TSTP Solution File: QUA006^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : QUA006^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 13:31:29 EDT 2023
% Result : Theorem 36.82s 37.09s
% Output : Proof 36.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : QUA006^1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 16:39:25 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 % File : QUA006^1 : TPTP v8.1.2. Released v4.1.0.
% 0.21/0.51 % Domain : Quantales
% 0.21/0.51 % Problem : Zero is left-annihilator
% 0.21/0.51 % Version : [Hoe09] axioms.
% 0.21/0.51 % English :
% 0.21/0.51
% 0.21/0.51 % Refs : [Con71] Conway (1971), Regular Algebra and Finite Machines
% 0.21/0.51 % : [Hoe09] Hoefner (2009), Email to Geoff Sutcliffe
% 0.21/0.51 % Source : [Hoe09]
% 0.21/0.51 % Names : QUA06 [Hoe09]
% 0.21/0.51
% 0.21/0.51 % Status : Theorem
% 0.21/0.51 % Rating : 0.31 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v6.0.0, 0.57 v5.5.0, 0.83 v5.4.0, 1.00 v4.1.0
% 0.21/0.51 % Syntax : Number of formulae : 27 ( 14 unt; 12 typ; 7 def)
% 0.21/0.51 % Number of atoms : 42 ( 18 equ; 0 cnn)
% 0.21/0.51 % Maximal formula atoms : 2 ( 2 avg)
% 0.21/0.51 % Number of connectives : 45 ( 0 ~; 1 |; 4 &; 39 @)
% 0.21/0.51 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.21/0.51 % Maximal formula depth : 6 ( 2 avg)
% 0.21/0.51 % Number of types : 2 ( 0 usr)
% 0.21/0.51 % Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% 0.21/0.51 % Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% 0.21/0.51 % Number of variables : 28 ( 15 ^; 9 !; 4 ?; 28 :)
% 0.21/0.51 % SPC : TH0_THM_EQU_NAR
% 0.21/0.51
% 0.21/0.51 % Comments :
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %----Include axioms for Quantales
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %----Usual Definition of Set Theory
% 0.21/0.51 thf(emptyset_type,type,
% 0.21/0.51 emptyset: $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(emptyset_def,definition,
% 0.21/0.51 ( emptyset
% 0.21/0.51 = ( ^ [X: $i] : $false ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(union_type,type,
% 0.21/0.51 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(union_def,definition,
% 0.21/0.51 ( union
% 0.21/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.51 ( ( X @ U )
% 0.21/0.51 | ( Y @ U ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(singleton_type,type,
% 0.21/0.51 singleton: $i > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(singleton_def,definition,
% 0.21/0.51 ( singleton
% 0.21/0.51 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Supremum Definition
% 0.21/0.51 thf(zero_type,type,
% 0.21/0.51 zero: $i ).
% 0.21/0.51
% 0.21/0.51 thf(sup_type,type,
% 0.21/0.51 sup: ( $i > $o ) > $i ).
% 0.21/0.51
% 0.21/0.51 thf(sup_es,axiom,
% 0.21/0.51 ( ( sup @ emptyset )
% 0.21/0.51 = zero ) ).
% 0.21/0.51
% 0.21/0.51 thf(sup_singleset,axiom,
% 0.21/0.51 ! [X: $i] :
% 0.21/0.51 ( ( sup @ ( singleton @ X ) )
% 0.21/0.51 = X ) ).
% 0.21/0.51
% 0.21/0.51 thf(supset_type,type,
% 0.21/0.51 supset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(supset,definition,
% 0.21/0.51 ( supset
% 0.21/0.51 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.21/0.51 ? [Y: $i > $o] :
% 0.21/0.51 ( ( F @ Y )
% 0.21/0.51 & ( ( sup @ Y )
% 0.21/0.51 = X ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(unionset_type,type,
% 0.21/0.51 unionset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(unionset,definition,
% 0.21/0.51 ( unionset
% 0.21/0.51 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.21/0.51 ? [Y: $i > $o] :
% 0.21/0.51 ( ( F @ Y )
% 0.21/0.51 & ( Y @ X ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(sup_set,axiom,
% 0.21/0.51 ! [X: ( $i > $o ) > $o] :
% 0.21/0.51 ( ( sup @ ( supset @ X ) )
% 0.21/0.51 = ( sup @ ( unionset @ X ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Definition of binary sums and lattice order
% 0.21/0.51 thf(addition_type,type,
% 0.21/0.51 addition: $i > $i > $i ).
% 0.21/0.51
% 0.21/0.51 thf(addition_def,definition,
% 0.21/0.51 ( addition
% 0.21/0.51 = ( ^ [X: $i,Y: $i] : ( sup @ ( union @ ( singleton @ X ) @ ( singleton @ Y ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(order_type,type,
% 0.21/0.51 leq: $i > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(order_def,axiom,
% 0.21/0.51 ! [X1: $i,X2: $i] :
% 0.21/0.51 ( ( leq @ X1 @ X2 )
% 0.21/0.51 <=> ( ( addition @ X1 @ X2 )
% 0.21/0.51 = X2 ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Definition of multiplication
% 0.21/0.51 thf(multiplication_type,type,
% 0.21/0.51 multiplication: $i > $i > $i ).
% 0.21/0.51
% 0.21/0.51 thf(crossmult_type,type,
% 0.21/0.51 crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(crossmult_def,definition,
% 0.21/0.51 ( crossmult
% 0.21/0.51 = ( ^ [X: $i > $o,Y: $i > $o,A: $i] :
% 0.21/0.51 ? [X1: $i,Y1: $i] :
% 0.21/0.51 ( ( X @ X1 )
% 0.21/0.51 & ( Y @ Y1 )
% 0.21/0.51 & ( A
% 0.21/0.51 = ( multiplication @ X1 @ Y1 ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(multiplication_def,axiom,
% 0.21/0.51 ! [X: $i > $o,Y: $i > $o] :
% 0.21/0.51 ( ( multiplication @ ( sup @ X ) @ ( sup @ Y ) )
% 0.21/0.51 = ( sup @ ( crossmult @ X @ Y ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(one_type,type,
% 0.21/0.51 one: $i ).
% 0.21/0.51
% 0.21/0.51 thf(multiplication_neutral_right,axiom,
% 0.21/0.51 ! [X: $i] :
% 0.21/0.51 ( ( multiplication @ X @ one )
% 0.21/0.51 = X ) ).
% 0.21/0.51
% 0.21/0.51 thf(multiplication_neutral_left,axiom,
% 36.82/37.09 ! [X: $i] :
% 36.82/37.09 ( ( multiplication @ one @ X )
% 36.82/37.09 = X ) ).
% 36.82/37.09
% 36.82/37.09 %------------------------------------------------------------------------------
% 36.82/37.09 %------------------------------------------------------------------------------
% 36.82/37.09 thf(multiplication_anni,conjecture,
% 36.82/37.09 ! [X1: $i] :
% 36.82/37.09 ( ( multiplication @ zero @ X1 )
% 36.82/37.09 = zero ) ).
% 36.82/37.09
% 36.82/37.09 %------------------------------------------------------------------------------
% 36.82/37.09 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.yhyqKGv5En/cvc5---1.0.5_19963.p...
% 36.82/37.09 (declare-sort $$unsorted 0)
% 36.82/37.09 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 36.82/37.09 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 36.82/37.09 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 36.82/37.09 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 36.82/37.09 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 36.82/37.09 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 36.82/37.09 (declare-fun tptp.zero () $$unsorted)
% 36.82/37.09 (declare-fun tptp.sup ((-> $$unsorted Bool)) $$unsorted)
% 36.82/37.09 (assert (= (@ tptp.sup tptp.emptyset) tptp.zero))
% 36.82/37.09 (assert (forall ((X $$unsorted)) (= (@ tptp.sup (@ tptp.singleton X)) X)))
% 36.82/37.09 (declare-fun tptp.supset ((-> (-> $$unsorted Bool) Bool) $$unsorted) Bool)
% 36.82/37.09 (assert (= tptp.supset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (= (@ tptp.sup Y) X))))))
% 36.82/37.09 (declare-fun tptp.unionset ((-> (-> $$unsorted Bool) Bool) $$unsorted) Bool)
% 36.82/37.09 (assert (= tptp.unionset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (@ Y X))))))
% 36.82/37.09 (assert (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (@ tptp.sup (@ tptp.supset X)) (@ tptp.sup (@ tptp.unionset X)))))
% 36.82/37.09 (declare-fun tptp.addition ($$unsorted $$unsorted) $$unsorted)
% 36.82/37.09 (assert (= tptp.addition (lambda ((X $$unsorted) (Y $$unsorted)) (@ tptp.sup (@ (@ tptp.union (@ tptp.singleton X)) (@ tptp.singleton Y))))))
% 36.82/37.09 (declare-fun tptp.leq ($$unsorted $$unsorted) Bool)
% 36.82/37.09 (assert (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.leq X1) X2) (= (@ (@ tptp.addition X1) X2) X2))))
% 36.82/37.09 (declare-fun tptp.multiplication ($$unsorted $$unsorted) $$unsorted)
% 36.82/37.09 (declare-fun tptp.crossmult ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 36.82/37.09 (assert (= tptp.crossmult (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A $$unsorted)) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (and (@ X X1) (@ Y Y1) (= A (@ (@ tptp.multiplication X1) Y1)))))))
% 36.82/37.09 (assert (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) (@ tptp.sup Y)) (@ tptp.sup (@ (@ tptp.crossmult X) Y)))))
% 36.82/37.09 (declare-fun tptp.one () $$unsorted)
% 36.82/37.09 (assert (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication X) tptp.one) X)))
% 36.82/37.09 (assert (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication tptp.one) X) X)))
% 36.82/37.09 (assert (not (forall ((X1 $$unsorted)) (= (@ (@ tptp.multiplication tptp.zero) X1) tptp.zero))))
% 36.82/37.09 (set-info :filename cvc5---1.0.5_19963)
% 36.82/37.09 (check-sat-assuming ( true ))
% 36.82/37.09 ------- get file name : TPTP file name is QUA006^1
% 36.82/37.09 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19963.smt2...
% 36.82/37.09 --- Run --ho-elim --full-saturate-quant at 10...
% 36.82/37.09 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 36.82/37.09 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 36.82/37.09 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 36.82/37.09 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 36.82/37.09 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 36.82/37.09 % SZS status Theorem for QUA006^1
% 36.82/37.09 % SZS output start Proof for QUA006^1
% 36.82/37.09 (
% 36.82/37.09 (let ((_let_1 (not (forall ((X1 $$unsorted)) (= (@ (@ tptp.multiplication tptp.zero) X1) tptp.zero))))) (let ((_let_2 (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication X) tptp.one) X)))) (let ((_let_3 (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) (@ tptp.sup Y)) (@ tptp.sup (@ (@ tptp.crossmult X) Y)))))) (let ((_let_4 (= tptp.crossmult (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A $$unsorted)) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (and (@ X X1) (@ Y Y1) (= A (@ (@ tptp.multiplication X1) Y1)))))))) (let ((_let_5 (= tptp.addition (lambda ((X $$unsorted) (Y $$unsorted)) (@ tptp.sup (@ (@ tptp.union (@ tptp.singleton X)) (@ tptp.singleton Y))))))) (let ((_let_6 (= tptp.unionset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (@ Y X))))))) (let ((_let_7 (= tptp.supset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (= (@ tptp.sup Y) X))))))) (let ((_let_8 (forall ((X $$unsorted)) (= (@ tptp.sup (@ tptp.singleton X)) X)))) (let ((_let_9 (@ tptp.sup tptp.emptyset))) (let ((_let_10 (= _let_9 tptp.zero))) (let ((_let_11 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))) (let ((_let_12 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_13 (= tptp.emptyset (lambda ((X $$unsorted)) false)))) (let ((_let_14 (tptp.sup lambdaF_3))) (let ((_let_15 (tptp.multiplication _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (= _let_14 _let_15))) (let ((_let_17 (tptp.multiplication _let_14 tptp.one))) (let ((_let_18 (= _let_14 _let_17))) (let ((_let_19 (tptp.sup lambdaF_10))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_19))) (let ((_let_21 (tptp.multiplication _let_14 _let_19))) (let ((_let_22 (tptp.sup lambdaF_144))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (= _let_14 k_176))) (let ((_let_25 (= lambdaF_3 lambdaF_144))) (let ((_let_26 (forall ((X1 $$unsorted)) (let ((_let_1 (@ tptp.sup (lambda ((BOUND_VARIABLE_1391 $$unsorted)) false)))) (= _let_1 (@ (@ tptp.multiplication _let_1) X1)))))) (let ((_let_27 (not _let_16))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (ASSUME :args (_let_12)))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (EQ_RESOLVE (SYMM (ASSUME :args (_let_10))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_30 _let_29 _let_28) :args ((= tptp.zero _let_9) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_33 _let_32 _let_31 _let_30 _let_29 _let_28) :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) _let_33 _let_32 _let_31 _let_30 _let_29 _let_28))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_34 :args ((not (forall ((X1 $$unsorted)) (= tptp.zero (@ (@ tptp.multiplication tptp.zero) X1)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_36 (or))) (let ((_let_37 (_let_27))) (let ((_let_38 (not _let_26))) (let ((_let_39 (=>))) (let ((_let_40 (not))) (let ((_let_41 (=))) (let ((_let_42 (@ tptp.multiplication _let_14))) (let ((_let_43 (@))) (let ((_let_44 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_45 (THEORY_PREPROCESS :args ((= (@ tptp.sup lambdaF_3) _let_14))))) (let ((_let_46 (REFL :args (tptp.sup)))) (let ((_let_47 (TRANS (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (lambda ((BOUND_VARIABLE_1391 $$unsorted)) false) lambdaF_3))) :args _let_43) _let_45))) (let ((_let_48 (REFL :args (tptp.multiplication)))) (let ((_let_49 (_let_38))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_35) :args _let_49) (CONG (REFL :args _let_49) (CONG (CONG _let_47 (TRANS (CONG (CONG _let_48 _let_47 :args _let_43) _let_44 :args _let_43) (THEORY_PREPROCESS :args ((= (@ _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_15)))) :args _let_41) :args _let_40) :args _let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_26))) (REFL :args _let_37) :args _let_36)) _let_35 :args (_let_27 true _let_26)))) (let ((_let_51 (forall ((X $$unsorted)) (= X (@ (@ tptp.multiplication X) tptp.one))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (REFL :args (_let_14)))) (let ((_let_54 (_let_51))) (let ((_let_55 (forall ((X $$unsorted)) (= X (@ tptp.sup (lambda ((U $$unsorted)) (= U X))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_31 _let_30 _let_29 _let_28) :args ((forall ((X $$unsorted)) (= X (@ tptp.sup (@ tptp.singleton X)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_57 (THEORY_PREPROCESS :args ((= (@ tptp.sup lambdaF_10) _let_19))))) (let ((_let_58 (_let_55))) (let ((_let_59 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM))) (let ((_let_60 (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) (@ tptp.sup Y)) (@ tptp.sup (lambda ((A $$unsorted)) (not (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (@ X X1)) (not (@ Y Y1)) (not (= A (@ (@ tptp.multiplication X1) Y1)))))))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO _let_34 :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (CONG 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(CNF_OR_NEG :args (_let_154 0)) (CONG (REFL :args (_let_154)) (MACRO_SR_PRED_INTRO :args ((= (not _let_153) _let_152))) :args _let_36)) :args ((or _let_152 _let_154))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_190 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_112)) _let_111 :args (_let_153 false _let_109)) :args (_let_154 true _let_152)) :args (_let_143 false _let_154)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_149 :args (k_167 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_144 A)))) :args (_let_147)))) _let_149 :args (_let_145 false _let_147)) :args (_let_146 false _let_143 false _let_145)) :args (_let_142 true _let_141 true _let_140)) :args (_let_25 false _let_142)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_24 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_133) :args ((or _let_74 _let_135 _let_132))) _let_139 _let_131 :args (_let_135 true _let_74 false _let_127)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or _let_136 _let_66 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_130) :args ((or _let_74 _let_67 _let_75))) _let_139 _let_126 :args (_let_67 true _let_74 true _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_71 :args _let_73) :args _let_72))) _let_71 :args (_let_68 false _let_69)) :args (_let_66 false _let_67 false _let_68)) :args (_let_24 true _let_65 false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_61 :args (lambdaF_3 lambdaF_10 QUANTIFIERS_INST_ENUM)) :args _let_63) (CONG _let_64 (TRANS (CONG (TRANS (CONG _let_62 _let_57 :args _let_43) (THEORY_PREPROCESS :args ((= (@ _let_42 _let_19) _let_21)))) (TRANS (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (lambda ((A $$unsorted)) (not (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (@ lambdaF_3 X1)) (not (@ lambdaF_10 Y1)) (not (= A (@ (@ tptp.multiplication X1) Y1))))))) lambdaF_144))) :args _let_43) (THEORY_PREPROCESS :args ((= (@ tptp.sup lambdaF_144) _let_22)))) :args _let_41) (REWRITE :args ((= _let_21 _let_22)))) :args _let_39))) _let_61 :args (_let_23 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_56 :args _let_59) :args _let_58) (CONG (REFL :args _let_58) (CONG _let_44 (TRANS (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (lambda ((U $$unsorted)) (= U SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) lambdaF_10))) :args _let_43) _let_57) :args _let_41) :args _let_39))) _let_56 :args (_let_20 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_52 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((@ tptp.multiplication X)))) :args _let_54) (CONG (REFL :args _let_54) (CONG _let_53 (THEORY_PREPROCESS :args ((= (@ _let_42 tptp.one) _let_17))) :args _let_41) :args _let_39))) _let_52 :args (_let_18 false _let_51)) _let_50 :args (false false _let_25 false _let_24 false _let_23 false _let_20 false _let_18 true _let_16)) :args (_let_13 _let_12 _let_11 _let_10 _let_8 _let_7 _let_6 (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (@ tptp.sup (@ tptp.supset X)) (@ tptp.sup (@ tptp.unionset X)))) _let_5 (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.leq X1) X2) (= (@ (@ tptp.addition X1) X2) X2))) _let_4 _let_3 _let_2 (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication tptp.one) X) X)) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 36.82/37.09 )
% 36.82/37.09 % SZS output end Proof for QUA006^1
% 36.82/37.09 % cvc5---1.0.5 exiting
% 36.82/37.09 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------