TSTP Solution File: QUA002^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : QUA002^1 : TPTP v8.1.2. Released v4.1.0.
% 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 13:31:28 EDT 2023
% Result : Theorem 0.19s 0.58s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : QUA002^1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.13 % Command : do_cvc5 %s %d
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 16:38:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.48 %----Proving TH0
% 0.19/0.49 %------------------------------------------------------------------------------
% 0.19/0.49 % File : QUA002^1 : TPTP v8.1.2. Released v4.1.0.
% 0.19/0.49 % Domain : Quantales
% 0.19/0.49 % Problem : Addition (Sumpremum) is commutative
% 0.19/0.49 % Version : [Hoe09] axioms.
% 0.19/0.49 % English :
% 0.19/0.49
% 0.19/0.49 % Refs : [Con71] Conway (1971), Regular Algebra and Finite Machines
% 0.19/0.49 % : [Hoe09] Hoefner (2009), Email to Geoff Sutcliffe
% 0.19/0.49 % Source : [Hoe09]
% 0.19/0.49 % Names : QUA02 [Hoe09]
% 0.19/0.49
% 0.19/0.49 % Status : Theorem
% 0.19/0.49 % Rating : 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.0.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.3.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0
% 0.19/0.49 % Syntax : Number of formulae : 27 ( 14 unt; 12 typ; 7 def)
% 0.19/0.49 % Number of atoms : 38 ( 18 equ; 0 cnn)
% 0.19/0.49 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.49 % Number of connectives : 47 ( 0 ~; 1 |; 4 &; 41 @)
% 0.19/0.49 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.49 % Maximal formula depth : 6 ( 2 avg)
% 0.19/0.49 % Number of types : 2 ( 0 usr)
% 0.19/0.49 % Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% 0.19/0.49 % Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% 0.19/0.49 % Number of variables : 29 ( 15 ^; 10 !; 4 ?; 29 :)
% 0.19/0.49 % SPC : TH0_THM_EQU_NAR
% 0.19/0.49
% 0.19/0.49 % Comments :
% 0.19/0.49 %------------------------------------------------------------------------------
% 0.19/0.49 %----Include axioms for Quantales
% 0.19/0.49 %------------------------------------------------------------------------------
% 0.19/0.49 %----Usual Definition of Set Theory
% 0.19/0.49 thf(emptyset_type,type,
% 0.19/0.49 emptyset: $i > $o ).
% 0.19/0.49
% 0.19/0.49 thf(emptyset_def,definition,
% 0.19/0.49 ( emptyset
% 0.19/0.49 = ( ^ [X: $i] : $false ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(union_type,type,
% 0.19/0.49 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.49
% 0.19/0.49 thf(union_def,definition,
% 0.19/0.49 ( union
% 0.19/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.19/0.49 ( ( X @ U )
% 0.19/0.49 | ( Y @ U ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(singleton_type,type,
% 0.19/0.49 singleton: $i > $i > $o ).
% 0.19/0.49
% 0.19/0.49 thf(singleton_def,definition,
% 0.19/0.49 ( singleton
% 0.19/0.49 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.19/0.49
% 0.19/0.49 %----Supremum Definition
% 0.19/0.49 thf(zero_type,type,
% 0.19/0.49 zero: $i ).
% 0.19/0.49
% 0.19/0.49 thf(sup_type,type,
% 0.19/0.49 sup: ( $i > $o ) > $i ).
% 0.19/0.49
% 0.19/0.49 thf(sup_es,axiom,
% 0.19/0.49 ( ( sup @ emptyset )
% 0.19/0.49 = zero ) ).
% 0.19/0.49
% 0.19/0.49 thf(sup_singleset,axiom,
% 0.19/0.49 ! [X: $i] :
% 0.19/0.49 ( ( sup @ ( singleton @ X ) )
% 0.19/0.49 = X ) ).
% 0.19/0.49
% 0.19/0.49 thf(supset_type,type,
% 0.19/0.49 supset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.19/0.49
% 0.19/0.49 thf(supset,definition,
% 0.19/0.49 ( supset
% 0.19/0.49 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.19/0.49 ? [Y: $i > $o] :
% 0.19/0.49 ( ( F @ Y )
% 0.19/0.49 & ( ( sup @ Y )
% 0.19/0.49 = X ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(unionset_type,type,
% 0.19/0.49 unionset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.19/0.49
% 0.19/0.49 thf(unionset,definition,
% 0.19/0.49 ( unionset
% 0.19/0.49 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.19/0.49 ? [Y: $i > $o] :
% 0.19/0.49 ( ( F @ Y )
% 0.19/0.49 & ( Y @ X ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(sup_set,axiom,
% 0.19/0.49 ! [X: ( $i > $o ) > $o] :
% 0.19/0.49 ( ( sup @ ( supset @ X ) )
% 0.19/0.49 = ( sup @ ( unionset @ X ) ) ) ).
% 0.19/0.49
% 0.19/0.49 %----Definition of binary sums and lattice order
% 0.19/0.49 thf(addition_type,type,
% 0.19/0.49 addition: $i > $i > $i ).
% 0.19/0.49
% 0.19/0.49 thf(addition_def,definition,
% 0.19/0.49 ( addition
% 0.19/0.49 = ( ^ [X: $i,Y: $i] : ( sup @ ( union @ ( singleton @ X ) @ ( singleton @ Y ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(order_type,type,
% 0.19/0.49 leq: $i > $i > $o ).
% 0.19/0.49
% 0.19/0.49 thf(order_def,axiom,
% 0.19/0.49 ! [X1: $i,X2: $i] :
% 0.19/0.49 ( ( leq @ X1 @ X2 )
% 0.19/0.49 <=> ( ( addition @ X1 @ X2 )
% 0.19/0.49 = X2 ) ) ).
% 0.19/0.49
% 0.19/0.49 %----Definition of multiplication
% 0.19/0.49 thf(multiplication_type,type,
% 0.19/0.49 multiplication: $i > $i > $i ).
% 0.19/0.49
% 0.19/0.49 thf(crossmult_type,type,
% 0.19/0.49 crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.49
% 0.19/0.49 thf(crossmult_def,definition,
% 0.19/0.49 ( crossmult
% 0.19/0.49 = ( ^ [X: $i > $o,Y: $i > $o,A: $i] :
% 0.19/0.49 ? [X1: $i,Y1: $i] :
% 0.19/0.49 ( ( X @ X1 )
% 0.19/0.49 & ( Y @ Y1 )
% 0.19/0.49 & ( A
% 0.19/0.49 = ( multiplication @ X1 @ Y1 ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(multiplication_def,axiom,
% 0.19/0.49 ! [X: $i > $o,Y: $i > $o] :
% 0.19/0.49 ( ( multiplication @ ( sup @ X ) @ ( sup @ Y ) )
% 0.19/0.49 = ( sup @ ( crossmult @ X @ Y ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(one_type,type,
% 0.19/0.49 one: $i ).
% 0.19/0.49
% 0.19/0.49 thf(multiplication_neutral_right,axiom,
% 0.19/0.49 ! [X: $i] :
% 0.19/0.49 ( ( multiplication @ X @ one )
% 0.19/0.58 = X ) ).
% 0.19/0.58
% 0.19/0.58 thf(multiplication_neutral_left,axiom,
% 0.19/0.58 ! [X: $i] :
% 0.19/0.58 ( ( multiplication @ one @ X )
% 0.19/0.58 = X ) ).
% 0.19/0.58
% 0.19/0.58 %------------------------------------------------------------------------------
% 0.19/0.58 %------------------------------------------------------------------------------
% 0.19/0.58 thf(addition_comm,conjecture,
% 0.19/0.58 ! [X1: $i,X2: $i] :
% 0.19/0.58 ( ( addition @ X1 @ X2 )
% 0.19/0.58 = ( addition @ X2 @ X1 ) ) ).
% 0.19/0.58
% 0.19/0.58 %------------------------------------------------------------------------------
% 0.19/0.58 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.7AvIOIEEfa/cvc5---1.0.5_2502.p...
% 0.19/0.58 (declare-sort $$unsorted 0)
% 0.19/0.58 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.19/0.58 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.19/0.58 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.19/0.58 (declare-fun tptp.zero () $$unsorted)
% 0.19/0.58 (declare-fun tptp.sup ((-> $$unsorted Bool)) $$unsorted)
% 0.19/0.58 (assert (= (@ tptp.sup tptp.emptyset) tptp.zero))
% 0.19/0.58 (assert (forall ((X $$unsorted)) (= (@ tptp.sup (@ tptp.singleton X)) X)))
% 0.19/0.58 (declare-fun tptp.supset ((-> (-> $$unsorted Bool) Bool) $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.supset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (= (@ tptp.sup Y) X))))))
% 0.19/0.58 (declare-fun tptp.unionset ((-> (-> $$unsorted Bool) Bool) $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.unionset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (@ Y X))))))
% 0.19/0.58 (assert (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (@ tptp.sup (@ tptp.supset X)) (@ tptp.sup (@ tptp.unionset X)))))
% 0.19/0.58 (declare-fun tptp.addition ($$unsorted $$unsorted) $$unsorted)
% 0.19/0.58 (assert (= tptp.addition (lambda ((X $$unsorted) (Y $$unsorted)) (@ tptp.sup (@ (@ tptp.union (@ tptp.singleton X)) (@ tptp.singleton Y))))))
% 0.19/0.58 (declare-fun tptp.leq ($$unsorted $$unsorted) Bool)
% 0.19/0.58 (assert (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.leq X1) X2) (= (@ (@ tptp.addition X1) X2) X2))))
% 0.19/0.58 (declare-fun tptp.multiplication ($$unsorted $$unsorted) $$unsorted)
% 0.19/0.58 (declare-fun tptp.crossmult ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.crossmult (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A $$unsorted)) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (and (@ X X1) (@ Y Y1) (= A (@ (@ tptp.multiplication X1) Y1)))))))
% 0.19/0.58 (assert (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) (@ tptp.sup Y)) (@ tptp.sup (@ (@ tptp.crossmult X) Y)))))
% 0.19/0.58 (declare-fun tptp.one () $$unsorted)
% 0.19/0.58 (assert (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication X) tptp.one) X)))
% 0.19/0.58 (assert (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication tptp.one) X) X)))
% 0.19/0.58 (assert (not (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.addition X1) X2) (@ (@ tptp.addition X2) X1)))))
% 0.19/0.58 (set-info :filename cvc5---1.0.5_2502)
% 0.19/0.58 (check-sat-assuming ( true ))
% 0.19/0.58 ------- get file name : TPTP file name is QUA002^1
% 0.19/0.58 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2502.smt2...
% 0.19/0.58 --- Run --ho-elim --full-saturate-quant at 10...
% 0.19/0.58 % SZS status Theorem for QUA002^1
% 0.19/0.58 % SZS output start Proof for QUA002^1
% 0.19/0.58 (
% 0.19/0.58 (let ((_let_1 (not (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.addition X1) X2) (@ (@ tptp.addition X2) X1)))))) (let ((_let_2 (= tptp.crossmult (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A $$unsorted)) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (and (@ X X1) (@ Y Y1) (= A (@ (@ tptp.multiplication X1) Y1)))))))) (let ((_let_3 (= tptp.addition (lambda ((X $$unsorted) (Y $$unsorted)) (@ tptp.sup (@ (@ tptp.union (@ tptp.singleton X)) (@ tptp.singleton Y))))))) (let ((_let_4 (= tptp.unionset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (@ Y X))))))) (let ((_let_5 (= tptp.supset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (= (@ tptp.sup Y) X))))))) (let ((_let_6 (@ tptp.sup tptp.emptyset))) (let ((_let_7 (= _let_6 tptp.zero))) (let ((_let_8 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))) (let ((_let_9 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_10 (= tptp.emptyset (lambda ((X $$unsorted)) false)))) (let ((_let_11 (ho_11 (ho_10 k_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_12 (ho_10 k_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_13 (ho_11 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_14 (= (ho_22 k_21 _let_13) (ho_22 k_21 _let_11)))) (let ((_let_15 (= _let_13 _let_11))) (let ((_let_16 (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (ho_22 k_21 (ho_11 (ho_10 k_9 X1) X2)) (ho_22 k_21 (ho_11 (ho_10 k_13 X2) X1)))))) (let ((_let_17 (not _let_14))) (let ((_let_18 (not _let_16))) (let ((_let_19 (not (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ tptp.sup (@ (@ ll_7 X2) X1)) (@ tptp.sup (@ (@ ll_8 X1) X2))))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (ASSUME :args (_let_9)))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (EQ_RESOLVE (SYMM (ASSUME :args (_let_7))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_22 _let_21 _let_20) :args ((= tptp.zero _let_6) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (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 (AND_INTRO _let_25 _let_24 _let_23 _let_22 _let_21 _let_20) :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) _let_25 _let_24 _let_23 _let_22 _let_21 _let_20) :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ tptp.sup (lambda ((U $$unsorted)) (or (= U X1) (= U X2)))) (@ tptp.sup (lambda ((U $$unsorted)) (or (= U X2) (= U X1))))))) _let_19))) (PREPROCESS :args ((= _let_19 _let_18))))))) (let ((_let_27 (or))) (let ((_let_28 (forall ((z $$unsorted)) (= (ho_12 (ho_11 (ho_10 k_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29) z) (ho_12 (ho_11 (ho_10 k_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30) z))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_15))) (let ((_let_31 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_12 x z) (ho_12 y z)))) (= x y))))) (let ((_let_32 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_12 v ii) (ite (= i ii) e (ho_12 u ii)))))))))) (let ((_let_33 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_11 v ii) (ite (= i ii) e (ho_11 u ii)))))))))) (let ((_let_34 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_11 x z) (ho_11 y z)))) (= x y))))) (let ((_let_35 (forall ((u |u_(-> $$unsorted $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_10 v ii) (ite (= i ii) e (ho_10 u ii)))))))))) (let ((_let_36 (forall ((x |u_(-> $$unsorted $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_10 x z) (ho_10 y z)))) (= x y))))) (let ((_let_37 (forall ((u |u_(-> $$unsorted $$unsorted)|) (e $$unsorted) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_16 v ii) (ite (= i ii) e (ho_16 u ii)))))))))) (let ((_let_38 (forall ((x |u_(-> $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_16 x z) (ho_16 y z)))) (= x y))))) (let ((_let_39 (forall ((u |u_(-> _u_(-> $$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_19 v ii) (ite (= i ii) e (ho_19 u ii)))))))))) (let ((_let_40 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_19 x z) (ho_19 y z)))) (= x y))))) (let ((_let_41 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (e $$unsorted) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_22 v ii) (ite (= i ii) e (ho_22 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_22 x z) (ho_22 y z)))) (= x y))))) (let ((_let_43 (forall ((u |u_(-> $$unsorted $$unsorted $$unsorted)|) (e |u_(-> $$unsorted $$unsorted)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_15 v ii) (ite (= i ii) e (ho_15 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> $$unsorted $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_15 x z) (ho_15 y z)))) (= x y))))) (let ((_let_45 (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_18 v ii) (ite (= i ii) e (ho_18 u ii)))))))))) (let ((_let_46 (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_(-> $$unsorted Bool)|)) (= (ho_18 x z) (ho_18 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (e Bool) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_51 (forall ((BOUND_VARIABLE_1128 $$unsorted) (BOUND_VARIABLE_1129 $$unsorted) (BOUND_VARIABLE_1130 $$unsorted)) (= (or (= BOUND_VARIABLE_1128 BOUND_VARIABLE_1130) (= BOUND_VARIABLE_1129 BOUND_VARIABLE_1130)) (ho_12 (ho_11 (ho_10 k_9 BOUND_VARIABLE_1128) BOUND_VARIABLE_1129) BOUND_VARIABLE_1130))))) (let ((_let_52 (forall ((BOUND_VARIABLE_1118 $$unsorted) (BOUND_VARIABLE_1119 $$unsorted) (BOUND_VARIABLE_1120 $$unsorted)) (= (or (= BOUND_VARIABLE_1118 BOUND_VARIABLE_1120) (= BOUND_VARIABLE_1119 BOUND_VARIABLE_1120)) (ho_12 (ho_11 (ho_10 k_13 BOUND_VARIABLE_1118) BOUND_VARIABLE_1119) BOUND_VARIABLE_1120))))) (let ((_let_53 (forall ((BOUND_VARIABLE_1228 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1225 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1104 $$unsorted)) (= (ho_12 (ho_19 (ho_18 k_17 BOUND_VARIABLE_1228) BOUND_VARIABLE_1225) BOUND_VARIABLE_1104) (not (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (ho_12 BOUND_VARIABLE_1228 X1)) (not (ho_12 BOUND_VARIABLE_1225 Y1)) (not (= BOUND_VARIABLE_1104 (ho_16 (ho_15 k_14 X1) Y1)))))))))) (let ((_let_54 (forall ((BOUND_VARIABLE_1092 $$unsorted) (BOUND_VARIABLE_1093 $$unsorted) (BOUND_VARIABLE_1094 $$unsorted)) (= (or (= BOUND_VARIABLE_1092 BOUND_VARIABLE_1094) (= BOUND_VARIABLE_1093 BOUND_VARIABLE_1094)) (ho_12 (ho_11 (ho_10 k_20 BOUND_VARIABLE_1092) BOUND_VARIABLE_1093) BOUND_VARIABLE_1094))))) (let ((_let_55 (forall ((BOUND_VARIABLE_1271 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (BOUND_VARIABLE_1080 $$unsorted)) (= (ho_12 (ho_25 k_24 BOUND_VARIABLE_1271) BOUND_VARIABLE_1080) (not (forall ((BOUND_VARIABLE_1260 |u_(-> $$unsorted Bool)|)) (or (not (ho_23 BOUND_VARIABLE_1271 BOUND_VARIABLE_1260)) (not (= BOUND_VARIABLE_1080 (ho_22 k_21 BOUND_VARIABLE_1260)))))))))) (let ((_let_56 (forall ((BOUND_VARIABLE_1294 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (BOUND_VARIABLE_1067 $$unsorted)) (= (ho_12 (ho_25 k_26 BOUND_VARIABLE_1294) BOUND_VARIABLE_1067) (not (forall ((BOUND_VARIABLE_1298 |u_(-> $$unsorted Bool)|)) (or (not (ho_23 BOUND_VARIABLE_1294 BOUND_VARIABLE_1298)) (not (ho_12 BOUND_VARIABLE_1298 BOUND_VARIABLE_1067))))))))) (let ((_let_57 (forall ((BOUND_VARIABLE_1059 $$unsorted) (BOUND_VARIABLE_1060 $$unsorted)) (= (= BOUND_VARIABLE_1059 BOUND_VARIABLE_1060) (ho_12 (ho_11 k_27 BOUND_VARIABLE_1059) BOUND_VARIABLE_1060))))) (let ((_let_58 (and (forall ((BOUND_VARIABLE_1059 $$unsorted) (BOUND_VARIABLE_1060 $$unsorted)) (= (ll_2 BOUND_VARIABLE_1059 BOUND_VARIABLE_1060) (= BOUND_VARIABLE_1059 BOUND_VARIABLE_1060))) (forall ((BOUND_VARIABLE_1066 (-> (-> $$unsorted Bool) Bool)) (BOUND_VARIABLE_1067 $$unsorted)) (= (not (forall ((Y (-> $$unsorted Bool))) (or (not (@ BOUND_VARIABLE_1066 Y)) (not (@ Y BOUND_VARIABLE_1067))))) (ll_3 BOUND_VARIABLE_1066 BOUND_VARIABLE_1067))) (forall ((BOUND_VARIABLE_1079 (-> (-> $$unsorted Bool) Bool)) (BOUND_VARIABLE_1080 $$unsorted)) (= (ll_4 BOUND_VARIABLE_1079 BOUND_VARIABLE_1080) (not (forall ((Y (-> $$unsorted Bool))) (or (not (@ BOUND_VARIABLE_1079 Y)) (not (= (@ tptp.sup Y) BOUND_VARIABLE_1080))))))) (forall ((BOUND_VARIABLE_1092 $$unsorted) (BOUND_VARIABLE_1093 $$unsorted) (BOUND_VARIABLE_1094 $$unsorted)) (= (ll_5 BOUND_VARIABLE_1092 BOUND_VARIABLE_1093 BOUND_VARIABLE_1094) (or (= BOUND_VARIABLE_1092 BOUND_VARIABLE_1094) (= BOUND_VARIABLE_1093 BOUND_VARIABLE_1094)))) (forall ((BOUND_VARIABLE_1102 (-> $$unsorted Bool)) (BOUND_VARIABLE_1103 (-> $$unsorted Bool)) (BOUND_VARIABLE_1104 $$unsorted)) (= (ll_6 BOUND_VARIABLE_1102 BOUND_VARIABLE_1103 BOUND_VARIABLE_1104) (not (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (@ BOUND_VARIABLE_1102 X1)) (not (@ BOUND_VARIABLE_1103 Y1)) (not (= (@ (@ tptp.multiplication X1) Y1) BOUND_VARIABLE_1104))))))) (forall ((BOUND_VARIABLE_1118 $$unsorted) (BOUND_VARIABLE_1119 $$unsorted) (BOUND_VARIABLE_1120 $$unsorted)) (= (ll_7 BOUND_VARIABLE_1118 BOUND_VARIABLE_1119 BOUND_VARIABLE_1120) (or (= BOUND_VARIABLE_1118 BOUND_VARIABLE_1120) (= BOUND_VARIABLE_1119 BOUND_VARIABLE_1120)))) (forall ((BOUND_VARIABLE_1128 $$unsorted) (BOUND_VARIABLE_1129 $$unsorted) (BOUND_VARIABLE_1130 $$unsorted)) (= (ll_8 BOUND_VARIABLE_1128 BOUND_VARIABLE_1129 BOUND_VARIABLE_1130) (or (= BOUND_VARIABLE_1128 BOUND_VARIABLE_1130) (= BOUND_VARIABLE_1129 BOUND_VARIABLE_1130))))))) (let ((_let_59 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (PREPROCESS_LEMMA :args (_let_58)) (PREPROCESS :args ((= _let_58 (and _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51))))) (PREPROCESS :args ((and _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_31 _let_32)))) :args ((and _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_31 _let_32))))) (let ((_let_60 (AND_ELIM _let_59 :args (25)))) (let ((_let_61 (ho_12 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102))) (let ((_let_62 (ho_12 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102))) (let ((_let_63 (= _let_62 _let_61))) (let ((_let_64 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102))) (let ((_let_65 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102))) (let ((_let_66 (or _let_65 _let_64))) (let ((_let_67 (= _let_62 _let_66))) (let ((_let_68 (or _let_64 _let_65))) (let ((_let_69 (= _let_61 _let_68))) (let ((_let_70 (ho_12 (ho_11 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102))) (let ((_let_71 (ho_12 (ho_11 (ho_10 k_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102))) (let ((_let_72 (not _let_62))) (let ((_let_73 (_let_63))) (let ((_let_74 (AND_ELIM _let_59 :args (5)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_52)))) _let_74 :args (_let_67 false _let_52)))) (let ((_let_76 (not _let_67))) (let ((_let_77 (_let_67))) (let ((_let_78 (AND_ELIM _let_59 :args (6)))) (let ((_let_79 (_let_51))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79))) _let_78 :args (_let_70 false _let_51)))) (let ((_let_81 (not _let_61))) (let ((_let_82 (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_61))))) (let ((_let_83 (FALSE_INTRO (ASSUME :args (_let_81))))) (let ((_let_84 (APPLY_UF ho_12))) (let ((_let_85 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102)))) (let ((_let_86 (APPLY_UF ho_11))) (let ((_let_87 (not _let_66))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79))) _let_78 :args (_let_71 false _let_51)))) (let ((_let_89 (_let_29))) (let ((_let_90 (_let_15))) (let ((_let_91 (ASSUME :args _let_90))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_91 (SCOPE (CONG (REFL :args (k_21)) (SYMM (SYMM _let_91)) :args (APPLY_UF ho_22)) :args _let_90)) :args _let_90)) :args ((or _let_14 (not _let_15)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_15 (not _let_30)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_89)) :args _let_89)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) (REFL :args ((not _let_63))) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_65 _let_64 (not _let_68)))) (CNF_OR_NEG :args (_let_66 1)) (CNF_OR_NEG :args (_let_66 0)) (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_81 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79))) _let_78 :args (_let_69 false _let_51)) (REORDERING (CNF_EQUIV_POS2 :args _let_77) :args ((or _let_62 _let_87 _let_76))) _let_75 (REORDERING (CNF_EQUIV_NEG1 :args _let_73) :args ((or _let_62 _let_61 _let_63))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_88)) (CONG (CONG (CONG (REFL :args (k_9)) (SYMM (ASSUME :args (_let_64))) :args (APPLY_UF ho_10)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)) :args _let_86) _let_85 :args _let_84) _let_83)) :args (_let_81 _let_64 _let_71))) (CONG _let_82 (REFL :args ((not _let_64))) (REFL :args ((not _let_71))) :args _let_27)) _let_88 (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_64 _let_87))) (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_80)) (CONG (CONG (REFL :args (_let_12)) (SYMM (ASSUME :args (_let_65))) :args _let_86) _let_85 :args _let_84) _let_83)) :args (_let_81 _let_65 _let_70))) (CONG _let_82 (REFL :args ((not _let_65))) (REFL :args ((not _let_70))) :args _let_27)) _let_80 (REORDERING (CNF_EQUIV_POS1 :args _let_77) :args ((or _let_72 _let_66 _let_76))) _let_75 (CNF_EQUIV_NEG2 :args _let_73) :args ((or _let_63 _let_72) false _let_71 false _let_64 true _let_65 false _let_70 false _let_66 false _let_67 true _let_61)) :args (_let_63 true _let_64 true _let_65 false _let_68 false _let_69 true _let_66 false _let_67 false _let_61 true _let_62)) :args (_let_28 false _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_11 _let_13 QUANTIFIERS_INST_ENUM)) :args (_let_31)))) _let_60 :args (_let_30 false _let_31)) :args (_let_15 false _let_28 false _let_30)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_18))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_16))) (REFL :args (_let_17)) :args _let_27)) _let_26 :args (_let_17 true _let_16)) :args (false false _let_15 true _let_14)) :args (_let_10 _let_9 _let_8 _let_7 (forall ((X $$unsorted)) (= (@ tptp.sup (@ tptp.singleton X)) X)) _let_5 _let_4 (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (@ tptp.sup (@ tptp.supset X)) (@ tptp.sup (@ tptp.unionset X)))) _let_3 (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.leq X1) X2) (= (@ (@ tptp.addition X1) X2) X2))) _let_2 (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) (@ tptp.sup Y)) (@ tptp.sup (@ (@ tptp.crossmult X) Y)))) (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication X) tptp.one) X)) (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication tptp.one) X) X)) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.58 )
% 0.19/0.58 % SZS output end Proof for QUA002^1
% 0.19/0.59 % cvc5---1.0.5 exiting
% 0.19/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------