TSTP Solution File: SET622+3 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET622+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 21 03:06:32 EDT 2024
% Result : Theorem 5.90s 2.37s
% Output : Refutation 5.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 29 ( 21 unt; 7 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 246 ( 9 ~; 1 |; 0 &; 236 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 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 : 43 ( 0 ^ 43 !; 0 ?; 43 :)
% Comments :
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thf(difference_type,type,
difference: $i > $i > $i ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( symmetric_difference @ A @ B )
= ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( symmetric_difference @ A @ B )
= ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( symmetric_difference @ B @ C ) )
= ( union @ ( difference @ A @ ( union @ B @ C ) ) @ ( intersection @ ( intersection @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( symmetric_difference @ B @ C ) )
= ( union @ ( difference @ A @ ( union @ B @ C ) ) @ ( intersection @ ( intersection @ A @ B ) @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( symmetric_difference @ B @ C ) )
= ( union @ ( difference @ A @ ( union @ B @ C ) ) @ ( intersection @ ( intersection @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
( ( difference @ sk1 @ ( symmetric_difference @ sk2 @ sk3 ) )
!= ( union @ ( difference @ sk1 @ ( union @ sk2 @ sk3 ) ) @ ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
( ( union @ ( difference @ sk1 @ ( union @ sk2 @ sk3 ) ) @ ( intersection @ ( intersection @ sk1 @ sk2 ) @ sk3 ) )
!= ( difference @ sk1 @ ( symmetric_difference @ sk2 @ sk3 ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
thf(20,plain,
! [A: $i,B: $i,C: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( intersection @ ( intersection @ A @ B ) @ C )
= ( intersection @ A @ ( intersection @ B @ C ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(122,plain,
( ( union @ ( difference @ sk1 @ ( union @ sk2 @ sk3 ) ) @ ( intersection @ sk1 @ ( intersection @ sk2 @ sk3 ) ) )
!= ( difference @ sk1 @ ( symmetric_difference @ sk2 @ sk3 ) ) ),
inference(rewrite,[status(thm)],[19,22]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( difference @ B @ C ) )
= ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).
thf(23,plain,
! [A: $i,B: $i,C: $i] :
( ( difference @ A @ ( difference @ B @ C ) )
= ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ ( difference @ B @ C ) )
= ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( union @ ( difference @ A @ B ) @ ( intersection @ A @ C ) )
= ( difference @ A @ ( difference @ B @ C ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(334,plain,
( ( difference @ sk1 @ ( difference @ ( union @ sk2 @ sk3 ) @ ( intersection @ sk2 @ sk3 ) ) )
!= ( difference @ sk1 @ ( symmetric_difference @ sk2 @ sk3 ) ) ),
inference(rewrite,[status(thm)],[122,25]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( ( difference @ sk1 @ ( difference @ ( union @ A @ B ) @ ( intersection @ A @ B ) ) )
!= ( difference @ sk1 @ ( difference @ ( union @ sk2 @ sk3 ) @ ( intersection @ sk2 @ sk3 ) ) ) )
| ( ( symmetric_difference @ A @ B )
!= ( symmetric_difference @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[28,334]) ).
thf(390,plain,
( ( difference @ sk1 @ ( difference @ ( union @ sk2 @ sk3 ) @ ( intersection @ sk2 @ sk3 ) ) )
!= ( difference @ sk1 @ ( difference @ ( union @ sk2 @ sk3 ) @ ( intersection @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(415,plain,
$false,
inference(simp,[status(thm)],[390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET622+3 : TPTP v8.2.0. Released v2.2.0.
% 0.08/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n026.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 : Mon May 20 11:34:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.94/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.04 % [INFO] Parsing done (130ms).
% 1.25/1.05 % [INFO] Running in sequential loop mode.
% 1.75/1.27 % [INFO] nitpick registered as external prover.
% 1.75/1.27 % [INFO] Scanning for conjecture ...
% 1.86/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.03/1.36 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.10/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/1.39 % [INFO] Type checking passed.
% 2.10/1.39 % [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 ...
% 5.90/2.36 % [INFO] Killing All external provers ...
% 5.90/2.37 % Time passed: 1837ms (effective reasoning time: 1313ms)
% 5.90/2.37 % 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)>
% 5.90/2.37 % Axioms used in derivation (3): symmetric_difference_and_difference, associativity_of_intersection, difference_difference_union2
% 5.90/2.37 % No. of inferences in proof: 22
% 5.90/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1837 ms resp. 1313 ms w/o parsing
% 5.90/2.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.90/2.40 % [INFO] Killing All external provers ...
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