%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU957^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n019.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 08:29:39 AM UTC 2026
% Result : Theorem 4.45s 2.45s
% Output : Refutation 4.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 19 unt; 0 typ; 5 def)
% Number of atoms : 41 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 144 ( 13 ~; 3 |; 3 &; 110 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 68 ( 11 ^; 35 !; 17 ?; 68 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(sk1_decl,type,
sk1: ( a > $o ) > a ).
thf(sk2_decl,type,
sk2: a > b ).
thf(sk3_decl,type,
sk3: b > a ).
thf(sk4_decl,type,
sk4: ( b > a ) > b ).
thf(sk5_decl,type,
sk5: ( b > a ) > b ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( a > $o ) > a] :
! [B: a > $o] :
( ? [C: a] : ( B @ C )
=> ( B @ ( A @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > b] :
! [B: b] :
? [C: a] :
( ( A @ C )
= B ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: b] :
@+[B: a] :
( ( sk2 @ B )
= A ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: b > a] :
@+[B: b] :
~ ! [C: b] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: b > a] :
@+[B: b] :
~ ( ( ( A @ ( sk4 @ A ) )
= ( A @ B ) )
=> ( ( sk4 @ A )
= B ) ) ) ) ).
thf(1,conjecture,
( ? [A: ( a > $o ) > a] :
! [B: a > $o] :
( ? [C: a] : ( B @ C )
=> ( B @ ( A @ B ) ) )
=> ( ? [A: a > b] :
! [B: b] :
? [C: a] :
( ( A @ C )
= B )
=> ? [A: b > a] :
! [B: b,C: b] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM607_pme) ).
thf(2,negated_conjecture,
~ ( ? [A: ( a > $o ) > a] :
! [B: a > $o] :
( ? [C: a] : ( B @ C )
=> ( B @ ( A @ B ) ) )
=> ( ? [A: a > b] :
! [B: b] :
? [C: a] :
( ( A @ C )
= B )
=> ? [A: b > a] :
! [B: b,C: b] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ? [A: ( a > $o ) > a] :
! [B: a > $o] :
( ? [C: a] : ( B @ C )
=> ( B @ ( A @ B ) ) )
=> ( ? [A: a > b] :
! [B: b] :
? [C: a] :
( ( A @ C )
= B )
=> ? [A: b > a] :
! [B: b,C: b] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [D: b > a,C: b,B: a,A: a > $o] :
( ( ~ ( A @ B )
| ( A @ ( sk1 @ A ) ) )
& ( ( sk2 @ ( sk3 @ C ) )
= C )
& ( ( D @ ( sk4 @ D ) )
= ( D @ ( sk5 @ D ) ) )
& ( ( sk4 @ D )
!= ( sk5 @ D ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [A: b > a] :
( ( A @ ( sk4 @ A ) )
= ( A @ ( sk5 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [A: b > a] :
( ( A @ ( sk5 @ A ) )
= ( A @ ( sk4 @ A ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(12,plain,
! [A: b > a] :
( ( A @ ( sk5 @ A ) )
= ( A @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(6,plain,
! [A: b] :
( ( sk2 @ ( sk3 @ A ) )
= A ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: b] :
( ( sk2 @ ( sk3 @ A ) )
= A ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
! [A: b] :
( ( sk2 @ ( sk3 @ A ) )
= A ),
inference(simp,[status(thm)],[9]) ).
thf(15,plain,
! [B: b,A: b > a] :
( ( ( sk2 @ ( A @ ( sk4 @ A ) ) )
= B )
| ( ( A @ ( sk5 @ A ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(16,plain,
! [A: b > b] :
( ( sk2
@ ( sk3
@ ( A
@ ( sk4
@ ^ [B: b] : ( sk3 @ ( A @ B ) ) ) ) ) )
= ( A
@ ( sk5
@ ^ [B: b] : ( sk3 @ ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[15:[bind(A,$thf( ^ [D: b] : ( sk3 @ ( C @ D ) ) )),bind(B,$thf( C @ ( sk5 @ ^ [D: b] : ( sk3 @ ( C @ D ) ) ) ))]]) ).
thf(17,plain,
! [A: b > b] :
( ( sk2
@ ( sk3
@ ( A
@ ( sk4
@ ^ [B: b] : ( sk3 @ ( A @ B ) ) ) ) ) )
= ( A
@ ( sk5
@ ^ [B: b] : ( sk3 @ ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [A: b > b] :
( ( A
@ ( sk5
@ ^ [B: b] : ( sk3 @ ( A @ B ) ) ) )
= ( A
@ ( sk4
@ ^ [B: b] : ( sk3 @ ( A @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[17,10]) ).
thf(8,plain,
! [A: b > a] :
( ( sk4 @ A )
!= ( sk5 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(13,plain,
! [A: b > a] :
( ( sk5 @ A )
!= ( sk4 @ A ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(14,plain,
! [A: b > a] :
( ( sk5 @ A )
!= ( sk4 @ A ) ),
inference(simp,[status(thm)],[13]) ).
thf(23,plain,
! [B: b > a,A: b > b] :
( ( ( A
@ ( sk4
@ ^ [C: b] : ( sk3 @ ( A @ C ) ) ) )
!= ( sk4 @ B ) )
| ( ( A
@ ( sk5
@ ^ [C: b] : ( sk3 @ ( A @ C ) ) ) )
!= ( sk5 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18,14]) ).
thf(29,plain,
( ( sk4 @ sk3 )
!= ( sk4 @ sk3 ) ),
inference(pre_uni,[status(thm)],[23:[bind(A,$thf( ^ [C: b] : C )),bind(B,$thf( sk3 ))]]) ).
thf(30,plain,
$false,
inference(pattern_uni,[status(thm)],[29:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU957^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.21 % Computer : n019.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 14:51:02 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (186ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 2.01/1.40 % [INFO] eprover registered as external prover.
% 2.01/1.41 % [INFO] Scanning for conjecture ...
% 2.01/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.19/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.19/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.54 % [INFO] Type checking passed.
% 2.19/1.54 % [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 ...
% 4.45/2.44 % [INFO] Killing All external provers ...
% 4.45/2.45 % Time passed: 2087ms (effective reasoning time: 1443ms)
% 4.45/2.45 % 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)>
% 4.45/2.45 % Axioms used in derivation (0):
% 4.45/2.45 % No. of inferences in proof: 20
% 4.45/2.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2087 ms resp. 1443 ms w/o parsing
% 4.88/2.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.88/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------