%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU121+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 : n005.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 08:37:38 AM UTC 2026
% Result : Theorem 12.98s 4.56s
% Output : Refutation 12.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 143 ( 14 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 403 ( 38 ~; 48 |; 12 &; 288 @)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 2 ^; 85 !; 0 ?; 91 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ subset ) )
& ( A @ ( sk1 @ subset ) ) )
=> ( B @ ( sk1 @ subset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ ( sk2 @ subset ) )
& ( sk2 @ ( sk1 @ subset ) ) )
=> ( A @ ( sk1 @ subset ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
( ~ ( sk3 @ ( sk1 @ subset ) )
& ( sk3 @ ( sk2 @ subset ) )
& ( sk2 @ ( sk1 @ subset ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
sk2 @ ( sk1 @ subset ),
inference(cnfConj,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk4 ) @ in ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk4 ) @ in ) ) )
& ( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(123,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ in ) )
!= ( C @ ( E @ in ) ) )
| ( D @ ( E @ in ) )
| ~ $true
| ~ ( D @ ( C @ subset ) )
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[26,23]) ).
thf(124,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ in ) )
!= ( C @ ( E @ in ) ) )
| ( D @ ( E @ in ) )
| ~ ( D @ ( C @ subset ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ sk4 ) @ in ) )
| ~ ( A @ ( C @ subset ) )
| ( B @ ( C @ subset ) ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ sk4 ) @ in ) )
| ~ ( A @ ( C @ subset ) )
| ( B @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ subset ) )
!= ( A @ ( C @ subset ) ) )
| ( A @ ( C @ ( B @ sk4 ) @ in ) )
| ~ $true
| ( B @ ( C @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[15,143]) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ subset ) )
!= ( A @ ( C @ subset ) ) )
| ( A @ ( C @ ( B @ sk4 ) @ in ) )
| ( B @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[758]) ).
thf(760,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ ( A @ sk4 ) @ in ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[759:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(802,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ ( A @ sk4 ) @ in ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[760]) ).
thf(16,plain,
sk3 @ ( sk2 @ subset ),
inference(cnfConj,[status(thm)],[14]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,23]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(122,plain,
! [A: $i] :
( ( sk3 @ ( A @ in ) )
| ~ ( sk2 @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(141,plain,
! [A: $i] :
( ( sk3 @ ( A @ in ) )
| ~ ( sk2 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(2976,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( A @ sk4 ) @ in ) )
!= ( sk2 @ ( B @ in ) ) )
| ( sk3 @ ( B @ in ) )
| ~ $true
| ( A @ ( sk1 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[802,141]) ).
thf(2977,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( A @ sk4 ) @ in ) )
!= ( sk2 @ ( B @ in ) ) )
| ( sk3 @ ( B @ in ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[2976]) ).
thf(2978,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ ( A @ sk4 ) @ in ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[2977:[bind(A,$thf( C )),bind(B,$thf( sk1 @ ( C @ sk4 ) ))]]) ).
thf(3077,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ ( A @ sk4 ) @ in ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[2978]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(3111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ ( A @ sk4 ) @ in ) )
!= ( C @ ( B @ ( C @ sk4 ) @ in ) ) )
| ( C @ ( B @ subset ) )
| ~ $true
| ( A @ ( sk1 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[3077,27]) ).
thf(3112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ ( A @ sk4 ) @ in ) )
!= ( C @ ( B @ ( C @ sk4 ) @ in ) ) )
| ( C @ ( B @ subset ) )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[3111]) ).
thf(3113,plain,
( ( sk3 @ ( sk1 @ subset ) )
| ( sk3 @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[3112:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 ))]]) ).
thf(3200,plain,
sk3 @ ( sk1 @ subset ),
inference(simp,[status(thm)],[3113]) ).
thf(17,plain,
~ ( sk3 @ ( sk1 @ subset ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(3212,plain,
$false,
inference(rewrite,[status(thm)],[3200,17]) ).
thf(3213,plain,
$false,
inference(simp,[status(thm)],[3212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU121+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
% 0.15/0.40 % Computer : n005.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 08:37:31 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.16 % [INFO] Parsing done (185ms).
% 1.27/1.18 % [INFO] Running in sequential loop mode.
% 1.76/1.56 % [INFO] eprover registered as external prover.
% 1.76/1.57 % [INFO] Scanning for conjecture ...
% 1.97/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.11/1.70 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.11/1.72 % [INFO] Problem is first-order (TPTP FOF).
% 2.11/1.72 % [INFO] Type checking passed.
% 2.11/1.73 % [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 ...
% 12.98/4.55 % [INFO] Killing All external provers ...
% 12.98/4.56 % Time passed: 4012ms (effective reasoning time: 3370ms)
% 12.98/4.56 % 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)>
% 12.98/4.56 % Axioms used in derivation (1): d3_tarski
% 12.98/4.56 % No. of inferences in proof: 38
% 12.98/4.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4012 ms resp. 3370 ms w/o parsing
% 12.98/4.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.98/4.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------