%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU631^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:28:50 AM UTC 2026
% Result : Theorem 8.33s 3.36s
% Output : Refutation 7.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 15 unt; 0 typ; 8 def)
% Number of atoms : 114 ( 38 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 593 ( 33 ~; 20 |; 39 &; 490 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 93 ( 13 ^; 42 !; 33 ?; 93 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_decl,type,
dsetconstrER: $o ).
thf(binunion_decl,type,
binunion: $i > $i > $i ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(cartprod_decl,type,
cartprod: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(kpair_def,definition,
( kpair
= ( ^ [A: $i,B: $i] : ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ).
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_def,definition,
( sk1
= ( @+[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 ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( in @ B
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sk1 @ A ) ) )
@ ^ [C: $i] :
? [D: $i] :
( ( in @ D @ sk1 )
& ? [E: $i] :
( ( in @ E @ A )
& ( C
= ( setadjoin @ ( setadjoin @ D @ emptyset ) @ ( setadjoin @ ( setadjoin @ D @ ( setadjoin @ E @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ? [C: $i] :
( ( in @ C @ sk1 )
& ? [D: $i] :
( ( in @ D @ A )
& ( B
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( in @ A
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) )
@ ^ [B: $i] :
? [C: $i] :
( ( in @ C @ sk1 )
& ? [D: $i] :
( ( in @ D @ sk2 )
& ( B
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ? [B: $i] :
( ( in @ B @ sk1 )
& ? [C: $i] :
( ( in @ C @ sk2 )
& ( A
= ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ( in @ A @ sk1 )
& ? [B: $i] :
( ( in @ B @ sk2 )
& ( sk3
= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ( in @ A @ sk2 )
& ( sk3
= ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ A @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
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(4,plain,
! [E: $i,D: $i,C: $i,B: $i > $o,A: $i] :
( ( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) )
& ( in @ sk3
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sk1 @ sk2 ) ) )
@ ^ [F: $i] :
? [G: $i] :
( ( in @ G @ sk1 )
& ? [H: $i] :
( ( in @ H @ sk2 )
& ( F
= ( setadjoin @ ( setadjoin @ G @ emptyset ) @ ( setadjoin @ ( setadjoin @ G @ ( setadjoin @ H @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
& ( ~ ( in @ D @ sk1 )
| ~ ( in @ E @ sk2 )
| ( sk3
!= ( setadjoin @ ( setadjoin @ D @ emptyset ) @ ( setadjoin @ ( setadjoin @ D @ ( setadjoin @ E @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,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(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ $true
| ( 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)],[6,5]) ).
thf(13,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(simp,[status(thm)],[12]) ).
thf(14,plain,
? [A: $i] :
( ( in @ A @ sk1 )
& ? [B: $i] :
( ( in @ B @ sk2 )
& ( sk3
= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(pattern_uni,[status(thm)],[13:[bind(A,$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(32,plain,
( ( in @ sk4 @ sk1 )
& ( in @ sk5 @ sk2 )
& ( sk3
= ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(35,plain,
( sk3
= ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(36,plain,
( ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) )
= sk3 ),
inference(lifteq,[status(thm)],[35]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ B @ sk2 )
| ( sk3
!= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnfConj,[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(lifteq,[status(thm)],[7]) ).
thf(9,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)],[8]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( sk3 != sk3 )
| ~ ( 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)],[36,9]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ B @ sk2 )
| ( ( setadjoin @ ( setadjoin @ sk4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk4 @ ( setadjoin @ sk5 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(126,plain,
( ~ ( in @ sk4 @ sk1 )
| ~ ( in @ sk5 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(33,plain,
in @ sk4 @ sk1,
inference(cnfConj,[status(thm)],[32]) ).
thf(34,plain,
in @ sk5 @ sk2,
inference(cnfConj,[status(thm)],[32]) ).
thf(227,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[126,33,34]) ).
thf(228,plain,
$false,
inference(simp,[status(thm)],[227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU631^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n008.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:00:09 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.99 % [INFO] Parsing done (204ms).
% 1.18/1.01 % [INFO] Running in sequential loop mode.
% 1.82/1.40 % [INFO] eprover registered as external prover.
% 1.99/1.40 % [INFO] Scanning for conjecture ...
% 2.16/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.16/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.16/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.56 % [INFO] Type checking passed.
% 2.16/1.57 % [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 ...
% 8.33/3.35 % [INFO] Killing All external provers ...
% 8.33/3.36 % Time passed: 3009ms (effective reasoning time: 2339ms)
% 8.33/3.36 % 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)>
% 8.33/3.36 % Axioms used in derivation (0):
% 8.33/3.36 % No. of inferences in proof: 22
% 8.33/3.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3009 ms resp. 2339 ms w/o parsing
% 7.93/3.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.93/3.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------