%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU780^2 : 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 : n026.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 08:29:17 AM UTC 2026
% Result : Theorem 8.40s 3.16s
% Output : Refutation 8.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 30 ( 16 unt; 0 typ; 10 def)
% Number of atoms : 162 ( 14 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 658 ( 32 ~; 18 |; 50 &; 519 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 115 ( 29 ^; 60 !; 20 ?; 115 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(cartprod_decl,type,
cartprod: $i > $i > $i ).
thf(breln_decl,type,
breln: $i > $i > $i > $o ).
thf(dpsetconstr_decl,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(dpsetconstrER_decl,type,
dpsetconstrER: $o ).
thf(breln1_decl,type,
breln1: $i > $i > $o ).
thf(breln1compset_decl,type,
breln1compset: $i > $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(sk6_decl,type,
sk6: $i ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(dpsetconstrER_def,definition,
( dpsetconstrER
= ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( C @ D @ E ) ) ) ) ).
thf(breln1_def,definition,
( breln1
= ( ^ [A: $i] : ( breln @ A @ A ) ) ) ).
thf(breln1compset_def,definition,
( breln1compset
= ( ^ [A: $i,B: $i,C: $i] :
( dpsetconstr @ A @ A
@ ^ [D: $i,E: $i] :
? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( subset @ B @ ( cartprod @ A @ A ) )
=> ! [C: $i] :
( ( subset @ C @ ( cartprod @ A @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E )
@ ( dpsetconstr @ A @ A
@ ^ [F: $i,G: $i] :
? [H: $i] :
( ( in @ H @ A )
& ( in @ ( kpair @ F @ H ) @ B )
& ( in @ ( kpair @ H @ G ) @ C ) ) ) )
=> ? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( subset @ A @ ( cartprod @ sk1 @ sk1 ) )
=> ! [B: $i] :
( ( subset @ B @ ( cartprod @ sk1 @ sk1 ) )
=> ! [C: $i] :
( ( in @ C @ sk1 )
=> ! [D: $i] :
( ( in @ D @ sk1 )
=> ( ( in @ ( kpair @ C @ D )
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [E: $i,F: $i] :
? [G: $i] :
( ( in @ G @ sk1 )
& ( in @ ( kpair @ E @ G ) @ A )
& ( in @ ( kpair @ G @ F ) @ B ) ) ) )
=> ? [E: $i] :
( ( in @ E @ sk1 )
& ( in @ ( kpair @ C @ E ) @ A )
& ( in @ ( kpair @ E @ D ) @ B ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( subset @ A @ ( cartprod @ sk1 @ sk1 ) )
=> ! [B: $i] :
( ( in @ B @ sk1 )
=> ! [C: $i] :
( ( in @ C @ sk1 )
=> ( ( in @ ( kpair @ B @ C )
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [D: $i,E: $i] :
? [F: $i] :
( ( in @ F @ sk1 )
& ( in @ ( kpair @ D @ F ) @ sk2 )
& ( in @ ( kpair @ F @ E ) @ A ) ) ) )
=> ? [D: $i] :
( ( in @ D @ sk1 )
& ( in @ ( kpair @ B @ D ) @ sk2 )
& ( in @ ( kpair @ D @ C ) @ A ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( in @ A @ sk1 )
=> ! [B: $i] :
( ( in @ B @ sk1 )
=> ( ( in @ ( kpair @ A @ B )
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [C: $i,D: $i] :
? [E: $i] :
( ( in @ E @ sk1 )
& ( in @ ( kpair @ C @ E ) @ sk2 )
& ( in @ ( kpair @ E @ D ) @ sk3 ) ) ) )
=> ? [C: $i] :
( ( in @ C @ sk1 )
& ( in @ ( kpair @ A @ C ) @ sk2 )
& ( in @ ( kpair @ C @ B ) @ sk3 ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( in @ A @ sk1 )
=> ( ( in @ ( kpair @ sk4 @ A )
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [B: $i,C: $i] :
? [D: $i] :
( ( in @ D @ sk1 )
& ( in @ ( kpair @ B @ D ) @ sk2 )
& ( in @ ( kpair @ D @ C ) @ sk3 ) ) ) )
=> ? [B: $i] :
( ( in @ B @ sk1 )
& ( in @ ( kpair @ sk4 @ B ) @ sk2 )
& ( in @ ( kpair @ B @ A ) @ sk3 ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ( in @ A @ sk1 )
& ( in @ ( kpair @ sk4 @ A ) @ sk2 )
& ( in @ ( kpair @ A @ sk5 ) @ sk3 ) ) ) ) ).
thf(1,conjecture,
( dpsetconstrER
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compE) ).
thf(2,negated_conjecture,
~ ( dpsetconstrER
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( C @ D @ E ) )
=> ! [A: $i,B: $i] :
( ( subset @ B @ ( cartprod @ A @ A ) )
=> ! [C: $i] :
( ( subset @ C @ ( cartprod @ A @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E )
@ ( dpsetconstr @ A @ A
@ ^ [F: $i,G: $i] :
? [H: $i] :
( ( in @ H @ A )
& ( in @ ( kpair @ F @ H ) @ B )
& ( in @ ( kpair @ H @ G ) @ C ) ) ) )
=> ? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [F: $i,E: $i,D: $i,C: $i > $i > $o,B: $i,A: $i] :
( ( ~ ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
| ( C @ D @ E ) )
& ( subset @ sk2 @ ( cartprod @ sk1 @ sk1 ) )
& ( subset @ sk3 @ ( cartprod @ sk1 @ sk1 ) )
& ( in @ sk4 @ sk1 )
& ( in @ sk5 @ sk1 )
& ( in @ ( kpair @ sk4 @ sk5 )
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [G: $i,H: $i] :
? [I: $i] :
( ( in @ I @ sk1 )
& ( in @ ( kpair @ G @ I ) @ sk2 )
& ( in @ ( kpair @ I @ H ) @ sk3 ) ) ) )
& ( ~ ( in @ F @ sk1 )
| ~ ( in @ ( kpair @ sk4 @ F ) @ sk2 )
| ~ ( in @ ( kpair @ F @ sk5 ) @ sk3 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
( in @ ( kpair @ sk4 @ sk5 )
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [A: $i,B: $i] :
? [C: $i] :
( ( in @ C @ sk1 )
& ( in @ ( kpair @ A @ C ) @ sk2 )
& ( in @ ( kpair @ C @ B ) @ sk3 ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [E: $i,D: $i,C: $i > $i > $o,B: $i,A: $i] :
( ~ ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
| ( C @ D @ E ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(114,plain,
! [E: $i,D: $i,C: $i > $i > $o,B: $i,A: $i] :
( ~ $true
| ( C @ D @ E )
| ( ( in @ ( kpair @ sk4 @ sk5 )
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [F: $i,G: $i] :
? [H: $i] :
( ( in @ H @ sk1 )
& ( in @ ( kpair @ F @ H ) @ sk2 )
& ( in @ ( kpair @ H @ G ) @ sk3 ) ) ) )
!= ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,9]) ).
thf(115,plain,
! [E: $i,D: $i,C: $i > $i > $o,B: $i,A: $i] :
( ( C @ D @ E )
| ( ( in @ ( kpair @ sk4 @ sk5 )
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [F: $i,G: $i] :
? [H: $i] :
( ( in @ H @ sk1 )
& ( in @ ( kpair @ F @ H ) @ sk2 )
& ( in @ ( kpair @ H @ G ) @ sk3 ) ) ) )
!= ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
? [A: $i] :
( ( in @ A @ sk1 )
& ( in @ ( kpair @ sk4 @ A ) @ sk2 )
& ( in @ ( kpair @ A @ sk5 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( ^ [F: $i] : ^ [G: $i] : ? [H: $i] : ( ( in @ H @ sk1 ) & ( in @ ( kpair @ F @ H ) @ sk2 ) & ( in @ ( kpair @ H @ G ) @ sk3 ) ) )),bind(D,$thf( sk4 )),bind(E,$thf( sk5 ))]]) ).
thf(217,plain,
( ( in @ sk6 @ sk1 )
& ( in @ ( kpair @ sk4 @ sk6 ) @ sk2 )
& ( in @ ( kpair @ sk6 @ sk5 ) @ sk3 ) ),
inference(cnf,[status(esa)],[116]) ).
thf(219,plain,
in @ ( kpair @ sk4 @ sk6 ) @ sk2,
inference(cnfConj,[status(thm)],[217]) ).
thf(10,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ ( kpair @ sk4 @ A ) @ sk2 )
| ~ ( in @ ( kpair @ A @ sk5 ) @ sk3 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ ( kpair @ sk4 @ A ) @ sk2 )
| ~ ( in @ ( kpair @ A @ sk5 ) @ sk3 ) ),
inference(simp,[status(thm)],[10]) ).
thf(260,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ~ $true
| ~ ( in @ ( kpair @ A @ sk5 ) @ sk3 )
| ( ( in @ ( kpair @ sk4 @ sk6 ) @ sk2 )
!= ( in @ ( kpair @ sk4 @ A ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[219,12]) ).
thf(261,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ ( kpair @ A @ sk5 ) @ sk3 )
| ( ( in @ ( kpair @ sk4 @ sk6 ) @ sk2 )
!= ( in @ ( kpair @ sk4 @ A ) @ sk2 ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(262,plain,
( ~ ( in @ sk6 @ sk1 )
| ~ ( in @ ( kpair @ sk6 @ sk5 ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( sk6 ))]]) ).
thf(218,plain,
in @ sk6 @ sk1,
inference(cnfConj,[status(thm)],[217]) ).
thf(220,plain,
in @ ( kpair @ sk6 @ sk5 ) @ sk3,
inference(cnfConj,[status(thm)],[217]) ).
thf(340,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[262,218,220]) ).
thf(341,plain,
$false,
inference(simp,[status(thm)],[340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU780^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.21 % Computer : n026.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 14:30:57 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (207ms).
% 1.24/1.02 % [INFO] Running in sequential loop mode.
% 2.11/1.43 % [INFO] eprover registered as external prover.
% 2.11/1.44 % [INFO] Scanning for conjecture ...
% 2.31/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.49/1.61 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.49/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.49/1.61 % [INFO] Type checking passed.
% 2.49/1.62 % [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 ...
% 8.40/3.15 % [INFO] Killing All external provers ...
% 8.40/3.15 % Time passed: 2798ms (effective reasoning time: 2127ms)
% 8.40/3.15 % 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)>
% 8.40/3.15 % Axioms used in derivation (0):
% 8.40/3.15 % No. of inferences in proof: 20
% 8.40/3.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2798 ms resp. 2127 ms w/o parsing
% 8.40/3.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.40/3.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------