%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV385^5 : 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 : n015.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 08:37:13 AM UTC 2026
% Result : Theorem 4.06s 2.48s
% Output : Refutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 74 ( 73 equ; 12 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 119 ( 20 ~; 11 |; 16 &; 64 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 14 ^; 18 !; 7 ?; 41 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(x_decl,type,
x: b ).
thf(y_decl,type,
y: a ).
thf(sk1_decl,type,
sk1: ( b > a ) > b ).
thf(sk2_decl,type,
sk2: ( b > a ) > a ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: b > a] :
@+[B: b] :
~ ( ( x = B )
=> ( y
= ( A @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: b > a] :
@+[B: a] :
~ ( ( y = B )
=> ? [C: b] :
( ( ^ [D: b] :
( ( x = D )
& ( B
= ( A @ D ) ) ) )
= ( (=) @ b @ C ) ) ) ) ) ).
thf(1,conjecture,
? [A: b > a] :
( ! [B: b] :
( ( x = B )
=> ( y
= ( A @ B ) ) )
& ! [B: a] :
( ( y = B )
=> ? [C: b] :
( ( ^ [D: b] :
( ( x = D )
& ( B
= ( A @ D ) ) ) )
= ( (=) @ b @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6004_pme) ).
thf(2,negated_conjecture,
~ ? [A: b > a] :
( ! [B: b] :
( ( x = B )
=> ( y
= ( A @ B ) ) )
& ! [B: a] :
( ( y = B )
=> ? [C: b] :
( ( ^ [D: b] :
( ( x = D )
& ( B
= ( A @ D ) ) ) )
= ( (=) @ b @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: b > a] :
( ! [B: b] :
( ( x = B )
=> ( y
= ( A @ B ) ) )
& ! [B: a] :
( ( y = B )
=> ? [C: b] :
( ( ^ [D: b] :
( ( x = D )
& ( B
= ( A @ D ) ) ) )
= ( (=) @ b @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: b,A: b > a] :
( ( ( x
= ( sk1 @ A ) )
| ( y
= ( sk2 @ A ) ) )
& ( ( x
= ( sk1 @ A ) )
| ( ( ^ [C: b] :
( ( x = C )
& ( ( sk2 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ b @ B ) ) )
& ( ( y
!= ( A @ ( sk1 @ A ) ) )
| ( y
= ( sk2 @ A ) ) )
& ( ( y
!= ( A @ ( sk1 @ A ) ) )
| ( ( ^ [C: b] :
( ( x = C )
& ( ( sk2 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ b @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [A: b > a] :
( ( y
!= ( A @ ( sk1 @ A ) ) )
| ( y
= ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [A: b > a] :
( ( y
!= ( A @ ( sk1 @ A ) ) )
| ( ( sk2 @ A )
= y ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
( ( sk2
@ ^ [A: b] : y )
= y ),
inference(pre_uni,[status(thm)],[11:[bind(A,$thf( ^ [B: b] : y ))]]) ).
thf(8,plain,
! [B: b,A: b > a] :
( ( y
!= ( A @ ( sk1 @ A ) ) )
| ( ( ^ [C: b] :
( ( x = C )
& ( ( sk2 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ b @ B ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
! [B: b,A: b > a] :
( ( y
!= ( A @ ( sk1 @ A ) ) )
| ( ( ^ [C: b] :
( ( x = C )
& ( ( sk2 @ A )
= ( A @ C ) ) ) )
!= ( (=) @ b @ B ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(55,plain,
! [B: b,A: b > a] :
( ( y
!= ( A @ ( sk1 @ A ) ) )
| ( ( ^ [C: b] :
( ( x = C )
& ( y
= ( A @ C ) ) ) )
!= ( (=) @ b @ B ) )
| ( ( sk2
@ ^ [C: b] : y )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13,12]) ).
thf(56,plain,
! [A: b] :
( ( y != y )
| ( ( ^ [B: b] :
( ( x = B )
& ( y = y ) ) )
!= ( (=) @ b @ A ) ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( ^ [C: b] : y ))]]) ).
thf(62,plain,
! [A: b] :
( ( (=) @ b @ x )
!= ( (=) @ b @ A ) ),
inference(simp,[status(thm)],[56]) ).
thf(67,plain,
$false,
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( x ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV385^5 : 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
% 0.10/0.22 % Computer : n015.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 15:46:33 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.00 % [INFO] Parsing done (198ms).
% 1.20/1.02 % [INFO] Running in sequential loop mode.
% 1.96/1.44 % [INFO] eprover registered as external prover.
% 1.96/1.45 % [INFO] Scanning for conjecture ...
% 2.17/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.17/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.17/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.17/1.59 % [INFO] Type checking passed.
% 2.17/1.59 % [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 ...
% 4.06/2.47 % [INFO] Killing All external provers ...
% 4.06/2.48 % Time passed: 2119ms (effective reasoning time: 1443ms)
% 4.06/2.48 % 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)>
% 4.06/2.48 % Axioms used in derivation (0):
% 4.06/2.48 % No. of inferences in proof: 13
% 4.06/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2119 ms resp. 1443 ms w/o parsing
% 4.35/2.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.35/2.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------