%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU303+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n013.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 : Sun Sep 27 08:38:23 AM UTC 2026
% Result : Theorem 4.91s 2.72s
% Output : Refutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 92 ( 14 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 218 ( 30 ~; 25 |; 11 &; 140 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 25 !; 0 ?; 26 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(finite_decl,type,
finite: $i > $o ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(relation_image_decl,type,
relation_image: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_dom @ finite )
=> ( A @ relation_rng @ finite ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_dom @ finite )
=> ( A @ relation_rng @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_dom @ finite )
=> ( A @ relation_rng @ finite ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ relation_dom @ finite )
=> ( A @ relation_rng @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
( ~ ( sk1 @ relation_rng @ finite )
& ( sk1 @ relation_dom @ finite )
& ( sk1 @ function )
& ( sk1 @ relation ) ),
inference(cnf,[status(esa)],[10]) ).
thf(14,plain,
sk1 @ relation_dom @ finite,
inference(cnfConj,[status(thm)],[11]) ).
thf(13,plain,
sk1 @ function,
inference(cnfConj,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ function )
& ( A @ relation ) )
=> ( B @ ( A @ relation_image ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ function )
& ( A @ relation ) )
=> ( B @ ( A @ relation_image ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ relation_image ) @ finite )
| ~ ( B @ finite )
| ~ ( A @ function )
| ~ ( A @ relation ) ),
inference(cnf,[status(esa)],[19]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ function )
!= ( A @ function ) )
| ( B @ ( A @ relation_image ) @ finite )
| ~ ( B @ finite )
| ~ $true
| ~ ( A @ relation ) ),
inference(paramod_ordered,[status(thm)],[13,20]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ function )
!= ( A @ function ) )
| ( B @ ( A @ relation_image ) @ finite )
| ~ ( B @ finite )
| ~ ( A @ relation ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( sk1 @ relation_image ) @ finite )
| ~ ( A @ finite )
| ~ ( sk1 @ relation ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( sk1 ))]]) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( sk1 @ relation_image ) @ finite )
| ~ ( A @ finite )
| ~ ( sk1 @ relation ) ),
inference(simp,[status(thm)],[38]) ).
thf(12,plain,
sk1 @ relation,
inference(cnfConj,[status(thm)],[11]) ).
thf(59,plain,
! [A: $i] :
( ( A @ ( sk1 @ relation_image ) @ finite )
| ~ ( A @ finite )
| ~ $true ),
inference(rewrite,[status(thm)],[50,12]) ).
thf(60,plain,
! [A: $i] :
( ( A @ ( sk1 @ relation_image ) @ finite )
| ~ ( A @ finite ) ),
inference(simp,[status(thm)],[59]) ).
thf(61,plain,
! [A: $i] :
( ( ( sk1 @ relation_dom @ finite )
!= ( A @ finite ) )
| ( A @ ( sk1 @ relation_image ) @ finite )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,60]) ).
thf(62,plain,
! [A: $i] :
( ( ( sk1 @ relation_dom @ finite )
!= ( A @ finite ) )
| ( A @ ( sk1 @ relation_image ) @ finite ) ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
sk1 @ relation_dom @ ( sk1 @ relation_image ) @ finite,
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( sk1 @ relation_dom ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(25,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,plain,
! [A: $i] :
( ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) )
| ~ ( A @ relation ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [A: $i] :
( ~ ( A @ relation )
| ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(83,plain,
! [A: $i] :
( ( ( sk1 @ relation )
!= ( A @ relation ) )
| ~ $true
| ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
inference(paramod_ordered,[status(thm)],[12,27]) ).
thf(84,plain,
! [A: $i] :
( ( ( sk1 @ relation )
!= ( A @ relation ) )
| ( ( A @ relation_dom @ ( A @ relation_image ) )
= ( A @ relation_rng ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
( ( sk1 @ relation_dom @ ( sk1 @ relation_image ) )
= ( sk1 @ relation_rng ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( sk1 ))]]) ).
thf(101,plain,
sk1 @ relation_rng @ finite,
inference(rewrite,[status(thm)],[63,85]) ).
thf(15,plain,
~ ( sk1 @ relation_rng @ finite ),
inference(cnfConj,[status(thm)],[11]) ).
thf(110,plain,
$false,
inference(rewrite,[status(thm)],[101,15]) ).
thf(111,plain,
$false,
inference(simp,[status(thm)],[110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU303+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.15/0.41 % Computer : n013.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 09:08:06 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.17 % [INFO] Parsing done (181ms).
% 1.31/1.19 % [INFO] Running in sequential loop mode.
% 1.88/1.58 % [INFO] eprover registered as external prover.
% 1.88/1.59 % [INFO] Scanning for conjecture ...
% 2.10/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.27/1.72 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.27/1.73 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/1.74 % [INFO] Type checking passed.
% 2.27/1.74 % [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 ...
% 4.91/2.72 % [INFO] Killing All external provers ...
% 4.91/2.72 % Time passed: 2161ms (effective reasoning time: 1525ms)
% 4.91/2.72 % 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)>
% 4.91/2.72 % Axioms used in derivation (2): fc13_finset_1, t146_relat_1
% 4.91/2.72 % No. of inferences in proof: 30
% 4.91/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2161 ms resp. 1525 ms w/o parsing
% 4.91/2.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.91/2.77 % [INFO] Killing All external provers ...
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