TSTP Solution File: SET669^3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET669^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 : Tue May 7 10:50:18 EDT 2024
% Result : Theorem 3.32s 1.98s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 28 ( 11 unt; 8 typ; 5 def)
% Number of atoms : 64 ( 19 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 97 ( 16 ~; 6 |; 4 &; 65 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 61 ( 29 ^ 22 !; 10 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(subset_def,definition,
( subset
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(id_rel_type,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(id_rel_def,definition,
( id_rel
= ( ^ [A: $i > $o,B: $i,C: $i] :
( ( A @ B )
& ( B = C ) ) ) ) ).
thf(sub_rel_type,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(sub_rel_def,definition,
( sub_rel
= ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) ) ) ) ).
thf(rel_codomain_type,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(rel_codomain_def,definition,
( rel_codomain
= ( ^ [A: $i > $i > $o,B: $i] :
? [C: $i] : ( A @ C @ B ) ) ) ).
thf(rel_domain_type,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(rel_domain_def,definition,
( rel_domain
= ( ^ [A: $i > $i > $o,B: $i] :
? [C: $i] : ( A @ B @ C ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [B: $i] : $true )
@ A )
=> ( ( subset
@ ^ [B: $i] : $true
@ ( rel_domain @ A ) )
& ( ( ^ [B: $i] : $true )
= ( rel_codomain @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [B: $i] : $true )
@ A )
=> ( ( subset
@ ^ [B: $i] : $true
@ ( rel_domain @ A ) )
& ( ( ^ [B: $i] : $true )
= ( rel_codomain @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ! [B: $i,C: $i] :
( ( B = C )
=> ( A @ B @ C ) )
=> ( ! [B: $i] :
? [C: $i] : ( A @ B @ C )
& ( ( ^ [B: $i] : $true )
= ( ^ [B: $i] :
? [C: $i] : ( A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( sk1 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( sk1 @ A @ B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(9,plain,
! [A: $i] : ( sk1 @ A @ A ),
inference(simp,[status(thm)],[8]) ).
thf(4,plain,
! [A: $i] :
( ~ ( sk1 @ sk2 @ A )
| ( ( ^ [B: $i] : $true )
!= ( ^ [B: $i] :
? [C: $i] : ( sk1 @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [A: $i] :
( ( ( ^ [B: $i] :
? [C: $i] : ( sk1 @ C @ B ) )
!= ( ^ [B: $i] : $true ) )
| ~ ( sk1 @ sk2 @ A ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
! [A: $i] :
( ( ( ^ [B: $i] :
? [C: $i] : ( sk1 @ C @ B ) )
!= ( ^ [B: $i] : $true ) )
| ~ ( sk1 @ sk2 @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i] :
? [D: $i] : ( sk1 @ D @ C ) )
!= ( ^ [C: $i] : $true ) )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,7]) ).
thf(12,plain,
( ( ^ [A: $i] :
? [B: $i] : ( sk1 @ B @ A ) )
!= ( ^ [A: $i] : $true ) ),
inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(14,plain,
~ ? [A: $i] : ( sk1 @ A @ sk4 ),
inference(func_ext,[status(esa)],[12]) ).
thf(15,plain,
! [A: $i] :
~ ( sk1 @ A @ sk4 ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( sk1 @ A @ A )
!= ( sk1 @ B @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[9,15]) ).
thf(17,plain,
$false,
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET669^3 : TPTP v8.1.2. Released v3.6.0.
% 0.14/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 6 20:32:09 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.81/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.02 % [INFO] Parsing done (192ms).
% 1.20/1.03 % [INFO] Running in sequential loop mode.
% 1.88/1.36 % [INFO] nitpick registered as external prover.
% 1.99/1.36 % [INFO] Scanning for conjecture ...
% 2.31/1.50 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.31/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.31/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.46/1.53 % [INFO] Type checking passed.
% 2.46/1.54 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.14/1.97 % [INFO] Killing All external provers ...
% 3.32/1.98 % Time passed: 1506ms (effective reasoning time: 944ms)
% 3.32/1.98 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.32/1.98 % Axioms used in derivation (0):
% 3.32/1.98 % No. of inferences in proof: 15
% 3.32/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1506 ms resp. 944 ms w/o parsing
% 3.32/2.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.32/2.03 % [INFO] Killing All external provers ...
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