%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU810^2 : 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 : n004.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 08:29:22 AM UTC 2026
% Result : Theorem 3.80s 2.38s
% Output : Refutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 70 ( 27 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 151 ( 20 ~; 7 |; 4 &; 94 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 1 ^; 47 !; 1 ?; 50 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(omega_decl,type,
omega: $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(setadjoinIL_decl,type,
setadjoinIL: $o ).
thf(in__Cong_decl,type,
in__Cong: $o ).
thf(omegaS_decl,type,
omegaS: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(setadjoinIL_def,definition,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(omegaS_def,definition,
( omegaS
= ( ^ [A: $i] : ( setadjoin @ A @ A ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( in @ A @ omega )
=> ( ( setadjoin @ A @ A )
!= emptyset ) ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ( setadjoinIL
=> ( in__Cong
=> ! [A: $i] :
( ( in @ A @ omega )
=> ( ( omegaS @ A )
!= emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',peano0notS) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( setadjoinIL
=> ( in__Cong
=> ! [A: $i] :
( ( in @ A @ omega )
=> ( ( omegaS @ A )
!= emptyset ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ! [A: $i] :
( ( in @ A @ omega )
=> ( ( setadjoin @ A @ A )
!= emptyset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ! [A: $i] :
( ( in @ A @ omega )
=> ( ( setadjoin @ A @ A )
!= emptyset ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $o,A: $i] :
( ( ~ ( in @ A @ emptyset )
| B )
& ( in @ C @ ( setadjoin @ C @ D ) )
& ( ( E != F )
| ( G != H )
| ( ( in @ G @ E )
= ( in @ H @ F ) ) )
& ( in @ sk1 @ omega )
& ( ( setadjoin @ sk1 @ sk1 )
= emptyset ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
( ( setadjoin @ sk1 @ sk1 )
= emptyset ),
inference(cnfConj,[status(thm)],[5]) ).
thf(14,plain,
( ( setadjoin @ sk1 @ sk1 )
= emptyset ),
inference(lifteq,[status(thm)],[8]) ).
thf(9,plain,
! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( in @ A @ emptyset )
| ( ( setadjoin @ sk1 @ sk1 )
!= ( setadjoin @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,13]) ).
thf(16,plain,
in @ sk1 @ emptyset,
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(7,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnfConj,[status(thm)],[5]) ).
thf(27,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ( B
!= ( ~ ( in @ A @ emptyset ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7]) ).
thf(33,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( D )),bind(B,$thf( ~ ( in @ D @ emptyset ) ))]]) ).
thf(38,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(simp,[status(thm)],[33]) ).
thf(47,plain,
$false,
inference(rewrite,[status(thm)],[16,38]) ).
thf(48,plain,
$false,
inference(simp,[status(thm)],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU810^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n004.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:33:22 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.00/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/1.01 % [INFO] Parsing done (183ms).
% 1.16/1.03 % [INFO] Running in sequential loop mode.
% 1.88/1.43 % [INFO] eprover registered as external prover.
% 1.88/1.43 % [INFO] Scanning for conjecture ...
% 2.04/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.59 % [INFO] Type checking passed.
% 2.04/1.59 % [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 ...
% 3.80/2.37 % [INFO] Killing All external provers ...
% 3.80/2.38 % Time passed: 2020ms (effective reasoning time: 1339ms)
% 3.80/2.38 % 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)>
% 3.80/2.38 % Axioms used in derivation (0):
% 3.80/2.38 % No. of inferences in proof: 17
% 3.80/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2020 ms resp. 1339 ms w/o parsing
% 4.14/2.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.14/2.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------