%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU247+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n003.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 08:38:12 AM UTC 2026
% Result : Theorem 25.31s 7.23s
% Output : Refutation 25.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 56 ( 30 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 217 ( 18 ~; 10 |; 1 &; 179 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 41 !; 0 ?; 43 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(relation_restriction_decl,type,
relation_restriction: $i > $i > $i ).
thf(relation_rng_restriction_decl,type,
relation_rng_restriction: $i > $i > $i ).
thf(relation_dom_restriction_decl,type,
relation_dom_restriction: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ relation )
=> ( ( sk1 @ ( A @ relation_restriction ) )
= ( sk1 @ ( A @ relation_dom_restriction ) @ ( sk1 @ relation_rng_restriction ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_wellord1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
( ( ( sk1 @ ( sk2 @ relation_restriction ) )
!= ( sk1 @ ( sk2 @ relation_dom_restriction ) @ ( sk1 @ relation_rng_restriction ) ) )
& ( sk2 @ relation ) ),
inference(cnf,[status(esa)],[13]) ).
thf(16,plain,
( ( sk1 @ ( sk2 @ relation_restriction ) )
!= ( sk1 @ ( sk2 @ relation_dom_restriction ) @ ( sk1 @ relation_rng_restriction ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(17,plain,
( ( sk1 @ ( sk2 @ relation_dom_restriction ) @ ( sk1 @ relation_rng_restriction ) )
!= ( sk1 @ ( sk2 @ relation_restriction ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(15,plain,
sk2 @ relation,
inference(cnfConj,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_wellord1) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ relation_restriction ) )
= ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) ) )
| ~ ( B @ relation ) ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( B @ relation )
| ( ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( A @ ( B @ relation_restriction ) ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(731,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ relation )
!= ( B @ relation ) )
| ~ $true
| ( ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( A @ ( B @ relation_restriction ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,42]) ).
thf(732,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ relation )
!= ( B @ relation ) )
| ( ( A @ ( B @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( A @ ( B @ relation_restriction ) ) ) ),
inference(simp,[status(thm)],[731]) ).
thf(733,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( A @ ( sk2 @ relation_restriction ) ) ),
inference(pattern_uni,[status(thm)],[732:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ relation ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ relation )
| ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ relation )
!= ( C @ relation ) )
| ~ $true
| ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,39]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ relation )
!= ( C @ relation ) )
| ( ( B @ ( C @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( C @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ) ),
inference(simp,[status(thm)],[395]) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ ( A @ relation_rng_restriction ) @ relation_dom_restriction ) )
= ( B @ ( sk2 @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) ) ),
inference(pattern_uni,[status(thm)],[396:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(3808,plain,
! [A: $i] :
( ( A @ ( sk2 @ relation_dom_restriction ) @ ( A @ relation_rng_restriction ) )
= ( A @ ( sk2 @ relation_restriction ) ) ),
inference(rewrite,[status(thm)],[733,397]) ).
thf(4005,plain,
( ( sk1 @ ( sk2 @ relation_restriction ) )
!= ( sk1 @ ( sk2 @ relation_restriction ) ) ),
inference(rewrite,[status(thm)],[17,3808]) ).
thf(4006,plain,
$false,
inference(simp,[status(thm)],[4005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU247+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.15/0.42 % Computer : n003.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 08:59:54 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 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
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.18 % [INFO] Parsing done (178ms).
% 1.26/1.19 % [INFO] Running in sequential loop mode.
% 1.84/1.59 % [INFO] eprover registered as external prover.
% 2.03/1.60 % [INFO] Scanning for conjecture ...
% 2.03/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.20/1.74 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.20/1.76 % [INFO] Problem is first-order (TPTP FOF).
% 2.20/1.76 % [INFO] Type checking passed.
% 2.20/1.77 % [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 ...
% 25.31/7.22 % [INFO] Killing All external provers ...
% 25.31/7.23 % Time passed: 6653ms (effective reasoning time: 6024ms)
% 25.31/7.23 % 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)>
% 25.31/7.23 % Axioms used in derivation (2): t17_wellord1, t140_relat_1
% 25.31/7.23 % No. of inferences in proof: 24
% 25.31/7.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6653 ms resp. 6024 ms w/o parsing
% 25.31/7.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.31/7.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------