TSTP Solution File: SEU755^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU755^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 03:43:39 EDT 2024
% Result : Theorem 37.73s 7.19s
% Output : Refutation 38.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 44 ( 13 unt; 11 typ; 3 def)
% Number of atoms : 128 ( 8 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 451 ( 56 ~; 39 |; 0 &; 316 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 66 ( 0 ^ 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(binunion_type,type,
binunion: $i > $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(binunionTEcontra_type,type,
binunionTEcontra: $o ).
thf(binunionTEcontra_def,definition,
( binunionTEcontra
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ B )
=> ( ~ ( in @ D @ C )
=> ~ ( in @ D @ ( binunion @ B @ C ) ) ) ) ) ) ) ) ) ).
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
=> ( setminusER
=> ( binunionTEcontra
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( setminus @ A @ B ) )
=> ( ( in @ D @ ( setminus @ A @ C ) )
=> ( in @ D @ ( setminus @ A @ ( binunion @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2) ).
thf(2,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ( binunionTEcontra
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( setminus @ A @ B ) )
=> ( ( in @ D @ ( setminus @ A @ C ) )
=> ( in @ D @ ( setminus @ A @ ( binunion @ B @ C ) ) ) ) ) ) ) ) ) ) ),
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 @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ B )
=> ( ~ ( in @ D @ C )
=> ~ ( in @ D @ ( binunion @ B @ C ) ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( setminus @ A @ B ) )
=> ( ( in @ D @ ( setminus @ A @ C ) )
=> ( in @ D @ ( setminus @ A @ ( binunion @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
in @ sk3 @ ( powerset @ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
~ ( in @ sk4 @ ( setminus @ sk1 @ ( binunion @ sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( ( in @ C @ ( setminus @ A @ B ) )
!= ( in @ sk4 @ ( setminus @ sk1 @ ( binunion @ sk2 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,5]) ).
thf(31,plain,
( ~ ( in @ sk4 @ sk1 )
| ( in @ sk4 @ ( binunion @ sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk1 )),bind(B,$thf( binunion @ sk2 @ sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(9,plain,
in @ sk4 @ sk1,
inference(cnf,[status(esa)],[3]) ).
thf(56,plain,
( ~ $true
| ( in @ sk4 @ ( binunion @ sk2 @ sk3 ) ) ),
inference(rewrite,[status(thm)],[31,9]) ).
thf(57,plain,
in @ sk4 @ ( binunion @ sk2 @ sk3 ),
inference(simp,[status(thm)],[56]) ).
thf(11,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ A ) )
| ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C )
| ~ ( in @ D @ ( binunion @ B @ C ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ A ) )
| ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C )
| ~ ( in @ D @ ( binunion @ B @ C ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ C @ ( powerset @ A ) )
| ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C )
| ( ( in @ sk4 @ ( binunion @ sk2 @ sk3 ) )
!= ( in @ D @ ( binunion @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,14]) ).
thf(232,plain,
! [A: $i] :
( ~ ( in @ sk2 @ ( powerset @ A ) )
| ~ ( in @ sk3 @ ( powerset @ A ) )
| ~ ( in @ sk4 @ A )
| ( in @ sk4 @ sk2 )
| ( in @ sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 )),bind(D,$thf( sk4 ))]]) ).
thf(10,plain,
in @ sk4 @ ( setminus @ sk1 @ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setminus @ A @ B ) )
| ~ ( in @ C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setminus @ A @ B ) )
| ~ ( in @ C @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ sk4 @ ( setminus @ sk1 @ sk3 ) )
!= ( in @ C @ ( setminus @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,13]) ).
thf(83,plain,
~ ( in @ sk4 @ sk3 ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(7,plain,
in @ sk4 @ ( setminus @ sk1 @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
!= ( in @ C @ ( setminus @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,13]) ).
thf(90,plain,
~ ( in @ sk4 @ sk2 ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(2299,plain,
! [A: $i] :
( ~ ( in @ sk2 @ ( powerset @ A ) )
| ~ ( in @ sk3 @ ( powerset @ A ) )
| ~ ( in @ sk4 @ A )
| $false
| $false ),
inference(rewrite,[status(thm)],[232,83,90]) ).
thf(2300,plain,
! [A: $i] :
( ~ ( in @ sk2 @ ( powerset @ A ) )
| ~ ( in @ sk3 @ ( powerset @ A ) )
| ~ ( in @ sk4 @ A ) ),
inference(simp,[status(thm)],[2299]) ).
thf(2331,plain,
! [A: $i] :
( ~ ( in @ sk2 @ ( powerset @ A ) )
| ~ ( in @ sk4 @ A )
| ( ( in @ sk3 @ ( powerset @ sk1 ) )
!= ( in @ sk3 @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,2300]) ).
thf(2332,plain,
( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
| ~ ( in @ sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2331:[bind(A,$thf( sk1 ))]]) ).
thf(4,plain,
in @ sk2 @ ( powerset @ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(2463,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[2332,4,9]) ).
thf(2464,plain,
$false,
inference(simp,[status(thm)],[2463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEU755^2 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.13 % Command : run_Leo-III %s %d
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun May 19 16:05:39 EDT 2024
% 0.13/0.33 % CPUTime :
% 1.07/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/1.21 % [INFO] Parsing done (185ms).
% 1.37/1.22 % [INFO] Running in sequential loop mode.
% 2.01/1.62 % [INFO] nitpick registered as external prover.
% 2.01/1.62 % [INFO] Scanning for conjecture ...
% 2.40/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.40/1.80 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.40/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 2.40/1.80 % [INFO] Type checking passed.
% 2.40/1.81 % [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 ...
% 37.73/7.16 % [INFO] Killing All external provers ...
% 37.73/7.19 % Time passed: 6688ms (effective reasoning time: 5957ms)
% 37.73/7.19 % 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)>
% 37.73/7.19 % Axioms used in derivation (0):
% 37.73/7.19 % No. of inferences in proof: 30
% 37.73/7.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6688 ms resp. 5957 ms w/o parsing
% 38.04/7.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.04/7.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------