TSTP Solution File: ITP366_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 : n010.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 04:18:51 EDT 2022
% Result : Theorem 0.19s 0.55s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Sep 1 07:22:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55 % SZS output start Proof
% 0.19/0.55 tff(tptp_fun__semantics_ltln___type, type, (
% 0.19/0.55 tptp_fun__semantics_ltln__: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > $o)).
% 0.19/0.55 tff(tptp_fun__gF_advice___type, type, (
% 0.19/0.55 tptp_fun__gF_advice__: ( 'A_ltln$' * 'A_ltln_set$' ) > 'A_ltln$')).
% 0.19/0.55 tff(tptp_fun__x___type, type, (
% 0.19/0.55 tptp_fun__x__: 'A_ltln_set$')).
% 0.19/0.55 tff(tptp_fun__fun_app_i__type, type, (
% 0.19/0.55 tptp_fun__fun_app_i_: ( 'A_ltln_a_ltln_fun$' * 'A_ltln$' ) > 'A_ltln$')).
% 0.19/0.55 tff(tptp_fun__phi___type, type, (
% 0.19/0.55 tptp_fun__phi__: 'A_ltln$')).
% 0.19/0.55 tff(tptp_fun__next_ltln___type, type, (
% 0.19/0.55 tptp_fun__next_ltln__: 'A_ltln_a_ltln_fun$')).
% 0.19/0.55 tff(tptp_fun__unf___type, type, (
% 0.19/0.55 tptp_fun__unf__: 'A_ltln_a_ltln_fun$')).
% 0.19/0.55 tff(tptp_fun__w___type, type, (
% 0.19/0.55 tptp_fun__w__: 'Nat_a_set_fun$')).
% 0.19/0.55 tff(tptp_fun__build___type, type, (
% 0.19/0.55 tptp_fun__build__: ( 'A_set$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$')).
% 0.19/0.55 tff(tptp_fun__suffix___type, type, (
% 0.19/0.55 tptp_fun__suffix__: ( 'Nat$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$')).
% 0.19/0.55 tff(tptp_fun__nat___type, type, (
% 0.19/0.55 tptp_fun__nat__: $int > 'Nat$')).
% 0.19/0.55 tff(tptp_fun__fun_app_j__type, type, (
% 0.19/0.55 tptp_fun__fun_app_j_: ( 'Nat_a_set_fun$' * 'Nat$' ) > 'A_set$')).
% 0.19/0.55 tff(tptp_fun__fun_app_g__type, type, (
% 0.19/0.55 tptp_fun__fun_app_g_: ( 'A_set_a_ltln_fun$' * 'A_set$' ) > 'A_ltln$')).
% 0.19/0.55 tff(tptp_fun__fun_app_h__type, type, (
% 0.19/0.55 tptp_fun__fun_app_h_: ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' ) > 'A_set_a_ltln_fun$')).
% 0.19/0.55 tff(tptp_fun__af_letter___type, type, (
% 0.19/0.55 tptp_fun__af_letter__: 'A_ltln_a_set_a_ltln_fun_fun$')).
% 0.19/0.55 tff(1,plain,
% 0.19/0.55 (^[A__questionmark_v0: 'A_ltln$'] : refl((tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) <=> (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(2,plain,
% 0.19/0.55 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) <=> ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.55 tff(3,plain,
% 0.19/0.55 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) <=> ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(4,axiom,(![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom21')).
% 0.19/0.55 tff(5,plain,
% 0.19/0.55 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.55 tff(6,plain,(
% 0.19/0.55 ![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0))),
% 0.19/0.55 inference(skolemize,[status(sab)],[5])).
% 0.19/0.55 tff(7,plain,
% 0.19/0.55 (![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.55 tff(8,plain,
% 0.19/0.55 ((~![A__questionmark_v0: 'A_ltln$'] : (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0)) = tptp_fun__fun_app_i_(|'next_ltln$'|, A__questionmark_v0))) | (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)) = tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(9,plain,
% 0.19/0.55 (tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)) = tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.55 tff(10,plain,
% 0.19/0.55 (tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|) = tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|)),
% 0.19/0.55 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.55 tff(11,plain,
% 0.19/0.55 (^[A__questionmark_v0: 'Nat_a_set_fun$'] : refl((A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0))) <=> (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(12,plain,
% 0.19/0.55 (![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0))) <=> ![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.55 tff(13,plain,
% 0.19/0.55 (![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0))) <=> ![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(14,axiom,(![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom26')).
% 0.19/0.55 tff(15,plain,
% 0.19/0.55 (![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.55 tff(16,plain,(
% 0.19/0.55 ![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0)))),
% 0.19/0.55 inference(skolemize,[status(sab)],[15])).
% 0.19/0.55 tff(17,plain,
% 0.19/0.55 (![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.55 tff(18,plain,
% 0.19/0.55 ((~![A__questionmark_v0: 'Nat_a_set_fun$'] : (A__questionmark_v0 = tptp_fun__build__(tptp_fun__fun_app_j_(A__questionmark_v0, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), A__questionmark_v0)))) | (|'w$'| = tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(19,plain,
% 0.19/0.55 (|'w$'| = tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.55 tff(20,plain,
% 0.19/0.55 (tptp_fun__semantics_ltln__(|'w$'|, tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|)) <=> tptp_fun__semantics_ltln__(tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)), tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[19, 10])).
% 0.19/0.56 tff(21,plain,
% 0.19/0.56 (tptp_fun__semantics_ltln__(tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)), tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|)) <=> tptp_fun__semantics_ltln__(|'w$'|, tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|))),
% 0.19/0.56 inference(symmetry,[status(thm)],[20])).
% 0.19/0.56 tff(22,plain,
% 0.19/0.56 ((~tptp_fun__semantics_ltln__(tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)), tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|))) <=> (~tptp_fun__semantics_ltln__(|'w$'|, tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|)))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.56 tff(23,plain,
% 0.19/0.56 (^[A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : refl(((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))) <=> ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(24,plain,
% 0.19/0.56 (![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))) <=> ![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.56 tff(25,plain,
% 0.19/0.56 (![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))) <=> ![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(26,plain,
% 0.19/0.56 (^[A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : rewrite((tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3)) => tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))) <=> ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(27,plain,
% 0.19/0.56 (![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : (tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3)) => tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3))) <=> ![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.56 tff(28,axiom,(![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : (tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3)) => tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom27')).
% 0.19/0.56 tff(29,plain,
% 0.19/0.56 (![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.56 tff(30,plain,
% 0.19/0.56 (![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.56 tff(31,plain,(
% 0.19/0.56 ![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))),
% 0.19/0.56 inference(skolemize,[status(sab)],[30])).
% 0.19/0.56 tff(32,plain,
% 0.19/0.56 (![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.56 tff(33,plain,
% 0.19/0.56 ((~tptp_fun__semantics_ltln__(tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|), tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0))), |'x$'|))) <=> (~tptp_fun__semantics_ltln__(tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|), tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0))), |'x$'|)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(34,axiom,(~tptp_fun__semantics_ltln__(tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|), tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0))), |'x$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture11')).
% 0.19/0.56 tff(35,plain,
% 0.19/0.56 (~tptp_fun__semantics_ltln__(tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|), tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0))), |'x$'|))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.56 tff(36,plain,
% 0.19/0.56 (((~![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))) | ((~tptp_fun__semantics_ltln__(tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)), tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|))) | tptp_fun__semantics_ltln__(tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|), tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0))), |'x$'|)))) <=> ((~![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))) | (~tptp_fun__semantics_ltln__(tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)), tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|))) | tptp_fun__semantics_ltln__(tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|), tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0))), |'x$'|)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(37,plain,
% 0.19/0.56 ((~![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))) | ((~tptp_fun__semantics_ltln__(tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)), tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|))) | tptp_fun__semantics_ltln__(tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|), tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0))), |'x$'|)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(38,plain,
% 0.19/0.59 ((~![A__questionmark_v0: 'A_set$', A__questionmark_v1: 'Nat_a_set_fun$', A__questionmark_v2: 'A_ltln$', A__questionmark_v3: 'A_ltln_set$'] : ((~tptp_fun__semantics_ltln__(tptp_fun__build__(A__questionmark_v0, A__questionmark_v1), tptp_fun__gF_advice__(A__questionmark_v2, A__questionmark_v3))) | tptp_fun__semantics_ltln__(A__questionmark_v1, tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, A__questionmark_v2), A__questionmark_v0), A__questionmark_v3)))) | (~tptp_fun__semantics_ltln__(tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)), tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|))) | tptp_fun__semantics_ltln__(tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|), tptp_fun__gF_advice__(tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'af_letter$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0))), |'x$'|))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.59 tff(39,plain,
% 0.19/0.59 (~tptp_fun__semantics_ltln__(tptp_fun__build__(tptp_fun__fun_app_j_(|'w$'|, tptp_fun__nat__(0)), tptp_fun__suffix__(tptp_fun__nat__(1), |'w$'|)), tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|), |'x$'|))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[38, 35, 32])).
% 0.19/0.59 tff(40,plain,
% 0.19/0.59 (~tptp_fun__semantics_ltln__(|'w$'|, tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[39, 22])).
% 0.19/0.59 tff(41,plain,
% 0.19/0.59 (tptp_fun__semantics_ltln__(|'w$'|, tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|)) <=> tptp_fun__semantics_ltln__(|'w$'|, tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(42,axiom,(tptp_fun__semantics_ltln__(|'w$'|, tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom12')).
% 0.19/0.59 tff(43,plain,
% 0.19/0.59 (tptp_fun__semantics_ltln__(|'w$'|, tptp_fun__gF_advice__(tptp_fun__fun_app_i_(|'unf$'|, tptp_fun__fun_app_i_(|'next_ltln$'|, |'phi$'|)), |'x$'|))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.59 tff(44,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.19/0.59 % SZS output end Proof
%------------------------------------------------------------------------------