TSTP Solution File: QUA011^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : QUA011^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 13:31:30 EDT 2023
% Result : Theorem 40.58s 40.78s
% Output : Proof 40.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : QUA011^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 16:42:47 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.51 %----Proving TH0
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 % File : QUA011^1 : TPTP v8.1.2. Released v4.1.0.
% 0.23/0.52 % Domain : Quantales
% 0.23/0.52 % Problem : 0 annihilates arbitrary sums from the right
% 0.23/0.52 % Version : [Hoe09] axioms.
% 0.23/0.52 % English :
% 0.23/0.52
% 0.23/0.52 % Refs : [Con71] Conway (1971), Regular Algebra and Finite Machines
% 0.23/0.52 % : [Hoe09] Hoefner (2009), Email to Geoff Sutcliffe
% 0.23/0.52 % Source : [Hoe09]
% 0.23/0.52 % Names : QUA11 [Hoe09]
% 0.23/0.52
% 0.23/0.52 % Status : Theorem
% 0.23/0.52 % Rating : 0.23 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v6.0.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0
% 0.23/0.52 % Syntax : Number of formulae : 27 ( 14 unt; 12 typ; 7 def)
% 0.23/0.52 % Number of atoms : 52 ( 18 equ; 0 cnn)
% 0.23/0.52 % Maximal formula atoms : 2 ( 3 avg)
% 0.23/0.52 % Number of connectives : 46 ( 0 ~; 1 |; 4 &; 40 @)
% 0.23/0.52 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.23/0.52 % Maximal formula depth : 6 ( 2 avg)
% 0.23/0.52 % Number of types : 2 ( 0 usr)
% 0.23/0.52 % Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% 0.23/0.52 % Number of symbols : 17 ( 15 usr; 6 con; 0-3 aty)
% 0.23/0.52 % Number of variables : 28 ( 15 ^; 9 !; 4 ?; 28 :)
% 0.23/0.52 % SPC : TH0_THM_EQU_NAR
% 0.23/0.52
% 0.23/0.52 % Comments :
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 %----Include axioms for Quantales
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 %----Usual Definition of Set Theory
% 0.23/0.52 thf(emptyset_type,type,
% 0.23/0.52 emptyset: $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(emptyset_def,definition,
% 0.23/0.52 ( emptyset
% 0.23/0.52 = ( ^ [X: $i] : $false ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(union_type,type,
% 0.23/0.52 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(union_def,definition,
% 0.23/0.52 ( union
% 0.23/0.52 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.52 ( ( X @ U )
% 0.23/0.52 | ( Y @ U ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(singleton_type,type,
% 0.23/0.52 singleton: $i > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(singleton_def,definition,
% 0.23/0.52 ( singleton
% 0.23/0.52 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Supremum Definition
% 0.23/0.52 thf(zero_type,type,
% 0.23/0.52 zero: $i ).
% 0.23/0.52
% 0.23/0.52 thf(sup_type,type,
% 0.23/0.52 sup: ( $i > $o ) > $i ).
% 0.23/0.52
% 0.23/0.52 thf(sup_es,axiom,
% 0.23/0.52 ( ( sup @ emptyset )
% 0.23/0.52 = zero ) ).
% 0.23/0.52
% 0.23/0.52 thf(sup_singleset,axiom,
% 0.23/0.52 ! [X: $i] :
% 0.23/0.52 ( ( sup @ ( singleton @ X ) )
% 0.23/0.52 = X ) ).
% 0.23/0.52
% 0.23/0.52 thf(supset_type,type,
% 0.23/0.52 supset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(supset,definition,
% 0.23/0.52 ( supset
% 0.23/0.52 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.23/0.52 ? [Y: $i > $o] :
% 0.23/0.52 ( ( F @ Y )
% 0.23/0.52 & ( ( sup @ Y )
% 0.23/0.52 = X ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(unionset_type,type,
% 0.23/0.52 unionset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(unionset,definition,
% 0.23/0.52 ( unionset
% 0.23/0.52 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.23/0.52 ? [Y: $i > $o] :
% 0.23/0.52 ( ( F @ Y )
% 0.23/0.52 & ( Y @ X ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(sup_set,axiom,
% 0.23/0.52 ! [X: ( $i > $o ) > $o] :
% 0.23/0.52 ( ( sup @ ( supset @ X ) )
% 0.23/0.52 = ( sup @ ( unionset @ X ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Definition of binary sums and lattice order
% 0.23/0.52 thf(addition_type,type,
% 0.23/0.52 addition: $i > $i > $i ).
% 0.23/0.52
% 0.23/0.52 thf(addition_def,definition,
% 0.23/0.52 ( addition
% 0.23/0.52 = ( ^ [X: $i,Y: $i] : ( sup @ ( union @ ( singleton @ X ) @ ( singleton @ Y ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(order_type,type,
% 0.23/0.52 leq: $i > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(order_def,axiom,
% 0.23/0.52 ! [X1: $i,X2: $i] :
% 0.23/0.52 ( ( leq @ X1 @ X2 )
% 0.23/0.52 <=> ( ( addition @ X1 @ X2 )
% 0.23/0.52 = X2 ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Definition of multiplication
% 0.23/0.52 thf(multiplication_type,type,
% 0.23/0.52 multiplication: $i > $i > $i ).
% 0.23/0.52
% 0.23/0.52 thf(crossmult_type,type,
% 0.23/0.52 crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(crossmult_def,definition,
% 0.23/0.52 ( crossmult
% 0.23/0.52 = ( ^ [X: $i > $o,Y: $i > $o,A: $i] :
% 0.23/0.52 ? [X1: $i,Y1: $i] :
% 0.23/0.52 ( ( X @ X1 )
% 0.23/0.52 & ( Y @ Y1 )
% 0.23/0.52 & ( A
% 0.23/0.52 = ( multiplication @ X1 @ Y1 ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(multiplication_def,axiom,
% 0.23/0.52 ! [X: $i > $o,Y: $i > $o] :
% 0.23/0.52 ( ( multiplication @ ( sup @ X ) @ ( sup @ Y ) )
% 0.23/0.52 = ( sup @ ( crossmult @ X @ Y ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(one_type,type,
% 0.23/0.52 one: $i ).
% 0.23/0.52
% 0.23/0.52 thf(multiplication_neutral_right,axiom,
% 0.23/0.52 ! [X: $i] :
% 0.23/0.52 ( ( multiplication @ X @ one )
% 0.23/0.52 = X ) ).
% 0.23/0.52
% 0.23/0.52 thf(multiplication_neutral_left,axiom,
% 40.58/40.78 ! [X: $i] :
% 40.58/40.78 ( ( multiplication @ one @ X )
% 40.58/40.78 = X ) ).
% 40.58/40.78
% 40.58/40.78 %------------------------------------------------------------------------------
% 40.58/40.78 %------------------------------------------------------------------------------
% 40.58/40.78 thf(multiplication_anni,conjecture,
% 40.58/40.78 ! [X: $i > $o] :
% 40.58/40.78 ( ( multiplication @ ( sup @ X ) @ zero )
% 40.58/40.78 = zero ) ).
% 40.58/40.78
% 40.58/40.78 %------------------------------------------------------------------------------
% 40.58/40.78 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.UIrmDduCQf/cvc5---1.0.5_14171.p...
% 40.58/40.78 (declare-sort $$unsorted 0)
% 40.58/40.78 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 40.58/40.78 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 40.58/40.78 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 40.58/40.78 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 40.58/40.78 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 40.58/40.78 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 40.58/40.78 (declare-fun tptp.zero () $$unsorted)
% 40.58/40.78 (declare-fun tptp.sup ((-> $$unsorted Bool)) $$unsorted)
% 40.58/40.78 (assert (= (@ tptp.sup tptp.emptyset) tptp.zero))
% 40.58/40.78 (assert (forall ((X $$unsorted)) (= (@ tptp.sup (@ tptp.singleton X)) X)))
% 40.58/40.78 (declare-fun tptp.supset ((-> (-> $$unsorted Bool) Bool) $$unsorted) Bool)
% 40.58/40.78 (assert (= tptp.supset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (= (@ tptp.sup Y) X))))))
% 40.58/40.78 (declare-fun tptp.unionset ((-> (-> $$unsorted Bool) Bool) $$unsorted) Bool)
% 40.58/40.78 (assert (= tptp.unionset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (@ Y X))))))
% 40.58/40.78 (assert (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (@ tptp.sup (@ tptp.supset X)) (@ tptp.sup (@ tptp.unionset X)))))
% 40.58/40.78 (declare-fun tptp.addition ($$unsorted $$unsorted) $$unsorted)
% 40.58/40.78 (assert (= tptp.addition (lambda ((X $$unsorted) (Y $$unsorted)) (@ tptp.sup (@ (@ tptp.union (@ tptp.singleton X)) (@ tptp.singleton Y))))))
% 40.58/40.78 (declare-fun tptp.leq ($$unsorted $$unsorted) Bool)
% 40.58/40.78 (assert (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.leq X1) X2) (= (@ (@ tptp.addition X1) X2) X2))))
% 40.58/40.78 (declare-fun tptp.multiplication ($$unsorted $$unsorted) $$unsorted)
% 40.58/40.78 (declare-fun tptp.crossmult ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 40.58/40.78 (assert (= tptp.crossmult (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A $$unsorted)) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (and (@ X X1) (@ Y Y1) (= A (@ (@ tptp.multiplication X1) Y1)))))))
% 40.58/40.78 (assert (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) (@ tptp.sup Y)) (@ tptp.sup (@ (@ tptp.crossmult X) Y)))))
% 40.58/40.78 (declare-fun tptp.one () $$unsorted)
% 40.58/40.78 (assert (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication X) tptp.one) X)))
% 40.58/40.78 (assert (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication tptp.one) X) X)))
% 40.58/40.78 (assert (not (forall ((X (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) tptp.zero) tptp.zero))))
% 40.58/40.78 (set-info :filename cvc5---1.0.5_14171)
% 40.58/40.78 (check-sat-assuming ( true ))
% 40.58/40.78 ------- get file name : TPTP file name is QUA011^1
% 40.58/40.78 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_14171.smt2...
% 40.58/40.78 --- Run --ho-elim --full-saturate-quant at 10...
% 40.58/40.78 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 40.58/40.78 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 40.58/40.78 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 40.58/40.78 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 40.58/40.78 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 40.58/40.78 % SZS status Theorem for QUA011^1
% 40.58/40.78 % SZS output start Proof for QUA011^1
% 40.58/40.78 (
% 40.58/40.78 (let ((_let_1 (not (forall ((X (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) tptp.zero) tptp.zero))))) (let ((_let_2 (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) (@ tptp.sup Y)) (@ tptp.sup (@ (@ tptp.crossmult X) Y)))))) (let ((_let_3 (= tptp.crossmult (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A $$unsorted)) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (and (@ X X1) (@ Y Y1) (= A (@ (@ tptp.multiplication X1) Y1)))))))) (let ((_let_4 (= tptp.addition (lambda ((X $$unsorted) (Y $$unsorted)) (@ tptp.sup (@ (@ tptp.union (@ tptp.singleton X)) (@ tptp.singleton Y))))))) (let ((_let_5 (= tptp.unionset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (@ Y X))))))) (let ((_let_6 (= tptp.supset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (= (@ tptp.sup Y) X))))))) (let ((_let_7 (@ tptp.sup tptp.emptyset))) (let ((_let_8 (= _let_7 tptp.zero))) (let ((_let_9 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))) (let ((_let_10 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_11 (= tptp.emptyset (lambda ((X $$unsorted)) false)))) (let ((_let_12 (tptp.sup lambdaF_3))) (let ((_let_13 (tptp.sup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.multiplication _let_13 _let_12))) (let ((_let_15 (= _let_12 _let_14))) (let ((_let_16 (tptp.sup lambdaF_364))) (let ((_let_17 (= _let_14 _let_16))) (let ((_let_18 (= lambdaF_3 lambdaF_364))) (let ((_let_19 (forall ((X (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.sup (lambda ((BOUND_VARIABLE_1393 $$unsorted)) false)))) (= _let_1 (@ (@ tptp.multiplication (@ tptp.sup X)) _let_1)))))) (let ((_let_20 (not _let_15))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (ASSUME :args (_let_10)))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (EQ_RESOLVE (SYMM (ASSUME :args (_let_8))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_23 _let_22 _let_21) :args ((= tptp.zero _let_7) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (AND_INTRO (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_26 _let_25 _let_24 _let_23 _let_22 _let_21) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_26 _let_25 _let_24 _let_23 _let_22 _let_21))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_27 :args ((not (forall ((X (-> $$unsorted Bool))) (= tptp.zero (@ (@ tptp.multiplication (@ tptp.sup X)) tptp.zero)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_19))) (let ((_let_31 (=>))) (let ((_let_32 (not))) (let ((_let_33 (=))) (let ((_let_34 (THEORY_PREPROCESS :args ((= (@ (@ tptp.multiplication _let_13) _let_12) _let_14))))) (let ((_let_35 (@))) (let ((_let_36 (THEORY_PREPROCESS :args ((= (@ tptp.sup lambdaF_3) _let_12))))) (let ((_let_37 (REFL :args (tptp.sup)))) (let ((_let_38 (TRANS (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (lambda ((BOUND_VARIABLE_1393 $$unsorted)) false) lambdaF_3))) :args _let_35) _let_36))) (let ((_let_39 (CONG (REFL :args (tptp.multiplication)) (THEORY_PREPROCESS :args ((= (@ tptp.sup SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_13))) :args _let_35))) (let ((_let_40 (_let_30))) (let ((_let_41 (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 $$unsorted)) (or (not (@ X X1)) (not (@ Y Y1)) (not (= A (@ (@ tptp.multiplication X1) Y1)))))))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO _let_27 :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 (lambdaF_364 k_396))) (let ((_let_45 (lambdaF_3 k_396))) (let ((_let_46 (= _let_45 _let_44))) (let ((_let_47 (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1)) (not (@ lambdaF_3 Y1)) (not (= (@ (@ tptp.multiplication X1) Y1) k_396)))))) (let ((_let_48 (not _let_47))) (let ((_let_49 (= _let_44 _let_48))) (let ((_let_50 (not _let_44))) (let ((_let_51 (forall ((A $$unsorted)) (= (not (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1)) (not (@ lambdaF_3 Y1)) (not (= A (@ (@ tptp.multiplication X1) Y1)))))) (lambdaF_364 A))))) (let ((_let_52 ((forall ((A $$unsorted)) (= (lambdaF_364 A) (@ (lambda ((A $$unsorted)) (not (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1)) (not (@ lambdaF_3 Y1)) (not (= A (@ (@ tptp.multiplication X1) Y1))))))) A)))))) (let ((_let_53 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_52) (REWRITE :args _let_52)))) (let ((_let_54 (tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_431 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_432))) (let ((_let_55 (lambdaF_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_432))) (let ((_let_56 (not _let_55))) (let ((_let_57 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_431))) (let ((_let_58 (or (not _let_57) _let_56 (not (= k_396 _let_54))))) (let ((_let_59 (forall ((BOUND_VARIABLE_1393 $$unsorted)) (not (lambdaF_3 BOUND_VARIABLE_1393))))) (let ((_let_60 ((forall ((BOUND_VARIABLE_1393 $$unsorted)) (= (lambdaF_3 BOUND_VARIABLE_1393) (@ (lambda ((BOUND_VARIABLE_1393 $$unsorted)) false) BOUND_VARIABLE_1393)))))) (let ((_let_61 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_60) (REWRITE :args _let_60)))) (let ((_let_62 (_let_59))) (let ((_let_63 (@ (@ tptp.multiplication SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_431) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_432))) (let ((_let_64 (@ lambdaF_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_432))) (let ((_let_65 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_431))) (let ((_let_66 (_let_48))) (let ((_let_67 (and _let_17 _let_18))) (let ((_let_68 (_let_17 _let_18))) (let ((_let_69 (ASSUME :args (_let_17)))) (let ((_let_70 (ASSUME :args (_let_18)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_67)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_69 _let_70) (SCOPE (TRANS (CONG (SYMM (SYMM _let_70)) :args (APPLY_UF tptp.sup)) (SYMM _let_69)) :args _let_68)) :args _let_68)) :args (true _let_67)) :args ((or _let_15 (not _let_17) (not _let_18)))) (MACRO_RESOLUTION_TRUST (THEORY_LEMMA :args ((or _let_18 (not _let_46)) THEORY_UF)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args (_let_46)) :args ((or _let_45 _let_44 _let_46))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (k_396 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_62)) _let_61 :args ((not _let_45) false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_49)) :args ((or _let_50 _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66) (TRANS (REWRITE :args ((=> _let_48 (not (or (not _let_65) (not _let_64) (not (= _let_63 k_396))))))) (CONG (REFL :args _let_66) (CONG (CONG (CONG (THEORY_PREPROCESS :args ((= _let_65 _let_57))) :args _let_32) (CONG (THEORY_PREPROCESS :args ((= _let_64 _let_55))) :args _let_32) (CONG (CONG (REFL :args (k_396)) (THEORY_PREPROCESS :args ((= _let_63 _let_54))) :args _let_33) :args _let_32) :args _let_29) :args _let_32) :args _let_31)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) (REFL :args ((not _let_58))) :args _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 1)) (CONG (REFL :args (_let_58)) (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) :args _let_29)) :args ((or _let_55 _let_58))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_432 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_62)) _let_61 :args (_let_56 false _let_59)) :args (_let_58 true _let_55)) :args (_let_47 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (k_396 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_364 A)))) :args (_let_51)))) _let_53 :args (_let_49 false _let_51)) :args (_let_50 false _let_47 false _let_49)) :args (_let_46 true _let_45 true _let_44)) :args (_let_18 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_3 QUANTIFIERS_INST_ENUM)) :args _let_43) (CONG (REFL :args _let_43) (CONG (TRANS (CONG _let_39 _let_36 :args _let_35) _let_34) (TRANS (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (lambda ((A $$unsorted)) (not (forall ((X1 $$unsorted) (Y1 $$unsorted)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1)) (not (@ lambdaF_3 Y1)) (not (= A (@ (@ tptp.multiplication X1) Y1))))))) lambdaF_364))) :args _let_35) (THEORY_PREPROCESS :args ((= (@ tptp.sup lambdaF_364) _let_16)))) :args _let_33) :args _let_31))) _let_42 :args (_let_17 false _let_41)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_28) :args _let_40) (CONG (REFL :args _let_40) (CONG (CONG _let_38 (TRANS (CONG _let_39 _let_38 :args _let_35) _let_34) :args _let_33) :args _let_32) :args _let_31))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_19))) (REFL :args (_let_20)) :args _let_29)) _let_28 :args (_let_20 true _let_19)) :args (false false _let_18 false _let_17 true _let_15)) :args (_let_11 _let_10 _let_9 _let_8 (forall ((X $$unsorted)) (= (@ tptp.sup (@ tptp.singleton X)) X)) _let_6 _let_5 (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (@ tptp.sup (@ tptp.supset X)) (@ tptp.sup (@ tptp.unionset X)))) _let_4 (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.leq X1) X2) (= (@ (@ tptp.addition X1) X2) X2))) _let_3 _let_2 (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication X) tptp.one) X)) (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication tptp.one) X) X)) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 40.58/40.78 )
% 40.58/40.78 % SZS output end Proof for QUA011^1
% 40.58/40.78 % cvc5---1.0.5 exiting
% 40.58/40.78 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------