TSTP Solution File: SET680^3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET680^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 10:50:20 EDT 2024
% Result : Theorem 4.59s 2.44s
% Output : Refutation 4.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 12 unt; 6 typ; 2 def)
% Number of atoms : 53 ( 10 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 134 ( 18 ~; 9 |; 11 &; 88 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 35 ( 6 ^ 20 !; 9 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_rel_on_type,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(is_rel_on_def,definition,
( is_rel_on
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
! [D: $i,E: $i] :
( ( A @ D @ E )
=> ( ( B @ D )
& ( C @ E ) ) ) ) ) ).
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(sk3_type,type,
sk3: $i > $o ).
thf(sk4_type,type,
sk4: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(1,conjecture,
! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
( ( is_rel_on @ A @ B @ C )
=> ! [D: $i] :
( ( B @ D )
=> ( ( rel_domain @ A @ D )
= ( ? [E: $i] :
( ( C @ E )
& ( A @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
( ( is_rel_on @ A @ B @ C )
=> ! [D: $i] :
( ( B @ D )
=> ( ( rel_domain @ A @ D )
= ( ? [E: $i] :
( ( C @ E )
& ( A @ D @ E ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
( ! [D: $i,E: $i] :
( ( A @ D @ E )
=> ( ( B @ D )
& ( C @ E ) ) )
=> ! [D: $i] :
( ( B @ D )
=> ( ( ? [E: $i] : ( A @ D @ E ) )
= ( ? [E: $i] :
( ( C @ E )
& ( A @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [A: $i] : ( sk1 @ sk4 @ A ) )
!= ( ? [A: $i] :
( ( sk3 @ A )
& ( sk1 @ sk4 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
( ( ? [A: $i] :
( ( sk3 @ A )
& ( sk1 @ sk4 @ A ) ) )
!= ( ? [A: $i] : ( sk1 @ sk4 @ A ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(9,plain,
( ( ^ [A: $i] :
( ( sk3 @ A )
& ( sk1 @ sk4 @ A ) ) )
!= ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[8]) ).
thf(15,plain,
( ( ( sk3 @ sk7 )
& ( sk1 @ sk4 @ sk7 ) )
!= ( sk1 @ sk4 @ sk7 ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(17,plain,
( ( ( sk3 @ sk7 )
& ( sk1 @ sk4 @ sk7 ) )
| ( sk1 @ sk4 @ sk7 ) ),
inference(bool_ext,[status(thm)],[15]) ).
thf(20,plain,
( ( sk1 @ sk4 @ sk7 )
| ( sk1 @ sk4 @ sk7 ) ),
inference(cnf,[status(esa)],[17]) ).
thf(22,plain,
sk1 @ sk4 @ sk7,
inference(simp,[status(thm)],[20]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A @ B )
| ( sk3 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( sk3 @ B )
| ( ( sk1 @ sk4 @ sk7 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,7]) ).
thf(77,plain,
sk3 @ sk7,
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( sk4 )),bind(B,$thf( sk7 ))]]) ).
thf(16,plain,
( ~ ( ( sk3 @ sk7 )
& ( sk1 @ sk4 @ sk7 ) )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(bool_ext,[status(thm)],[15]) ).
thf(18,plain,
( ~ ( sk1 @ sk4 @ sk7 )
| ~ ( sk3 @ sk7 )
| ~ ( sk1 @ sk4 @ sk7 ) ),
inference(cnf,[status(esa)],[16]) ).
thf(19,plain,
( ~ ( sk1 @ sk4 @ sk7 )
| ~ ( sk3 @ sk7 ) ),
inference(simp,[status(thm)],[18]) ).
thf(25,plain,
( ~ $true
| ~ ( sk3 @ sk7 ) ),
inference(rewrite,[status(thm)],[19,22]) ).
thf(26,plain,
~ ( sk3 @ sk7 ),
inference(simp,[status(thm)],[25]) ).
thf(78,plain,
$false,
inference(rewrite,[status(thm)],[77,26]) ).
thf(79,plain,
$false,
inference(simp,[status(thm)],[78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET680^3 : TPTP v8.1.2. Released v3.6.0.
% 0.16/0.17 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n022.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.39 % DateTime : Mon May 6 20:31:09 EDT 2024
% 0.16/0.39 % CPUTime :
% 0.92/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.60/1.19 % [INFO] Parsing done (244ms).
% 1.60/1.20 % [INFO] Running in sequential loop mode.
% 2.03/1.54 % [INFO] nitpick registered as external prover.
% 2.15/1.55 % [INFO] Scanning for conjecture ...
% 2.45/1.71 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.45/1.74 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.45/1.74 % [INFO] Problem is higher-order (TPTP THF).
% 2.45/1.75 % [INFO] Type checking passed.
% 2.45/1.75 % [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 ...
% 4.59/2.43 % [INFO] Killing All external provers ...
% 4.59/2.44 % Time passed: 1874ms (effective reasoning time: 1227ms)
% 4.59/2.44 % 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)>
% 4.59/2.44 % Axioms used in derivation (0):
% 4.59/2.44 % No. of inferences in proof: 20
% 4.59/2.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1874 ms resp. 1227 ms w/o parsing
% 4.59/2.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.59/2.48 % [INFO] Killing All external provers ...
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