TSTP Solution File: NUM863^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM863^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 10:48:36 EDT 2023
% Result : Timeout 299.17s 300.23s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM863^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n027.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 : Fri Aug 25 13:31:33 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 % File : NUM863^1 : TPTP v8.1.2. Released v4.1.0.
% 0.22/0.51 % Domain : Number Theory
% 0.22/0.51 % Problem : A property of cardinal numbers.
% 0.22/0.51 % Version : Especial.
% 0.22/0.51 % English : |A|=|A'| & |B|=|B'| & A' disjoint B', then |A U B| <= |A' U B'|.
% 0.22/0.51
% 0.22/0.51 % Refs :
% 0.22/0.51 % Source : [TPTP]
% 0.22/0.51 % Names :
% 0.22/0.51
% 0.22/0.51 % Status : Theorem
% 0.22/0.51 % Rating : 1.00 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 1.00 v4.1.0
% 0.22/0.51 % Syntax : Number of formulae : 41 ( 20 unt; 20 typ; 20 def)
% 0.22/0.51 % Number of atoms : 64 ( 28 equ; 0 cnn)
% 0.22/0.51 % Maximal formula atoms : 6 ( 3 avg)
% 0.22/0.51 % Number of connectives : 88 ( 5 ~; 3 |; 14 &; 61 @)
% 0.22/0.51 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.22/0.51 % Maximal formula depth : 10 ( 1 avg)
% 0.22/0.51 % Number of types : 2 ( 0 usr)
% 0.22/0.51 % Number of type conns : 124 ( 124 >; 0 *; 0 +; 0 <<)
% 0.22/0.51 % Number of symbols : 25 ( 23 usr; 4 con; 0-3 aty)
% 0.22/0.51 % Number of variables : 62 ( 48 ^; 9 !; 5 ?; 62 :)
% 0.22/0.51 % SPC : TH0_THM_EQU_NAR
% 0.22/0.51
% 0.22/0.51 % Comments : Originally suggested by Viktor Kuncak.
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 %----Basic set theory definitions
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 thf(in_decl,type,
% 0.22/0.51 in: $i > ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(in,definition,
% 0.22/0.51 ( in
% 0.22/0.51 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(is_a_decl,type,
% 0.22/0.51 is_a: $i > ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(is_a,definition,
% 0.22/0.51 ( is_a
% 0.22/0.51 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(emptyset_decl,type,
% 0.22/0.51 emptyset: $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(emptyset,definition,
% 0.22/0.51 ( emptyset
% 0.22/0.51 = ( ^ [X: $i] : $false ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(unord_pair_decl,type,
% 0.22/0.51 unord_pair: $i > $i > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(unord_pair,definition,
% 0.22/0.51 ( unord_pair
% 0.22/0.51 = ( ^ [X: $i,Y: $i,U: $i] :
% 0.22/0.51 ( ( U = X )
% 0.22/0.51 | ( U = Y ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(singleton_decl,type,
% 0.22/0.51 singleton: $i > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(singleton,definition,
% 0.22/0.51 ( singleton
% 0.22/0.51 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(union_decl,type,
% 0.22/0.51 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(union,definition,
% 0.22/0.51 ( union
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.22/0.51 ( ( X @ U )
% 0.22/0.51 | ( Y @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(excl_union_decl,type,
% 0.22/0.51 excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(excl_union,definition,
% 0.22/0.51 ( excl_union
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.22/0.51 ( ( ( X @ U )
% 0.22/0.51 & ~ ( Y @ U ) )
% 0.22/0.51 | ( ~ ( X @ U )
% 0.22/0.51 & ( Y @ U ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(intersection_decl,type,
% 0.22/0.51 intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(intersection,definition,
% 0.22/0.51 ( intersection
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.22/0.51 ( ( X @ U )
% 0.22/0.51 & ( Y @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(setminus_decl,type,
% 0.22/0.51 setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(setminus,definition,
% 0.22/0.51 ( setminus
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.22/0.51 ( ( X @ U )
% 0.22/0.51 & ~ ( Y @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(complement_decl,type,
% 0.22/0.51 complement: ( $i > $o ) > $i > $o ).
% 0.22/0.51
% 0.22/0.51 thf(complement,definition,
% 0.22/0.51 ( complement
% 0.22/0.51 = ( ^ [X: $i > $o,U: $i] :
% 0.22/0.51 ~ ( X @ U ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(disjoint_decl,type,
% 0.22/0.51 disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(disjoint,definition,
% 0.22/0.51 ( disjoint
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.22/0.51 ( ( intersection @ X @ Y )
% 0.22/0.51 = emptyset ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(subset_decl,type,
% 0.22/0.51 subset: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(subset,definition,
% 0.22/0.51 ( subset
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.22/0.51 ! [U: $i] :
% 0.22/0.51 ( ( X @ U )
% 0.22/0.51 => ( Y @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(meets_decl,type,
% 0.22/0.51 meets: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(meets,definition,
% 0.22/0.51 ( meets
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.22/0.51 ? [U: $i] :
% 0.22/0.51 ( ( X @ U )
% 0.22/0.51 & ( Y @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(misses_decl,type,
% 0.22/0.51 misses: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(misses,definition,
% 0.22/0.51 ( misses
% 0.22/0.51 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.22/0.51 ~ ? [U: $i] :
% 0.22/0.51 ( ( X @ U )
% 0.22/0.51 & ( Y @ U ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 thf(is_function_type,type,
% 0.22/0.52 is_function: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(is_function,definition,
% 0.22/0.52 ( is_function
% 0.22/0.52 = ( ^ [X: $i > $o,F: $i > $i,Y: $i > $o] :
% 0.22/0.52 ! [E: $i] :
% 0.22/0.52 ( ( X @ E )
% 0.22/0.52 => ( Y @ ( F @ E ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(injection_type,type,
% 0.22/0.52 injection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(injection,definition,
% 0.22/0.52 ( injection
% 0.22/0.52 = ( ^ [X: $i > $o,F: $i > $i,Y: $i > $o] :
% 0.22/0.52 ( ( is_function @ X @ F @ Y )
% 0.22/0.52 & ! [E1: $i,E2: $i] :
% 0.22/0.52 ( ( ( X @ E1 )
% 0.22/0.52 & ( X @ E2 )
% 0.22/0.52 & ( ( F @ E1 )
% 0.22/0.52 = ( F @ E2 ) ) )
% 0.22/0.52 => ( E1 = E2 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(surjection_type,type,
% 0.22/0.52 surjection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(surjection,definition,
% 0.22/0.52 ( surjection
% 0.22/0.52 = ( ^ [X: $i > $o,F: $i > $i,Y: $i > $o] :
% 0.22/0.52 ( ( is_function @ X @ F @ Y )
% 0.22/0.52 & ! [E1: $i] :
% 0.22/0.52 ( ( Y @ E1 )
% 0.22/0.52 => ? [E2: $i] :
% 0.22/0.52 ( ( X @ E2 )
% 0.22/0.52 & ( ( F @ E2 )
% 0.22/0.52 = E1 ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(bijection_type,type,
% 0.22/0.52 bijection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(bijection,definition,
% 0.22/0.52 ( bijection
% 0.22/0.52 = ( ^ [X: $i > $o,F: $i > $i,Y: $i > $o] :
% 0.22/0.52 ( ( injection @ X @ F @ Y )
% 0.22/0.52 & ( surjection @ X @ F @ Y ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(equinumerous_type,type,
% 0.22/0.52 equinumerous: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(equinumerous,definition,
% 0.22/0.52 ( equinumerous
% 0.22/0.52 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.22/0.52 ? [F: $i > $i] : ( bijection @ X @ F @ Y ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(embedding_type,type,
% 0.22/0.52 embedding: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(embedding,definition,
% 0.22/0.52 ( embedding
% 0.22/0.52 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.22/0.52 ? [F: $i > $i] : ( injection @ X @ F @ Y ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(prove,conjecture,
% 0.22/0.52 ! [A: $i > $o,Ap: $i > $o,B: $i > $o,Bp: $i > $o] :
% 0.22/0.52 ( ( ( equinumerous @ A @ Ap )
% 0.22/0.52 & ( equinumerous @ B @ Bp )
% 0.22/0.52 & ( ( intersection @ Ap @ Bp )
% 0.22/0.52 = emptyset ) )
% 0.22/0.52 => ( embedding @ ( union @ A @ B ) @ ( union @ Ap @ Bp ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qfCtM0ajqg/cvc5---1.0.5_27688.p...
% 0.22/0.52 (declare-sort $$unsorted 0)
% 0.22/0.52 (declare-fun tptp.in ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.52 (assert (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.22/0.52 (declare-fun tptp.is_a ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.52 (assert (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.22/0.52 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.22/0.52 (declare-fun tptp.unord_pair ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))
% 0.22/0.52 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.22/0.52 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.22/0.52 (declare-fun tptp.excl_union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))
% 0.22/0.52 (declare-fun tptp.intersection ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.22/0.52 (declare-fun tptp.setminus ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.52 (assert (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 9383 Alarm clock ( read result; case "$result" in
% 299.17/300.23 unsat)
% 299.17/300.23 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.17/300.23 ;;
% 299.17/300.23 sat)
% 299.17/300.23 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.17/300.23 ;;
% 299.17/300.23 esac; exit 1 )
% 299.17/300.23 Alarm clock
% 299.17/300.23 % cvc5---1.0.5 exiting
% 299.17/300.24 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------