> ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))) | (~status(F!28, F!29, csa)) | (~status(F!28, F!29, sat)))),
% 19.61/12.77 inference(transitivity,[status(thm)],[200, 198])).
% 19.61/12.77 tff(202,plain,
% 19.61/12.77 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))) | ((~status(F!28, F!29, sat)) | (~status(F!28, F!29, csa)))),
% 19.61/12.77 inference(quant_inst,[status(thm)],[])).
% 19.61/12.77 tff(203,plain,
% 19.61/12.77 ((~![Ax: $i, C: $i] : ((~status(Ax, C, sat)) | (~status(Ax, C, csa)))) | (~status(F!28, F!29, csa)) | (~status(F!28, F!29, sat))),
% 19.61/12.77 inference(modus_ponens,[status(thm)],[202, 201])).
% 19.61/12.77 tff(204,plain,
% 19.61/12.77 ($false),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[203, 197, 196, 44])).
% 19.61/12.77 tff(205,plain,(~status(F!28, F!29, csa)), inference(lemma,lemma(discharge,[]))).
% 19.61/12.77 tff(206,plain,
% 19.61/12.77 ((~![Ax: $i, C: $i] : (~((~((~status(Ax, C, csa)) | (~((~model(tptp_fun_I1_14(C, Ax), Ax)) | (~model(tptp_fun_I1_14(C, Ax), not(C))))))) | (~(status(Ax, C, csa) | ![I1: $i] : ((~model(I1, Ax)) | (~model(I1, not(C))))))))) | (~((~((~status(F!28, F!29, csa)) | (~((~model(tptp_fun_I1_14(F!29, F!28), F!28)) | (~model(tptp_fun_I1_14(F!29, F!28), not(F!29))))))) | (~(status(F!28, F!29, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))))))),
% 19.61/12.77 inference(quant_inst,[status(thm)],[])).
% 19.61/12.77 tff(207,plain,
% 19.61/12.77 (~((~((~status(F!28, F!29, csa)) | (~((~model(tptp_fun_I1_14(F!29, F!28), F!28)) | (~model(tptp_fun_I1_14(F!29, F!28), not(F!29))))))) | (~(status(F!28, F!29, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29)))))))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[206, 75])).
% 19.61/12.77 tff(208,plain,
% 19.61/12.77 (((~((~status(F!28, F!29, csa)) | (~((~model(tptp_fun_I1_14(F!29, F!28), F!28)) | (~model(tptp_fun_I1_14(F!29, F!28), not(F!29))))))) | (~(status(F!28, F!29, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))))) | (status(F!28, F!29, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29)))))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(209,plain,
% 19.61/12.77 (status(F!28, F!29, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[208, 207])).
% 19.61/12.77 tff(210,plain,
% 19.61/12.77 ((~(status(F!28, F!29, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29)))))) | status(F!28, F!29, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))),
% 19.61/12.77 inference(tautology,[status(thm)],[])).
% 19.61/12.77 tff(211,plain,
% 19.61/12.77 (status(F!28, F!29, csa) | ![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[210, 209])).
% 19.61/12.77 tff(212,plain,
% 19.61/12.77 (![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[211, 205])).
% 19.61/12.77 tff(213,plain,
% 19.61/12.77 ((~![I: $i] : model(I, F!28)) | model(I2!31, F!28)),
% 19.61/12.77 inference(quant_inst,[status(thm)],[])).
% 19.61/12.77 tff(214,plain,
% 19.61/12.77 (model(I2!31, F!28)),
% 19.61/12.77 inference(unit_resolution,[status(thm)],[213, 30])).
% 19.61/12.77 tff(215,plain,
% 19.61/12.77 (((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))) | ((~model(I2!31, F!28)) | (~model(I2!31, not(F!29))))) <=> ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))) | (~model(I2!31, F!28)) | (~model(I2!31, not(F!29))))),
% 19.61/12.78 inference(rewrite,[status(thm)],[])).
% 19.61/12.78 tff(216,plain,
% 19.61/12.78 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))) | ((~model(I2!31, F!28)) | (~model(I2!31, not(F!29))))),
% 19.61/12.78 inference(quant_inst,[status(thm)],[])).
% 19.61/12.78 tff(217,plain,
% 19.61/12.78 ((~![I1: $i] : ((~model(I1, F!28)) | (~model(I1, not(F!29))))) | (~model(I2!31, F!28)) | (~model(I2!31, not(F!29)))),
% 19.61/12.78 inference(modus_ponens,[status(thm)],[216, 215])).
% 19.61/12.78 tff(218,plain,
% 19.61/12.78 (~model(I2!31, not(F!29))),
% 19.61/12.78 inference(unit_resolution,[status(thm)],[217, 214, 212])).
% 19.61/12.78 tff(219,plain,
% 19.61/12.78 (~model(I2!31, F!29)),
% 19.61/12.78 inference(and_elim,[status(thm)],[35])).
% 19.61/12.78 tff(220,plain,
% 19.61/12.78 ((~((~model(I2!31, F!29)) <=> model(I2!31, not(F!29)))) | model(I2!31, F!29) | model(I2!31, not(F!29))),
% 19.61/12.78 inference(tautology,[status(thm)],[])).
% 19.61/12.78 tff(221,plain,
% 19.61/12.78 (~((~model(I2!31, F!29)) <=> model(I2!31, not(F!29)))),
% 19.61/12.78 inference(unit_resolution,[status(thm)],[220, 219, 218])).
% 19.61/12.78 tff(222,plain,
% 19.61/12.78 ((~![I: $i, F: $i] : ((~model(I, F)) <=> model(I, not(F)))) | ((~model(I2!31, F!29)) <=> model(I2!31, not(F!29)))),
% 19.61/12.78 inference(quant_inst,[status(thm)],[])).
% 19.61/12.78 tff(223,plain,
% 19.61/12.78 ($false),
% 19.61/12.78 inference(unit_resolution,[status(thm)],[222, 54, 221])).
% 19.61/12.78 % SZS output end Proof
%------------------------------------------------------------------------------