TSTP Solution File: SEU631^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU631^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 03:43:04 EDT 2024
% Result : Theorem 5.87s 2.33s
% Output : Refutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 35 ( 10 unt; 14 typ; 3 def)
% Number of atoms : 61 ( 18 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 306 ( 20 ~; 12 |; 16 &; 250 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 53 ( 8 ^ 29 !; 16 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(kpair_def,definition,
( kpair
= ( ^ [A: $i,B: $i] : ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(cartprod_def,definition,
( cartprod
= ( ^ [A: $i,B: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
@ ^ [C: $i] :
? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) ) ) ) ).
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(sk5_type,type,
sk5: $i ).
thf(1,conjecture,
( dsetconstrER
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ A )
& ? [F: $i] :
( ( in @ F @ B )
& ( D
= ( setadjoin @ ( setadjoin @ E @ emptyset ) @ ( setadjoin @ ( setadjoin @ E @ ( setadjoin @ F @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( setadjoin @ ( setadjoin @ D @ emptyset ) @ ( setadjoin @ ( setadjoin @ D @ ( setadjoin @ E @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( in @ sk3
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) )
@ ^ [A: $i] :
? [B: $i] :
( ( in @ B @ sk1 )
& ? [C: $i] :
( ( in @ C @ sk2 )
& ( A
= ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk3
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ sk1 )
& ? [F: $i] :
( ( in @ F @ sk2 )
& ( D
= ( setadjoin @ ( setadjoin @ E @ emptyset ) @ ( setadjoin @ ( setadjoin @ E @ ( setadjoin @ F @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(10,plain,
? [A: $i] :
( ( in @ A @ sk1 )
& ? [B: $i] :
( ( in @ B @ sk2 )
& ( sk3
= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(pattern_uni,[status(thm)],[9:[bind(A,$thf( powerset @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) )),bind(B,$thf( ^ [D: $i] : ? [E: $i] : ( ( in @ E @ sk1 ) & ? [F: $i] : ( ( in @ F @ sk2 ) & ( D = ( setadjoin @ ( setadjoin @ E @ emptyset ) @ ( setadjoin @ ( setadjoin @ E @ ( setadjoin @ F @ emptyset ) ) @ emptyset ) ) ) ) ) )),bind(C,$thf( sk3 ))]]) ).
thf(25,plain,
( sk3
= ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(28,plain,
( ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) )
= sk3 ),
inference(lifteq,[status(thm)],[25]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ B @ sk2 )
| ( sk3
!= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
!= sk3 )
| ~ ( in @ A @ sk1 )
| ~ ( in @ B @ sk2 ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
!= sk3 )
| ~ ( in @ A @ sk1 )
| ~ ( in @ B @ sk2 ) ),
inference(simp,[status(thm)],[7]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ B @ sk2 )
| ( ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,8]) ).
thf(104,plain,
( ~ ( in @ sk4 @ sk1 )
| ~ ( in @ sk5 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(26,plain,
in @ sk5 @ sk2,
inference(cnf,[status(esa)],[10]) ).
thf(27,plain,
in @ sk4 @ sk1,
inference(cnf,[status(esa)],[10]) ).
thf(189,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[104,26,27]) ).
thf(190,plain,
$false,
inference(simp,[status(thm)],[189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU631^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 17:30:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (113ms).
% 1.17/0.99 % [INFO] Running in sequential loop mode.
% 1.75/1.22 % [INFO] nitpick registered as external prover.
% 1.75/1.22 % [INFO] Scanning for conjecture ...
% 1.88/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.88/1.32 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.88/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.88/1.33 % [INFO] Type checking passed.
% 1.88/1.33 % [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 ...
% 5.87/2.32 % [INFO] Killing All external provers ...
% 5.87/2.33 % Time passed: 1797ms (effective reasoning time: 1332ms)
% 5.87/2.33 % 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)>
% 5.87/2.33 % Axioms used in derivation (0):
% 5.87/2.33 % No. of inferences in proof: 18
% 5.87/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1797 ms resp. 1332 ms w/o parsing
% 5.87/2.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.87/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------