TSTP Solution File: ITP355_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 04:18:49 EDT 2022
% Result : Theorem 0.55s 0.64s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 07:28:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.55/0.64 % SZS status Theorem
% 0.55/0.64 % SZS output start Proof
% 0.55/0.64 tff(tptp_fun__fun_app___type, type, (
% 0.55/0.64 tptp_fun__fun_app__: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > $o)).
% 0.55/0.64 tff(tptp_fun__until_ltln___type, type, (
% 0.55/0.64 tptp_fun__until_ltln__: ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$')).
% 0.55/0.64 tff(tptp_fun__release_ltln___type, type, (
% 0.55/0.64 tptp_fun__release_ltln__: ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$')).
% 0.55/0.64 tff(tptp_fun_A__questionmark_v2_50_type, type, (
% 0.55/0.64 tptp_fun_A__questionmark_v2_50: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$')).
% 0.55/0.64 tff(tptp_fun__uu___type, type, (
% 0.55/0.64 tptp_fun__uu__: 'A_ltln_bool_fun$')).
% 0.55/0.64 tff(tptp_fun__uua___type, type, (
% 0.55/0.64 tptp_fun__uua__: 'A_ltln_bool_fun$')).
% 0.55/0.64 tff(tptp_fun__false_ltln___type, type, (
% 0.55/0.64 tptp_fun__false_ltln__: 'A_ltln$')).
% 0.55/0.64 tff(tptp_fun__true_ltln___type, type, (
% 0.55/0.64 tptp_fun__true_ltln__: 'A_ltln$')).
% 0.55/0.64 tff(tptp_fun__semantics_ltln___type, type, (
% 0.55/0.64 tptp_fun__semantics_ltln__: 'Nat_a_set_fun$' > 'A_ltln_bool_fun$')).
% 0.55/0.64 tff(tptp_fun__w___type, type, (
% 0.55/0.64 tptp_fun__w__: 'Nat_a_set_fun$')).
% 0.55/0.64 tff(tptp_fun__suffix___type, type, (
% 0.55/0.64 tptp_fun__suffix__: ( 'Nat$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$')).
% 0.55/0.64 tff(tptp_fun__i___type, type, (
% 0.55/0.64 tptp_fun__i__: 'Nat$')).
% 0.55/0.64 tff(tptp_fun__member___type, type, (
% 0.55/0.64 tptp_fun__member__: ( 'A_ltln$' * 'A_ltln_set$' ) > $o)).
% 0.55/0.64 tff(tptp_fun__subformulas_nu___type, type, (
% 0.55/0.64 tptp_fun__subformulas_nu__: 'A_ltln$' > 'A_ltln_set$')).
% 0.55/0.64 tff(tptp_fun__phi___type, type, (
% 0.55/0.64 tptp_fun__phi__: 'A_ltln$')).
% 0.55/0.64 tff(tptp_fun__less_eq___type, type, (
% 0.55/0.64 tptp_fun__less_eq__: ( 'A_ltln_set$' * 'A_ltln_set$' ) > $o)).
% 0.55/0.64 tff(tptp_fun__fun_app_i__type, type, (
% 0.55/0.64 tptp_fun__fun_app_i_: ( 'A_ltln_bool_fun_a_ltln_set_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln_set$')).
% 0.55/0.64 tff(tptp_fun__collect___type, type, (
% 0.55/0.64 tptp_fun__collect__: 'A_ltln_bool_fun_a_ltln_set_fun$')).
% 0.55/0.64 tff(1,plain,
% 0.55/0.64 (^[A__questionmark_v0: 'A_ltln$'] : refl((tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))))) <=> (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(2,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))))) <=> ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[1])).
% 0.55/0.64 tff(3,plain,
% 0.55/0.64 (^[A__questionmark_v0: 'A_ltln$'] : rewrite((tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))) <=> (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(4,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))) <=> ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[3])).
% 0.55/0.64 tff(5,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))) <=> ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(6,axiom,(![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom0')).
% 0.55/0.64 tff(7,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.55/0.64 tff(8,plain,(
% 0.55/0.64 ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))),
% 0.55/0.64 inference(skolemize,[status(sab)],[7])).
% 0.55/0.64 tff(9,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.55/0.64 tff(10,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.55/0.64 tff(11,plain,
% 0.55/0.64 ((~![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uu$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))) | (tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) <=> (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))))),
% 0.55/0.64 inference(quant_inst,[status(thm)],[])).
% 0.55/0.64 tff(12,plain,
% 0.55/0.64 (tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) <=> (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))))),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.55/0.64 tff(13,plain,
% 0.55/0.64 (^[A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : refl(((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))) <=> ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(14,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))) <=> ![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[13])).
% 0.55/0.64 tff(15,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))) <=> ![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(16,plain,
% 0.55/0.64 (^[A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : trans(monotonicity(quant_intro(proof_bind(^[A__questionmark_v2: 'A_ltln$'] : rewrite((tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2) => tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)) <=> ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)))), (![A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2) => tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)) <=> ![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)))), ((![A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2) => tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)) => tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))) <=> (![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)) => tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))))), rewrite((![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)) => tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))) <=> ((~![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))), ((![A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2) => tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)) => tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))) <=> ((~![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(17,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : (![A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2) => tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)) => tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1))) <=> ![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[16])).
% 0.55/0.64 tff(18,axiom,(![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : (![A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2) => tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2)) => tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom167')).
% 0.55/0.64 tff(19,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.55/0.64 tff(20,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~![A__questionmark_v2: 'A_ltln$'] : ((~tptp_fun__fun_app__(A__questionmark_v0, A__questionmark_v2)) | tptp_fun__fun_app__(A__questionmark_v1, A__questionmark_v2))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.55/0.65 tff(21,plain,(
% 0.55/0.65 ![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))),
% 0.55/0.65 inference(skolemize,[status(sab)],[20])).
% 0.55/0.65 tff(22,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.55/0.65 tff(23,plain,
% 0.55/0.65 ((~tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, |'uu$'|), tptp_fun__fun_app_i_(|'collect$'|, |'uua$'|))) <=> (~tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, |'uu$'|), tptp_fun__fun_app_i_(|'collect$'|, |'uua$'|)))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(24,axiom,(~tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, |'uu$'|), tptp_fun__fun_app_i_(|'collect$'|, |'uua$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture24')).
% 0.55/0.65 tff(25,plain,
% 0.55/0.65 (~tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, |'uu$'|), tptp_fun__fun_app_i_(|'collect$'|, |'uua$'|))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.55/0.65 tff(26,plain,
% 0.55/0.65 (((~![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))) | ((~((~tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, |'uu$'|), tptp_fun__fun_app_i_(|'collect$'|, |'uua$'|)))) <=> ((~![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))) | (~((~tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, |'uu$'|), tptp_fun__fun_app_i_(|'collect$'|, |'uua$'|)))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(27,plain,
% 0.55/0.65 ((~![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))) | ((~((~tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, |'uu$'|), tptp_fun__fun_app_i_(|'collect$'|, |'uua$'|)))),
% 0.55/0.65 inference(quant_inst,[status(thm)],[])).
% 0.55/0.65 tff(28,plain,
% 0.55/0.65 ((~![A__questionmark_v0: 'A_ltln_bool_fun$', A__questionmark_v1: 'A_ltln_bool_fun$'] : ((~((~tptp_fun__fun_app__(A__questionmark_v0, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0))) | tptp_fun__fun_app__(A__questionmark_v1, tptp_fun_A__questionmark_v2_50(A__questionmark_v1, A__questionmark_v0)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v0), tptp_fun__fun_app_i_(|'collect$'|, A__questionmark_v1)))) | (~((~tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))) | tptp_fun__less_eq__(tptp_fun__fun_app_i_(|'collect$'|, |'uu$'|), tptp_fun__fun_app_i_(|'collect$'|, |'uua$'|))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.55/0.65 tff(29,plain,
% 0.55/0.65 (~((~tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[28, 25, 22])).
% 0.55/0.65 tff(30,plain,
% 0.55/0.65 (((~tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(31,plain,
% 0.55/0.65 (tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.55/0.65 tff(32,plain,
% 0.55/0.65 ((~(tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) <=> (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))))) | (~tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(33,plain,
% 0.55/0.65 ((~(tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) <=> (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))))) | (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.55/0.65 tff(34,plain,
% 0.55/0.65 (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[33, 12])).
% 0.55/0.65 tff(35,plain,
% 0.55/0.65 (((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))) | tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(36,plain,
% 0.55/0.65 (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.55/0.65 tff(37,plain,
% 0.55/0.65 (^[A__questionmark_v0: 'A_ltln$'] : refl((tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))))) <=> (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))))))),
% 0.55/0.65 inference(bind,[status(th)],[])).
% 0.55/0.65 tff(38,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))))) <=> ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))),
% 0.55/0.65 inference(quant_intro,[status(thm)],[37])).
% 0.55/0.65 tff(39,plain,
% 0.55/0.65 (^[A__questionmark_v0: 'A_ltln$'] : rewrite((tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))) <=> (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))))))),
% 0.55/0.65 inference(bind,[status(th)],[])).
% 0.55/0.65 tff(40,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))) <=> ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))),
% 0.55/0.65 inference(quant_intro,[status(thm)],[39])).
% 0.55/0.65 tff(41,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0))))) <=> ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(42,axiom,(![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom1')).
% 0.55/0.65 tff(43,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.55/0.65 tff(44,plain,(
% 0.55/0.65 ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|)) & tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))),
% 0.55/0.65 inference(skolemize,[status(sab)],[43])).
% 0.55/0.65 tff(45,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.55/0.65 tff(46,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.55/0.65 tff(47,plain,
% 0.55/0.65 ((~![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app__(|'uua$'|, A__questionmark_v0) <=> (~((~tptp_fun__member__(A__questionmark_v0, tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v0)))))))) | (tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) <=> (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))))),
% 0.55/0.65 inference(quant_inst,[status(thm)],[])).
% 0.55/0.65 tff(48,plain,
% 0.55/0.65 (tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) <=> (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.55/0.65 tff(49,plain,
% 0.55/0.65 (((~tptp_fun__fun_app__(|'uu$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))) | (~tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(50,plain,
% 0.55/0.65 (~tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[49, 29])).
% 0.55/0.65 tff(51,plain,
% 0.55/0.65 ((~(tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) <=> (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))))) | tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) | ((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(52,plain,
% 0.55/0.65 ((~(tptp_fun__fun_app__(|'uua$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)) <=> (~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))))) | ((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.55/0.65 tff(53,plain,
% 0.55/0.65 ((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[52, 48])).
% 0.55/0.65 tff(54,plain,
% 0.55/0.65 (((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))) | tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(55,plain,
% 0.55/0.65 (tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[54, 34])).
% 0.55/0.65 tff(56,plain,
% 0.55/0.65 ((~((~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))))) | (~tptp_fun__member__(tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|), tptp_fun__subformulas_nu__(|'phi$'|))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(57,plain,
% 0.55/0.65 (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[56, 55, 53])).
% 0.55/0.65 tff(58,plain,
% 0.55/0.65 ((~(tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))) | (~tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))) | tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|))))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(59,plain,
% 0.55/0.65 (~(tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[58, 57, 36])).
% 0.55/0.65 tff(60,plain,
% 0.55/0.65 (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : refl((tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2)))) <=> (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2)))))),
% 0.55/0.65 inference(bind,[status(th)],[])).
% 0.55/0.65 tff(61,plain,
% 0.55/0.65 (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2)))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))))),
% 0.55/0.65 inference(quant_intro,[status(thm)],[60])).
% 0.55/0.65 tff(62,plain,
% 0.55/0.65 (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2)))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))))),
% 0.60/0.70 inference(rewrite,[status(thm)],[])).
% 0.60/0.70 tff(63,axiom,(![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom35')).
% 0.60/0.70 tff(64,plain,
% 0.60/0.70 (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))))),
% 0.60/0.70 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.60/0.70 tff(65,plain,(
% 0.60/0.70 ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))))),
% 0.60/0.70 inference(skolemize,[status(sab)],[64])).
% 0.60/0.70 tff(66,plain,
% 0.60/0.70 (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))))),
% 0.60/0.70 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.60/0.70 tff(67,plain,
% 0.60/0.70 ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$'] : (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(A__questionmark_v0, A__questionmark_v1)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(A__questionmark_v1), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, A__questionmark_v2))))) | (tptp_fun__fun_app__(tptp_fun__semantics_ltln__(tptp_fun__suffix__(|'i$'|, |'w$'|)), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))) <=> tptp_fun__fun_app__(tptp_fun__semantics_ltln__(|'w$'|), tptp_fun__until_ltln__(|'true_ltln$'|, tptp_fun__release_ltln__(|'false_ltln$'|, tptp_fun_A__questionmark_v2_50(|'uua$'|, |'uu$'|)))))),
% 0.60/0.70 inference(quant_inst,[status(thm)],[])).
% 0.60/0.70 tff(68,plain,
% 0.60/0.70 ($false),
% 0.60/0.70 inference(unit_resolution,[status(thm)],[67, 66, 59])).
% 0.60/0.70 % SZS output end Proof
%------------------------------------------------------------------------------