TSTP Solution File: SEU736^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU736^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 03:43:34 EDT 2024
% Result : Theorem 5.50s 2.30s
% Output : Refutation 5.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 37 ( 10 unt; 10 typ; 2 def)
% Number of atoms : 111 ( 5 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 377 ( 55 ~; 39 |; 0 &; 248 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 49 ( 0 ^ 49 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
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(contrasubsetT_type,type,
contrasubsetT: $o ).
thf(contrasubsetT_def,definition,
( contrasubsetT
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( subset @ B @ ( setminus @ A @ C ) )
=> ( ( in @ D @ C )
=> ~ ( in @ D @ B ) ) ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
( setminusI
=> ( contrasubsetT
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( ( subset @ B @ ( setminus @ A @ C ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ C )
=> ( in @ D @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(2,negated_conjecture,
~ ( setminusI
=> ( contrasubsetT
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( ( subset @ B @ ( setminus @ A @ C ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ C )
=> ( in @ D @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( subset @ B @ ( setminus @ A @ C ) )
=> ( ( in @ D @ C )
=> ~ ( in @ D @ B ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( ( subset @ B @ ( setminus @ A @ C ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ C )
=> ( in @ D @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
in @ sk4 @ sk3,
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
subset @ sk2 @ ( setminus @ sk1 @ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ A ) )
| ~ ( in @ D @ A )
| ~ ( subset @ B @ ( setminus @ A @ C ) )
| ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ A ) )
| ~ ( in @ D @ A )
| ~ ( subset @ B @ ( setminus @ A @ C ) )
| ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ A ) )
| ~ ( in @ D @ A )
| ~ ( in @ D @ C )
| ~ ( in @ D @ B )
| ( ( subset @ sk2 @ ( setminus @ sk1 @ sk3 ) )
!= ( subset @ B @ ( setminus @ A @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,12]) ).
thf(114,plain,
! [A: $i] :
( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
| ~ ( in @ sk3 @ ( powerset @ sk1 ) )
| ~ ( in @ A @ sk1 )
| ~ ( in @ A @ sk3 )
| ~ ( in @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(189,plain,
! [A: $i] :
( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
| ~ ( in @ sk3 @ ( powerset @ sk1 ) )
| ~ ( in @ A @ sk1 )
| ~ ( in @ A @ sk3 )
| ~ ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[114]) ).
thf(8,plain,
in @ sk2 @ ( powerset @ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
in @ sk3 @ ( powerset @ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(193,plain,
! [A: $i] :
( ~ $true
| ~ $true
| ~ ( in @ A @ sk1 )
| ~ ( in @ A @ sk3 )
| ~ ( in @ A @ sk2 ) ),
inference(rewrite,[status(thm)],[189,8,9]) ).
thf(194,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ A @ sk3 )
| ~ ( in @ A @ sk2 ) ),
inference(simp,[status(thm)],[193]) ).
thf(196,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ A @ sk2 )
| ( ( in @ sk4 @ sk3 )
!= ( in @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[10,194]) ).
thf(197,plain,
( ~ ( in @ sk4 @ sk1 )
| ~ ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( sk4 ))]]) ).
thf(4,plain,
in @ sk4 @ sk1,
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
~ ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( ( in @ C @ ( setminus @ A @ B ) )
!= ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,11]) ).
thf(30,plain,
( ~ ( in @ sk4 @ sk1 )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(44,plain,
( ~ $true
| ( in @ sk4 @ sk2 ) ),
inference(rewrite,[status(thm)],[30,4]) ).
thf(45,plain,
in @ sk4 @ sk2,
inference(simp,[status(thm)],[44]) ).
thf(297,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[197,4,45]) ).
thf(298,plain,
$false,
inference(simp,[status(thm)],[297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU736^2 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n002.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun May 19 17:32:24 EDT 2024
% 0.17/0.38 % CPUTime :
% 1.07/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.07 % [INFO] Parsing done (126ms).
% 1.41/1.08 % [INFO] Running in sequential loop mode.
% 1.72/1.31 % [INFO] nitpick registered as external prover.
% 1.72/1.31 % [INFO] Scanning for conjecture ...
% 2.13/1.38 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.13/1.41 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.13/1.41 % [INFO] Problem is higher-order (TPTP THF).
% 2.13/1.41 % [INFO] Type checking passed.
% 2.13/1.41 % [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 ...
% 5.50/2.29 % [INFO] Killing All external provers ...
% 5.50/2.30 % Time passed: 1741ms (effective reasoning time: 1207ms)
% 5.50/2.30 % 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)>
% 5.50/2.30 % Axioms used in derivation (0):
% 5.50/2.30 % No. of inferences in proof: 25
% 5.50/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1741 ms resp. 1207 ms w/o parsing
% 5.50/2.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.50/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------