TSTP Solution File: QUA001^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : QUA001^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 : Timeout 299.85s 300.14s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : QUA001^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 16:59:38 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.50 %----Proving TH0
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 % File : QUA001^1 : TPTP v8.1.2. Released v4.1.0.
% 0.20/0.50 % Domain : Quantales
% 0.20/0.50 % Problem : Addition is associative
% 0.20/0.50 % Version : [Hoe09] axioms.
% 0.20/0.50 % English :
% 0.20/0.50
% 0.20/0.50 % Refs : [Con71] Conway (1971), Regular Algebra and Finite Machines
% 0.20/0.50 % : [Hoe09] Hoefner (2009), Email to Geoff Sutcliffe
% 0.20/0.50 % Source : [Hoe09]
% 0.20/0.50 % Names : QUA01 [Hoe09]
% 0.20/0.50
% 0.20/0.50 % Status : Theorem
% 0.20/0.50 % Rating : 1.00 v4.1.0
% 0.20/0.50 % Syntax : Number of formulae : 27 ( 14 unt; 12 typ; 7 def)
% 0.20/0.50 % Number of atoms : 40 ( 18 equ; 0 cnn)
% 0.20/0.50 % Maximal formula atoms : 2 ( 2 avg)
% 0.20/0.50 % Number of connectives : 51 ( 0 ~; 1 |; 4 &; 45 @)
% 0.20/0.50 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.50 % Maximal formula depth : 6 ( 2 avg)
% 0.20/0.50 % Number of types : 2 ( 0 usr)
% 0.20/0.50 % Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% 0.20/0.50 % Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% 0.20/0.50 % Number of variables : 30 ( 15 ^; 11 !; 4 ?; 30 :)
% 0.20/0.50 % SPC : TH0_THM_EQU_NAR
% 0.20/0.50
% 0.20/0.50 % Comments :
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 %----Include axioms for Quantales
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 %----Usual Definition of Set Theory
% 0.20/0.50 thf(emptyset_type,type,
% 0.20/0.50 emptyset: $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(emptyset_def,definition,
% 0.20/0.50 ( emptyset
% 0.20/0.50 = ( ^ [X: $i] : $false ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(union_type,type,
% 0.20/0.50 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(union_def,definition,
% 0.20/0.50 ( union
% 0.20/0.50 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.20/0.50 ( ( X @ U )
% 0.20/0.50 | ( Y @ U ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(singleton_type,type,
% 0.20/0.50 singleton: $i > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(singleton_def,definition,
% 0.20/0.50 ( singleton
% 0.20/0.50 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Supremum Definition
% 0.20/0.50 thf(zero_type,type,
% 0.20/0.50 zero: $i ).
% 0.20/0.50
% 0.20/0.50 thf(sup_type,type,
% 0.20/0.50 sup: ( $i > $o ) > $i ).
% 0.20/0.50
% 0.20/0.50 thf(sup_es,axiom,
% 0.20/0.50 ( ( sup @ emptyset )
% 0.20/0.50 = zero ) ).
% 0.20/0.50
% 0.20/0.50 thf(sup_singleset,axiom,
% 0.20/0.50 ! [X: $i] :
% 0.20/0.50 ( ( sup @ ( singleton @ X ) )
% 0.20/0.50 = X ) ).
% 0.20/0.50
% 0.20/0.50 thf(supset_type,type,
% 0.20/0.50 supset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(supset,definition,
% 0.20/0.50 ( supset
% 0.20/0.50 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.20/0.50 ? [Y: $i > $o] :
% 0.20/0.50 ( ( F @ Y )
% 0.20/0.50 & ( ( sup @ Y )
% 0.20/0.50 = X ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(unionset_type,type,
% 0.20/0.50 unionset: ( ( $i > $o ) > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(unionset,definition,
% 0.20/0.50 ( unionset
% 0.20/0.50 = ( ^ [F: ( $i > $o ) > $o,X: $i] :
% 0.20/0.50 ? [Y: $i > $o] :
% 0.20/0.50 ( ( F @ Y )
% 0.20/0.50 & ( Y @ X ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(sup_set,axiom,
% 0.20/0.50 ! [X: ( $i > $o ) > $o] :
% 0.20/0.50 ( ( sup @ ( supset @ X ) )
% 0.20/0.50 = ( sup @ ( unionset @ X ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Definition of binary sums and lattice order
% 0.20/0.50 thf(addition_type,type,
% 0.20/0.50 addition: $i > $i > $i ).
% 0.20/0.50
% 0.20/0.50 thf(addition_def,definition,
% 0.20/0.50 ( addition
% 0.20/0.50 = ( ^ [X: $i,Y: $i] : ( sup @ ( union @ ( singleton @ X ) @ ( singleton @ Y ) ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(order_type,type,
% 0.20/0.50 leq: $i > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(order_def,axiom,
% 0.20/0.50 ! [X1: $i,X2: $i] :
% 0.20/0.50 ( ( leq @ X1 @ X2 )
% 0.20/0.50 <=> ( ( addition @ X1 @ X2 )
% 0.20/0.50 = X2 ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Definition of multiplication
% 0.20/0.50 thf(multiplication_type,type,
% 0.20/0.50 multiplication: $i > $i > $i ).
% 0.20/0.50
% 0.20/0.50 thf(crossmult_type,type,
% 0.20/0.50 crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(crossmult_def,definition,
% 0.20/0.50 ( crossmult
% 0.20/0.50 = ( ^ [X: $i > $o,Y: $i > $o,A: $i] :
% 0.20/0.50 ? [X1: $i,Y1: $i] :
% 0.20/0.50 ( ( X @ X1 )
% 0.20/0.50 & ( Y @ Y1 )
% 0.20/0.50 & ( A
% 0.20/0.50 = ( multiplication @ X1 @ Y1 ) ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(multiplication_def,axiom,
% 0.20/0.50 ! [X: $i > $o,Y: $i > $o] :
% 0.20/0.50 ( ( multiplication @ ( sup @ X ) @ ( sup @ Y ) )
% 0.20/0.50 = ( sup @ ( crossmult @ X @ Y ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(one_type,type,
% 0.20/0.50 one: $i ).
% 0.20/0.50
% 0.20/0.50 thf(multiplication_neutral_right,axiom,
% 0.20/0.50 ! [X: $i] :
% 0.20/0.50 ( ( multiplication @ X @ one )
% 0.20/0.50 = X ) ).
% 0.20/0.50
% 0.20/0.50 thf(multiplication_neutral_left,axiom,
% 0.20/0.50 ! [X: $i] :
% 0.20/0.50 ( ( multiplication @ one @ X )
% 0.20/0.50 = X ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 %--/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 23828 Alarm clock ( read result; case "$result" in
% 299.85/300.14 unsat)
% 299.85/300.14 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.85/300.14 ;;
% 299.85/300.14 sat)
% 299.85/300.14 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.85/300.14 ;;
% 299.85/300.14 esac; exit 1 )
% 299.85/300.14 Alarm clock
% 299.85/300.14 % cvc5---1.0.5 exiting
% 299.85/300.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------