%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP305_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:12:41 AM UTC 2025
% Result : Theorem 0.43s 0.60s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP305_1 : TPTP v9.0.0. Released v8.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 18:44:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.43/0.60 % SZS status Theorem
% 0.43/0.60 % SZS output start Proof
% 0.43/0.60 tff(tptp_fun__yMapInv___type, type, (
% 0.43/0.60 tptp_fun__yMapInv__: ( |'A_b_b_c_LSCategory_ext_Category_ext$'| * |'A$'| * |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'| * |'ZF$'| ) > |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)).
% 0.43/0.60 tff(tptp_fun__yMap___type, type, (
% 0.43/0.60 tptp_fun__yMap__: ( |'A_b_b_c_LSCategory_ext_Category_ext$'| * |'A$'| * |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'| ) > |'ZF$'|)).
% 0.43/0.60 tff(tptp_fun__eta___type, type, (
% 0.43/0.60 tptp_fun__eta__: |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'|)).
% 0.43/0.60 tff(tptp_fun__x___type, type, (
% 0.43/0.60 tptp_fun__x__: |'A$'|)).
% 0.43/0.60 tff(tptp_fun__c___type, type, (
% 0.43/0.60 tptp_fun__c__: |'A_b_b_c_LSCategory_ext_Category_ext$'|)).
% 0.43/0.60 tff(tptp_fun__mapO___type, type, (
% 0.43/0.60 tptp_fun__mapO__: ( |'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'| * |'A$'| ) > |'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)).
% 0.43/0.60 tff(tptp_fun__y___type, type, (
% 0.43/0.60 tptp_fun__y__: |'A$'|)).
% 0.43/0.60 tff(tptp_fun__yFtor___type, type, (
% 0.43/0.60 tptp_fun__yFtor__: |'A_b_b_c_LSCategory_ext_Category_ext$'| > |'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'|)).
% 0.43/0.60 tff(tptp_fun__fun_app_p__type, type, (
% 0.43/0.60 tptp_fun__fun_app_p_: ( |'B_ZF_fun$'| * |'B$'| ) > |'ZF$'|)).
% 0.43/0.60 tff(tptp_fun__zF2mor___type, type, (
% 0.43/0.60 tptp_fun__zF2mor__: ( |'A_b_b_c_LSCategory_ext_Category_ext$'| * |'ZF$'| ) > |'B$'|)).
% 0.43/0.60 tff(tptp_fun__mor2ZF___type, type, (
% 0.43/0.60 tptp_fun__mor2ZF__: |'A_b_b_c_LSCategory_ext_Category_ext$'| > |'B_ZF_fun$'|)).
% 0.43/0.60 tff(tptp_fun__fun_app_l__type, type, (
% 0.43/0.60 tptp_fun__fun_app_l_: ( |'A_bool_fun$'| * |'A$'| ) > $o)).
% 0.43/0.60 tff(tptp_fun__mapsTo___type, type, (
% 0.43/0.60 tptp_fun__mapsTo__: ( |'A_b_b_c_LSCategory_ext_Category_ext$'| * |'B$'| * |'A$'| ) > |'A_bool_fun$'|)).
% 0.43/0.60 tff(tptp_fun__fun_app_b__type, type, (
% 0.43/0.60 tptp_fun__fun_app_b_: ( |'ZF_bool_fun$'| * |'ZF$'| ) > $o)).
% 0.43/0.60 tff(tptp_fun__homSet___type, type, (
% 0.43/0.60 tptp_fun__homSet__: ( |'A_b_b_c_LSCategory_ext_Category_ext$'| * |'A$'| * |'A$'| ) > |'ZF$'|)).
% 0.43/0.60 tff(tptp_fun__elem___type, type, (
% 0.43/0.60 tptp_fun__elem__: |'ZF$'| > |'ZF_bool_fun$'|)).
% 0.43/0.60 tff(tptp_fun__member_i__type, type, (
% 0.43/0.60 tptp_fun__member_i_: ( |'A$'| * |'A_set$'| ) > $o)).
% 0.43/0.60 tff(tptp_fun__obj_b__type, type, (
% 0.43/0.60 tptp_fun__obj_b_: |'A_b_b_c_LSCategory_ext_Category_ext$'| > |'A_set$'|)).
% 0.43/0.60 tff(tptp_fun__lSCategory___type, type, (
% 0.43/0.60 tptp_fun__lSCategory__: |'A_b_b_c_LSCategory_ext_Category_ext$'| > $o)).
% 0.43/0.60 tff(1,plain,
% 0.43/0.60 (^[A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : refl(((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))))) <=> ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(2,plain,
% 0.43/0.60 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[1])).
% 0.43/0.60 tff(3,plain,
% 0.43/0.60 (^[A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) <=> (~((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))))), ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) <=> (~(~((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))))))), rewrite((~(~((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))))) <=> ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))))), ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) <=> ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))))), rewrite((tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)) <=> (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))))), (((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))) <=> (((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))))))), rewrite((((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))))) <=> ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))), (((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))) <=> ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(4,plain,
% 0.43/0.61 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[3])).
% 0.43/0.61 tff(5,plain,
% 0.43/0.61 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(6,plain,
% 0.43/0.61 (^[A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : trans(monotonicity(trans(monotonicity(rewrite(((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) <=> (tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)))), ((((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) <=> ((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))))), rewrite(((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) <=> (tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))), ((((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) <=> (tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))))), (((((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) => (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))) <=> ((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) => (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))))), rewrite(((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) => (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))) <=> ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))), (((((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) => (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))) <=> ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(7,plain,
% 0.43/0.61 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) => (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3))) <=> ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[6])).
% 0.43/0.61 tff(8,axiom,(![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((((tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) => (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom71')).
% 0.43/0.61 tff(9,plain,
% 0.43/0.61 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.43/0.61 tff(10,plain,
% 0.43/0.61 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.43/0.61 tff(11,plain,(
% 0.43/0.61 ![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~(tptp_fun__lSCategory__(A__questionmark_v0) & tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0)) & tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2)))) | (tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2) & (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))),
% 0.45/0.61 inference(skolemize,[status(sab)],[10])).
% 0.45/0.61 tff(12,plain,
% 0.45/0.61 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.45/0.61 tff(13,plain,
% 0.45/0.61 (![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.45/0.61 tff(14,plain,
% 0.45/0.61 (tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|)) <=> tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(15,axiom,(tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom39')).
% 0.45/0.61 tff(16,plain,
% 0.45/0.61 (tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.45/0.61 tff(17,plain,
% 0.45/0.61 (tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|)) <=> tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(18,axiom,(tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom37')).
% 0.45/0.61 tff(19,plain,
% 0.45/0.61 (tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.45/0.61 tff(20,plain,
% 0.45/0.61 (tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|)) <=> tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(21,axiom,(tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom36')).
% 0.45/0.61 tff(22,plain,
% 0.45/0.61 (tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.45/0.61 tff(23,plain,
% 0.45/0.61 (tptp_fun__lSCategory__(|'c$'|) <=> tptp_fun__lSCategory__(|'c$'|)),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(24,axiom,(tptp_fun__lSCategory__(|'c$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom35')).
% 0.45/0.61 tff(25,plain,
% 0.45/0.61 (tptp_fun__lSCategory__(|'c$'|)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.45/0.61 tff(26,plain,
% 0.45/0.61 (((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))) | ((~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))))) <=> ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))) | (~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(27,plain,
% 0.45/0.61 (((~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))))) <=> ((~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(28,plain,
% 0.45/0.61 (((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))) | ((~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))))) <=> ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))) | ((~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[27])).
% 0.45/0.61 tff(29,plain,
% 0.45/0.61 (((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))) | ((~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))))) <=> ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))) | (~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[28, 26])).
% 0.45/0.61 tff(30,plain,
% 0.45/0.61 ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))) | ((~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(31,plain,
% 0.45/0.61 ((~![A__questionmark_v0: |'A_b_b_c_LSCategory_ext_Category_ext$'|, A__questionmark_v1: |'A$'|, A__questionmark_v2: |'A$'|, A__questionmark_v3: |'ZF$'|] : ((~tptp_fun__lSCategory__(A__questionmark_v0)) | (~tptp_fun__member_i_(A__questionmark_v2, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__member_i_(A__questionmark_v1, tptp_fun__obj_b_(A__questionmark_v0))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(A__questionmark_v3), tptp_fun__homSet__(A__questionmark_v0, A__questionmark_v1, A__questionmark_v2))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(A__questionmark_v0, tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3), A__questionmark_v1), A__questionmark_v2)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(A__questionmark_v0), tptp_fun__zF2mor__(A__questionmark_v0, A__questionmark_v3)) = A__questionmark_v3)))))) | (~tptp_fun__member_i_(|'y$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__lSCategory__(|'c$'|)) | (~tptp_fun__member_i_(|'x$'|, tptp_fun__obj_b_(|'c$'|))) | (~tptp_fun__fun_app_b_(tptp_fun__elem__(tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), tptp_fun__homSet__(|'c$'|, |'x$'|, |'y$'|))) | (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.45/0.61 tff(32,plain,
% 0.45/0.61 (~((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[31, 25, 22, 19, 16, 13])).
% 0.45/0.61 tff(33,plain,
% 0.45/0.61 (((~tptp_fun__fun_app_l_(tptp_fun__mapsTo__(|'c$'|, tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)), |'x$'|), |'y$'|)) | (~(tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))) | (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))),
% 0.45/0.61 inference(tautology,[status(thm)],[])).
% 0.45/0.61 tff(34,plain,
% 0.45/0.61 (tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))) = tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.45/0.61 tff(35,plain,
% 0.45/0.61 (tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|) = tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))),
% 0.45/0.61 inference(symmetry,[status(thm)],[34])).
% 0.45/0.61 tff(36,plain,
% 0.45/0.61 (tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)) = tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[35])).
% 0.45/0.61 tff(37,plain,
% 0.45/0.61 (tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))) = tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))),
% 0.45/0.61 inference(symmetry,[status(thm)],[36])).
% 0.45/0.61 tff(38,plain,
% 0.45/0.61 ((~(tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))) = tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))) <=> (~(tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))) = tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(39,axiom,(~(tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))) = tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture34')).
% 0.47/0.66 tff(40,plain,
% 0.47/0.66 (~(tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__fun_app_p_(tptp_fun__mor2ZF__(|'c$'|), tptp_fun__zF2mor__(|'c$'|, tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))) = tptp_fun__yMapInv__(|'c$'|, |'x$'|, tptp_fun__mapO__(tptp_fun__yFtor__(|'c$'|), |'y$'|), tptp_fun__yMap__(|'c$'|, |'x$'|, |'eta$'|)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.47/0.66 tff(41,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.47/0.66 % SZS output end Proof
% 0.47/0.66 % E exiting
%------------------------------------------------------------------------------