TSTP Solution File: SET194+3 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET194+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 03:05:40 EDT 2024
% Result : Theorem 8.19s 3.10s
% Output : Refutation 8.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 7 unt; 6 typ; 0 def)
% Number of atoms : 65 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 223 ( 10 ~; 18 |; 4 &; 176 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 ^ 65 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(union_type,type,
union: $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 > $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i] : ( subset @ A @ ( union @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_of_union) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] : ( subset @ A @ ( union @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] : ( subset @ A @ ( union @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
~ ( subset @ sk1 @ ( union @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,plain,
( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( member @ C @ A )
=> ( member @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( member @ ( sk3 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[18]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( member @ ( sk3 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(10,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
( ! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[10]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ C @ A )
| ( member @ C @ ( union @ A @ B ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(89,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ E @ ( union @ C @ D ) )
| ( ( member @ ( sk3 @ B @ A ) @ A )
!= ( member @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,15]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk3 @ B @ C ) @ ( union @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( sk3 @ F @ G ))]]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( member @ ( sk3 @ B @ C ) @ ( union @ C @ A ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk3 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[18]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( sk3 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[20]) ).
thf(509,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( subset @ C @ B )
| ( subset @ D @ E )
| ( ( member @ ( sk3 @ B @ C ) @ ( union @ C @ A ) )
!= ( member @ ( sk3 @ E @ D ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[106,23]) ).
thf(510,plain,
! [B: $i,A: $i] :
( ( subset @ A @ ( union @ A @ B ) )
| ( subset @ A @ ( union @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[509:[bind(A,$thf( G )),bind(B,$thf( union @ F @ G )),bind(C,$thf( F )),bind(D,$thf( F )),bind(E,$thf( union @ F @ G ))]]) ).
thf(526,plain,
! [B: $i,A: $i] : ( subset @ A @ ( union @ A @ B ) ),
inference(simp,[status(thm)],[510]) ).
thf(527,plain,
~ $true,
inference(rewrite,[status(thm)],[9,526]) ).
thf(528,plain,
$false,
inference(simp,[status(thm)],[527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET194+3 : TPTP v8.2.0. Released v2.2.0.
% 0.02/0.12 % Command : run_Leo-III %s %d
% 0.13/0.32 % Computer : n017.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 20 12:21:09 EDT 2024
% 0.13/0.32 % CPUTime :
% 0.98/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.09 % [INFO] Parsing done (150ms).
% 1.27/1.11 % [INFO] Running in sequential loop mode.
% 1.71/1.45 % [INFO] nitpick registered as external prover.
% 1.71/1.46 % [INFO] Scanning for conjecture ...
% 1.98/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.98/1.57 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.98/1.58 % [INFO] Problem is first-order (TPTP FOF).
% 1.98/1.59 % [INFO] Type checking passed.
% 1.98/1.59 % [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 ...
% 8.19/3.09 % [INFO] Killing All external provers ...
% 8.19/3.10 % Time passed: 2618ms (effective reasoning time: 1979ms)
% 8.19/3.10 % 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)>
% 8.19/3.10 % Axioms used in derivation (2): subset_defn, union_defn
% 8.19/3.10 % No. of inferences in proof: 24
% 8.19/3.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2618 ms resp. 1979 ms w/o parsing
% 8.19/3.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.19/3.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------