TSTP Solution File: QUA018^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : QUA018^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 13:31:31 EDT 2023
% Result : Timeout 299.86s 300.10s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : QUA018^1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 17:01:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.49 %----Proving TH0
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 % File : QUA018^1 : TPTP v8.1.2. Released v4.1.0.
% 0.20/0.49 % Domain : Quantales
% 0.20/0.49 % Problem : Tests are commutative with respect to multiplication
% 0.20/0.49 % Version : [Hoe09] axioms.
% 0.20/0.49 % English :
% 0.20/0.49
% 0.20/0.49 % Refs : [Con71] Conway (1971), Regular Algebra and Finite Machines
% 0.20/0.49 % : [Koz97] Kozen (1997), Kleene Algebra with Tests
% 0.20/0.49 % : [Hoe09] Hoefner (2009), Email to Geoff Sutcliffe
% 0.20/0.49 % Source : [Hoe09]
% 0.20/0.49 % Names : QUA18 [Hoe09]
% 0.20/0.49
% 0.20/0.49 % Status : Theorem
% 0.20/0.49 % Rating : 1.00 v4.1.0
% 0.20/0.49 % Syntax : Number of formulae : 29 ( 13 unt; 13 typ; 7 def)
% 0.20/0.49 % Number of atoms : 48 ( 21 equ; 0 cnn)
% 0.20/0.49 % Maximal formula atoms : 4 ( 3 avg)
% 0.20/0.49 % Number of connectives : 61 ( 0 ~; 1 |; 7 &; 50 @)
% 0.20/0.49 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.49 % Maximal formula depth : 6 ( 2 avg)
% 0.20/0.49 % Number of types : 2 ( 0 usr)
% 0.20/0.49 % Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% 0.20/0.49 % Number of symbols : 17 ( 15 usr; 5 con; 0-3 aty)
% 0.20/0.49 % Number of variables : 31 ( 15 ^; 11 !; 5 ?; 31 :)
% 0.20/0.49 % SPC : TH0_THM_EQU_NAR
% 0.20/0.49
% 0.20/0.49 % Comments :
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 %----Include axioms for Quantales
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 %----Usual Definition of Set Theory
% 0.20/0.49 thf(emptyset_type,type,
% 0.20/0.49 emptyset: $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(emptyset_def,definition,
% 0.20/0.49 ( emptyset
% 0.20/0.49 = ( ^ [X: $i] : $false ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(union_type,type,
% 0.20/0.49 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(union_def,definition,
% 0.20/0.49 ( union
% 0.20/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.20/0.49 ( ( X @ U )
% 0.20/0.49 | ( Y @ U ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(singleton_type,type,
% 0.20/0.49 singleton: $i > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(singleton_def,definition,
% 0.20/0.49 ( singleton
% 0.20/0.49 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----Supremum Definition
% 0.20/0.49 thf(zero_type,type,
% 0.20/0.49 zero: $i ).
% 0.20/0.49
% 0.20/0.49 thf(sup_type,type,
% 0.20/0.49 sup: ( $i > $o ) > $i ).
% 0.20/0.49
% 0.20/0.49 thf(sup_es,axiom,
% 0.20/0.49 ( ( sup @ emptyset )
% 0.20/0.49 = zero ) ).
% 0.20/0.49
% 0.20/0.49 thf(sup_singleset,axiom,
% 0.20/0.49 ! [X: $i] :
% 0.20/0.49 ( ( sup @ ( singleton @ X ) )
% 0.20/0.49 = X ) ).
% 0.20/0.49
% 0.20/0.49 thf(supset_type,type,
% 0.20/0.49 supset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(supset,definition,
% 0.20/0.49 ( supset
% 0.20/0.49 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.20/0.49 ? [Y: $i > $o] :
% 0.20/0.49 ( ( F @ Y )
% 0.20/0.49 & ( ( sup @ Y )
% 0.20/0.49 = X ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(unionset_type,type,
% 0.20/0.49 unionset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(unionset,definition,
% 0.20/0.49 ( unionset
% 0.20/0.49 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.20/0.49 ? [Y: $i > $o] :
% 0.20/0.49 ( ( F @ Y )
% 0.20/0.49 & ( Y @ X ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(sup_set,axiom,
% 0.20/0.49 ! [X: ( $i > $o ) > $o] :
% 0.20/0.49 ( ( sup @ ( supset @ X ) )
% 0.20/0.49 = ( sup @ ( unionset @ X ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----Definition of binary sums and lattice order
% 0.20/0.49 thf(addition_type,type,
% 0.20/0.49 addition: $i > $i > $i ).
% 0.20/0.49
% 0.20/0.49 thf(addition_def,definition,
% 0.20/0.49 ( addition
% 0.20/0.49 = ( ^ [X: $i,Y: $i] : ( sup @ ( union @ ( singleton @ X ) @ ( singleton @ Y ) ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(order_type,type,
% 0.20/0.49 leq: $i > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(order_def,axiom,
% 0.20/0.49 ! [X1: $i,X2: $i] :
% 0.20/0.49 ( ( leq @ X1 @ X2 )
% 0.20/0.49 <=> ( ( addition @ X1 @ X2 )
% 0.20/0.49 = X2 ) ) ).
% 0.20/0.49
% 0.20/0.49 %----Definition of multiplication
% 0.20/0.49 thf(multiplication_type,type,
% 0.20/0.49 multiplication: $i > $i > $i ).
% 0.20/0.49
% 0.20/0.49 thf(crossmult_type,type,
% 0.20/0.49 crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(crossmult_def,definition,
% 0.20/0.49 ( crossmult
% 0.20/0.49 = ( ^ [X: $i > $o,Y: $i > $o,A: $i] :
% 0.20/0.49 ? [X1: $i,Y1: $i] :
% 0.20/0.49 ( ( X @ X1 )
% 0.20/0.49 & ( Y @ Y1 )
% 0.20/0.49 & ( A
% 0.20/0.49 = ( multiplication @ X1 @ Y1 ) ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(multiplication_def,axiom,
% 0.20/0.49 ! [X: $i > $o,Y: $i > $o] :
% 0.20/0.49 ( ( multiplication @ ( sup @ X ) @ ( sup @ Y ) )
% 0.20/0.49 = ( sup @ ( crossmult @ X @ Y ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(one_type,type,
% 0.20/0.49 one: $i ).
% 0.20/0.49
% 0.20/0.49 thf(multiplication_neutral_right,axiom,
% 0.20/0.49 ! [X: $i] :
% 0.20/0.49 ( ( multiplication @ X @ one )
% 0.20/0.49 = X ) ).
% 0.20/0.49
% 0.20/0.49 thf(multiplication_neutral_left,axiom,
% 0.20/0.49 ! [X: $i] :
% 0.20/0.49 ( ( multiplication @ one @ X )
% 0.20/0.49 = X ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 %----Include axioms for Tests for Quantales (Boolean sub-algebra below 1)
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 thf(tests,type,
% 0.20/0.50 test: $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(test_definition,axiom,
% 0.20/0.50 ! [X: $i] :
% 0.20/0.50 ( ( test @ X )
% 0.20/0.50 => ? [Y: $i] :
% 0.20/0.50 ( ( ( addition @ X @ Y )
% 0.20/0.50 = one )
% 0.20/0.50 & ( ( multiplication @ X @ Y )
% 0.20/0.50 = zero )
% 0.20/0.50 & ( ( multiplication @ Y @ X )
% 0.20/0.50 = zero ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 thf(test_comm,conjecture,
% 0.20/0.50 ! [X: $i,Y: $i] :
% 0.20/0.50 ( ( ( test @ X )
% 0.20/0.50 & ( test @ Y ) )
% 0.20/0.50 => ( ( multiplication @ X @ Y )
% 0.20/0.50 = ( multiplication @ Y @ X ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.q9akSkJ18d/cvc5---1.0.5_19390.p...
% 0.20/0.50 (declare-sort $$unsorted 0)
% 0.20/0.50 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.20/0.50 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.20/0.50 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.20/0.50 (declare-fun tptp.zero () $$unsorted)
% 0.20/0.50 (declare-fun tptp.sup ((-> $$unsorted Bool)) $$unsorted)
% 0.20/0.50 (assert (= (@ tptp.sup tptp.emptyset) tptp.zero))
% 0.20/0.50 (assert (forall ((X $$unsorted)) (= (@ tptp.sup (@ tptp.singleton X)) X)))
% 0.20/0.50 (declare-fun tptp.supset ((-> (-> $$unsorted Bool) Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.supset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (= (@ tptp.sup Y) X))))))
% 0.20/0.50 (declare-fun tptp.unionset ((-> (-> $$unsorted Bool) Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.unionset (lambda ((F (-> (-> $$unsorted Bool) Bool)) (X $$unsorted)) (exists ((Y (-> $$unsorted Bool))) (and (@ F Y) (@ Y X))))))
% 0.20/0.50 (assert (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (@ tptp.sup (@ tptp.supset X)) (@ tptp.sup (@ tptp.unionset X)))))
% 0.20/0.50 (declare-fun tptp.addition ($$unsorted $$unsorted) $$unsorted)
% 0.20/0.50 (assert (= tptp.addition (lambda ((X $$unsorted) (Y $$unsorted)) (@ tptp.sup (@ (@ tptp.union (@ tptp.singleton X)) (@ tptp.singleton Y))))))
% 0.20/0.50 (declare-fun tptp.leq ($$unsorted $$unsorted) Bool)
% 0.20/0.50 (assert (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (@ (@ tptp.leq X1) X2) (= (@ (@ tptp.addition X1) X2) X2))))
% 0.20/0.50 (declare-fun tptp.multiplication ($$unsorted $$unsorted) $$unsorted)
% 0.20/0.50 (declare-fun tptp.crossmult ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.crossmult (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (A $$unsorted)) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (and (@ X X1) (@ Y Y1) (= A (@ (@ tptp.multiplication X1) Y1)))))))
% 0.20/0.50 (assert (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.multiplication (@ tptp.sup X)) (@ tptp.sup Y)) (@ tptp.sup (@ (@ tptp.crossmult X) Y)))))
% 0.20/0.50 (declare-fun tptp.one () $$unsorted)
% 0.20/0.50 (assert (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication X) tptp.one) X)))
% 0.20/0.50 (assert (forall ((X $$unsorted)) (= (@ (@ tptp.multiplication tptp.one) X) X)))
% 0.20/0.50 (declare-fun tptp.test ($$unsorted) Bool)
% 0.20/0.50 (assert (forall ((X $$unsorted)) (=> (@ tptp.test X) (exists ((Y $$unsorted)) (and (= (@ (@ tptp.addition X) Y) tptp.one) (= (@ (@ tptp.multiplication X) Y) tptp.zero) (= (@ (@ tptp.multiplication Y) X) tptp.zero))))))
% 0.20/0.50 (assert (not (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (@ tptp.test X) (@ tptp.test Y)) (= (@ (@ tptp.multiplication X) Y) (@ (@ tptp.multiplication Y) X))))))
% 0.20/0.50 (set-info :filename cvc5---1.0.5_19390)
% 0.20/0.50 (check-sat-assuming ( true ))
% 0.20/0.50 ------- get file name : TPTP file name is QUA018^1
% 0.20/0.50 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19390.smt2...
% 0.20/0.50 --- Run --ho-elim -/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 22764 Alarm clock ( read result; case "$result" in
% 299.86/300.10 unsat)
% 299.86/300.10 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.86/300.10 ;;
% 299.86/300.10 sat)
% 299.86/300.10 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.86/300.10 ;;
% 299.86/300.10 esac; exit 1 )
% 299.86/300.11 -full-saturate-quant at 10...
% 299.86/300.11 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 299.86/300.11 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 299.86/300.11 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 299.86/300.11 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 299.86/300.11 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 299.86/300.11 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 299.86/300.11 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 299.86/300.11 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 299.86/300.11 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 299.86/300.11 % cvc5---1.0.5 exiting
% 299.86/300.11 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------