TSTP Solution File: ITP410_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 : n015.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 04:18:59 EDT 2022
% Result : Theorem 0.54s 0.66s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.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 07:52:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 0.54/0.66 % SZS status Theorem
% 0.54/0.66 % SZS output start Proof
% 0.54/0.66 tff(tptp_fun__fun_app_e__type, type, (
% 0.54/0.66 tptp_fun__fun_app_e_: ( 'A_run_set_a_run_set_fun$' * 'A_run_set$' ) > 'A_run_set$')).
% 0.54/0.66 tff(tptp_fun__tESL_interpretation_stepwise___type, type, (
% 0.54/0.66 tptp_fun__tESL_interpretation_stepwise__: ( 'A_TESL_atomic_list$' * 'Nat$' ) > 'A_run_set$')).
% 0.54/0.66 tff(tptp_fun__nat___type, type, (
% 0.54/0.66 tptp_fun__nat__: $int > 'Nat$')).
% 0.54/0.66 tff(tptp_fun__fun_app_g__type, type, (
% 0.54/0.66 tptp_fun__fun_app_g_: ( 'Nat_int_fun$' * 'Nat$' ) > $int)).
% 0.54/0.66 tff(tptp_fun__of_nat___type, type, (
% 0.54/0.66 tptp_fun__of_nat__: 'Nat_int_fun$')).
% 0.54/0.66 tff(tptp_fun__fun_app_f__type, type, (
% 0.54/0.66 tptp_fun__fun_app_f_: ( 'A_run_set_a_run_set_a_run_set_fun_fun$' * 'A_run_set$' ) > 'A_run_set_a_run_set_fun$')).
% 0.54/0.66 tff(tptp_fun__symbolic_run_interpretation___type, type, (
% 0.54/0.66 tptp_fun__symbolic_run_interpretation__: 'A_constr_list$' > 'A_run_set$')).
% 0.54/0.66 tff(tptp_fun__inf___type, type, (
% 0.54/0.66 tptp_fun__inf__: 'A_run_set_a_run_set_a_run_set_fun_fun$')).
% 0.54/0.66 tff(tptp_fun__heronConf_interpretation___type, type, (
% 0.54/0.66 tptp_fun__heronConf_interpretation__: 'A_constr_list_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_prod$' > 'A_run_set$')).
% 0.54/0.66 tff(tptp_fun__pair___type, type, (
% 0.54/0.66 tptp_fun__pair__: ( 'A_constr_list$' * 'Nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod$' ) > 'A_constr_list_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_prod$')).
% 0.54/0.66 tff(tptp_fun__pair_a__type, type, (
% 0.54/0.66 tptp_fun__pair_a_: ( 'Nat$' * 'A_TESL_atomic_list_a_TESL_atomic_list_prod$' ) > 'Nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod$')).
% 0.54/0.66 tff(tptp_fun__pair_b__type, type, (
% 0.54/0.66 tptp_fun__pair_b_: ( 'A_TESL_atomic_list$' * 'A_TESL_atomic_list$' ) > 'A_TESL_atomic_list_a_TESL_atomic_list_prod$')).
% 0.54/0.66 tff(tptp_fun__n___type, type, (
% 0.54/0.66 tptp_fun__n__: 'Nat$')).
% 0.54/0.66 tff(tptp_fun__phi___type, type, (
% 0.54/0.66 tptp_fun__phi__: 'A_TESL_atomic_list$')).
% 0.54/0.66 tff(tptp_fun__psi___type, type, (
% 0.54/0.66 tptp_fun__psi__: 'A_TESL_atomic_list$')).
% 0.54/0.66 tff(tptp_fun__cons___type, type, (
% 0.54/0.66 tptp_fun__cons__: ( 'A_constr$' * 'A_constr_list$' ) > 'A_constr_list$')).
% 0.54/0.66 tff(tptp_fun__gamma___type, type, (
% 0.54/0.66 tptp_fun__gamma__: 'A_constr_list$')).
% 0.54/0.66 tff(tptp_fun__timestamp___type, type, (
% 0.54/0.66 tptp_fun__timestamp__: ( 'Clock$' * 'Nat$' * 'A_tag_const$' ) > 'A_constr$')).
% 0.54/0.66 tff(tptp_fun__tau___type, type, (
% 0.54/0.66 tptp_fun__tau__: 'A_tag_const$')).
% 0.54/0.66 tff(tptp_fun__k_2___type, type, (
% 0.54/0.66 tptp_fun__k_2__: 'Clock$')).
% 0.54/0.66 tff(tptp_fun__ticks___type, type, (
% 0.54/0.66 tptp_fun__ticks__: ( 'Clock$' * 'Nat$' ) > 'A_constr$')).
% 0.54/0.66 tff(tptp_fun__k_1___type, type, (
% 0.54/0.66 tptp_fun__k_1__: 'Clock$')).
% 0.54/0.66 tff(1,plain,
% 0.54/0.66 (^[A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : refl((tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1)))))) <=> (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1)))))))),
% 0.54/0.66 inference(bind,[status(th)],[])).
% 0.54/0.66 tff(2,plain,
% 0.54/0.66 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1)))))) <=> ![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.54/0.66 inference(quant_intro,[status(thm)],[1])).
% 0.54/0.66 tff(3,plain,
% 0.54/0.66 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1)))))) <=> ![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.54/0.66 inference(rewrite,[status(thm)],[])).
% 0.54/0.66 tff(4,plain,
% 0.54/0.66 (^[A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : rewrite((tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1), 1))))) <=> (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1)))))))),
% 0.54/0.66 inference(bind,[status(th)],[])).
% 0.54/0.66 tff(5,plain,
% 0.54/0.66 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1), 1))))) <=> ![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.54/0.66 inference(quant_intro,[status(thm)],[4])).
% 0.54/0.66 tff(6,axiom,(![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1), 1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom8')).
% 0.54/0.66 tff(7,plain,
% 0.54/0.66 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.54/0.66 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.54/0.66 tff(8,plain,
% 0.54/0.66 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.54/0.66 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.54/0.66 tff(9,plain,(
% 0.54/0.66 ![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.54/0.66 inference(skolemize,[status(sab)],[8])).
% 0.54/0.66 tff(10,plain,
% 0.54/0.66 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.54/0.66 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.54/0.66 tff(11,plain,
% 0.54/0.66 (tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))) = tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|)))),
% 0.54/0.66 inference(rewrite,[status(thm)],[])).
% 0.54/0.66 tff(12,plain,
% 0.54/0.66 (tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|)))) = tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))),
% 0.54/0.66 inference(monotonicity,[status(thm)],[11])).
% 0.54/0.66 tff(13,plain,
% 0.54/0.66 (tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|)))))),
% 0.54/0.66 inference(monotonicity,[status(thm)],[12])).
% 0.54/0.66 tff(14,plain,
% 0.54/0.66 ((tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|)))))) <=> (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))))),
% 0.54/0.66 inference(monotonicity,[status(thm)],[13])).
% 0.54/0.66 tff(15,plain,
% 0.54/0.66 ((~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))))) <=> (~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|)))))))),
% 0.54/0.66 inference(monotonicity,[status(thm)],[14])).
% 0.54/0.66 tff(16,plain,
% 0.54/0.66 ((~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))))) <=> (~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|)))))))),
% 0.54/0.66 inference(rewrite,[status(thm)],[])).
% 0.54/0.66 tff(17,plain,
% 0.54/0.66 ((~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|), 1)))))) <=> (~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|)))))))),
% 0.54/0.66 inference(rewrite,[status(thm)],[])).
% 0.54/0.66 tff(18,axiom,(~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|), 1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture5')).
% 0.54/0.66 tff(19,plain,
% 0.54/0.66 (~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))))),
% 0.54/0.66 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.54/0.66 tff(20,plain,
% 0.54/0.66 (~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))))),
% 0.54/0.66 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.54/0.66 tff(21,plain,
% 0.54/0.66 (~(tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))))),
% 0.62/0.71 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.62/0.71 tff(22,plain,
% 0.62/0.71 ((~![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(A__questionmark_v0, tptp_fun__pair_a_(A__questionmark_v1, tptp_fun__pair_b_(A__questionmark_v2, A__questionmark_v3)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2, A__questionmark_v1))), tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, A__questionmark_v1))))))) | (tptp_fun__heronConf_interpretation__(tptp_fun__pair__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)), tptp_fun__pair_a_(|'n$'|, tptp_fun__pair_b_(|'psi$'|, |'phi$'|)))) = tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__fun_app_e_(tptp_fun__fun_app_f_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(tptp_fun__cons__(tptp_fun__ticks__(|'k_1$'|, |'n$'|), tptp_fun__cons__(tptp_fun__timestamp__(|'k_2$'|, |'n$'|, |'tau$'|), |'gamma$'|)))), tptp_fun__tESL_interpretation_stepwise__(|'psi$'|, |'n$'|))), tptp_fun__tESL_interpretation_stepwise__(|'phi$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_g_(|'of_nat$'|, |'n$'|))))))),
% 0.62/0.71 inference(quant_inst,[status(thm)],[])).
% 0.62/0.71 tff(23,plain,
% 0.62/0.71 ($false),
% 0.62/0.71 inference(unit_resolution,[status(thm)],[22, 21, 10])).
% 0.62/0.71 % SZS output end Proof
%------------------------------------------------------------------------------