%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP303_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:12:41 AM UTC 2025
% Result : Theorem 0.39s 0.60s
% Output : Proof 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ITP303_1 : TPTP v9.0.0. Released v8.0.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.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 18:46:41 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.39/0.60 % SZS status Theorem
% 0.39/0.60 % SZS output start Proof
% 0.39/0.60 tff(tptp_fun__catDom___type, type, (
% 0.39/0.60 tptp_fun__catDom__: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'| > |'A_b_b_c_LSCategory_ext_Category_ext$'|)).
% 0.39/0.60 tff(tptp_fun__fun_app_r__type, type, (
% 0.39/0.60 tptp_fun__fun_app_r_: ( |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'| * |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'| ) > |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)).
% 0.39/0.60 tff(tptp_fun__yFtorNT___type, type, (
% 0.39/0.60 tptp_fun__yFtorNT__: ( |'A_b_b_c_LSCategory_ext_Category_ext$'| * |'B$'| ) > |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)).
% 0.39/0.60 tff(tptp_fun__f___type, type, (
% 0.39/0.60 tptp_fun__f__: |'B$'|)).
% 0.39/0.60 tff(tptp_fun__c___type, type, (
% 0.39/0.60 tptp_fun__c__: |'A_b_b_c_LSCategory_ext_Category_ext$'|)).
% 0.39/0.60 tff(tptp_fun__nTCod___type, type, (
% 0.39/0.60 tptp_fun__nTCod__: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'|)).
% 0.39/0.60 tff(tptp_fun__nTDom___type, type, (
% 0.39/0.60 tptp_fun__nTDom__: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'|)).
% 0.39/0.60 tff(tptp_fun__fun_app_s__type, type, (
% 0.39/0.60 tptp_fun__fun_app_s_: ( |'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$'| * |'A_b_b_c_LSCategory_ext_Category_ext$'| ) > |'A_b_b_c_LSCategory_ext_Category_ext$'|)).
% 0.39/0.60 tff(tptp_fun__oppositeCategory___type, type, (
% 0.39/0.60 tptp_fun__oppositeCategory__: |'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$'|)).
% 0.39/0.60 tff(tptp_fun__fun_app_w__type, type, (
% 0.39/0.60 tptp_fun__fun_app_w_: ( |'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun$'| * |'ZF_ZF_unit_Category_ext$'| ) > |'ZF_ZF_unit_Category_ext$'|)).
% 0.39/0.60 tff(tptp_fun__set_a__type, type, (
% 0.39/0.60 tptp_fun__set_a_: |'ZF_ZF_unit_Category_ext$'|)).
% 0.39/0.60 tff(tptp_fun__makeCat___type, type, (
% 0.39/0.60 tptp_fun__makeCat__: |'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun$'|)).
% 0.39/0.60 tff(tptp_fun__catCod___type, type, (
% 0.39/0.60 tptp_fun__catCod__: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'| > |'ZF_ZF_unit_Category_ext$'|)).
% 0.39/0.60 tff(tptp_fun__fun_app_a__type, type, (
% 0.39/0.60 tptp_fun__fun_app_a_: ( |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'| * |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'| ) > $o)).
% 0.39/0.60 tff(tptp_fun__functor___type, type, (
% 0.39/0.60 tptp_fun__functor__: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'|)).
% 0.39/0.60 tff(tptp_fun__functor_abbrev___type, type, (
% 0.39/0.60 tptp_fun__functor_abbrev__: ( |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'| * |'A_b_b_c_LSCategory_ext_Category_ext$'| * |'ZF_ZF_unit_Category_ext$'| ) > $o)).
% 0.39/0.60 tff(tptp_fun__set___type, type, (
% 0.39/0.60 tptp_fun__set__: |'ZF_ZF_unit_Category_ext$'|)).
% 0.39/0.60 tff(tptp_fun__nTCatDom___type, type, (
% 0.39/0.60 tptp_fun__nTCatDom__: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'| > |'A_b_b_c_LSCategory_ext_Category_ext$'|)).
% 0.39/0.60 tff(1,plain,
% 0.39/0.60 (^[A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : refl((~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) <=> (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(2,plain,
% 0.39/0.60 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) <=> ![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[1])).
% 0.39/0.60 tff(3,plain,
% 0.39/0.60 (^[A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : trans(trans(monotonicity(rewrite((tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2)) <=> (~((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))))), ((tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (~((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))))))), rewrite((tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (~((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))))) <=> (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))), ((tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))))), rewrite((~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) <=> (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))), ((tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(4,plain,
% 0.39/0.60 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> ![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[3])).
% 0.39/0.60 tff(5,plain,
% 0.39/0.60 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> ![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2)))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(6,plain,
% 0.39/0.60 (^[A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : rewrite((tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> ((tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(7,plain,
% 0.39/0.60 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> ((tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> ![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2)))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[6])).
% 0.39/0.60 tff(8,axiom,(![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> ((tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom75')).
% 0.39/0.60 tff(9,plain,
% 0.39/0.60 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.39/0.60 tff(10,plain,
% 0.39/0.60 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.39/0.60 tff(11,plain,(
% 0.39/0.60 ![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2) <=> (tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0) & (tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1) & (tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2)))),
% 0.39/0.60 inference(skolemize,[status(sab)],[10])).
% 0.39/0.60 tff(12,plain,
% 0.39/0.60 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.39/0.60 tff(13,plain,
% 0.39/0.60 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.39/0.60 tff(14,plain,
% 0.39/0.60 ((~![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (~(((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(15,plain,
% 0.39/0.60 (~(((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.39/0.60 tff(16,plain,
% 0.39/0.60 ((|'set$'| = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)) <=> (|'set$'| = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(17,axiom,(|'set$'| = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom244')).
% 0.39/0.60 tff(18,plain,
% 0.39/0.60 (|'set$'| = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.39/0.60 tff(19,plain,
% 0.39/0.60 (tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|) = |'set$'|),
% 0.39/0.60 inference(symmetry,[status(thm)],[18])).
% 0.39/0.60 tff(20,plain,
% 0.39/0.60 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|)),
% 0.39/0.60 inference(monotonicity,[status(thm)],[19])).
% 0.39/0.60 tff(21,plain,
% 0.39/0.60 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))),
% 0.39/0.60 inference(symmetry,[status(thm)],[20])).
% 0.39/0.60 tff(22,plain,
% 0.39/0.60 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|)),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(23,axiom,(tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom32')).
% 0.39/0.60 tff(24,plain,
% 0.39/0.60 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|)),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.39/0.60 tff(25,plain,
% 0.39/0.60 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.39/0.60 tff(26,plain,
% 0.39/0.60 ((((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))) | (~((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))))) | (~tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))),
% 0.39/0.60 inference(tautology,[status(thm)],[])).
% 0.39/0.60 tff(27,plain,
% 0.39/0.60 (~((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[26, 25, 15])).
% 0.39/0.60 tff(28,plain,
% 0.39/0.60 (((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))) | (tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))),
% 0.39/0.60 inference(tautology,[status(thm)],[])).
% 0.39/0.60 tff(29,plain,
% 0.39/0.60 (tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|)),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.39/0.60 tff(30,plain,
% 0.39/0.60 ((tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) <=> (tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[29])).
% 0.39/0.60 tff(31,plain,
% 0.39/0.60 ((tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|)) <=> (tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))))),
% 0.39/0.60 inference(symmetry,[status(thm)],[30])).
% 0.39/0.60 tff(32,plain,
% 0.39/0.60 ((~![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|, A__questionmark_v1: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v2: |'ZF_ZF_unit_Category_ext$'|] : (~(((~tptp_fun__fun_app_a_(|'functor$'|, A__questionmark_v0)) | (~(tptp_fun__catDom__(A__questionmark_v0) = A__questionmark_v1)) | (~(tptp_fun__catCod__(A__questionmark_v0) = A__questionmark_v2))) <=> tptp_fun__functor_abbrev__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (~(((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(33,plain,
% 0.39/0.61 (~(((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[32, 13])).
% 0.39/0.61 tff(34,plain,
% 0.39/0.61 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|)),
% 0.39/0.61 inference(monotonicity,[status(thm)],[19])).
% 0.39/0.61 tff(35,plain,
% 0.39/0.61 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))),
% 0.39/0.61 inference(symmetry,[status(thm)],[34])).
% 0.39/0.61 tff(36,plain,
% 0.39/0.61 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|)),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(37,axiom,(tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom37')).
% 0.39/0.61 tff(38,plain,
% 0.39/0.61 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), |'set$'|)),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.39/0.61 tff(39,plain,
% 0.39/0.61 (tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.39/0.61 tff(40,plain,
% 0.39/0.61 ((((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))) <=> tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))) | (~((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))))) | (~tptp_fun__functor_abbrev__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)), tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|), tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))),
% 0.39/0.61 inference(tautology,[status(thm)],[])).
% 0.39/0.61 tff(41,plain,
% 0.39/0.61 (~((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[40, 39, 33])).
% 0.39/0.61 tff(42,plain,
% 0.39/0.61 (((~tptp_fun__fun_app_a_(|'functor$'|, tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) | (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))) | (~(tptp_fun__catCod__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_w_(|'makeCat$'|, |'set$a'|)))) | (tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|))),
% 0.39/0.61 inference(tautology,[status(thm)],[])).
% 0.39/0.61 tff(43,plain,
% 0.39/0.61 (tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__fun_app_s_(|'oppositeCategory$'|, |'c$'|)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.39/0.61 tff(44,plain,
% 0.39/0.61 (tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[43, 31])).
% 0.39/0.61 tff(45,plain,
% 0.39/0.61 (^[A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : refl((tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0))) <=> (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(46,plain,
% 0.39/0.61 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0)))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[45])).
% 0.39/0.61 tff(47,plain,
% 0.39/0.61 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(48,axiom,(![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom36')).
% 0.39/0.61 tff(49,plain,
% 0.39/0.61 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.39/0.61 tff(50,plain,(
% 0.39/0.61 ![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0)))),
% 0.39/0.61 inference(skolemize,[status(sab)],[49])).
% 0.39/0.61 tff(51,plain,
% 0.39/0.61 (![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.39/0.61 tff(52,plain,
% 0.39/0.61 ((~![A__questionmark_v0: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|] : (tptp_fun__nTCatDom__(A__questionmark_v0) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, A__questionmark_v0)))) | (tptp_fun__nTCatDom__(tptp_fun__yFtorNT__(|'c$'|, |'f$'|)) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(53,plain,
% 0.49/0.65 (tptp_fun__nTCatDom__(tptp_fun__yFtorNT__(|'c$'|, |'f$'|)) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.49/0.65 tff(54,plain,
% 0.49/0.65 ((tptp_fun__nTCatDom__(tptp_fun__yFtorNT__(|'c$'|, |'f$'|)) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))) <=> (tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[53])).
% 0.49/0.65 tff(55,plain,
% 0.49/0.65 ((~(tptp_fun__nTCatDom__(tptp_fun__yFtorNT__(|'c$'|, |'f$'|)) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))))) <=> (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[54])).
% 0.49/0.65 tff(56,plain,
% 0.49/0.65 ((~(tptp_fun__nTCatDom__(tptp_fun__yFtorNT__(|'c$'|, |'f$'|)) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))))) <=> (~(tptp_fun__nTCatDom__(tptp_fun__yFtorNT__(|'c$'|, |'f$'|)) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|)))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(57,axiom,(~(tptp_fun__nTCatDom__(tptp_fun__yFtorNT__(|'c$'|, |'f$'|)) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture27')).
% 0.49/0.65 tff(58,plain,
% 0.49/0.65 (~(tptp_fun__nTCatDom__(tptp_fun__yFtorNT__(|'c$'|, |'f$'|)) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.49/0.65 tff(59,plain,
% 0.49/0.65 (~(tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTDom$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))) = tptp_fun__catDom__(tptp_fun__fun_app_r_(|'nTCod$'|, tptp_fun__yFtorNT__(|'c$'|, |'f$'|))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.49/0.65 tff(60,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[59, 44])).
% 0.49/0.65 % SZS output end Proof
% 0.49/0.66 % E exiting
%------------------------------------------------------------------------------