%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU503^1 : 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 : n017.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 08:28:18 AM UTC 2026
% Result : Theorem 3.26s 1.96s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 25 ( 23 unt; 0 typ; 21 def)
% Number of atoms : 158 ( 32 equ; 0 cnn)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 254 ( 7 ~; 3 |; 18 &; 156 @)
% ( 0 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 23 con; 0-2 aty)
% Number of variables : 71 ( 3 ^; 55 !; 13 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(exu_decl,type,
exu: ( $i > $o ) > $o ).
thf(setextAx_decl,type,
setextAx: $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(emptysetAx_decl,type,
emptysetAx: $o ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setadjoinAx_decl,type,
setadjoinAx: $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(powersetAx_decl,type,
powersetAx: $o ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(setunionAx_decl,type,
setunionAx: $o ).
thf(omega_decl,type,
omega: $i ).
thf(omega0Ax_decl,type,
omega0Ax: $o ).
thf(omegaSAx_decl,type,
omegaSAx: $o ).
thf(omegaIndAx_decl,type,
omegaIndAx: $o ).
thf(replAx_decl,type,
replAx: $o ).
thf(foundationAx_decl,type,
foundationAx: $o ).
thf(wellorderingAx_decl,type,
wellorderingAx: $o ).
thf(descr_decl,type,
descr: ( $i > $o ) > $i ).
thf(descrp_decl,type,
descrp: $o ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrI_decl,type,
dsetconstrI: $o ).
thf(dsetconstrEL_decl,type,
dsetconstrEL: $o ).
thf(dsetconstrER_decl,type,
dsetconstrER: $o ).
thf(exuE1_decl,type,
exuE1: $o ).
thf(prop2set_decl,type,
prop2set: $o > $i ).
thf(prop2setE_decl,type,
prop2setE: $o ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(emptysetimpfalse_decl,type,
emptysetimpfalse: $o ).
thf(exu_def,definition,
( exu
= ( ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) ) ) ) ).
thf(setextAx_def,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
= ( in @ C @ B ) )
=> ( A = B ) ) ) ) ).
thf(emptysetAx_def,definition,
( emptysetAx
= ( ! [A: $i] :
~ ( in @ A @ emptyset ) ) ) ).
thf(setadjoinAx_def,definition,
( setadjoinAx
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
= ( ( C = A )
| ( in @ C @ B ) ) ) ) ) ).
thf(powersetAx_def,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
= ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) ) ) ) ).
thf(setunionAx_def,definition,
( setunionAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
= ( ? [C: $i] :
( ( in @ B @ C )
& ( in @ C @ A ) ) ) ) ) ) ).
thf(omega0Ax_def,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ) ).
thf(omegaSAx_def,definition,
( omegaSAx
= ( ! [A: $i] :
( ( in @ A @ omega )
=> ( in @ ( setadjoin @ A @ A ) @ omega ) ) ) ) ).
thf(omegaIndAx_def,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [B: $i] :
( ( ( in @ B @ omega )
& ( in @ B @ A ) )
=> ( in @ ( setadjoin @ B @ B ) @ A ) ) )
=> ! [B: $i] :
( ( in @ B @ omega )
=> ( in @ B @ A ) ) ) ) ) ).
thf(replAx_def,definition,
( replAx
= ( ! [A: $i > $i > $o,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( exu @ ( A @ C ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ B )
& ( A @ E @ D ) ) ) ) ) ) ) ).
thf(foundationAx_def,definition,
( foundationAx
= ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) ) ) ) ).
thf(wellorderingAx_def,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ C )
=> ( in @ D @ A ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ A )
& ( in @ D @ A ) )
=> ( ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ C @ E )
= ( in @ D @ E ) ) )
=> ( C = D ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ C )
=> ( in @ E @ D ) )
| ! [E: $i] :
( ( in @ E @ D )
=> ( in @ E @ C ) ) ) )
& ! [C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ( in @ D @ A ) )
& ? [D: $i] : ( in @ D @ C ) )
=> ? [D: $i,E: $i] :
( ( in @ D @ B )
& ( in @ E @ C )
& ~ ? [F: $i] :
( ( in @ F @ D )
& ( in @ F @ C ) )
& ! [F: $i] :
( ( in @ F @ B )
=> ( ! [G: $i] :
( ( in @ G @ F )
=> ( in @ G @ D ) )
| ( in @ E @ F ) ) ) ) ) ) ) ) ).
thf(descrp_def,definition,
( descrp
= ( ! [A: $i > $o] :
( ( exu @ A )
=> ( A @ ( descr @ A ) ) ) ) ) ).
thf(dsetconstrI_def,definition,
( dsetconstrI
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).
thf(dsetconstrEL_def,definition,
( dsetconstrEL
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) ) ) ) ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(exuE1_def,definition,
( exuE1
= ( ! [A: $i > $o] :
( ( exu @ A )
=> ? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) ) ) ) ) ).
thf(prop2set_def,definition,
( prop2set
= ( ^ [A: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [B: $i] : A ) ) ) ).
thf(prop2setE_def,definition,
( prop2setE
= ( ! [A: $o,B: $i] :
( ( in @ B @ ( prop2set @ A ) )
=> A ) ) ) ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(emptysetimpfalse_def,definition,
( emptysetimpfalse
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> $false ) ) ) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ! [A: $i] :
~ ( in @ A @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(2,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ! [A: $i] :
~ ( in @ A @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
$false,
inference(simp,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU503^1 : 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
% 0.12/0.20 % Computer : n017.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Sep 29 13:42:06 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.55/1.04 % [INFO] Parsing done (246ms).
% 1.55/1.05 % [INFO] Running in sequential loop mode.
% 2.16/1.45 % [INFO] eprover registered as external prover.
% 2.16/1.46 % [INFO] Scanning for conjecture ...
% 2.59/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.85/1.70 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.85/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.85/1.70 % [INFO] Type checking passed.
% 2.85/1.71 % [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 ...
% 3.26/1.95 % [INFO] Killing All external provers ...
% 3.26/1.95 % Time passed: 1604ms (effective reasoning time: 888ms)
% 3.26/1.95 % 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)>
% 3.26/1.96 % Axioms used in derivation (0):
% 3.26/1.96 % No. of inferences in proof: 4
% 3.26/1.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1604 ms resp. 888 ms w/o parsing
% 3.57/2.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.57/2.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------