TSTP Solution File: SEU610^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU610^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 03:42:57 EDT 2024
% Result : Theorem 4.04s 2.13s
% Output : Refutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 42 ( 12 unt; 11 typ; 4 def)
% Number of atoms : 109 ( 24 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 288 ( 21 ~; 20 |; 0 &; 206 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 73 ( 0 ^ 72 !; 1 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetI2_type,type,
subsetI2: $o ).
thf(subsetI2_def,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(setminus_type,type,
setminus: $i > $i > $i ).
thf(setminusI_type,type,
setminusI: $o ).
thf(setminusI_def,definition,
( setminusI
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ B ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ B ) ) ) )
=> ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ B ) ) ) )
=> ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(7,plain,
( ( setminus @ sk2 @ sk3 )
= emptyset ),
inference(cnf,[status(esa)],[4]) ).
thf(14,plain,
( ( setminus @ sk2 @ sk3 )
= emptyset ),
inference(lifteq,[status(thm)],[7]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(10,plain,
~ ( subset @ sk2 @ sk3 ),
inference(cnf,[status(esa)],[4]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( ( subset @ A @ B )
!= ( subset @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(44,plain,
in @ ( sk1 @ sk3 @ sk2 ) @ sk2,
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) )
| ( ( in @ ( sk1 @ sk3 @ sk2 ) @ sk2 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,15]) ).
thf(86,plain,
! [A: $i] :
( ( in @ ( sk1 @ sk3 @ sk2 ) @ A )
| ( in @ ( sk1 @ sk3 @ sk2 ) @ ( setminus @ sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk1 @ sk3 @ sk2 ))]]) ).
thf(94,plain,
! [A: $i] :
( ( in @ ( sk1 @ sk3 @ sk2 ) @ A )
| ( in @ ( sk1 @ sk3 @ sk2 ) @ ( setminus @ sk2 @ A ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(104,plain,
! [A: $i] :
( ( in @ ( sk1 @ sk3 @ sk2 ) @ A )
| ( in @ ( sk1 @ sk3 @ sk2 ) @ emptyset )
| ( ( setminus @ sk2 @ sk3 )
!= ( setminus @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,94]) ).
thf(105,plain,
( ( in @ ( sk1 @ sk3 @ sk2 ) @ sk3 )
| ( in @ ( sk1 @ sk3 @ sk2 ) @ emptyset ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( sk3 ))]]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( ( subset @ A @ B )
!= ( subset @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(50,plain,
~ ( in @ ( sk1 @ sk3 @ sk2 ) @ sk3 ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(6,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnf,[status(esa)],[4]) ).
thf(20,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ( B
!= ( subset @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[6,10]) ).
thf(21,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( A )),bind(B,$thf( subset @ sk2 @ sk3 ))]]) ).
thf(163,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[105,50,21]) ).
thf(164,plain,
$false,
inference(simp,[status(thm)],[163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU610^2 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 17:54:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.97/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.00 % [INFO] Parsing done (108ms).
% 1.18/1.01 % [INFO] Running in sequential loop mode.
% 1.62/1.23 % [INFO] nitpick registered as external prover.
% 1.75/1.23 % [INFO] Scanning for conjecture ...
% 1.99/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.99/1.34 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.99/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 1.99/1.35 % [INFO] Type checking passed.
% 1.99/1.35 % [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 ...
% 4.04/2.13 % [INFO] Killing All external provers ...
% 4.04/2.13 % Time passed: 1579ms (effective reasoning time: 1116ms)
% 4.04/2.13 % 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)>
% 4.04/2.13 % Axioms used in derivation (0):
% 4.04/2.13 % No. of inferences in proof: 27
% 4.04/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1579 ms resp. 1116 ms w/o parsing
% 4.06/2.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.06/2.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------