TSTP Solution File: SEU752^2 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU752^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 03:43:38 EDT 2024
% Result : Theorem 178.94s 25.89s
% Output : Refutation 178.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 65 ( 14 unt; 14 typ; 5 def)
% Number of atoms : 212 ( 16 equ; 0 cnn)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 740 ( 91 ~; 78 |; 0 &; 520 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 112 ( 0 ^ 112 !; 0 ?; 112 :)
% 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(binunionE_type,type,
binunionE: $o ).
thf(binunionE_def,definition,
( binunionE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) ) ) ) ).
thf(binintersect_type,type,
binintersect: $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(binintersectTELcontra_type,type,
binintersectTELcontra: $o ).
thf(binintersectTELcontra_def,definition,
( binintersectTELcontra
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ B )
=> ~ ( in @ D @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ).
thf(binintersectTERcontra_type,type,
binintersectTERcontra: $o ).
thf(binintersectTERcontra_def,definition,
( binintersectTERcontra
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ C )
=> ~ ( in @ D @ ( binintersect @ 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,
( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) )
=> ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1b) ).
thf(2,negated_conjecture,
~ ( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) )
=> ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) )
=> ( ! [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 @ ( binintersect @ B @ C ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ ( in @ D @ C )
=> ~ ( in @ D @ ( binintersect @ B @ C ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( binunion @ ( setminus @ A @ B ) @ ( setminus @ A @ C ) ) )
=> ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
in @ sk4 @ sk1,
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) )
| ( ( in @ sk4 @ sk1 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,16]) ).
thf(503,plain,
! [A: $i] :
( ( in @ sk4 @ A )
| ( in @ sk4 @ ( setminus @ sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[502:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(537,plain,
! [A: $i] :
( ( in @ sk4 @ A )
| ( in @ sk4 @ ( setminus @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[503]) ).
thf(4,plain,
~ ( in @ sk4 @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(619,plain,
! [A: $i] :
( ( in @ sk4 @ A )
| ( ( in @ sk4 @ ( setminus @ sk1 @ A ) )
!= ( in @ sk4 @ ( setminus @ sk1 @ ( binintersect @ sk2 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[537,4]) ).
thf(620,plain,
in @ sk4 @ ( binintersect @ sk2 @ sk3 ),
inference(pattern_uni,[status(thm)],[619:[bind(A,$thf( binintersect @ sk2 @ sk3 ))]]) ).
thf(7,plain,
in @ sk2 @ ( powerset @ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(6,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 @ ( binintersect @ B @ C ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,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 @ ( binintersect @ B @ C ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( powerset @ A ) )
| ~ ( in @ D @ A )
| ( in @ D @ C )
| ~ ( in @ D @ ( binintersect @ B @ C ) )
| ( ( in @ sk2 @ ( powerset @ sk1 ) )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,15]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk1 ) )
| ~ ( in @ B @ sk1 )
| ( in @ B @ A )
| ~ ( in @ B @ ( binintersect @ sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk1 ) )
| ~ ( in @ B @ sk1 )
| ( in @ B @ A )
| ~ ( in @ B @ ( binintersect @ sk2 @ A ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(33890,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk1 ) )
| ~ ( in @ B @ sk1 )
| ( in @ B @ A )
| ( ( in @ sk4 @ ( binintersect @ sk2 @ sk3 ) )
!= ( in @ B @ ( binintersect @ sk2 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[620,307]) ).
thf(33891,plain,
( ~ ( in @ sk3 @ ( powerset @ sk1 ) )
| ~ ( in @ sk4 @ sk1 )
| ( in @ sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[33890:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(11,plain,
in @ sk4 @ ( binunion @ ( setminus @ sk1 @ sk2 ) @ ( setminus @ sk1 @ sk3 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| ( ( in @ sk4 @ ( binunion @ ( setminus @ sk1 @ sk2 ) @ ( setminus @ sk1 @ sk3 ) ) )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,5]) ).
thf(31,plain,
( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
| ( in @ sk4 @ ( setminus @ sk1 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( setminus @ sk1 @ sk2 )),bind(B,$thf( setminus @ sk1 @ sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setminus @ A @ B ) )
| ~ ( in @ C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setminus @ A @ B ) )
| ~ ( in @ C @ B ) ),
inference(simp,[status(thm)],[12]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
| ~ ( in @ C @ B )
| ( ( in @ sk4 @ ( setminus @ sk1 @ sk3 ) )
!= ( in @ C @ ( setminus @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,17]) ).
thf(73,plain,
( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
| ~ ( in @ sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(372,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ sk4 @ sk3 )
| ~ ( in @ C @ B )
| ( ( in @ sk4 @ ( setminus @ sk1 @ sk2 ) )
!= ( in @ C @ ( setminus @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,17]) ).
thf(373,plain,
( ~ ( in @ sk4 @ sk3 )
| ~ ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[372:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).
thf(433,plain,
( ~ ( in @ sk4 @ sk2 )
| ( ( in @ sk4 @ sk3 )
!= ( in @ sk4 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[373]) ).
thf(441,plain,
( ~ ( in @ sk4 @ sk2 )
| ( ( in @ sk4 @ sk3 )
!= ( in @ sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[433]) ).
thf(9,plain,
in @ sk3 @ ( powerset @ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(10,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 @ ( binintersect @ 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 @ ( binintersect @ B @ C ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ~ ( in @ D @ A )
| ( in @ D @ B )
| ~ ( in @ D @ ( binintersect @ B @ C ) )
| ( ( in @ sk3 @ ( powerset @ sk1 ) )
!= ( in @ C @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,14]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk1 ) )
| ~ ( in @ B @ sk1 )
| ( in @ B @ A )
| ~ ( in @ B @ ( binintersect @ A @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk1 ) )
| ~ ( in @ B @ sk1 )
| ( in @ B @ A )
| ~ ( in @ B @ ( binintersect @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(21327,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( powerset @ sk1 ) )
| ~ ( in @ B @ sk1 )
| ( in @ B @ A )
| ( ( in @ sk4 @ ( binintersect @ sk2 @ sk3 ) )
!= ( in @ B @ ( binintersect @ A @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[620,195]) ).
thf(21328,plain,
( ~ ( in @ sk2 @ ( powerset @ sk1 ) )
| ~ ( in @ sk4 @ sk1 )
| ( in @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[21327:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(31414,plain,
( ~ $true
| ~ $true
| ( in @ sk4 @ sk2 ) ),
inference(rewrite,[status(thm)],[21328,7,8]) ).
thf(31415,plain,
in @ sk4 @ sk2,
inference(simp,[status(thm)],[31414]) ).
thf(31446,plain,
( ~ $true
| ~ ( in @ sk4 @ sk3 ) ),
inference(rewrite,[status(thm)],[441,31415]) ).
thf(31447,plain,
~ ( in @ sk4 @ sk3 ),
inference(simp,[status(thm)],[31446]) ).
thf(38657,plain,
( ~ $true
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[33891,31447,8,9]) ).
thf(38658,plain,
$false,
inference(simp,[status(thm)],[38657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU752^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 16:06:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 1.05/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.21 % [INFO] Parsing done (195ms).
% 1.38/1.22 % [INFO] Running in sequential loop mode.
% 2.04/1.61 % [INFO] nitpick registered as external prover.
% 2.04/1.61 % [INFO] Scanning for conjecture ...
% 2.44/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.48/1.79 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.48/1.79 % [INFO] Problem is higher-order (TPTP THF).
% 2.48/1.79 % [INFO] Type checking passed.
% 2.48/1.80 % [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 ...
% 178.94/25.88 % [INFO] Killing All external provers ...
% 178.94/25.88 % Time passed: 25380ms (effective reasoning time: 24645ms)
% 178.94/25.88 % 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)>
% 178.94/25.89 % Axioms used in derivation (0):
% 178.94/25.89 % No. of inferences in proof: 46
% 178.94/25.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 25380 ms resp. 24645 ms w/o parsing
% 178.94/25.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 178.94/25.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------