TSTP Solution File: SET724^4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET724^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 14:40:04 EDT 2023
% Result : Theorem 35.77s 35.99s
% Output : Proof 35.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET724^4 : TPTP v8.1.2. Released v3.6.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 16:17:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 % File : SET724^4 : TPTP v8.1.2. Released v3.6.0.
% 0.21/0.49 % Domain : Set Theory
% 0.21/0.49 % Problem : If GoF = HoF and F is surjective, then G = H
% 0.21/0.49 % Version : [BS+08] axioms.
% 0.21/0.49 % English :
% 0.21/0.49
% 0.21/0.49 % Refs : [BS+05] Benzmueller et al. (2005), Can a Higher-Order and a Fi
% 0.21/0.49 % : [BS+08] Benzmueller et al. (2008), Combined Reasoning by Autom
% 0.21/0.49 % : [Ben08] Benzmueller (2008), Email to Geoff Sutcliffe
% 0.21/0.49 % Source : [Ben08]
% 0.21/0.49 % Names :
% 0.21/0.49
% 0.21/0.49 % Status : Theorem
% 0.21/0.49 % Rating : 0.15 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.33 v3.7.0
% 0.21/0.49 % Syntax : Number of formulae : 17 ( 8 unt; 8 typ; 8 def)
% 0.21/0.49 % Number of atoms : 28 ( 15 equ; 0 cnn)
% 0.21/0.49 % Maximal formula atoms : 3 ( 3 avg)
% 0.21/0.49 % Number of connectives : 36 ( 0 ~; 0 |; 4 &; 28 @)
% 0.21/0.49 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.21/0.49 % Maximal formula depth : 7 ( 2 avg)
% 0.21/0.49 % Number of types : 2 ( 0 usr)
% 0.21/0.49 % Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% 0.21/0.49 % Number of symbols : 11 ( 10 usr; 2 con; 0-3 aty)
% 0.21/0.49 % Number of variables : 29 ( 16 ^; 10 !; 3 ?; 29 :)
% 0.21/0.49 % SPC : TH0_THM_EQU_NAR
% 0.21/0.49
% 0.21/0.49 % Comments :
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 %----Include definitions for functions
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 thf(fun_image_decl,type,
% 0.21/0.49 fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(fun_image,definition,
% 0.21/0.49 ( fun_image
% 0.21/0.49 = ( ^ [F: $i > $i,A: $i > $o,Y: $i] :
% 0.21/0.49 ? [X: $i] :
% 0.21/0.49 ( ( A @ X )
% 0.21/0.49 & ( Y
% 0.21/0.49 = ( F @ X ) ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(fun_composition_decl,type,
% 0.21/0.49 fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.21/0.49
% 0.21/0.49 thf(fun_composition,definition,
% 0.21/0.49 ( fun_composition
% 0.21/0.49 = ( ^ [F: $i > $i,G: $i > $i,X: $i] : ( G @ ( F @ X ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(fun_inv_image_decl,type,
% 0.21/0.49 fun_inv_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
% 0.21/0.49
% 0.21/0.49 thf(fun_inv_image,definition,
% 0.21/0.49 ( fun_inv_image
% 0.21/0.49 = ( ^ [F: $i > $i,B: $i > $o,X: $i] :
% 0.21/0.49 ? [Y: $i] :
% 0.21/0.49 ( ( B @ Y )
% 0.21/0.49 & ( Y
% 0.21/0.49 = ( F @ X ) ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(fun_injective_decl,type,
% 0.21/0.49 fun_injective: ( $i > $i ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(fun_injective,definition,
% 0.21/0.49 ( fun_injective
% 0.21/0.49 = ( ^ [F: $i > $i] :
% 0.21/0.49 ! [X: $i,Y: $i] :
% 0.21/0.49 ( ( ( F @ X )
% 0.21/0.49 = ( F @ Y ) )
% 0.21/0.49 => ( X = Y ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(fun_surjective_decl,type,
% 0.21/0.49 fun_surjective: ( $i > $i ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(fun_surjective,definition,
% 0.21/0.49 ( fun_surjective
% 0.21/0.49 = ( ^ [F: $i > $i] :
% 0.21/0.49 ! [Y: $i] :
% 0.21/0.49 ? [X: $i] :
% 0.21/0.49 ( Y
% 0.21/0.49 = ( F @ X ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(fun_bijective_decl,type,
% 0.21/0.49 fun_bijective: ( $i > $i ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(fun_bijective,definition,
% 0.21/0.49 ( fun_bijective
% 0.21/0.49 = ( ^ [F: $i > $i] :
% 0.21/0.49 ( ( fun_injective @ F )
% 0.21/0.49 & ( fun_surjective @ F ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(fun_decreasing_decl,type,
% 0.21/0.49 fun_decreasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(fun_decreasing,definition,
% 0.21/0.49 ( fun_decreasing
% 0.21/0.49 = ( ^ [F: $i > $i,SMALLER: $i > $i > $o] :
% 0.21/0.49 ! [X: $i,Y: $i] :
% 0.21/0.49 ( ( SMALLER @ X @ Y )
% 0.21/0.49 => ( SMALLER @ ( F @ Y ) @ ( F @ X ) ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 thf(fun_increasing_decl,type,
% 0.21/0.49 fun_increasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
% 0.21/0.49
% 0.21/0.49 thf(fun_increasing,definition,
% 0.21/0.49 ( fun_increasing
% 0.21/0.49 = ( ^ [F: $i > $i,SMALLER: $i > $i > $o] :
% 0.21/0.49 ! [X: $i,Y: $i] :
% 0.21/0.49 ( ( SMALLER @ X @ Y )
% 0.21/0.49 => ( SMALLER @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.21/0.49
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 thf(thm,conjecture,
% 0.21/0.49 ! [F: $i > $i,G: $i > $i,H: $i > $i] :
% 0.21/0.49 ( ( ( ( fun_composition @ F @ G )
% 0.21/0.49 = ( fun_composition @ F @ H ) )
% 0.21/0.49 & ( fun_surjective @ F ) )
% 0.21/0.49 => ( G = H ) ) ).
% 0.21/0.49
% 0.21/0.49 %------------------------------------------------------------------------------
% 35.77/35.99 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.9uUz5o7BSD/cvc5---1.0.5_25436.p...
% 35.77/35.99 (declare-sort $$unsorted 0)
% 35.77/35.99 (declare-fun tptp.fun_image ((-> $$unsorted $$unsorted) (-> $$unsorted Bool) $$unsorted) Bool)
% 35.77/35.99 (assert (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))))))
% 35.77/35.99 (declare-fun tptp.fun_composition ((-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 35.77/35.99 (assert (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X)))))
% 35.77/35.99 (declare-fun tptp.fun_inv_image ((-> $$unsorted $$unsorted) (-> $$unsorted Bool) $$unsorted) Bool)
% 35.77/35.99 (assert (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))))))
% 35.77/35.99 (declare-fun tptp.fun_injective ((-> $$unsorted $$unsorted)) Bool)
% 35.77/35.99 (assert (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))))))
% 35.77/35.99 (declare-fun tptp.fun_surjective ((-> $$unsorted $$unsorted)) Bool)
% 35.77/35.99 (assert (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))))))
% 35.77/35.99 (declare-fun tptp.fun_bijective ((-> $$unsorted $$unsorted)) Bool)
% 35.77/35.99 (assert (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F)))))
% 35.77/35.99 (declare-fun tptp.fun_decreasing ((-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted Bool)) Bool)
% 35.77/35.99 (assert (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F Y)) (@ F X)))))))
% 35.77/35.99 (declare-fun tptp.fun_increasing ((-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted Bool)) Bool)
% 35.77/35.99 (assert (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F X)) (@ F Y)))))))
% 35.77/35.99 (assert (not (forall ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (H (-> $$unsorted $$unsorted))) (let ((_let_1 (@ tptp.fun_composition F))) (=> (and (= (@ _let_1 G) (@ _let_1 H)) (@ tptp.fun_surjective F)) (= G H))))))
% 35.77/35.99 (set-info :filename cvc5---1.0.5_25436)
% 35.77/35.99 (check-sat-assuming ( true ))
% 35.77/35.99 ------- get file name : TPTP file name is SET724^4
% 35.77/35.99 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25436.smt2...
% 35.77/35.99 --- Run --ho-elim --full-saturate-quant at 10...
% 35.77/35.99 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 35.77/35.99 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 35.77/35.99 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 35.77/35.99 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 35.77/35.99 % SZS status Theorem for SET724^4
% 35.77/35.99 % SZS output start Proof for SET724^4
% 35.77/35.99 (
% 35.77/35.99 (let ((_let_1 (not (forall ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (H (-> $$unsorted $$unsorted))) (let ((_let_1 (@ tptp.fun_composition F))) (=> (and (= (@ _let_1 G) (@ _let_1 H)) (@ tptp.fun_surjective F)) (= G H))))))) (let ((_let_2 (= tptp.fun_increasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F X)) (@ F Y)))))))) (let ((_let_3 (= tptp.fun_decreasing (lambda ((F (-> $$unsorted $$unsorted)) (SMALLER (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ SMALLER X) Y) (@ (@ SMALLER (@ F Y)) (@ F X)))))))) (let ((_let_4 (= tptp.fun_bijective (lambda ((F (-> $$unsorted $$unsorted))) (and (@ tptp.fun_injective F) (@ tptp.fun_surjective F)))))) (let ((_let_5 (= tptp.fun_surjective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= Y (@ F X)))))))) (let ((_let_6 (= tptp.fun_injective (lambda ((F (-> $$unsorted $$unsorted))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (@ F X) (@ F Y)) (= X Y))))))) (let ((_let_7 (= tptp.fun_inv_image (lambda ((F (-> $$unsorted $$unsorted)) (B (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ B Y) (= Y (@ F X)))))))) (let ((_let_8 (= tptp.fun_composition (lambda ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (X $$unsorted)) (@ G (@ F X)))))) (let ((_let_9 (= tptp.fun_image (lambda ((F (-> $$unsorted $$unsorted)) (A (-> $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (and (@ A X) (= Y (@ F X)))))))) (let ((_let_10 (= lambdaF_5 lambdaF_6))) (let ((_let_11 (= (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 k_7) (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 k_7)))) (let ((_let_12 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_13 (= k_7 _let_12))) (let ((_let_14 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12))) (let ((_let_15 (lambdaF_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12))) (let ((_let_18 (lambdaF_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_19 (= _let_18 _let_17))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X)))))))) (let ((_let_22 (not _let_21))) (let ((_let_23 (not _let_10))) (let ((_let_24 (or _let_23 _let_22 _let_20))) (let ((_let_25 (forall ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (H (-> $$unsorted $$unsorted))) (or (not (= (lambda ((X $$unsorted)) (@ G (@ F X))) (lambda ((X $$unsorted)) (@ H (@ F X))))) (not (forall ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (= Y (@ F X))))))) (= G H))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (ASSUME :args (_let_8)))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_31 _let_30 _let_29 _let_28 _let_27) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_31 _let_30 _let_29 _let_28 _let_27) :args ((not (forall ((F (-> $$unsorted $$unsorted)) (G (-> $$unsorted $$unsorted)) (H (-> $$unsorted $$unsorted))) (let ((_let_1 (@ tptp.fun_composition F))) (or (not (= (@ _let_1 G) (@ _let_1 H))) (not (@ tptp.fun_surjective F)) (= G H))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_25))) (let ((_let_35 (=>))) (let ((_let_36 (not))) (let ((_let_37 (=))) (let ((_let_38 (_let_34))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_32) :args _let_38) (CONG (REFL :args _let_38) (CONG (CONG (CONG (TRANS (CONG (MACRO_SR_PRED_INTRO :args ((= (lambda ((X $$unsorted)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X))) lambdaF_6))) (MACRO_SR_PRED_INTRO :args ((= (lambda ((X $$unsorted)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X))) lambdaF_5))) :args _let_37) (REWRITE :args ((= lambdaF_6 lambdaF_5)))) :args _let_36) (REFL :args (_let_22)) (REFL :args (_let_20)) :args _let_33) :args _let_36) :args _let_35))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_25))) (REFL :args (_let_26)) :args _let_33)) _let_32 :args (_let_26 true _let_25)))) (let ((_let_40 (REFL :args (_let_24)))) (let ((_let_41 (not _let_11))) (let ((_let_42 (forall ((X $$unsorted)) (not (= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X) k_7))))) (let ((_let_43 (not _let_42))) (let ((_let_44 (_let_21))) (let ((_let_45 (_let_13))) (let ((_let_46 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_47 (THEORY_PREPROCESS :args ((= _let_46 _let_12))))) (let ((_let_48 (_let_43))) (let ((_let_49 (forall ((X $$unsorted)) (= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X)) (lambdaF_5 X))))) (let ((_let_50 ((forall ((X $$unsorted)) (= (lambdaF_5 X) (@ (lambda ((X $$unsorted)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X))) X)))))) (let ((_let_51 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_50) (REWRITE :args _let_50)))) (let ((_let_52 (@))) (let ((_let_53 (_let_49))) (let ((_let_54 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_FMF_FMC_EXH))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_51 :args _let_54) :args _let_53) (CONG (REFL :args _let_53) (TRANS (CONG (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_47 :args _let_52) (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12) _let_14)))) (REFL :args (_let_15)) :args _let_37) (REWRITE :args ((= _let_14 _let_15)))) :args _let_35))) _let_51 :args (_let_16 false _let_49)))) (let ((_let_56 (forall ((X $$unsorted)) (= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X)) (lambdaF_6 X))))) (let ((_let_57 ((forall ((X $$unsorted)) (= (lambdaF_6 X) (@ (lambda ((X $$unsorted)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X))) X)))))) (let ((_let_58 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_57) (REWRITE :args _let_57)))) (let ((_let_59 (_let_56))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_58 :args _let_54) :args _let_59) (CONG (REFL :args _let_59) (TRANS (CONG (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_47 :args _let_52) (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_12) _let_17)))) (REFL :args (_let_18)) :args _let_37) (REWRITE :args ((= _let_17 _let_18)))) :args _let_35))) _let_58 :args (_let_19 false _let_56)))) (let ((_let_61 (and _let_10 _let_13 _let_16 _let_19))) (let ((_let_62 (ASSUME :args _let_45))) (let ((_let_63 (ASSUME :args (_let_10)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_61)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_62 _let_55 _let_63 _let_60) (SCOPE (TRANS (CONG _let_62 :args (APPLY_UF SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (SYMM _let_60) (HO_CONG (SYMM _let_63) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) _let_55 (CONG (SYMM _let_62) :args (APPLY_UF SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) :args (_let_13 _let_16 _let_10 _let_19))) :args (_let_10 _let_13 _let_16 _let_19))) :args (true _let_61)) :args ((or _let_23 _let_11 (not _let_13) (not _let_16) (not _let_19)))) _let_60 _let_55 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_48)) :args _let_48) (TRANS (REWRITE :args ((=> _let_43 (not (not (= _let_46 k_7)))))) (CONG (REFL :args _let_48) (CONG (REFL :args (k_7)) _let_47 :args _let_37) :args _let_35)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) (REFL :args _let_45) :args _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (k_7 QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_44))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 1)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_33)) :args ((or _let_21 _let_24))) _let_39 :args (_let_21 true _let_24)) :args (_let_43 false _let_21)) :args (_let_13 true _let_42)) (MACRO_RESOLUTION_TRUST (THEORY_LEMMA :args ((or _let_20 _let_41) THEORY_UF)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 2)) _let_39 :args ((not _let_20) true _let_24)) :args (_let_41 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_10))) :args _let_33)) :args ((or _let_10 _let_24))) _let_39 :args (_let_10 true _let_24)) :args (false false _let_19 false _let_16 false _let_13 true _let_11 false _let_10)) :args (_let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 35.77/36.00 )
% 35.77/36.00 % SZS output end Proof for SET724^4
% 35.77/36.00 % cvc5---1.0.5 exiting
% 35.77/36.00 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------