TSTP Solution File: SET619+3 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET619+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 03:06:31 EDT 2024
% Result : Theorem 93.72s 14.56s
% Output : Refutation 93.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 39 unt; 6 typ; 0 def)
% Number of atoms : 60 ( 59 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 380 ( 32 ~; 12 |; 0 &; 336 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 0 ^ 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_type,type,
union: $i > $i > $i ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_difference) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[29]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( union @ ( union @ A @ B ) @ C )
= ( union @ A @ ( union @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).
thf(22,plain,
! [A: $i,B: $i,C: $i] :
( ( union @ ( union @ A @ B ) @ C )
= ( union @ A @ ( union @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( union @ ( union @ A @ B ) @ C )
= ( union @ A @ ( union @ B @ C ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( union @ ( union @ A @ B ) @ C )
= ( union @ A @ ( union @ B @ C ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ ( symmetric_difference @ A @ B ) @ ( intersection @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th95) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ ( symmetric_difference @ A @ B ) @ ( intersection @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ ( symmetric_difference @ A @ B ) @ ( intersection @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
( ( union @ sk1 @ sk2 )
!= ( union @ ( symmetric_difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
( ( union @ ( symmetric_difference @ sk1 @ sk2 ) @ ( intersection @ sk1 @ sk2 ) )
!= ( union @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( union @ ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) @ ( intersection @ sk1 @ sk2 ) )
!= ( union @ sk1 @ sk2 ) )
| ( ( symmetric_difference @ A @ B )
!= ( symmetric_difference @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[21,18]) ).
thf(257,plain,
( ( union @ ( union @ ( difference @ sk1 @ sk2 ) @ ( difference @ sk2 @ sk1 ) ) @ ( intersection @ sk1 @ sk2 ) )
!= ( union @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(724,plain,
( ( union @ ( difference @ sk1 @ sk2 ) @ ( union @ ( difference @ sk2 @ sk1 ) @ ( intersection @ sk1 @ sk2 ) ) )
!= ( union @ sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[257,24]) ).
thf(862,plain,
! [B: $i,A: $i] :
( ( ( union @ B @ A )
!= ( union @ sk1 @ sk2 ) )
| ( ( union @ A @ B )
!= ( union @ ( difference @ sk1 @ sk2 ) @ ( union @ ( difference @ sk2 @ sk1 ) @ ( intersection @ sk1 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,724]) ).
thf(863,plain,
( ( union @ ( union @ ( difference @ sk2 @ sk1 ) @ ( intersection @ sk1 @ sk2 ) ) @ ( difference @ sk1 @ sk2 ) )
!= ( union @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[862:[bind(A,$thf( difference @ sk1 @ sk2 )),bind(B,$thf( union @ ( difference @ sk2 @ sk1 ) @ ( intersection @ sk1 @ sk2 ) ))]]) ).
thf(907,plain,
( ( union @ ( difference @ sk2 @ sk1 ) @ ( union @ ( intersection @ sk1 @ sk2 ) @ ( difference @ sk1 @ sk2 ) ) )
!= ( union @ sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[863,24]) ).
thf(1330,plain,
( ( union @ ( difference @ sk2 @ sk1 ) @ sk1 )
!= ( union @ sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[907,30]) ).
thf(1468,plain,
! [B: $i,A: $i] :
( ( ( union @ B @ A )
!= ( union @ sk1 @ sk2 ) )
| ( ( union @ A @ B )
!= ( union @ ( difference @ sk2 @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[57,1330]) ).
thf(1469,plain,
( ( union @ sk1 @ ( difference @ sk2 @ sk1 ) )
!= ( union @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1468:[bind(A,$thf( difference @ sk2 @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ( ( union @ A @ ( union @ B @ C ) )
!= ( union @ sk1 @ sk2 ) )
| ( ( union @ ( union @ A @ B ) @ C )
!= ( union @ sk1 @ ( difference @ sk2 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,1469]) ).
thf(1526,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk1 )
| ( ( union @ B @ C )
!= sk2 )
| ( ( union @ A @ B )
!= sk1 )
| ( C
!= ( difference @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[1495]) ).
thf(1537,plain,
! [A: $i] :
( ( ( union @ A @ ( difference @ sk2 @ sk1 ) )
!= sk2 )
| ( ( union @ sk1 @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[1526]) ).
thf(18954,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk2 )
| ( ( union @ sk1 @ C )
!= sk1 )
| ( ( union @ ( intersection @ A @ B ) @ ( difference @ A @ B ) )
!= ( union @ C @ ( difference @ sk2 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,1537]) ).
thf(18955,plain,
( ( sk2 != sk2 )
| ( ( union @ sk1 @ ( intersection @ sk2 @ sk1 ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[18954:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( intersection @ sk2 @ sk1 ))]]) ).
thf(18989,plain,
( ( union @ sk1 @ ( intersection @ sk2 @ sk1 ) )
!= sk1 ),
inference(simp,[status(thm)],[18955]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( union @ A @ ( intersection @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( union @ A @ ( intersection @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( union @ A @ ( intersection @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( union @ A @ ( intersection @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[26]) ).
thf(631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( union @ C @ ( intersection @ B @ A ) )
= C )
| ( ( intersection @ A @ B )
!= ( intersection @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[60,27]) ).
thf(632,plain,
! [B: $i,A: $i] :
( ( union @ A @ ( intersection @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[631:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(19575,plain,
sk1 != sk1,
inference(rewrite,[status(thm)],[18989,632]) ).
thf(19576,plain,
$false,
inference(simp,[status(thm)],[19575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET619+3 : TPTP v8.2.0. Released v2.2.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 12:47:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.01/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.15 % [INFO] Parsing done (167ms).
% 1.28/1.17 % [INFO] Running in sequential loop mode.
% 1.98/1.54 % [INFO] nitpick registered as external prover.
% 1.98/1.54 % [INFO] Scanning for conjecture ...
% 2.13/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.13/1.67 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.28/1.71 % [INFO] Problem is first-order (TPTP FOF).
% 2.28/1.71 % [INFO] Type checking passed.
% 2.28/1.72 % [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 ...
% 93.72/14.55 % [INFO] Killing All external provers ...
% 93.72/14.55 % Time passed: 14052ms (effective reasoning time: 13374ms)
% 93.72/14.55 % 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)>
% 93.72/14.56 % Axioms used in derivation (6): union_intersection, associativity_of_union, union_intersection_difference, symmetric_difference_defn, commutativity_of_intersection, commutativity_of_union
% 93.72/14.56 % No. of inferences in proof: 48
% 93.72/14.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14052 ms resp. 13374 ms w/o parsing
% 93.72/14.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 93.72/14.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------