TSTP Solution File: ITP412_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 : n009.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 04:19:00 EDT 2022
% Result : Theorem 0.55s 0.63s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 07:38:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.55/0.63 % SZS status Theorem
% 0.55/0.63 % SZS output start Proof
% 0.55/0.63 tff(tptp_fun__fun_app_q__type, type, (
% 0.55/0.63 tptp_fun__fun_app_q_: ( 'A_run_set_a_run_set_fun$' * 'A_run_set$' ) > 'A_run_set$')).
% 0.55/0.63 tff(tptp_fun__fun_app_s__type, type, (
% 0.55/0.63 tptp_fun__fun_app_s_: ( 'Nat_a_run_set_fun$' * 'Nat$' ) > 'A_run_set$')).
% 0.55/0.63 tff(tptp_fun__fun_app_t__type, type, (
% 0.55/0.63 tptp_fun__fun_app_t_: ( 'Int_nat_fun$' * $int ) > 'Nat$')).
% 0.55/0.63 tff(tptp_fun__fun_app_u__type, type, (
% 0.55/0.63 tptp_fun__fun_app_u_: ( 'Nat_int_fun$' * 'Nat$' ) > $int)).
% 0.55/0.63 tff(tptp_fun__n_1___type, type, (
% 0.55/0.63 tptp_fun__n_1__: 'Nat$')).
% 0.55/0.63 tff(tptp_fun__of_nat___type, type, (
% 0.55/0.63 tptp_fun__of_nat__: 'Nat_int_fun$')).
% 0.55/0.63 tff(tptp_fun__nat___type, type, (
% 0.55/0.63 tptp_fun__nat__: 'Int_nat_fun$')).
% 0.55/0.63 tff(tptp_fun__tESL_interpretation_stepwise___type, type, (
% 0.55/0.63 tptp_fun__tESL_interpretation_stepwise__: 'A_TESL_atomic_list$' > 'Nat_a_run_set_fun$')).
% 0.55/0.63 tff(tptp_fun__phi_1___type, type, (
% 0.55/0.63 tptp_fun__phi_1__: 'A_TESL_atomic_list$')).
% 0.55/0.63 tff(tptp_fun__fun_app_r__type, type, (
% 0.55/0.63 tptp_fun__fun_app_r_: ( 'A_run_set_a_run_set_a_run_set_fun_fun$' * 'A_run_set$' ) > 'A_run_set_a_run_set_fun$')).
% 0.55/0.63 tff(tptp_fun__psi_1___type, type, (
% 0.55/0.63 tptp_fun__psi_1__: 'A_TESL_atomic_list$')).
% 0.55/0.63 tff(tptp_fun__symbolic_run_interpretation___type, type, (
% 0.55/0.63 tptp_fun__symbolic_run_interpretation__: 'A_constr_list$' > 'A_run_set$')).
% 0.55/0.63 tff(tptp_fun__gamma_1___type, type, (
% 0.55/0.63 tptp_fun__gamma_1__: 'A_constr_list$')).
% 0.55/0.63 tff(tptp_fun__inf___type, type, (
% 0.55/0.63 tptp_fun__inf__: 'A_run_set_a_run_set_a_run_set_fun_fun$')).
% 0.55/0.63 tff(tptp_fun__n_2___type, type, (
% 0.55/0.63 tptp_fun__n_2__: 'Nat$')).
% 0.55/0.63 tff(tptp_fun__phi_2___type, type, (
% 0.55/0.63 tptp_fun__phi_2__: 'A_TESL_atomic_list$')).
% 0.55/0.63 tff(tptp_fun__psi_2___type, type, (
% 0.55/0.63 tptp_fun__psi_2__: 'A_TESL_atomic_list$')).
% 0.55/0.63 tff(tptp_fun__gamma_2___type, type, (
% 0.55/0.63 tptp_fun__gamma_2__: 'A_constr_list$')).
% 0.55/0.63 tff(tptp_fun__heronConf_interpretation___type, type, (
% 0.55/0.63 tptp_fun__heronConf_interpretation__: 'A_constr_list_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_prod$' > 'A_run_set$')).
% 0.55/0.63 tff(tptp_fun__fun_app_c__type, type, (
% 0.55/0.63 tptp_fun__fun_app_c_: ( 'Nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_a_constr_list_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_prod_fun$' * 'Nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod$' ) > 'A_constr_list_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_prod$')).
% 0.55/0.63 tff(tptp_fun__fun_app_k__type, type, (
% 0.55/0.63 tptp_fun__fun_app_k_: ( 'A_TESL_atomic_list_a_TESL_atomic_list_prod_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_fun$' * 'A_TESL_atomic_list_a_TESL_atomic_list_prod$' ) > 'Nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod$')).
% 0.55/0.63 tff(tptp_fun__fun_app_g__type, type, (
% 0.55/0.63 tptp_fun__fun_app_g_: ( 'A_TESL_atomic_list_a_TESL_atomic_list_a_TESL_atomic_list_prod_fun$' * 'A_TESL_atomic_list$' ) > 'A_TESL_atomic_list_a_TESL_atomic_list_prod$')).
% 0.55/0.63 tff(tptp_fun__fun_app_h__type, type, (
% 0.55/0.63 tptp_fun__fun_app_h_: ( 'A_TESL_atomic_list_a_TESL_atomic_list_a_TESL_atomic_list_a_TESL_atomic_list_prod_fun_fun$' * 'A_TESL_atomic_list$' ) > 'A_TESL_atomic_list_a_TESL_atomic_list_a_TESL_atomic_list_prod_fun$')).
% 0.55/0.63 tff(tptp_fun__pair_a__type, type, (
% 0.55/0.63 tptp_fun__pair_a_: 'A_TESL_atomic_list_a_TESL_atomic_list_a_TESL_atomic_list_a_TESL_atomic_list_prod_fun_fun$')).
% 0.55/0.63 tff(tptp_fun__fun_app_l__type, type, (
% 0.55/0.63 tptp_fun__fun_app_l_: ( 'Nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_fun_fun$' * 'Nat$' ) > 'A_TESL_atomic_list_a_TESL_atomic_list_prod_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_fun$')).
% 0.55/0.63 tff(tptp_fun__pair_b__type, type, (
% 0.55/0.63 tptp_fun__pair_b_: 'Nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_fun_fun$')).
% 0.55/0.63 tff(tptp_fun__fun_app_d__type, type, (
% 0.55/0.63 tptp_fun__fun_app_d_: ( '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_fun_fun$' * 'A_constr_list$' ) > '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_fun$')).
% 0.55/0.63 tff(tptp_fun__pair___type, type, (
% 0.55/0.63 tptp_fun__pair__: 'A_constr_list_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_a_constr_list_nat_a_TESL_atomic_list_a_TESL_atomic_list_prod_prod_prod_fun_fun$')).
% 0.55/0.63 tff(tptp_fun__phi___type, type, (
% 0.55/0.63 tptp_fun__phi__: 'A_TESL_atomic_list$')).
% 0.55/0.63 tff(tptp_fun__cons___type, type, (
% 0.55/0.63 tptp_fun__cons__: ( 'A_TESL_atomic$' * 'A_TESL_atomic_list$' ) > 'A_TESL_atomic_list$')).
% 0.55/0.63 tff(tptp_fun__psi___type, type, (
% 0.55/0.63 tptp_fun__psi__: 'A_TESL_atomic_list$')).
% 0.55/0.63 tff(tptp_fun__weaklyPrecedes___type, type, (
% 0.55/0.63 tptp_fun__weaklyPrecedes__: ( 'Clock$' * 'Clock$' ) > 'A_TESL_atomic$')).
% 0.55/0.63 tff(tptp_fun__k_2___type, type, (
% 0.55/0.63 tptp_fun__k_2__: 'Clock$')).
% 0.55/0.63 tff(tptp_fun__k_1___type, type, (
% 0.55/0.63 tptp_fun__k_1__: 'Clock$')).
% 0.55/0.63 tff(tptp_fun__n___type, type, (
% 0.55/0.63 tptp_fun__n__: 'Nat$')).
% 0.55/0.63 tff(tptp_fun__gamma___type, type, (
% 0.55/0.63 tptp_fun__gamma__: 'A_constr_list$')).
% 0.55/0.63 tff(tptp_fun__cons_a__type, type, (
% 0.55/0.63 tptp_fun__cons_a_: ( 'A_constr$' * 'A_constr_list$' ) > 'A_constr_list$')).
% 0.55/0.63 tff(tptp_fun__tickCntArith___type, type, (
% 0.55/0.63 tptp_fun__tickCntArith__: ( 'Cnt_expr$' * 'Cnt_expr$' * 'Nat_nat_prod_bool_fun$' ) > 'A_constr$')).
% 0.55/0.64 tff(tptp_fun__case_prod___type, type, (
% 0.55/0.64 tptp_fun__case_prod__: 'Nat_nat_bool_fun_fun$' > 'Nat_nat_prod_bool_fun$')).
% 0.55/0.64 tff(tptp_fun__less_eq_f__type, type, (
% 0.55/0.64 tptp_fun__less_eq_f_: 'Nat_nat_bool_fun_fun$')).
% 0.55/0.64 tff(tptp_fun__tickCountLeq___type, type, (
% 0.55/0.64 tptp_fun__tickCountLeq__: ( 'Clock$' * 'Nat$' ) > 'Cnt_expr$')).
% 0.55/0.64 tff(tptp_fun__less_eq___type, type, (
% 0.55/0.64 tptp_fun__less_eq__: ( 'A_run_set$' * 'A_run_set$' ) > $o)).
% 0.55/0.64 tff(1,plain,
% 0.55/0.64 (^[A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'A_TESL_atomic_list$', A__questionmark_v3: 'A_TESL_atomic_list$'] : refl((tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1)))))) <=> (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1)))))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(2,plain,
% 0.55/0.64 (![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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, 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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))),
% 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_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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, 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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(4,plain,
% 0.55/0.64 (^[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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1), 1))))) <=> (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1)))))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(5,plain,
% 0.55/0.64 (![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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(tptp_fun__fun_app_u_(|'of_nat$'|, 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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[4])).
% 0.55/0.64 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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1), 1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom287')).
% 0.55/0.64 tff(7,plain,
% 0.55/0.64 (![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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))),
% 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_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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.55/0.64 tff(9,plain,(
% 0.55/0.64 ![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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))),
% 0.55/0.64 inference(skolemize,[status(sab)],[8])).
% 0.55/0.64 tff(10,plain,
% 0.55/0.64 (![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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))),
% 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_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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))) | (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_1$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_1$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_1$'|), |'phi_1$'|)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))),
% 0.55/0.64 inference(quant_inst,[status(thm)],[])).
% 0.55/0.64 tff(12,plain,
% 0.55/0.64 (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_1$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_1$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_1$'|), |'phi_1$'|)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))))),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.55/0.64 tff(13,plain,
% 0.55/0.64 ((tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_1$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_1$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_1$'|), |'phi_1$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|)))) <=> (tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_1$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_1$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_1$'|), |'phi_1$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|))))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(14,axiom,(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_1$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_1$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_1$'|), |'phi_1$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom15')).
% 0.55/0.64 tff(15,plain,
% 0.55/0.64 (tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_1$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_1$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_1$'|), |'phi_1$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|)))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.55/0.64 tff(16,plain,
% 0.55/0.64 (tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_1$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_1$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_1$'|), |'phi_1$'|)))),
% 0.55/0.64 inference(symmetry,[status(thm)],[15])).
% 0.55/0.64 tff(17,plain,
% 0.55/0.64 (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_1$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_1$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_1$'|), |'phi_1$'|))))),
% 0.55/0.64 inference(monotonicity,[status(thm)],[16])).
% 0.55/0.64 tff(18,plain,
% 0.55/0.64 (^[A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : refl((tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5)))))) <=> (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5)))))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(19,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5)))))) <=> ![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5))))))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[18])).
% 0.55/0.64 tff(20,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5)))))) <=> ![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5))))))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(21,axiom,(![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom257')).
% 0.55/0.64 tff(22,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5))))))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.55/0.64 tff(23,plain,(
% 0.55/0.64 ![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5))))))),
% 0.55/0.64 inference(skolemize,[status(sab)],[22])).
% 0.55/0.64 tff(24,plain,
% 0.55/0.64 (![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5))))))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.55/0.64 tff(25,plain,
% 0.55/0.64 ((~![A__questionmark_v0: 'A_constr_list$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Clock$', A__questionmark_v3: 'Clock$', A__questionmark_v4: 'A_TESL_atomic_list$', A__questionmark_v5: 'A_TESL_atomic_list$'] : (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v4)), A__questionmark_v5)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(A__questionmark_v3, A__questionmark_v1), tptp_fun__tickCountLeq__(A__questionmark_v2, A__questionmark_v1), tptp_fun__case_prod__(|'less_eq$f'|)), A__questionmark_v0)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v4), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(A__questionmark_v2, A__questionmark_v3), A__questionmark_v5))))))) | (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(|'k_2$'|, |'n$'|), tptp_fun__tickCountLeq__(|'k_1$'|, |'n$'|), tptp_fun__case_prod__(|'less_eq$f'|)), |'gamma$'|)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi$'|), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'phi$'|))))))),
% 0.55/0.64 inference(quant_inst,[status(thm)],[])).
% 0.55/0.64 tff(26,plain,
% 0.55/0.64 (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(|'k_2$'|, |'n$'|), tptp_fun__tickCountLeq__(|'k_1$'|, |'n$'|), tptp_fun__case_prod__(|'less_eq$f'|)), |'gamma$'|)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi$'|), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'phi$'|)))))),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.55/0.64 tff(27,plain,
% 0.55/0.64 (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(|'k_2$'|, |'n$'|), tptp_fun__tickCountLeq__(|'k_1$'|, |'n$'|), tptp_fun__case_prod__(|'less_eq$f'|)), |'gamma$'|)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi$'|), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'phi$'|))))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'psi$'|)), |'phi$'|))))),
% 0.55/0.64 inference(symmetry,[status(thm)],[26])).
% 0.55/0.64 tff(28,plain,
% 0.55/0.64 ((tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_2$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_2$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_2$'|), |'phi_2$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(|'k_2$'|, |'n$'|), tptp_fun__tickCountLeq__(|'k_1$'|, |'n$'|), tptp_fun__case_prod__(|'less_eq$f'|)), |'gamma$'|)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi$'|), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'phi$'|))))) <=> (tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_2$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_2$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_2$'|), |'phi_2$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(|'k_2$'|, |'n$'|), tptp_fun__tickCountLeq__(|'k_1$'|, |'n$'|), tptp_fun__case_prod__(|'less_eq$f'|)), |'gamma$'|)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi$'|), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'phi$'|)))))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(29,axiom,(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_2$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_2$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_2$'|), |'phi_2$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(|'k_2$'|, |'n$'|), tptp_fun__tickCountLeq__(|'k_1$'|, |'n$'|), tptp_fun__case_prod__(|'less_eq$f'|)), |'gamma$'|)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi$'|), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'phi$'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom194')).
% 0.55/0.64 tff(30,plain,
% 0.55/0.64 (tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_2$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_2$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_2$'|), |'phi_2$'|))) = tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(|'k_2$'|, |'n$'|), tptp_fun__tickCountLeq__(|'k_1$'|, |'n$'|), tptp_fun__case_prod__(|'less_eq$f'|)), |'gamma$'|)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi$'|), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'phi$'|))))),
% 0.55/0.64 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.55/0.64 tff(31,plain,
% 0.55/0.64 (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_2$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_2$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_2$'|), |'phi_2$'|)))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, tptp_fun__cons_a_(tptp_fun__tickCntArith__(tptp_fun__tickCountLeq__(|'k_2$'|, |'n$'|), tptp_fun__tickCountLeq__(|'k_1$'|, |'n$'|), tptp_fun__case_prod__(|'less_eq$f'|)), |'gamma$'|)), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi$'|), tptp_fun__cons__(tptp_fun__weaklyPrecedes__(|'k_1$'|, |'k_2$'|), |'phi$'|)))))),
% 0.55/0.64 inference(monotonicity,[status(thm)],[30])).
% 0.55/0.64 tff(32,plain,
% 0.55/0.64 ((~![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__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, A__questionmark_v0), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, A__questionmark_v1), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, A__questionmark_v2), A__questionmark_v3)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(A__questionmark_v0)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v2), A__questionmark_v1))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(A__questionmark_v3), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, A__questionmark_v1))))))) | (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_2$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_2$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_2$'|), |'phi_2$'|)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))))),
% 0.55/0.64 inference(quant_inst,[status(thm)],[])).
% 0.55/0.64 tff(33,plain,
% 0.55/0.64 (tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_2$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_2$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_2$'|), |'phi_2$'|)))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|)))))),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[32, 10])).
% 0.55/0.64 tff(34,plain,
% 0.55/0.64 (tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))) = tptp_fun__heronConf_interpretation__(tptp_fun__fun_app_c_(tptp_fun__fun_app_d_(|'pair$'|, |'gamma_2$'|), tptp_fun__fun_app_k_(tptp_fun__fun_app_l_(|'pair$b'|, |'n_2$'|), tptp_fun__fun_app_g_(tptp_fun__fun_app_h_(|'pair$a'|, |'psi_2$'|), |'phi_2$'|))))),
% 0.55/0.64 inference(symmetry,[status(thm)],[33])).
% 0.55/0.64 tff(35,plain,
% 0.55/0.64 (tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))))),
% 0.55/0.64 inference(transitivity,[status(thm)],[34, 31, 27, 17, 12])).
% 0.55/0.64 tff(36,plain,
% 0.55/0.64 (tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))) = tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))),
% 0.55/0.64 inference(rewrite,[status(thm)],[])).
% 0.55/0.64 tff(37,plain,
% 0.55/0.64 (tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))) = tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))),
% 0.55/0.65 inference(monotonicity,[status(thm)],[36])).
% 0.55/0.65 tff(38,plain,
% 0.55/0.65 (tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))))),
% 0.55/0.65 inference(monotonicity,[status(thm)],[37])).
% 0.55/0.65 tff(39,plain,
% 0.55/0.65 (tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))) = tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|)))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(40,plain,
% 0.55/0.65 (tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|)))) = tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))),
% 0.55/0.65 inference(monotonicity,[status(thm)],[39])).
% 0.55/0.65 tff(41,plain,
% 0.55/0.65 (tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|)))))),
% 0.55/0.65 inference(monotonicity,[status(thm)],[40])).
% 0.55/0.65 tff(42,plain,
% 0.55/0.65 (tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))))) <=> tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))),
% 0.55/0.65 inference(monotonicity,[status(thm)],[41, 38])).
% 0.55/0.65 tff(43,plain,
% 0.55/0.65 ((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) <=> (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))))))),
% 0.55/0.65 inference(monotonicity,[status(thm)],[42])).
% 0.55/0.65 tff(44,plain,
% 0.55/0.65 ((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) <=> (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))))))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(45,plain,
% 0.55/0.65 ((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|), 1)))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|), 1)))))) <=> (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|)))))))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(46,axiom,(~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|), 1)))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|), 1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture12')).
% 0.55/0.65 tff(47,plain,
% 0.55/0.65 (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.55/0.65 tff(48,plain,
% 0.55/0.65 (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.55/0.65 tff(49,plain,
% 0.55/0.65 (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.55/0.65 tff(50,plain,
% 0.55/0.65 (((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|)))))))) | tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))),
% 0.55/0.65 inference(tautology,[status(thm)],[])).
% 0.55/0.65 tff(51,plain,
% 0.55/0.65 ((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|)))))))),
% 0.55/0.65 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.55/0.65 tff(52,plain,
% 0.55/0.65 (^[A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : refl(((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))) <=> ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))))),
% 0.55/0.65 inference(bind,[status(th)],[])).
% 0.55/0.65 tff(53,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))) <=> ![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(quant_intro,[status(thm)],[52])).
% 0.55/0.65 tff(54,plain,
% 0.55/0.65 (^[A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)) <=> (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))), ((~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))) <=> (~(~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))))), rewrite((~(~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))) <=> ((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))), ((~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))) <=> ((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))), (((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))) <=> ((A__questionmark_v0 = A__questionmark_v1) & ((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))), rewrite(((A__questionmark_v0 = A__questionmark_v1) & ((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))) <=> (~((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))))), (((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))) <=> (~((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))))), ((~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))) <=> (~(~((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))))))), rewrite((~(~((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))))) <=> ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))), ((~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))) <=> ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))))),
% 0.55/0.65 inference(bind,[status(th)],[])).
% 0.55/0.65 tff(55,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))) <=> ![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(quant_intro,[status(thm)],[54])).
% 0.55/0.65 tff(56,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))) <=> ![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(57,plain,
% 0.55/0.65 (^[A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : trans(monotonicity(rewrite(((A__questionmark_v0 = A__questionmark_v1) & ((tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)) => $false)) <=> ((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0))))), ((((A__questionmark_v0 = A__questionmark_v1) & ((tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)) => $false)) => $false) <=> (((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))) => $false))), rewrite((((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))) => $false) <=> (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))), ((((A__questionmark_v0 = A__questionmark_v1) & ((tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)) => $false)) => $false) <=> (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))))),
% 0.55/0.65 inference(bind,[status(th)],[])).
% 0.55/0.65 tff(58,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (((A__questionmark_v0 = A__questionmark_v1) & ((tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)) => $false)) => $false) <=> ![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(quant_intro,[status(thm)],[57])).
% 0.55/0.65 tff(59,axiom,(![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (((A__questionmark_v0 = A__questionmark_v1) & ((tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)) => $false)) => $false)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom84')).
% 0.55/0.65 tff(60,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.55/0.65 tff(61,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.55/0.65 tff(62,plain,(
% 0.55/0.65 ![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : (~((A__questionmark_v0 = A__questionmark_v1) & (~(tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1) & tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(skolemize,[status(sab)],[61])).
% 0.55/0.65 tff(63,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.55/0.65 tff(64,plain,
% 0.55/0.65 (![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.55/0.65 tff(65,plain,
% 0.55/0.65 (((~![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))) | ((~(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))))))))) <=> ((~![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))) | (~(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))))))))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(66,plain,
% 0.55/0.65 ((~![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))) | ((~(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))))))))),
% 0.55/0.65 inference(quant_inst,[status(thm)],[])).
% 0.55/0.65 tff(67,plain,
% 0.55/0.65 ((~![A__questionmark_v0: 'A_run_set$', A__questionmark_v1: 'A_run_set$'] : ((~(A__questionmark_v0 = A__questionmark_v1)) | (~((~tptp_fun__less_eq__(A__questionmark_v0, A__questionmark_v1)) | (~tptp_fun__less_eq__(A__questionmark_v1, A__questionmark_v0)))))) | (~(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~((~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))) | (~tptp_fun__less_eq__(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))), tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|)))))))))),
% 0.55/0.69 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.55/0.69 tff(68,plain,
% 0.55/0.69 (~(tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_2$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_2$'|), |'n_2$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_2$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_2$'|))))) = tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__fun_app_q_(tptp_fun__fun_app_r_(|'inf$'|, tptp_fun__symbolic_run_interpretation__(|'gamma_1$'|)), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'psi_1$'|), |'n_1$'|))), tptp_fun__fun_app_s_(tptp_fun__tESL_interpretation_stepwise__(|'phi_1$'|), tptp_fun__fun_app_t_(|'nat$'|, $sum(1, tptp_fun__fun_app_u_(|'of_nat$'|, |'n_1$'|))))))),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[67, 64, 51])).
% 0.55/0.69 tff(69,plain,
% 0.55/0.69 ($false),
% 0.55/0.69 inference(unit_resolution,[status(thm)],[68, 35])).
% 0.55/0.69 % SZS output end Proof
%------------------------------------------------------------------------------