TSTP Solution File: SET739+4 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET739+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n032.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 : Thu Aug 31 14:40:08 EDT 2023

% Result   : Theorem 97.19s 97.45s
% Output   : Proof 97.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET739+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.11  % Command    : do_cvc5 %s %d
% 0.12/0.30  % Computer : n032.cluster.edu
% 0.12/0.30  % Model    : x86_64 x86_64
% 0.12/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30  % Memory   : 8042.1875MB
% 0.12/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30  % CPULimit   : 300
% 0.12/0.30  % WCLimit    : 300
% 0.12/0.30  % DateTime   : Sat Aug 26 15:33:44 EDT 2023
% 0.12/0.30  % CPUTime    : 
% 0.14/0.39  %----Proving TF0_NAR, FOF, or CNF
% 97.19/97.45  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ISF06mORSX/cvc5---1.0.5_29395.p...
% 97.19/97.45  ------- get file name : TPTP file name is SET739+4
% 97.19/97.45  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29395.smt2...
% 97.19/97.45  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 97.19/97.45  --- Run --no-e-matching --full-saturate-quant at 5...
% 97.19/97.45  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 97.19/97.45  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 97.19/97.45  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 97.19/97.45  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 97.19/97.45  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 97.19/97.45  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 97.19/97.45  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 97.19/97.45  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 97.19/97.45  --- Run --relevant-triggers --full-saturate-quant at 5...
% 97.19/97.45  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 97.19/97.45  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 97.19/97.45  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 97.19/97.45  --- Run --no-cbqi --full-saturate-quant at 10...
% 97.19/97.45  --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 97.19/97.45  % SZS status Theorem for SET739+4
% 97.19/97.45  % SZS output start Proof for SET739+4
% 97.19/97.45  (
% 97.19/97.45  (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B C) (tptp.maps H C A) (tptp.injective (tptp.compose_function H (tptp.compose_function G F A B C) A C A) A A) (tptp.surjective (tptp.compose_function F (tptp.compose_function H G B C A) B A B) B B) (tptp.surjective (tptp.compose_function G (tptp.compose_function F H C A B) C B C) C C)) (tptp.one_to_one F A B)))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.isomorphism F A R B S) (and (tptp.maps F A B) (tptp.one_to_one F A B) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (= (tptp.apply R X1 X2) (tptp.apply S Y1 Y2))))))))) (let ((_let_3 (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.decreasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y2 Y1))))))) (let ((_let_4 (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.increasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y1 Y2))))))) (let ((_let_5 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.inverse_predicate G F A B) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))))) (let ((_let_6 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))))) (let ((_let_7 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (=> (tptp.member Y B) (exists ((E $$unsorted)) (and (tptp.member E A) (tptp.apply F E Y))))))))) (let ((_let_8 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A) (tptp.member Y B)) (=> (and (tptp.apply F X1 Y) (tptp.apply F X2 Y)) (= X1 X2)))))))) (let ((_let_9 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))))) (let ((_let_10 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply G X Y2)) (= Y1 Y2)))))))) (let ((_let_11 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (let ((_let_12 (forall ((H $$unsorted) (G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.compose_predicate H G F A B C) (forall ((X $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Z C)) (= (tptp.apply H X Z) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))))) (let ((_let_13 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.maps F A B) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y))))) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_17 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_20 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_21 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (tptp.apply _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.apply _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_25 (not _let_24))) (let ((_let_26 (not _let_18))) (let ((_let_27 (not _let_16))) (let ((_let_28 (not _let_17))) (let ((_let_29 (or _let_28 _let_27 _let_26 _let_25 _let_23 _let_19))) (let ((_let_30 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_27 _let_28 _let_35 _let_33 _let_31 _let_19))) (let ((_let_37 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_38 (not _let_37))) (let ((_let_39 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (and _let_36 _let_41))) (let ((_let_43 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_40 _let_44))) (let ((_let_46 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_47 (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48))) (let ((_let_52 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_53 (not _let_52))) (let ((_let_54 (= _let_47 _let_53))) (let ((_let_55 (or _let_50 _let_40 _let_54))) (let ((_let_56 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 (not (tptp.apply _let_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130)) _let_57))) (let ((_let_61 (or _let_59 _let_57))) (let ((_let_62 (or))) (let ((_let_63 (REFL :args (_let_41)))) (let ((_let_64 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) E Y))))))))) (let ((_let_65 (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) E Y)))))))))) (let ((_let_66 (not _let_64))) (let ((_let_67 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply _let_1 X1 Y)) (not (tptp.apply _let_1 X2 Y)) (= X1 X2)))))) (let ((_let_68 (not _let_67))) (let ((_let_69 (not (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y2)) (= Y1 Y2)))))) (let ((_let_70 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y))))))))) (let ((_let_71 (not _let_70))) (let ((_let_72 (not (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y2)) (= Y1 Y2)))))) (let ((_let_73 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y))))))))) (let ((_let_74 (not _let_73))) (let ((_let_75 (not (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2)))))) (let ((_let_76 (not (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)))))))))) (let ((_let_77 (or _let_76 _let_75 _let_74 _let_72 _let_71 _let_69 _let_68 _let_66 _let_65 _let_42))) (let ((_let_78 (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2028 $$unsorted) (BOUND_VARIABLE_2014 $$unsorted) (BOUND_VARIABLE_2012 $$unsorted) (BOUND_VARIABLE_2010 $$unsorted)) (or (not (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)))))))) (not (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))) (not (forall ((X $$unsorted)) (or (not (tptp.member X B)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y C)) (not (tptp.apply G X Y)))))))) (not (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X B)) (not (tptp.member Y1 C)) (not (tptp.member Y2 C)) (not (tptp.apply G X Y1)) (not (tptp.apply G X Y2)) (= Y1 Y2)))) (not (forall ((X $$unsorted)) (or (not (tptp.member X C)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y A)) (not (tptp.apply H X Y)))))))) (not (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X C)) (not (tptp.member Y1 A)) (not (tptp.member Y2 A)) (not (tptp.apply H X Y1)) (not (tptp.apply H X Y2)) (= Y1 Y2)))) (not (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.compose_function H (tptp.compose_function G F A B C) A C A))) (or (not (tptp.member X1 A)) (not (tptp.member X2 A)) (not (tptp.member Y A)) (not (tptp.apply _let_1 X1 Y)) (not (tptp.apply _let_1 X2 Y)) (= X1 X2))))) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (forall ((E $$unsorted)) (or (not (tptp.member E B)) (not (tptp.apply (tptp.compose_function F (tptp.compose_function H G B C A) B A B) E Y)))))))) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y C)) (not (forall ((E $$unsorted)) (or (not (tptp.member E C)) (not (tptp.apply (tptp.compose_function G (tptp.compose_function F H C A B) C B C) E Y)))))))) (and (or (not (tptp.member BOUND_VARIABLE_2010 A)) (not (tptp.member BOUND_VARIABLE_2012 A)) (not (tptp.member BOUND_VARIABLE_2014 B)) (not (tptp.apply F BOUND_VARIABLE_2010 BOUND_VARIABLE_2014)) (not (tptp.apply F BOUND_VARIABLE_2012 BOUND_VARIABLE_2014)) (= BOUND_VARIABLE_2010 BOUND_VARIABLE_2012)) (or (not (tptp.member BOUND_VARIABLE_2028 B)) (not (forall ((E $$unsorted)) (or (not (tptp.member E A)) (not (tptp.apply F E BOUND_VARIABLE_2028))))))))))) (let ((_let_79 (not _let_77))) (let ((_let_80 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.subset (lambda ((BOUND_VARIABLE_1352 $$unsorted) (BOUND_VARIABLE_1353 $$unsorted)) (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1352)) (tptp.member X BOUND_VARIABLE_1353))))))))) (let ((_let_81 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO _let_80 :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.equal_set (lambda ((BOUND_VARIABLE_1382 $$unsorted) (BOUND_VARIABLE_1383 $$unsorted)) (and (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1382)) (tptp.member X BOUND_VARIABLE_1383))) (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1383)) (tptp.member X BOUND_VARIABLE_1382)))))))))) (let ((_let_82 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.maps (lambda ((BOUND_VARIABLE_1409 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted) (BOUND_VARIABLE_1411 $$unsorted)) (and (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1410)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y BOUND_VARIABLE_1411)) (not (tptp.apply BOUND_VARIABLE_1409 X Y))))))) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1410)) (not (tptp.member Y1 BOUND_VARIABLE_1411)) (not (tptp.member Y2 BOUND_VARIABLE_1411)) (not (tptp.apply BOUND_VARIABLE_1409 X Y1)) (not (tptp.apply BOUND_VARIABLE_1409 X Y2)) (= Y1 Y2)))))))))) (let ((_let_83 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.compose_predicate (lambda ((BOUND_VARIABLE_1441 $$unsorted) (BOUND_VARIABLE_1442 $$unsorted) (BOUND_VARIABLE_1443 $$unsorted) (BOUND_VARIABLE_1444 $$unsorted) (BOUND_VARIABLE_1445 $$unsorted) (BOUND_VARIABLE_1446 $$unsorted)) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1444)) (not (tptp.member Z BOUND_VARIABLE_1446)) (= (tptp.apply BOUND_VARIABLE_1441 X Z) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y BOUND_VARIABLE_1445)) (not (tptp.apply BOUND_VARIABLE_1443 X Y)) (not (tptp.apply BOUND_VARIABLE_1442 Y Z)))))))))))))) (let ((_let_84 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.equal_maps (lambda ((BOUND_VARIABLE_1478 $$unsorted) (BOUND_VARIABLE_1479 $$unsorted) (BOUND_VARIABLE_1480 $$unsorted) (BOUND_VARIABLE_1481 $$unsorted)) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1480)) (not (tptp.member Y1 BOUND_VARIABLE_1481)) (not (tptp.member Y2 BOUND_VARIABLE_1481)) (not (tptp.apply BOUND_VARIABLE_1478 X Y1)) (not (tptp.apply BOUND_VARIABLE_1479 X Y2)) (= Y1 Y2))))))))) (let ((_let_85 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.identity (lambda ((BOUND_VARIABLE_1504 $$unsorted) (BOUND_VARIABLE_1505 $$unsorted)) (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1505)) (tptp.apply BOUND_VARIABLE_1504 X X))))))))) (let ((_let_86 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.injective (lambda ((BOUND_VARIABLE_1517 $$unsorted) (BOUND_VARIABLE_1518 $$unsorted) (BOUND_VARIABLE_1519 $$unsorted)) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 BOUND_VARIABLE_1518)) (not (tptp.member X2 BOUND_VARIABLE_1518)) (not (tptp.member Y BOUND_VARIABLE_1519)) (not (tptp.apply BOUND_VARIABLE_1517 X1 Y)) (not (tptp.apply BOUND_VARIABLE_1517 X2 Y)) (= X1 X2))))))))) (let ((_let_87 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.surjective (lambda ((BOUND_VARIABLE_1540 $$unsorted) (BOUND_VARIABLE_1541 $$unsorted) (BOUND_VARIABLE_1542 $$unsorted)) (forall ((Y $$unsorted)) (or (not (tptp.member Y BOUND_VARIABLE_1542)) (not (forall ((E $$unsorted)) (or (not (tptp.member E BOUND_VARIABLE_1541)) (not (tptp.apply BOUND_VARIABLE_1540 E Y))))))))))))) (let ((_let_88 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.one_to_one (lambda ((BOUND_VARIABLE_1594 $$unsorted) (BOUND_VARIABLE_1595 $$unsorted) (BOUND_VARIABLE_1596 $$unsorted)) (and (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 BOUND_VARIABLE_1595)) (not (tptp.member X2 BOUND_VARIABLE_1595)) (not (tptp.member Y BOUND_VARIABLE_1596)) (not (tptp.apply BOUND_VARIABLE_1594 X1 Y)) (not (tptp.apply BOUND_VARIABLE_1594 X2 Y)) (= X1 X2))) (forall ((Y $$unsorted)) (or (not (tptp.member Y BOUND_VARIABLE_1596)) (not (forall ((E $$unsorted)) (or (not (tptp.member E BOUND_VARIABLE_1595)) (not (tptp.apply BOUND_VARIABLE_1594 E Y)))))))))))))) (let ((_let_89 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.inverse_predicate (lambda ((BOUND_VARIABLE_1626 $$unsorted) (BOUND_VARIABLE_1627 $$unsorted) (BOUND_VARIABLE_1628 $$unsorted) (BOUND_VARIABLE_1629 $$unsorted)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1628)) (not (tptp.member Y BOUND_VARIABLE_1629)) (= (tptp.apply BOUND_VARIABLE_1627 X Y) (tptp.apply BOUND_VARIABLE_1626 Y X)))))))))) (let ((_let_90 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.increasing (lambda ((BOUND_VARIABLE_1649 $$unsorted) (BOUND_VARIABLE_1650 $$unsorted) (BOUND_VARIABLE_1651 $$unsorted) (BOUND_VARIABLE_1652 $$unsorted) (BOUND_VARIABLE_1653 $$unsorted)) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 BOUND_VARIABLE_1650)) (not (tptp.member Y1 BOUND_VARIABLE_1652)) (not (tptp.member X2 BOUND_VARIABLE_1650)) (not (tptp.member Y2 BOUND_VARIABLE_1652)) (not (tptp.apply BOUND_VARIABLE_1651 X1 X2)) (not (tptp.apply BOUND_VARIABLE_1649 X1 Y1)) (not (tptp.apply BOUND_VARIABLE_1649 X2 Y2)) (tptp.apply BOUND_VARIABLE_1653 Y1 Y2))))))))) (let ((_let_91 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.decreasing (lambda ((BOUND_VARIABLE_1683 $$unsorted) (BOUND_VARIABLE_1684 $$unsorted) (BOUND_VARIABLE_1685 $$unsorted) (BOUND_VARIABLE_1686 $$unsorted) (BOUND_VARIABLE_1687 $$unsorted)) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 BOUND_VARIABLE_1684)) (not (tptp.member Y1 BOUND_VARIABLE_1686)) (not (tptp.member X2 BOUND_VARIABLE_1684)) (not (tptp.member Y2 BOUND_VARIABLE_1686)) (not (tptp.apply BOUND_VARIABLE_1685 X1 X2)) (not (tptp.apply BOUND_VARIABLE_1683 X1 Y1)) (not (tptp.apply BOUND_VARIABLE_1683 X2 Y2)) (tptp.apply BOUND_VARIABLE_1687 Y2 Y1))))))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (TRUST_SUBS_EQ (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80) :args ((forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.isomorphism F A R B S) (and (tptp.maps F A B) (tptp.one_to_one F A B) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 A)) (not (tptp.member Y1 B)) (not (tptp.member X2 A)) (not (tptp.member Y2 B)) (not (tptp.apply F X1 Y1)) (not (tptp.apply F X2 Y2)) (= (tptp.apply R X1 X2) (tptp.apply S Y1 Y2))))))) SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.isomorphism (lambda ((BOUND_VARIABLE_1775 $$unsorted) (BOUND_VARIABLE_1776 $$unsorted) (BOUND_VARIABLE_1777 $$unsorted) (BOUND_VARIABLE_1778 $$unsorted) (BOUND_VARIABLE_1779 $$unsorted)) (and (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 BOUND_VARIABLE_1776)) (not (tptp.member Y1 BOUND_VARIABLE_1778)) (not (tptp.member X2 BOUND_VARIABLE_1776)) (not (tptp.member Y2 BOUND_VARIABLE_1778)) (not (tptp.apply BOUND_VARIABLE_1775 X1 Y1)) (not (tptp.apply BOUND_VARIABLE_1775 X2 Y2)) (= (tptp.apply BOUND_VARIABLE_1777 X1 X2) (tptp.apply BOUND_VARIABLE_1779 Y1 Y2)))) (forall ((X $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1776)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y BOUND_VARIABLE_1778)) (not (tptp.apply BOUND_VARIABLE_1775 X Y))))))) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X BOUND_VARIABLE_1776)) (not (tptp.member Y1 BOUND_VARIABLE_1778)) (not (tptp.member Y2 BOUND_VARIABLE_1778)) (not (tptp.apply BOUND_VARIABLE_1775 X Y1)) (not (tptp.apply BOUND_VARIABLE_1775 X Y2)) (= Y1 Y2))) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 BOUND_VARIABLE_1776)) (not (tptp.member X2 BOUND_VARIABLE_1776)) (not (tptp.member Y BOUND_VARIABLE_1778)) (not (tptp.apply BOUND_VARIABLE_1775 X1 Y)) (not (tptp.apply BOUND_VARIABLE_1775 X2 Y)) (= X1 X2))) (forall ((Y $$unsorted)) (or (not (tptp.member Y BOUND_VARIABLE_1778)) (not (forall ((E $$unsorted)) (or (not (tptp.member E BOUND_VARIABLE_1776)) (not (tptp.apply BOUND_VARIABLE_1775 E Y)))))))))))) _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80) :args ((not (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B C)) (not (tptp.maps H C A)) (not (tptp.injective (tptp.compose_function H (tptp.compose_function G F A B C) A C A) A A)) (not (tptp.surjective (tptp.compose_function F (tptp.compose_function H G B C A) B A B) B B)) (not (tptp.surjective (tptp.compose_function G (tptp.compose_function F H C A B) C B C) C C)) (tptp.one_to_one F A B)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_93 (not _let_78))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_92) :args (_let_93)) (REWRITE :args ((=> _let_93 (not (or _let_76 _let_75 _let_74 _let_72 _let_71 _let_69 _let_68 _let_66 _let_65 (and (or _let_27 _let_28 _let_35 _let_33 _let_31 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) _let_41)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_78))) (REFL :args (_let_79)) :args _let_62)) _let_92 :args (_let_79 true _let_78)))) (let ((_let_95 (REFL :args (_let_77)))) (let ((_let_96 (_let_64))) (let ((_let_97 (_let_44))) (let ((_let_98 (REFL :args (_let_51)))) (let ((_let_99 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)) (not (tptp.apply G Y Z)))))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (_let_99))) (let ((_let_102 ((tptp.apply (tptp.compose_function G F A B C) X Z)))) (let ((_let_103 (_let_53))) (let ((_let_104 (REFL :args (_let_60)))) (let ((_let_105 (_let_37))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_42)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_77 9)) _let_94 :args ((not _let_42) true _let_77)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_105) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_105)) (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_59 _let_57 (not _let_61)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 2)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_62)) :args ((or _let_56 _let_60))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 0)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) 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(REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG _let_98 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_62)) :args ((or _let_49 _let_51))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_97)) :args _let_97)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) (REFL :args ((not _let_51))) :args _let_62)) (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_40 _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_96) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 7)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_64))) :args _let_62)) :args ((or _let_64 _let_77))) _let_94 :args (_let_64 true _let_77)) :args (_let_45 false _let_64)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args 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SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING _let_102)) :args _let_101)) _let_100 :args (_let_141 false _let_99)) :args (_let_140 false _let_16 false _let_18 false _let_141)) :args (_let_22 true _let_138 false _let_140)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_137) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false)) (not (= (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false)) (not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_137)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 6)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_62)) :args ((or _let_67 _let_77))) _let_94 :args (_let_67 true _let_77)) :args (_let_29 false _let_67)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_36 5)) _let_106 :args ((not _let_19) true _let_36)) _let_136 _let_109 _let_108 :args (false false _let_24 false _let_22 false _let_29 true _let_19 false _let_18 false _let_17 false _let_16)) :args (_let_15 _let_14 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))) (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image3 F A B)) (and (tptp.member Y B) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y)))))) (forall ((F $$unsorted) (B $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image2 F B)) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y))))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image3 F B A)) (and (tptp.member X A) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))) _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 97.19/97.45  )
% 97.19/97.45  % SZS output end Proof for SET739+4
% 97.19/97.45  % cvc5---1.0.5 exiting
% 97.19/97.46  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------