%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV057^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n026.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 08:36:47 AM UTC 2026
% Result : Theorem 6.02s 2.86s
% Output : Refutation 6.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 84 ( 30 equ; 0 cnn)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 239 ( 36 ~; 29 |; 25 &; 133 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 11 ^; 32 !; 9 ?; 56 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: ( a > a ) > $o ).
thf(sk3_decl,type,
sk3: ( a > a ) > a ).
thf(sk4_decl,type,
sk4: ( a > a ) > a ).
thf(sk5_decl,type,
sk5: a > ( a > a ) > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ? [B: a > a] :
( ! [C: a] :
( ( A @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( A @ D )
& ( C
= ( B @ D ) )
& ! [E: a] :
( ( ( A @ E )
& ( C
= ( B @ E ) ) )
=> ( E = D ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: a > a] :
@+[B: a] :
~ ( ( sk1 @ B )
=> ( sk1 @ ( A @ B ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: a > a] :
@+[B: a] :
~ ( ( sk1 @ B )
=> ? [C: a] :
( ( sk1 @ C )
& ( B
= ( A @ C ) )
& ! [D: a] :
( ( ( sk1 @ D )
& ( B
= ( A @ D ) ) )
=> ( D = C ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: a,B: a > a] :
@+[C: a] :
~ ( ( ( sk1 @ C )
& ( ( sk4 @ B )
= ( B @ C ) ) )
=> ( C = A ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o] :
? [B: a > a] :
( ! [C: a] :
( ( A @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( A @ D )
& ( C
= ( B @ D ) )
& ! [E: a] :
( ( ( A @ E )
& ( C
= ( B @ E ) ) )
=> ( E = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQP1_1A_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o] :
? [B: a > a] :
( ! [C: a] :
( ( A @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( A @ D )
& ( C
= ( B @ D ) )
& ! [E: a] :
( ( ( A @ E )
& ( C
= ( B @ E ) ) )
=> ( E = D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o] :
? [B: a > a] :
( ! [C: a] :
( ( A @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( A @ D )
& ( C
= ( B @ D ) )
& ! [E: a] :
( ( ( A @ E )
& ( C
= ( B @ E ) ) )
=> ( E = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: a,A: a > a] :
( ( ( sk1 @ ( sk3 @ A ) )
| ~ ( sk2 @ A ) )
& ( ~ ( sk1 @ ( A @ ( sk3 @ A ) ) )
| ~ ( sk2 @ A ) )
& ( ( sk2 @ A )
| ( sk1 @ ( sk4 @ A ) ) )
& ( ( sk2 @ A )
| ~ ( sk1 @ B )
| ( ( sk4 @ A )
!= ( A @ B ) )
| ( sk1 @ ( sk5 @ B @ A ) ) )
& ( ( sk2 @ A )
| ~ ( sk1 @ B )
| ( ( sk4 @ A )
!= ( A @ B ) )
| ( ( sk4 @ A )
= ( A @ ( sk5 @ B @ A ) ) ) )
& ( ( sk2 @ A )
| ~ ( sk1 @ B )
| ( ( sk4 @ A )
!= ( A @ B ) )
| ( ( sk5 @ B @ A )
!= B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: a > a] :
( ~ ( sk1 @ ( A @ ( sk3 @ A ) ) )
| ~ ( sk2 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
! [A: a > a] :
( ( sk2 @ A )
| ( sk1 @ ( sk4 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: a > a] :
( ( sk1 @ ( sk3 @ A ) )
| ~ ( sk2 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(27,plain,
! [B: a > a,A: a > a] :
( ~ ( sk2 @ A )
| ~ $true
| ~ ( sk2 @ B )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk3 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,5]) ).
thf(28,plain,
! [B: a > a,A: a > a] :
( ~ ( sk2 @ A )
| ~ ( sk2 @ B )
| ( ( sk1 @ ( sk3 @ A ) )
!= ( sk1 @ ( B @ ( sk3 @ B ) ) ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(32,plain,
( ~ ( sk2
@ ^ [A: a] : A )
| ~ ( sk2
@ ^ [A: a] : A ) ),
inference(pre_uni,[status(thm)],[28:[bind(A,$thf( ^ [C: a] : C )),bind(B,$thf( ^ [C: a] : C ))]]) ).
thf(33,plain,
~ ( sk2
@ ^ [A: a] : A ),
inference(simp,[status(thm)],[32]) ).
thf(14,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk4 @ A ) )
| ( sk1 @ ( sk3 @ B ) )
| ~ $true
| ( ( sk2 @ A )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(15,plain,
! [B: a > a,A: a > a] :
( ( sk1 @ ( sk4 @ A ) )
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk2 @ A )
!= ( sk2 @ B ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(16,plain,
! [A: a > a] :
( ( sk1 @ ( sk4 @ A ) )
| ( sk1 @ ( sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(31,plain,
! [A: a > a > a] :
( ~ ( sk2
@ ( A
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) )
| ~ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[28:[bind(A,$thf( C @ ( sk3 @ ^ [D: a] : ( sk3 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk3 @ ( C @ D ) ) ))]]) ).
thf(36,plain,
! [A: a > a > a] :
( ~ ( sk2
@ ( A
@ ( sk3
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) )
| ~ ( sk2
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(96,plain,
$false,
inference(e,[status(thm)],[5,6,33,9,3,16,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV057^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:08:27 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 0.85/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (194ms).
% 1.20/0.98 % [INFO] Running in sequential loop mode.
% 1.81/1.39 % [INFO] eprover registered as external prover.
% 2.01/1.40 % [INFO] Scanning for conjecture ...
% 2.01/1.48 % [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).
% 2.19/1.53 % [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 ...
% 6.02/2.86 % External prover 'e' found a proof!
% 6.02/2.86 % [INFO] Killing All external provers ...
% 6.02/2.86 % Time passed: 2527ms (effective reasoning time: 1873ms)
% 6.02/2.86 % 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)>
% 6.02/2.86 % Axioms used in derivation (0):
% 6.02/2.86 % No. of inferences in proof: 17
% 6.02/2.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2527 ms resp. 1873 ms w/o parsing
% 6.42/2.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.42/2.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------