%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU688^2 : 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 : n002.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 08:29:02 AM UTC 2026
% Result : Theorem 5.17s 2.64s
% Output : Refutation 5.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 64 ( 14 equ; 0 cnn)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 191 ( 2 ~; 0 |; 6 &; 152 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 51 ( 14 ^; 34 !; 3 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
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(singleton_decl,type,
singleton: $i > $o ).
thf(ex1_decl,type,
ex1: $i > ( $i > $o ) > $o ).
thf(breln_decl,type,
breln: $i > $i > $i > $o ).
thf(func_decl,type,
func: $i > $i > $i > $o ).
thf(funcSet_decl,type,
funcSet: $i > $i > $i ).
thf(ap_decl,type,
ap: $i > $i > $i > $i > $i ).
thf(infuncsetfunc_decl,type,
infuncsetfunc: $o ).
thf(funcGraphProp2_decl,type,
funcGraphProp2: $o ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(ex1_def,definition,
( ex1
= ( ^ [A: $i,B: $i > $o] : ( singleton @ ( dsetconstr @ A @ B ) ) ) ) ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(func_def,definition,
( func
= ( ^ [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
& ! [D: $i] :
( ( in @ D @ A )
=> ( ex1 @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ).
thf(infuncsetfunc_def,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ C ) ) ) ) ).
thf(funcGraphProp2_def,definition,
( funcGraphProp2
= ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ C )
=> ( ( ap @ A @ B @ C @ D )
= E ) ) ) ) ) ) ) ).
thf(1,conjecture,
( infuncsetfunc
=> ( funcGraphProp2
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ C )
=> ( ( ap @ A @ B @ C @ D )
= E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(2,negated_conjecture,
~ ( infuncsetfunc
=> ( funcGraphProp2
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ C )
=> ( ( ap @ A @ B @ C @ D )
= E ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ( ( subset @ C @ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ C @ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ C )
=> ( ( ap @ A @ B @ C @ D )
= E ) ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ C )
=> ( ( ap @ A @ B @ C @ D )
= E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU688^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.12 % 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
% 0.25/0.34 % Computer : n002.cluster.edu
% 0.25/0.34 % Model : x86_64 x86_64
% 0.25/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.34 % Memory : 8046.5625MB
% 0.25/0.34 % OS : Linux 6.8.0-71-generic
% 0.25/0.34 % CPULimit : 300
% 0.25/0.34 % WCLimit : 300
% 0.25/0.34 % DateTime : Tue Sep 29 14:11:52 UTC 2026
% 0.25/0.34 % CPUTime :
% 0.25/0.34 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
% 1.09/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.10 % [INFO] Parsing done (202ms).
% 1.53/1.11 % [INFO] Running in sequential loop mode.
% 2.25/1.46 % [INFO] eprover registered as external prover.
% 2.25/1.47 % [INFO] Scanning for conjecture ...
% 2.70/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.70/1.64 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.70/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.70/1.65 % [INFO] Type checking passed.
% 2.70/1.65 % [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 ...
% 5.17/2.63 % External prover 'e' found a proof!
% 5.17/2.63 % [INFO] Killing All external provers ...
% 5.17/2.63 % Time passed: 2166ms (effective reasoning time: 1518ms)
% 5.17/2.63 % 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)>
% 5.17/2.63 % Axioms used in derivation (0):
% 5.17/2.63 % No. of inferences in proof: 4
% 5.17/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2166 ms resp. 1518 ms w/o parsing
% 5.40/2.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.40/2.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------