TSTP Solution File: SET601^3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET601^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 14:39:21 EDT 2023
% Result : Theorem 3.03s 3.22s
% Output : Proof 3.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET601^3 : TPTP v8.1.2. Released v3.6.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat Aug 26 10:43:23 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.23/0.50 %----Proving TH0
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 % File : SET601^3 : TPTP v8.1.2. Released v3.6.0.
% 0.23/0.51 % Domain : Set Theory
% 0.23/0.51 % Problem : X ^ Y U Y ^ Z U Z ^ X = (X U Y) ^ (Y U Z) ^ (Z U X)
% 0.23/0.51 % Version : [BS+08] axioms.
% 0.23/0.51 % English : The intersection of X and the union of Y and the intersection
% 0.23/0.51 % of Y and the union of Z and the intersection of Z and X is the
% 0.23/0.51 % intersection of (the union of X and Y) and the intersection of
% 0.23/0.51 % (the union of Y and Z) and (the union of Z and X).
% 0.23/0.51
% 0.23/0.51 % Refs : [BS+05] Benzmueller et al. (2005), Can a Higher-Order and a Fi
% 0.23/0.51 % : [BS+08] Benzmueller et al. (2008), Combined Reasoning by Autom
% 0.23/0.51 % : [Ben08] Benzmueller (2008), Email to Geoff Sutcliffe
% 0.23/0.51 % Source : [Ben08]
% 0.23/0.51 % Names :
% 0.23/0.51
% 0.23/0.51 % Status : Theorem
% 0.23/0.51 % Rating : 0.31 v8.1.0, 0.09 v7.5.0, 0.14 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, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.23/0.51 % Syntax : Number of formulae : 29 ( 15 unt; 14 typ; 14 def)
% 0.23/0.51 % Number of atoms : 46 ( 19 equ; 0 cnn)
% 0.23/0.51 % Maximal formula atoms : 1 ( 3 avg)
% 0.23/0.51 % Number of connectives : 56 ( 5 ~; 3 |; 6 &; 41 @)
% 0.23/0.51 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.23/0.51 % Maximal formula depth : 4 ( 1 avg)
% 0.23/0.51 % Number of types : 2 ( 0 usr)
% 0.23/0.51 % Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% 0.23/0.51 % Number of symbols : 18 ( 16 usr; 3 con; 0-3 aty)
% 0.23/0.51 % Number of variables : 38 ( 32 ^; 4 !; 2 ?; 38 :)
% 0.23/0.51 % SPC : TH0_THM_EQU_NAR
% 0.23/0.51
% 0.23/0.51 % Comments :
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 %----Basic set theory definitions
% 0.23/0.51 %------------------------------------------------------------------------------
% 0.23/0.51 thf(in_decl,type,
% 0.23/0.51 in: $i > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(in,definition,
% 0.23/0.51 ( in
% 0.23/0.51 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(is_a_decl,type,
% 0.23/0.51 is_a: $i > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(is_a,definition,
% 0.23/0.51 ( is_a
% 0.23/0.51 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(emptyset_decl,type,
% 0.23/0.51 emptyset: $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(emptyset,definition,
% 0.23/0.51 ( emptyset
% 0.23/0.51 = ( ^ [X: $i] : $false ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(unord_pair_decl,type,
% 0.23/0.51 unord_pair: $i > $i > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(unord_pair,definition,
% 0.23/0.51 ( unord_pair
% 0.23/0.51 = ( ^ [X: $i,Y: $i,U: $i] :
% 0.23/0.51 ( ( U = X )
% 0.23/0.51 | ( U = Y ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(singleton_decl,type,
% 0.23/0.51 singleton: $i > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(singleton,definition,
% 0.23/0.51 ( singleton
% 0.23/0.51 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(union_decl,type,
% 0.23/0.51 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(union,definition,
% 0.23/0.51 ( union
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.51 ( ( X @ U )
% 0.23/0.51 | ( Y @ U ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(excl_union_decl,type,
% 0.23/0.51 excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(excl_union,definition,
% 0.23/0.51 ( excl_union
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.51 ( ( ( X @ U )
% 0.23/0.51 & ~ ( Y @ U ) )
% 0.23/0.51 | ( ~ ( X @ U )
% 0.23/0.51 & ( Y @ U ) ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(intersection_decl,type,
% 0.23/0.51 intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(intersection,definition,
% 0.23/0.51 ( intersection
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.51 ( ( X @ U )
% 0.23/0.51 & ( Y @ U ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(setminus_decl,type,
% 0.23/0.51 setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(setminus,definition,
% 0.23/0.51 ( setminus
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.51 ( ( X @ U )
% 0.23/0.51 & ~ ( Y @ U ) ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(complement_decl,type,
% 0.23/0.51 complement: ( $i > $o ) > $i > $o ).
% 0.23/0.51
% 0.23/0.51 thf(complement,definition,
% 0.23/0.51 ( complement
% 0.23/0.51 = ( ^ [X: $i > $o,U: $i] :
% 0.23/0.51 ~ ( X @ U ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(disjoint_decl,type,
% 0.23/0.51 disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(disjoint,definition,
% 0.23/0.51 ( disjoint
% 0.23/0.51 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.23/0.51 ( ( intersection @ X @ Y )
% 0.23/0.51 = emptyset ) ) ) ).
% 0.23/0.51
% 0.23/0.51 thf(subset_decl,type,
% 0.23/0.51 subset: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.23/0.51
% 0.23/0.51 thf(subset,definition,
% 0.23/0.52 ( subset
% 0.23/0.52 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.23/0.52 ! [U: $i] :
% 0.23/0.52 ( ( X @ U )
% 0.23/0.52 => ( Y @ U ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(meets_decl,type,
% 0.23/0.52 meets: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(meets,definition,
% 0.23/0.52 ( meets
% 0.23/0.52 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.23/0.52 ? [U: $i] :
% 0.23/0.52 ( ( X @ U )
% 0.23/0.52 & ( Y @ U ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(misses_decl,type,
% 0.23/0.52 misses: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(misses,definition,
% 0.23/0.52 ( misses
% 0.23/0.52 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.23/0.52 ~ ? [U: $i] :
% 0.23/0.52 ( ( X @ U )
% 0.23/0.52 & ( Y @ U ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 thf(thm,conjecture,
% 0.23/0.52 ! [X: $i > $o,Y: $i > $o,Z: $i > $o] :
% 0.23/0.52 ( ( union @ ( intersection @ X @ Y ) @ ( union @ ( intersection @ Y @ Z ) @ ( intersection @ Z @ X ) ) )
% 0.23/0.52 = ( intersection @ ( union @ X @ Y ) @ ( intersection @ ( union @ Y @ Z ) @ ( union @ Z @ X ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.r59ELEOGiT/cvc5---1.0.5_11705.p...
% 0.23/0.52 (declare-sort $$unsorted 0)
% 0.23/0.52 (declare-fun tptp.in ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.23/0.52 (assert (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.23/0.52 (declare-fun tptp.is_a ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.23/0.52 (assert (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.23/0.52 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 0.23/0.52 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.23/0.52 (declare-fun tptp.unord_pair ($$unsorted $$unsorted $$unsorted) Bool)
% 0.23/0.52 (assert (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))
% 0.23/0.52 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 0.23/0.52 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.23/0.52 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.52 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.23/0.52 (declare-fun tptp.excl_union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.52 (assert (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))
% 0.23/0.52 (declare-fun tptp.intersection ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.52 (assert (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.23/0.52 (declare-fun tptp.setminus ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.52 (assert (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))
% 0.23/0.52 (declare-fun tptp.complement ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.52 (assert (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.23/0.52 (declare-fun tptp.disjoint ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.23/0.52 (assert (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))
% 0.23/0.52 (declare-fun tptp.subset ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.23/0.52 (assert (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))
% 0.23/0.52 (declare-fun tptp.meets ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.23/0.52 (assert (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))
% 0.23/0.52 (declare-fun tptp.misses ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.23/0.52 (assert (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))
% 0.23/0.52 (assert (not (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (Z (-> $$unsorted Bool))) (= (@ (@ tptp.union (@ (@ tptp.intersection X) Y)) (@ (@ tptp.union (@ (@ tptp.intersection Y) Z)) (@ (@ tptp.intersection Z) X))) (@ (@ tptp.intersection (@ (@ tptp.union X) Y)) (@ (@ tptp.intersection (@ (@ tptp.union Y) Z)) (@ (@ tptp.union Z) X)))))))
% 3.03/3.22 (set-info :filename cvc5---1.0.5_11705)
% 3.03/3.22 (check-sat-assuming ( true ))
% 3.03/3.22 ------- get file name : TPTP file name is SET601^3
% 3.03/3.22 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11705.smt2...
% 3.03/3.22 --- Run --ho-elim --full-saturate-quant at 10...
% 3.03/3.22 % SZS status Theorem for SET601^3
% 3.03/3.22 % SZS output start Proof for SET601^3
% 3.03/3.22 (
% 3.03/3.22 (let ((_let_1 (not (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (Z (-> $$unsorted Bool))) (= (@ (@ tptp.union (@ (@ tptp.intersection X) Y)) (@ (@ tptp.union (@ (@ tptp.intersection Y) Z)) (@ (@ tptp.intersection Z) X))) (@ (@ tptp.intersection (@ (@ tptp.union X) Y)) (@ (@ tptp.intersection (@ (@ tptp.union Y) Z)) (@ (@ tptp.union Z) X)))))))) (let ((_let_2 (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) (let ((_let_3 (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (let ((_let_4 (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))) (let ((_let_5 (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))) (let ((_let_6 (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_7 (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))) (let ((_let_8 (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_9 (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))) (let ((_let_10 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_11 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))) (let ((_let_12 (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))) (let ((_let_13 (= tptp.emptyset (lambda ((X $$unsorted)) false)))) (let ((_let_14 (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) (let ((_let_15 (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) (let ((_let_16 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3539))) (let ((_let_17 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3539))) (let ((_let_18 (and _let_17 _let_16))) (let ((_let_19 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3539))) (let ((_let_20 (and _let_16 _let_19))) (let ((_let_21 (and _let_19 _let_17))) (let ((_let_22 (or _let_21 _let_18 _let_20))) (let ((_let_23 (not _let_18))) (let ((_let_24 (ho_8 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_25 (ho_4 _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3539))) (let ((_let_26 (= _let_25 _let_22))) (let ((_let_27 (not _let_22))) (let ((_let_28 (forall ((BOUND_VARIABLE_1080 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1079 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1076 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1052 $$unsorted)) (let ((_let_1 (ho_4 BOUND_VARIABLE_1076 BOUND_VARIABLE_1052))) (let ((_let_2 (ho_4 BOUND_VARIABLE_1079 BOUND_VARIABLE_1052))) (let ((_let_3 (ho_4 BOUND_VARIABLE_1080 BOUND_VARIABLE_1052))) (= (ho_4 (ho_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_1080) BOUND_VARIABLE_1079) BOUND_VARIABLE_1076) BOUND_VARIABLE_1052) (or (and _let_1 _let_3) (and _let_3 _let_2) (and _let_2 _let_1))))))))) (let ((_let_29 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_30 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_31 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_32 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_33 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_34 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_35 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_36 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_37 (forall ((BOUND_VARIABLE_1113 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1112 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1111 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1037 $$unsorted)) (let ((_let_1 (ho_4 BOUND_VARIABLE_1111 BOUND_VARIABLE_1037))) (let ((_let_2 (ho_4 BOUND_VARIABLE_1112 BOUND_VARIABLE_1037))) (let ((_let_3 (ho_4 BOUND_VARIABLE_1113 BOUND_VARIABLE_1037))) (= (ho_4 (ho_8 (ho_7 (ho_6 k_9 BOUND_VARIABLE_1113) BOUND_VARIABLE_1112) BOUND_VARIABLE_1111) BOUND_VARIABLE_1037) (and (or _let_1 _let_3) (or _let_3 _let_2) (or _let_2 _let_1))))))))) (let ((_let_38 (and (forall ((BOUND_VARIABLE_1034 (-> $$unsorted Bool)) (BOUND_VARIABLE_1035 (-> $$unsorted Bool)) (BOUND_VARIABLE_1036 (-> $$unsorted Bool)) (BOUND_VARIABLE_1037 $$unsorted)) (let ((_let_1 (@ BOUND_VARIABLE_1036 BOUND_VARIABLE_1037))) (let ((_let_2 (@ BOUND_VARIABLE_1035 BOUND_VARIABLE_1037))) (let ((_let_3 (@ BOUND_VARIABLE_1034 BOUND_VARIABLE_1037))) (= (and (or _let_1 _let_3) (or _let_3 _let_2) (or _let_2 _let_1)) (ll_2 BOUND_VARIABLE_1034 BOUND_VARIABLE_1035 BOUND_VARIABLE_1036 BOUND_VARIABLE_1037)))))) (forall ((BOUND_VARIABLE_1049 (-> $$unsorted Bool)) (BOUND_VARIABLE_1050 (-> $$unsorted Bool)) (BOUND_VARIABLE_1051 (-> $$unsorted Bool)) (BOUND_VARIABLE_1052 $$unsorted)) (let ((_let_1 (@ BOUND_VARIABLE_1051 BOUND_VARIABLE_1052))) (let ((_let_2 (@ BOUND_VARIABLE_1050 BOUND_VARIABLE_1052))) (let ((_let_3 (@ BOUND_VARIABLE_1049 BOUND_VARIABLE_1052))) (= (or (and _let_1 _let_3) (and _let_3 _let_2) (and _let_2 _let_1)) (ll_3 BOUND_VARIABLE_1049 BOUND_VARIABLE_1050 BOUND_VARIABLE_1051 BOUND_VARIABLE_1052))))))))) (let ((_let_39 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (PREPROCESS_LEMMA :args (_let_38)) (PREPROCESS :args ((= _let_38 (and _let_37 _let_28))))) (PREPROCESS :args ((and _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29)))) :args ((and _let_37 _let_28 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29))))) (let ((_let_40 (AND_ELIM _let_39 :args (1)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3539 QUANTIFIERS_INST_E_MATCHING ((ho_4 (ho_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_1080) BOUND_VARIABLE_1079) BOUND_VARIABLE_1076) BOUND_VARIABLE_1052)))) :args (_let_28))) _let_40 :args (_let_26 false _let_28)))) (let ((_let_42 (ho_8 (ho_7 (ho_6 k_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_43 (ho_4 _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3539))) (let ((_let_44 (= _let_43 _let_25))) (let ((_let_45 (not _let_25))) (let ((_let_46 (or _let_16 _let_19))) (let ((_let_47 (or _let_17 _let_16))) (let ((_let_48 (or _let_19 _let_17))) (let ((_let_49 (and _let_48 _let_47 _let_46))) (let ((_let_50 (= _let_43 _let_49))) (let ((_let_51 (forall ((z $$unsorted)) (= (ho_4 (ho_8 (ho_7 (ho_6 k_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) z) (ho_4 (ho_8 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) z))))) (let ((_let_52 (not _let_44))) (let ((_let_53 (= _let_24 _let_42))) (let ((_let_54 (not _let_51))) (let ((_let_55 (or _let_54 _let_53))) (let ((_let_56 (AND_ELIM _let_39 :args (8)))) (let ((_let_57 (forall ((BOUND_VARIABLE_1136 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1138 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1137 |u_(-> $$unsorted Bool)|)) (= (ho_8 (ho_7 (ho_6 k_5 BOUND_VARIABLE_1138) BOUND_VARIABLE_1137) BOUND_VARIABLE_1136) (ho_8 (ho_7 (ho_6 k_9 BOUND_VARIABLE_1138) BOUND_VARIABLE_1137) BOUND_VARIABLE_1136))))) (let ((_let_58 (not _let_53))) (let ((_let_59 (not _let_57))) (let ((_let_60 (not (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (Z (-> $$unsorted Bool))) (= (@ (@ (@ ll_2 Y) Z) X) (@ (@ (@ ll_3 Y) Z) X)))))) (let ((_let_61 (ASSUME :args (_let_15)))) (let ((_let_62 (ASSUME :args (_let_14)))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (ASSUME :args (_let_10)))) (let ((_let_67 (ASSUME :args (_let_9)))) (let ((_let_68 (ASSUME :args (_let_8)))) (let ((_let_69 (ASSUME :args (_let_7)))) (let ((_let_70 (ASSUME :args (_let_6)))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (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 :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61) :args ((= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) SB_DEFAULT SBA_FIXPOINT))) _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61) :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (Z (-> $$unsorted Bool))) (= (lambda ((U $$unsorted)) (let ((_let_1 (@ X U))) (let ((_let_2 (@ Z U))) (let ((_let_3 (@ Y U))) (or (and _let_1 _let_3) (and _let_3 _let_2) (and _let_2 _let_1)))))) (lambda ((U $$unsorted)) (let ((_let_1 (@ X U))) (let ((_let_2 (@ Z U))) (let ((_let_3 (@ Y U))) (and (or _let_1 _let_3) (or _let_3 _let_2) (or _let_2 _let_1))))))))) _let_60))) (PREPROCESS :args ((= _let_60 _let_59))))))) (let ((_let_72 (or))) (let ((_let_73 (_let_54))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_73)) :args _let_73)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_51))) (REFL :args (_let_52)) :args _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_53 _let_54 (not _let_55)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_71) :args (_let_59))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_57))) (REFL :args (_let_58)) :args _let_72)) _let_71 :args (_let_58 true _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_42 _let_24 QUANTIFIERS_INST_ENUM)) :args (_let_30)))) _let_56 :args (_let_55 false _let_30)) :args (_let_54 true _let_53 false _let_55)) :args (_let_52 true _let_51)))) (let ((_let_75 (_let_44))) (let ((_let_76 (AND_ELIM _let_39 :args (0)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3539 QUANTIFIERS_INST_E_MATCHING ((ho_4 (ho_8 (ho_7 (ho_6 k_9 BOUND_VARIABLE_1113) BOUND_VARIABLE_1112) BOUND_VARIABLE_1111) BOUND_VARIABLE_1037)))) :args (_let_37))) _let_76 :args (_let_50 false _let_37)))) (let ((_let_78 (not _let_50))) (let ((_let_79 (not _let_49))) (let ((_let_80 (_let_50))) (let ((_let_81 (not _let_26))) (let ((_let_82 (_let_26))) (let ((_let_83 (not _let_21))) (let ((_let_84 (REORDERING (CNF_AND_POS :args (_let_18 0)) :args ((or _let_17 _let_23))))) (let ((_let_85 (not _let_20))) (let ((_let_86 (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_18 _let_20 _let_27))))) (let ((_let_87 (not _let_47))) (let ((_let_88 (not _let_19))) (let ((_let_89 (CNF_AND_NEG :args (_let_49)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST _let_89 (CNF_OR_NEG :args (_let_46 0)) (CNF_OR_NEG :args (_let_48 1)) (REORDERING (CNF_AND_POS :args (_let_18 1)) :args ((or _let_16 _let_23))) _let_84 _let_86 (REORDERING (CNF_AND_POS :args (_let_20 1)) :args ((or _let_19 _let_85))) (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_19 _let_83))) (MACRO_RESOLUTION_TRUST _let_89 (CNF_OR_NEG :args (_let_46 1)) (CNF_OR_NEG :args (_let_48 0)) :args ((or _let_49 _let_88 _let_87) false _let_46 false _let_48)) (MACRO_RESOLUTION_TRUST _let_86 (REORDERING (CNF_AND_POS :args (_let_20 0)) :args ((or _let_16 _let_85))) _let_84 (REORDERING (CNF_AND_POS :args (_let_21 1)) :args ((or _let_17 _let_83))) (CNF_OR_NEG :args (_let_47 1)) (CNF_OR_NEG :args (_let_47 0)) :args ((or _let_47 _let_27) true _let_20 true _let_18 true _let_21 true _let_16 true _let_17)) (REORDERING (CNF_EQUIV_POS1 :args _let_82) :args ((or _let_45 _let_22 _let_81))) _let_41 (REORDERING (CNF_EQUIV_POS2 :args _let_80) :args ((or _let_43 _let_79 _let_78))) _let_77 (REORDERING (CNF_EQUIV_NEG1 :args _let_75) :args ((or _let_43 _let_25 _let_44))) _let_74 :args (_let_43 false _let_46 false _let_48 false _let_16 false _let_17 false _let_18 true _let_20 true _let_21 true _let_19 false _let_47 false _let_22 false _let_26 true _let_49 false _let_50 false _let_25 true _let_44)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_82) :args ((or _let_25 _let_27 _let_81))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_75) _let_74 _let_90 :args (_let_45 true _let_44 false _let_43)) _let_41 :args (_let_27 true _let_25 false _let_26)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_80) :args ((or (not _let_43) _let_49 _let_78))) _let_90 _let_77 :args (_let_49 false _let_43 false _let_50)))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_17 _let_16 _let_87))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 1)) :args ((or _let_47 _let_79))) _let_92 :args (_let_47 false _let_49)) (REORDERING (CNF_AND_NEG :args (_let_20)) :args ((or _let_20 _let_88 (not _let_16)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 2)) _let_91 :args (_let_85 true _let_22)) (CNF_AND_NEG :args (_let_21)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 0)) _let_91 :args (_let_83 true _let_22)) :args (_let_88 false _let_47 true _let_16 true _let_20 true _let_17 true _let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_19 _let_16 (not _let_46)))) _let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 2)) :args ((or _let_46 _let_79))) _let_92 :args (_let_46 false _let_49)) :args (_let_16 true _let_19 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_19 _let_17 (not _let_48)))) _let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_48 _let_79))) _let_92 :args (_let_48 false _let_49)) :args (_let_17 true _let_19 false _let_48)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 1)) _let_91 :args (_let_23 true _let_22)) :args (false false _let_16 false _let_17 true _let_18)) :args (_let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.03/3.23 )
% 3.03/3.23 % SZS output end Proof for SET601^3
% 3.03/3.23 % cvc5---1.0.5 exiting
% 3.03/3.23 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------