TSTP Solution File: SET626+3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 10:50:10 EDT 2024
% Result : Theorem 277.28s 47.73s
% Output : Refutation 277.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 9 unt; 7 typ; 0 def)
% Number of atoms : 92 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 306 ( 20 ~; 16 |; 14 &; 240 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 0 ^ 64 !; 6 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(intersect_type,type,
intersect: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( intersect @ A @ ( intersection @ B @ C ) )
=> ( intersect @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th102) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( intersect @ A @ ( intersection @ B @ C ) )
=> ( intersect @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( intersect @ A @ ( intersection @ B @ C ) )
=> ( intersect @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
~ ! [A: $i,B: $i] :
( ? [C: $i] : ( intersect @ A @ ( intersection @ B @ C ) )
=> ( intersect @ A @ B ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(11,plain,
intersect @ sk1 @ ( intersection @ sk2 @ sk3 ),
inference(cnf,[status(esa)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
<=> ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ( intersect @ A @ B )
=> ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( intersect @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
( ! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ? [C: $i] :
( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( intersect @ A @ B ) ) ),
inference(miniscope,[status(thm)],[18]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( intersect @ A @ B )
| ( member @ ( sk4 @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[19]) ).
thf(1561,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ B )
| ( ( intersect @ sk1 @ ( intersection @ sk2 @ sk3 ) )
!= ( intersect @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,22]) ).
thf(1562,plain,
member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ ( intersection @ sk2 @ sk3 ),
inference(pattern_uni,[status(thm)],[1561:[bind(A,$thf( sk1 )),bind(B,$thf( intersection @ sk2 @ sk3 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
<=> ( ( member @ C @ A )
& ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
thf(12,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( intersection @ A @ B ) )
=> ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( intersection @ A @ B ) )
=> ( ( member @ C @ A )
& ( member @ C @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ A )
& ( member @ C @ B ) )
=> ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ ( intersection @ A @ B ) )
| ( member @ C @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(2809,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ A )
| ( ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ ( intersection @ sk2 @ sk3 ) )
!= ( member @ C @ ( intersection @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1562,15]) ).
thf(2810,plain,
member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ sk2,
inference(pattern_uni,[status(thm)],[2809:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ))]]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( intersect @ A @ B )
| ( member @ ( sk4 @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[19]) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ( member @ ( sk4 @ B @ A ) @ A )
| ( ( intersect @ sk1 @ ( intersection @ sk2 @ sk3 ) )
!= ( intersect @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,21]) ).
thf(1174,plain,
member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ sk1,
inference(pattern_uni,[status(thm)],[1173:[bind(A,$thf( sk1 )),bind(B,$thf( intersection @ sk2 @ sk3 ))]]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( intersect @ A @ B ) ),
inference(cnf,[status(esa)],[19]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ~ ( member @ C @ B )
| ( intersect @ A @ B ) ),
inference(simp,[status(thm)],[20]) ).
thf(1349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( intersect @ A @ B )
| ( ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ sk1 )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1174,23]) ).
thf(1350,plain,
! [A: $i] :
( ~ ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ A )
| ( intersect @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1349:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ))]]) ).
thf(127429,plain,
! [A: $i] :
( ( intersect @ A @ sk1 )
| ( ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ sk2 )
!= ( member @ ( sk4 @ ( intersection @ sk2 @ sk3 ) @ sk1 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2810,1350]) ).
thf(127430,plain,
intersect @ sk2 @ sk1,
inference(pattern_uni,[status(thm)],[127429:[bind(A,$thf( sk2 ))]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ( intersect @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( intersect @ A @ B )
=> ( intersect @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( intersect @ A @ B )
| ( intersect @ B @ A ) ),
inference(cnf,[status(esa)],[27]) ).
thf(127946,plain,
! [B: $i,A: $i] :
( ( intersect @ B @ A )
| ( ( intersect @ sk2 @ sk1 )
!= ( intersect @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[127430,28]) ).
thf(127947,plain,
intersect @ sk1 @ sk2,
inference(pattern_uni,[status(thm)],[127946:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(10,plain,
~ ( intersect @ sk1 @ sk2 ),
inference(cnf,[status(esa)],[9]) ).
thf(128252,plain,
$false,
inference(rewrite,[status(thm)],[127947,10]) ).
thf(128253,plain,
$false,
inference(simp,[status(thm)],[128252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.11 % Command : run_Leo-III %s %d
% 0.10/0.32 % Computer : n028.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon May 6 20:52:24 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.07 % [INFO] Parsing done (154ms).
% 1.19/1.08 % [INFO] Running in sequential loop mode.
% 1.76/1.39 % [INFO] nitpick registered as external prover.
% 1.76/1.40 % [INFO] Scanning for conjecture ...
% 1.91/1.48 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.96/1.51 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.05/1.53 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/1.54 % [INFO] Type checking passed.
% 2.10/1.54 % [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 ...
% 277.28/47.73 % [INFO] Killing All external provers ...
% 277.28/47.73 % Time passed: 47259ms (effective reasoning time: 46646ms)
% 277.28/47.73 % 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)>
% 277.28/47.73 % Axioms used in derivation (3): intersect_defn, intersection_defn, symmetry_of_intersect
% 277.28/47.73 % No. of inferences in proof: 34
% 277.28/47.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 47259 ms resp. 46646 ms w/o parsing
% 277.28/47.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 277.28/47.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------