%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU499^1 : 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 : n007.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 08:28:17 AM UTC 2026
% Result : Theorem 4.33s 2.62s
% Output : Refutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 20 ( 18 unt; 0 typ; 16 def)
% Number of atoms : 137 ( 28 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 233 ( 5 ~; 3 |; 19 &; 145 @)
% ( 0 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 65 ( 1 ^; 50 !; 14 ?; 65 :)
% 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(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(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ! [A: $i > $o] :
( ( exu @ A )
=> ? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(2,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ! [A: $i > $o] :
( ( exu @ A )
=> ? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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
% 0.00/0.04 % Problem : SEU499^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.10 % 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
% 0.24/0.30 % Computer : n007.cluster.edu
% 0.24/0.30 % Model : x86_64 x86_64
% 0.24/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.30 % Memory : 8046.5625MB
% 0.24/0.30 % OS : Linux 6.8.0-71-generic
% 0.24/0.30 % CPULimit : 300
% 0.24/0.30 % WCLimit : 300
% 0.24/0.30 % DateTime : Tue Sep 29 13:43:56 UTC 2026
% 0.24/0.30 % CPUTime :
% 0.24/0.30 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
% 1.28/1.12 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.72/1.39 % [INFO] Parsing done (271ms).
% 1.99/1.41 % [INFO] Running in sequential loop mode.
% 2.86/1.93 % [INFO] eprover registered as external prover.
% 2.86/1.94 % [INFO] Scanning for conjecture ...
% 3.42/2.20 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.42/2.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.42/2.26 % [INFO] Problem is higher-order (TPTP THF).
% 3.42/2.27 % [INFO] Type checking passed.
% 3.42/2.28 % [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 ...
% 4.33/2.61 % [INFO] Killing All external provers ...
% 4.33/2.61 % Time passed: 2094ms (effective reasoning time: 1192ms)
% 4.33/2.61 % 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)>
% 4.33/2.62 % Axioms used in derivation (0):
% 4.33/2.62 % No. of inferences in proof: 4
% 4.33/2.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2094 ms resp. 1192 ms w/o parsing
% 4.58/2.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.58/2.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------