%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU684^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n009.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 08:29:01 AM UTC 2026
% Result : Theorem 4.48s 2.36s
% Output : Refutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 12 ( 9 unt; 0 typ; 8 def)
% Number of atoms : 68 ( 13 equ; 0 cnn)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 199 ( 2 ~; 0 |; 8 &; 163 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 59 ( 23 ^; 31 !; 5 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_decl,type,
dsetconstrER: $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(singleton_decl,type,
singleton: $i > $o ).
thf(ex1_decl,type,
ex1: $i > ( $i > $o ) > $o ).
thf(theprop_decl,type,
theprop: $o ).
thf(breln_decl,type,
breln: $i > $i > $i > $o ).
thf(func_decl,type,
func: $i > $i > $i > $o ).
thf(funcImageSingleton_decl,type,
funcImageSingleton: $o ).
thf(ap_decl,type,
ap: $i > $i > $i > $i > $i ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
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(theprop_def,definition,
( theprop
= ( ! [A: $i] :
( ( singleton @ A )
=> ( in @ ( setunion @ A ) @ A ) ) ) ) ).
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(funcImageSingleton_def,definition,
( funcImageSingleton
= ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ) ).
thf(ap_def,definition,
( ap
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
( setunion
@ ( dsetconstr @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ).
thf(1,conjecture,
( dsetconstrER
=> ( theprop
=> ( funcImageSingleton
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( kpair @ D @ ( ap @ A @ B @ C @ D ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ( theprop
=> ( funcImageSingleton
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( kpair @ D @ ( ap @ A @ B @ C @ D ) ) @ C ) ) ) ) ) ),
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] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) )
=> ( in @ ( setunion @ A ) @ A ) )
=> ( ! [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
@ ( 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 )
=> ( in
@ ( kpair @ D
@ ( setunion
@ ( dsetconstr @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) )
@ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU684^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:08:45 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.95/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/0.98 % [INFO] Parsing done (202ms).
% 1.32/0.99 % [INFO] Running in sequential loop mode.
% 2.08/1.39 % [INFO] eprover registered as external prover.
% 2.28/1.40 % [INFO] Scanning for conjecture ...
% 2.47/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.47/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.47/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.47/1.58 % [INFO] Type checking passed.
% 2.47/1.58 % [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 ...
% 4.48/2.36 % External prover 'e' found a proof!
% 4.48/2.36 % [INFO] Killing All external provers ...
% 4.48/2.36 % Time passed: 2024ms (effective reasoning time: 1360ms)
% 4.48/2.36 % 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)>
% 4.48/2.36 % Axioms used in derivation (0):
% 4.48/2.36 % No. of inferences in proof: 4
% 4.48/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2024 ms resp. 1360 ms w/o parsing
% 4.80/2.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.80/2.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------