%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP302_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 05:12:41 AM UTC 2025
% Result : Theorem 0.50s 0.67s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP302_1 : TPTP v9.0.0. Released v8.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 18:46:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.50/0.67 % SZS status Theorem
% 0.50/0.67 % SZS output start Proof
% 0.50/0.67 tff(tptp_fun__category___type, type, (
% 0.50/0.67 tptp_fun__category__: |'A_b_b_c_LSCategory_ext_Category_ext$'| > $o)).
% 0.50/0.67 tff(tptp_fun__c___type, type, (
% 0.50/0.67 tptp_fun__c__: |'A_b_b_c_LSCategory_ext_Category_ext$'|)).
% 0.50/0.67 tff(tptp_fun__fun_app_m__type, type, (
% 0.50/0.67 tptp_fun__fun_app_m_: ( |'B_set_bool_fun$'| * |'B_set$'| ) > $o)).
% 0.50/0.67 tff(tptp_fun__mor___type, type, (
% 0.50/0.67 tptp_fun__mor__: |'A_b_b_c_LSCategory_ext_Category_ext$'| > |'B_set$'|)).
% 0.50/0.67 tff(tptp_fun__member_b__type, type, (
% 0.50/0.67 tptp_fun__member_b_: |'B$'| > |'B_set_bool_fun$'|)).
% 0.50/0.67 tff(tptp_fun__fun_app_p__type, type, (
% 0.50/0.67 tptp_fun__fun_app_p_: ( |'A_set_bool_fun$'| * |'A_set$'| ) > $o)).
% 0.50/0.67 tff(tptp_fun__obj___type, type, (
% 0.50/0.67 tptp_fun__obj__: |'A_b_b_c_LSCategory_ext_Category_ext$'| > |'A_set$'|)).
% 0.50/0.67 tff(tptp_fun__member_c__type, type, (
% 0.50/0.67 tptp_fun__member_c_: |'A$'| > |'A_set_bool_fun$'|)).
% 0.50/0.67 tff(tptp_fun__fun_app_bk__type, type, (
% 0.50/0.67 tptp_fun__fun_app_bk_: ( |'B_a_fun$'| * |'B$'| ) > |'A$'|)).
% 0.50/0.67 tff(tptp_fun__dom___type, type, (
% 0.50/0.67 tptp_fun__dom__: |'A_b_b_c_LSCategory_ext_Category_ext$'| > |'B_a_fun$'|)).
% 0.50/0.67 tff(tptp_fun__f___type, type, (
% 0.50/0.67 tptp_fun__f__: |'B$'|)).
% 0.50/0.67 tff(tptp_fun__lSCategory___type, type, (
% 0.50/0.67 tptp_fun__lSCategory__: |'A_b_b_c_LSCategory_ext_Category_ext$'| > $o)).
% 0.50/0.67 tff(1,plain,
% 0.50/0.67 (^[A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : refl((tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0))) <=> (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(2,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[1])).
% 0.50/0.67 tff(3,plain,
% 0.50/0.67 (^[A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) <=> (~((~tptp_fun__category__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))))), ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) <=> (~(~((~tptp_fun__category__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))))))), rewrite((~(~((~tptp_fun__category__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))))) <=> ((~tptp_fun__category__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))))), ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) <=> ((~tptp_fun__category__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))))), (((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))) <=> (((~tptp_fun__category__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))))), rewrite((((~tptp_fun__category__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))) <=> (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))), (((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))) <=> (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(4,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[3])).
% 0.50/0.67 tff(5,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(6,plain,
% 0.50/0.67 (^[A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : rewrite(((tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) => tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))) <=> ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(7,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) => tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[6])).
% 0.50/0.67 tff(8,axiom,(![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) => tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom203')).
% 0.50/0.67 tff(9,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.50/0.67 tff(10,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.50/0.67 tff(11,plain,(
% 0.50/0.67 ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : ((~(tptp_fun__category__(A__questionmark_v0) & tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)))),
% 0.50/0.67 inference(skolemize,[status(sab)],[10])).
% 0.50/0.67 tff(12,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.50/0.67 tff(13,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.50/0.67 tff(14,plain,
% 0.50/0.67 (tptp_fun__fun_app_m_(tptp_fun__member_b_(|'f$'|), tptp_fun__mor__(|'c$'|)) <=> tptp_fun__fun_app_m_(tptp_fun__member_b_(|'f$'|), tptp_fun__mor__(|'c$'|))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(15,axiom,(tptp_fun__fun_app_m_(tptp_fun__member_b_(|'f$'|), tptp_fun__mor__(|'c$'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom187')).
% 0.50/0.67 tff(16,plain,
% 0.50/0.67 (tptp_fun__fun_app_m_(tptp_fun__member_b_(|'f$'|), tptp_fun__mor__(|'c$'|))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.50/0.67 tff(17,plain,
% 0.50/0.67 ((~tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(|'c$'|), |'f$'|)), tptp_fun__obj__(|'c$'|))) <=> (~tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(|'c$'|), |'f$'|)), tptp_fun__obj__(|'c$'|)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(18,axiom,(~tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(|'c$'|), |'f$'|)), tptp_fun__obj__(|'c$'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture185')).
% 0.50/0.67 tff(19,plain,
% 0.50/0.67 (~tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(|'c$'|), |'f$'|)), tptp_fun__obj__(|'c$'|))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.50/0.67 tff(20,plain,
% 0.50/0.67 (((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))) | (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(|'c$'|), |'f$'|)), tptp_fun__obj__(|'c$'|)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(|'f$'|), tptp_fun__mor__(|'c$'|))) | (~tptp_fun__category__(|'c$'|)))) <=> ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(|'c$'|), |'f$'|)), tptp_fun__obj__(|'c$'|)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(|'f$'|), tptp_fun__mor__(|'c$'|))) | (~tptp_fun__category__(|'c$'|)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(21,plain,
% 0.50/0.67 ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))) | (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(|'c$'|), |'f$'|)), tptp_fun__obj__(|'c$'|)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(|'f$'|), tptp_fun__mor__(|'c$'|))) | (~tptp_fun__category__(|'c$'|)))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(22,plain,
% 0.50/0.67 ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'B$'|] : (tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__obj__(A__questionmark_v0)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(A__questionmark_v1), tptp_fun__mor__(A__questionmark_v0))) | (~tptp_fun__category__(A__questionmark_v0)))) | tptp_fun__fun_app_p_(tptp_fun__member_c_(tptp_fun__fun_app_bk_(tptp_fun__dom__(|'c$'|), |'f$'|)), tptp_fun__obj__(|'c$'|)) | (~tptp_fun__fun_app_m_(tptp_fun__member_b_(|'f$'|), tptp_fun__mor__(|'c$'|))) | (~tptp_fun__category__(|'c$'|))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.50/0.67 tff(23,plain,
% 0.50/0.67 (~tptp_fun__category__(|'c$'|)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[22, 19, 16, 13])).
% 0.50/0.67 tff(24,plain,
% 0.50/0.67 (^[A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : refl((tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0))) <=> (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(25,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[24])).
% 0.50/0.67 tff(26,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(27,plain,
% 0.50/0.67 (^[A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : rewrite((tptp_fun__lSCategory__(A__questionmark_v0) => tptp_fun__category__(A__questionmark_v0)) <=> (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(28,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__lSCategory__(A__questionmark_v0) => tptp_fun__category__(A__questionmark_v0)) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[27])).
% 0.50/0.67 tff(29,axiom,(![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__lSCategory__(A__questionmark_v0) => tptp_fun__category__(A__questionmark_v0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom212')).
% 0.50/0.67 tff(30,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.50/0.67 tff(31,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.50/0.67 tff(32,plain,(
% 0.50/0.67 ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))),
% 0.50/0.67 inference(skolemize,[status(sab)],[31])).
% 0.50/0.67 tff(33,plain,
% 0.50/0.67 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.50/0.67 tff(34,plain,
% 0.50/0.67 (tptp_fun__lSCategory__(|'c$'|) <=> tptp_fun__lSCategory__(|'c$'|)),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(35,axiom,(tptp_fun__lSCategory__(|'c$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom186')).
% 0.50/0.67 tff(36,plain,
% 0.50/0.67 (tptp_fun__lSCategory__(|'c$'|)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.50/0.67 tff(37,plain,
% 0.50/0.67 (((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))) | (tptp_fun__category__(|'c$'|) | (~tptp_fun__lSCategory__(|'c$'|)))) <=> ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))) | tptp_fun__category__(|'c$'|) | (~tptp_fun__lSCategory__(|'c$'|)))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(38,plain,
% 0.57/0.74 ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))) | (tptp_fun__category__(|'c$'|) | (~tptp_fun__lSCategory__(|'c$'|)))),
% 0.57/0.74 inference(quant_inst,[status(thm)],[])).
% 0.57/0.74 tff(39,plain,
% 0.57/0.74 ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|] : (tptp_fun__category__(A__questionmark_v0) | (~tptp_fun__lSCategory__(A__questionmark_v0)))) | tptp_fun__category__(|'c$'|) | (~tptp_fun__lSCategory__(|'c$'|))),
% 0.57/0.74 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.57/0.74 tff(40,plain,
% 0.57/0.74 ($false),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[39, 36, 33, 23])).
% 0.57/0.74 % SZS output end Proof
% 0.57/0.74 % E exiting
%------------------------------------------------------------------------------