TSTP Solution File: SEU728^2 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU728^2 : 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 03:43:32 EDT 2024
% Result : Theorem 4.41s 2.36s
% Output : Refutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 28 ( 9 unt; 8 typ; 2 def)
% Number of atoms : 61 ( 5 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 195 ( 17 ~; 10 |; 0 &; 147 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 ^ 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
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(setminusER_type,type,
setminusER: $o ).
thf(setminusER_def,definition,
( setminusER
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setminus @ A @ B ) )
=> ~ ( in @ C @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( setminusI
=> ( setminusER
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) )
=> ( in @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(2,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) )
=> ( in @ C @ 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,C: $i] :
( ( in @ C @ ( setminus @ A @ B ) )
=> ~ ( in @ C @ B ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ ( setminus @ A @ ( setminus @ A @ B ) ) )
=> ( in @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
in @ sk3 @ sk1,
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) )
| ( ( in @ sk3 @ sk1 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,5]) ).
thf(52,plain,
! [A: $i] :
( ( in @ sk3 @ A )
| ( in @ sk3 @ ( setminus @ sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(65,plain,
! [A: $i] :
( ( in @ sk3 @ A )
| ( in @ sk3 @ ( setminus @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(9,plain,
in @ sk3 @ ( setminus @ sk1 @ ( setminus @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setminus @ A @ B ) )
| ~ ( in @ C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setminus @ A @ B ) )
| ~ ( in @ C @ B ) ),
inference(simp,[status(thm)],[8]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ sk3 @ ( setminus @ sk1 @ ( setminus @ sk1 @ sk2 ) ) )
!= ( in @ C @ ( setminus @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,10]) ).
thf(31,plain,
~ ( in @ sk3 @ ( setminus @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk1 )),bind(B,$thf( setminus @ sk1 @ sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(91,plain,
! [A: $i] :
( ( in @ sk3 @ A )
| ( ( in @ sk3 @ ( setminus @ sk1 @ A ) )
!= ( in @ sk3 @ ( setminus @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,31]) ).
thf(92,plain,
in @ sk3 @ sk2,
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( sk2 ))]]) ).
thf(4,plain,
~ ( in @ sk3 @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
thf(102,plain,
$false,
inference(rewrite,[status(thm)],[92,4]) ).
thf(103,plain,
$false,
inference(simp,[status(thm)],[102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU728^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n011.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 17:16:39 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.86/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.06 % [INFO] Parsing done (163ms).
% 1.29/1.08 % [INFO] Running in sequential loop mode.
% 1.78/1.42 % [INFO] nitpick registered as external prover.
% 1.78/1.43 % [INFO] Scanning for conjecture ...
% 2.00/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.00/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.00/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.00/1.56 % [INFO] Type checking passed.
% 2.00/1.56 % [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 ...
% 4.41/2.36 % [INFO] Killing All external provers ...
% 4.41/2.36 % Time passed: 1911ms (effective reasoning time: 1276ms)
% 4.41/2.36 % 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)>
% 4.41/2.36 % Axioms used in derivation (0):
% 4.41/2.36 % No. of inferences in proof: 18
% 4.41/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1911 ms resp. 1276 ms w/o parsing
% 4.41/2.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.41/2.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------