%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP384_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 Jun 21 05:12:47 AM UTC 2025
% Result : Theorem 0.39s 0.62s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ITP384_1 : TPTP v9.0.0. Released v8.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 18:49:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.39/0.62 % SZS status Theorem
% 0.39/0.62 % SZS output start Proof
% 0.39/0.62 tff(tptp_fun__id___type, type, (
% 0.39/0.62 tptp_fun__id__: |'C_update_c_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__comp___type, type, (
% 0.39/0.62 tptp_fun__comp__: ( |'B_update_c_update_fun$'| * |'C_update_b_update_fun$'| ) > |'C_update_c_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_x__type, type, (
% 0.39/0.62 tptp_fun__fun_app_x_: ( |'C_update_a_update_fun_c_update_b_update_fun_fun$'| * |'C_update_a_update_fun$'| ) > |'C_update_b_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__g_a__type, type, (
% 0.39/0.62 tptp_fun__g_a_: |'C_update_a_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_y__type, type, (
% 0.39/0.62 tptp_fun__fun_app_y_: ( |'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$'| * |'A_update_b_update_fun$'| ) > |'C_update_a_update_fun_c_update_b_update_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__f_a__type, type, (
% 0.39/0.62 tptp_fun__f_a_: |'A_update_b_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__comp_b__type, type, (
% 0.39/0.62 tptp_fun__comp_b_: |'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_v__type, type, (
% 0.39/0.62 tptp_fun__fun_app_v_: ( |'B_update_a_update_fun_b_update_c_update_fun_fun$'| * |'B_update_a_update_fun$'| ) > |'B_update_c_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__f___type, type, (
% 0.39/0.62 tptp_fun__f__: |'B_update_a_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_w__type, type, (
% 0.39/0.62 tptp_fun__fun_app_w_: ( |'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$'| * |'A_update_c_update_fun$'| ) > |'B_update_a_update_fun_b_update_c_update_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__g___type, type, (
% 0.39/0.62 tptp_fun__g__: |'A_update_c_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__comp_a__type, type, (
% 0.39/0.62 tptp_fun__comp_a_: |'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_ae__type, type, (
% 0.39/0.62 tptp_fun__fun_app_ae_: ( |'C_update_a_update_fun_c_update_c_update_fun_fun$'| * |'C_update_a_update_fun$'| ) > |'C_update_c_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_af__type, type, (
% 0.39/0.62 tptp_fun__fun_app_af_: ( |'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$'| * |'A_update_c_update_fun$'| ) > |'C_update_a_update_fun_c_update_c_update_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__comp_d__type, type, (
% 0.39/0.62 tptp_fun__comp_d_: |'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fcomp_a__type, type, (
% 0.39/0.62 tptp_fun__fcomp_a_: ( |'C_update_a_update_fun$'| * |'A_update_c_update_fun$'| ) > |'C_update_c_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__comp_aj__type, type, (
% 0.39/0.62 tptp_fun__comp_aj_: ( |'B_update_c_update_fun$'| * |'A_update_b_update_fun$'| ) > |'A_update_c_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__inv_into_b__type, type, (
% 0.39/0.62 tptp_fun__inv_into_b_: ( |'A_update_set$'| * |'A_update_b_update_fun$'| ) > |'B_update_a_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__top___type, type, (
% 0.39/0.62 tptp_fun__top__: |'A_update_set$'|)).
% 0.39/0.62 tff(tptp_fun__inj_on___type, type, (
% 0.39/0.62 tptp_fun__inj_on__: ( |'A_update_b_update_fun$'| * |'A_update_set$'| ) > $o)).
% 0.39/0.62 tff(tptp_fun__id_b__type, type, (
% 0.39/0.62 tptp_fun__id_b_: |'A_update_a_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_ac__type, type, (
% 0.39/0.62 tptp_fun__fun_app_ac_: ( |'A_update_b_update_fun_a_update_a_update_fun_fun$'| * |'A_update_b_update_fun$'| ) > |'A_update_a_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_ad__type, type, (
% 0.39/0.62 tptp_fun__fun_app_ad_: ( |'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$'| * |'B_update_a_update_fun$'| ) > |'A_update_b_update_fun_a_update_a_update_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__comp_c__type, type, (
% 0.39/0.62 tptp_fun__comp_c_: |'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__iso_register_a__type, type, (
% 0.39/0.62 tptp_fun__iso_register_a_: |'A_update_b_update_fun$'| > $o)).
% 0.39/0.62 tff(tptp_fun__id_a__type, type, (
% 0.39/0.62 tptp_fun__id_a_: |'B_update_b_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_aj__type, type, (
% 0.39/0.62 tptp_fun__fun_app_aj_: ( |'B_update_a_update_fun_b_update_b_update_fun_fun$'| * |'B_update_a_update_fun$'| ) > |'B_update_b_update_fun$'|)).
% 0.39/0.62 tff(tptp_fun__fun_app_ak__type, type, (
% 0.39/0.62 tptp_fun__fun_app_ak_: ( |'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$'| * |'A_update_b_update_fun$'| ) > |'B_update_a_update_fun_b_update_b_update_fun_fun$'|)).
% 0.39/0.62 tff(tptp_fun__comp_e__type, type, (
% 0.39/0.62 tptp_fun__comp_e_: |'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$'|)).
% 0.39/0.62 tff(1,plain,
% 0.39/0.62 ((tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, |'g$'|), |'g$a'|) = |'id$'|) <=> (tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, |'g$'|), |'g$a'|) = |'id$'|)),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(2,axiom,(tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, |'g$'|), |'g$a'|) = |'id$'|), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom42')).
% 0.39/0.62 tff(3,plain,
% 0.39/0.62 (tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, |'g$'|), |'g$a'|) = |'id$'|),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.39/0.62 tff(4,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : refl((tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0)) <=> (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0)))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(5,plain,
% 0.39/0.62 (![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0)) <=> ![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[4])).
% 0.39/0.62 tff(6,plain,
% 0.39/0.62 (![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0)) <=> ![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(7,axiom,(![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom230')).
% 0.39/0.62 tff(8,plain,
% 0.39/0.62 (![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.39/0.62 tff(9,plain,(
% 0.39/0.62 ![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0))),
% 0.39/0.62 inference(skolemize,[status(sab)],[8])).
% 0.39/0.62 tff(10,plain,
% 0.39/0.62 (![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.39/0.62 tff(11,plain,
% 0.39/0.62 ((~![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0))) | (tptp_fun__fcomp_a_(|'g$a'|, |'g$'|) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, |'g$'|), |'g$a'|))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(12,plain,
% 0.39/0.62 (tptp_fun__fcomp_a_(|'g$a'|, |'g$'|) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, |'g$'|), |'g$a'|)),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.39/0.62 tff(13,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'A_update_b_update_fun$'|] : refl((tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)) <=> (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(14,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[13])).
% 0.39/0.62 tff(15,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(16,axiom,(![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom575')).
% 0.39/0.62 tff(17,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.39/0.62 tff(18,plain,(
% 0.39/0.62 ![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(skolemize,[status(sab)],[17])).
% 0.39/0.62 tff(19,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.39/0.62 tff(20,plain,
% 0.39/0.62 ((~![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inj_on__(|'f$a'|, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(21,plain,
% 0.39/0.62 (tptp_fun__inj_on__(|'f$a'|, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|)),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.39/0.62 tff(22,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'A_update_b_update_fun$'|] : refl(((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)) <=> ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(23,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[22])).
% 0.39/0.62 tff(24,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(25,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'A_update_b_update_fun$'|] : rewrite((tptp_fun__iso_register_a_(A__questionmark_v0) => (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)) <=> ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(26,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__iso_register_a_(A__questionmark_v0) => (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[25])).
% 0.39/0.62 tff(27,axiom,(![A__questionmark_v0: |'A_update_b_update_fun$'|] : (tptp_fun__iso_register_a_(A__questionmark_v0) => (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom400')).
% 0.39/0.62 tff(28,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.39/0.62 tff(29,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.39/0.62 tff(30,plain,(
% 0.39/0.62 ![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(skolemize,[status(sab)],[29])).
% 0.39/0.62 tff(31,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.39/0.62 tff(32,plain,
% 0.39/0.62 (tptp_fun__iso_register_a_(|'f$a'|) <=> tptp_fun__iso_register_a_(|'f$a'|)),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(33,axiom,(tptp_fun__iso_register_a_(|'f$a'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom31')).
% 0.39/0.62 tff(34,plain,
% 0.39/0.62 (tptp_fun__iso_register_a_(|'f$a'|)),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.39/0.62 tff(35,plain,
% 0.39/0.62 (((~![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))) | ((~tptp_fun__iso_register_a_(|'f$a'|)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|))) <=> ((~![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))) | (~tptp_fun__iso_register_a_(|'f$a'|)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(36,plain,
% 0.39/0.62 ((~![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))) | ((~tptp_fun__iso_register_a_(|'f$a'|)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(37,plain,
% 0.39/0.62 ((~![A__questionmark_v0: |'A_update_b_update_fun$'|] : ((~tptp_fun__iso_register_a_(A__questionmark_v0)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = |'id$b'|))) | (~tptp_fun__iso_register_a_(|'f$a'|)) | (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|)),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.39/0.62 tff(38,plain,
% 0.39/0.62 (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[37, 34, 31])).
% 0.39/0.62 tff(39,plain,
% 0.39/0.62 ((~(tptp_fun__inj_on__(|'f$a'|, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|))) | tptp_fun__inj_on__(|'f$a'|, |'top$'|) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|))),
% 0.39/0.62 inference(tautology,[status(thm)],[])).
% 0.39/0.62 tff(40,plain,
% 0.39/0.62 ((~(tptp_fun__inj_on__(|'f$a'|, |'top$'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'id$b'|))) | tptp_fun__inj_on__(|'f$a'|, |'top$'|)),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.39/0.62 tff(41,plain,
% 0.39/0.62 (tptp_fun__inj_on__(|'f$a'|, |'top$'|)),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[40, 21])).
% 0.39/0.62 tff(42,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : refl(((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(43,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[42])).
% 0.39/0.62 tff(44,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(45,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : rewrite((tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) => (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(46,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) => (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[45])).
% 0.39/0.62 tff(47,axiom,(![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__inj_on__(A__questionmark_v0, |'top$'|) => (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom479')).
% 0.39/0.62 tff(48,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.39/0.62 tff(49,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.39/0.62 tff(50,plain,(
% 0.39/0.62 ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.62 inference(skolemize,[status(sab)],[49])).
% 0.39/0.62 tff(51,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.39/0.62 tff(52,plain,
% 0.39/0.62 (((~![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on__(|'f$a'|, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'g$'|))) <=> ((~![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on__(|'f$a'|, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'g$'|))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(53,plain,
% 0.39/0.62 ((~![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | ((~tptp_fun__inj_on__(|'f$a'|, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'g$'|))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(54,plain,
% 0.39/0.62 ((~![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : ((~tptp_fun__inj_on__(A__questionmark_v0, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, A__questionmark_v1), tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0)), A__questionmark_v0) = A__questionmark_v1))) | (~tptp_fun__inj_on__(|'f$a'|, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'g$'|)),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.39/0.62 tff(55,plain,
% 0.39/0.62 ((~tptp_fun__inj_on__(|'f$a'|, |'top$'|)) | (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'g$'|)),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.39/0.62 tff(56,plain,
% 0.39/0.62 (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|) = |'g$'|),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.39/0.62 tff(57,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : refl(((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) <=> ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(58,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[57])).
% 0.39/0.62 tff(59,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)) <=> (~((~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))))), ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) <=> (~(~((~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))))))), rewrite((~(~((~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))))) <=> ((~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))), ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) <=> ((~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))))), (((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> (((~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)))), rewrite((((~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))), (((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(60,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[59])).
% 0.39/0.62 tff(61,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(62,plain,
% 0.39/0.62 (^[A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : rewrite((((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)) => (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(63,plain,
% 0.39/0.62 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : (((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)) => (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1)) <=> ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[62])).
% 0.39/0.63 tff(64,axiom,(![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : (((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)) => (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom455')).
% 0.39/0.63 tff(65,plain,
% 0.39/0.63 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.39/0.63 tff(66,plain,
% 0.39/0.63 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.39/0.63 tff(67,plain,(
% 0.39/0.63 ![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((~((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|) & (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|))) | (tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1))),
% 0.39/0.63 inference(skolemize,[status(sab)],[66])).
% 0.39/0.63 tff(68,plain,
% 0.39/0.63 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.39/0.63 tff(69,plain,
% 0.39/0.63 (![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.39/0.63 tff(70,plain,
% 0.39/0.63 ((tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, |'f$'|), |'f$a'|) = |'id$b'|) <=> (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, |'f$'|), |'f$a'|) = |'id$b'|)),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(71,axiom,(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, |'f$'|), |'f$a'|) = |'id$b'|), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom69')).
% 0.39/0.63 tff(72,plain,
% 0.39/0.63 (tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, |'f$'|), |'f$a'|) = |'id$b'|),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.39/0.63 tff(73,plain,
% 0.39/0.63 ((tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, |'f$a'|), |'f$'|) = |'id$a'|) <=> (tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, |'f$a'|), |'f$'|) = |'id$a'|)),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(74,axiom,(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, |'f$a'|), |'f$'|) = |'id$a'|), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom67')).
% 0.39/0.63 tff(75,plain,
% 0.39/0.63 (tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, |'f$a'|), |'f$'|) = |'id$a'|),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.39/0.63 tff(76,plain,
% 0.39/0.63 (((~![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))) | ((tptp_fun__inv_into_b_(|'top$'|, |'f$a'|) = |'f$'|) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, |'f$a'|), |'f$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, |'f$'|), |'f$a'|) = |'id$b'|)))) <=> ((~![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))) | (tptp_fun__inv_into_b_(|'top$'|, |'f$a'|) = |'f$'|) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, |'f$a'|), |'f$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, |'f$'|), |'f$a'|) = |'id$b'|)))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(77,plain,
% 0.39/0.63 ((~![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))) | ((tptp_fun__inv_into_b_(|'top$'|, |'f$a'|) = |'f$'|) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, |'f$a'|), |'f$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, |'f$'|), |'f$a'|) = |'id$b'|)))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(78,plain,
% 0.39/0.63 ((~![A__questionmark_v0: |'A_update_b_update_fun$'|, A__questionmark_v1: |'B_update_a_update_fun$'|] : ((tptp_fun__inv_into_b_(|'top$'|, A__questionmark_v0) = A__questionmark_v1) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, A__questionmark_v0), A__questionmark_v1) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, A__questionmark_v1), A__questionmark_v0) = |'id$b'|)))) | (tptp_fun__inv_into_b_(|'top$'|, |'f$a'|) = |'f$'|) | (~(tptp_fun__fun_app_aj_(tptp_fun__fun_app_ak_(|'comp$e'|, |'f$a'|), |'f$'|) = |'id$a'|)) | (~(tptp_fun__fun_app_ac_(tptp_fun__fun_app_ad_(|'comp$c'|, |'f$'|), |'f$a'|) = |'id$b'|))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.39/0.63 tff(79,plain,
% 0.39/0.63 (tptp_fun__inv_into_b_(|'top$'|, |'f$a'|) = |'f$'|),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[78, 75, 72, 69])).
% 0.39/0.63 tff(80,plain,
% 0.39/0.63 (tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)) = tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|)),
% 0.39/0.63 inference(monotonicity,[status(thm)],[79])).
% 0.39/0.63 tff(81,plain,
% 0.39/0.63 (tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|) = tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|))),
% 0.39/0.63 inference(symmetry,[status(thm)],[80])).
% 0.39/0.63 tff(82,plain,
% 0.39/0.63 (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|) = tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), tptp_fun__inv_into_b_(|'top$'|, |'f$a'|)), |'f$a'|)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[81])).
% 0.48/0.63 tff(83,plain,
% 0.48/0.63 (tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|) = |'g$'|),
% 0.48/0.63 inference(transitivity,[status(thm)],[82, 56])).
% 0.48/0.63 tff(84,plain,
% 0.48/0.63 (tptp_fun__fcomp_a_(|'g$a'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|)) = tptp_fun__fcomp_a_(|'g$a'|, |'g$'|)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[83])).
% 0.48/0.63 tff(85,plain,
% 0.48/0.63 ((~![A__questionmark_v0: |'C_update_a_update_fun$'|, A__questionmark_v1: |'A_update_c_update_fun$'|] : (tptp_fun__fcomp_a_(A__questionmark_v0, A__questionmark_v1) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, A__questionmark_v1), A__questionmark_v0))) | (tptp_fun__fcomp_a_(|'g$a'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|)), |'g$a'|))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(86,plain,
% 0.48/0.63 (tptp_fun__fcomp_a_(|'g$a'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|)), |'g$a'|)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[85, 10])).
% 0.48/0.63 tff(87,plain,
% 0.48/0.63 (tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|)), |'g$a'|) = tptp_fun__fcomp_a_(|'g$a'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|))),
% 0.48/0.63 inference(symmetry,[status(thm)],[86])).
% 0.48/0.63 tff(88,plain,
% 0.48/0.63 (^[A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : refl((tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2)) <=> (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2)))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(89,plain,
% 0.48/0.63 (![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2)) <=> ![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[88])).
% 0.48/0.63 tff(90,plain,
% 0.48/0.63 (![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2)) <=> ![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(91,axiom,(![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom187')).
% 0.48/0.63 tff(92,plain,
% 0.48/0.63 (![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.48/0.63 tff(93,plain,(
% 0.48/0.63 ![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 0.48/0.63 inference(skolemize,[status(sab)],[92])).
% 0.48/0.63 tff(94,plain,
% 0.48/0.63 (![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.48/0.63 tff(95,plain,
% 0.48/0.63 ((~![A__questionmark_v0: |'B_update_c_update_fun$'|, A__questionmark_v1: |'A_update_b_update_fun$'|, A__questionmark_v2: |'C_update_a_update_fun$'|] : (tptp_fun__comp__(A__questionmark_v0, tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, A__questionmark_v1), A__questionmark_v2)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(A__questionmark_v0, A__questionmark_v1)), A__questionmark_v2))) | (tptp_fun__comp__(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, |'f$a'|), |'g$a'|)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|)), |'g$a'|))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(96,plain,
% 0.48/0.63 (tptp_fun__comp__(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, |'f$a'|), |'g$a'|)) = tptp_fun__fun_app_ae_(tptp_fun__fun_app_af_(|'comp$d'|, tptp_fun__comp_aj_(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), |'f$a'|)), |'g$a'|)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.48/0.63 tff(97,plain,
% 0.48/0.63 (tptp_fun__comp__(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, |'f$a'|), |'g$a'|)) = |'id$'|),
% 0.48/0.63 inference(transitivity,[status(thm)],[96, 87, 84, 12, 3])).
% 0.48/0.63 tff(98,plain,
% 0.48/0.63 ((~(tptp_fun__comp__(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, |'f$a'|), |'g$a'|)) = |'id$'|)) <=> (~(tptp_fun__comp__(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, |'f$a'|), |'g$a'|)) = |'id$'|))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(99,axiom,(~(tptp_fun__comp__(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, |'f$a'|), |'g$a'|)) = |'id$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture29')).
% 0.48/0.68 tff(100,plain,
% 0.48/0.68 (~(tptp_fun__comp__(tptp_fun__fun_app_v_(tptp_fun__fun_app_w_(|'comp$a'|, |'g$'|), |'f$'|), tptp_fun__fun_app_x_(tptp_fun__fun_app_y_(|'comp$b'|, |'f$a'|), |'g$a'|)) = |'id$'|)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.48/0.68 tff(101,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.48/0.68 % SZS output end Proof
% 0.54/0.69 % E exiting
%------------------------------------------------------------------------------