%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV429^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n006.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 08:37:17 AM UTC 2026
% Result : Theorem 4.21s 2.33s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 24 ( 23 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 55 ( 10 ~; 3 |; 0 &; 40 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 26 ( 1 ^; 19 !; 4 ?; 26 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i ).
thf(sk1_decl,type,
sk1: ( $i > $i ) > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $i] :
@+[B: $i] :
( ( A @ ( f @ B ) )
!= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
! [B: $i] :
( ( A @ ( f @ B ) )
= B ) ) ) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( f @ A )
= ( f @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finj) ).
thf(7,plain,
! [A: $i,B: $i] :
( ( ( f @ A )
= ( f @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( ( f @ A )
!= ( f @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( ( f @ A )
!= ( f @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
? [A: $i > $i] :
! [B: $i] :
( ( A @ ( f @ B ) )
= B ),
inference(detectInverse,[status(thm)],[9]) ).
thf(11,plain,
! [A: $i] :
( ( sk2 @ ( f @ A ) )
= A ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [A: $i] :
( ( sk2 @ ( f @ A ) )
= A ),
inference(lifteq,[status(thm)],[11]) ).
thf(1,conjecture,
? [A: $i > $i] :
! [B: $i] :
( ( A @ ( f @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',invexists) ).
thf(2,negated_conjecture,
~ ? [A: $i > $i] :
! [B: $i] :
( ( A @ ( f @ B ) )
= B ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ? [A: $i > $i] :
! [B: $i] :
( ( A @ ( f @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [A: $i > $i] :
( ( A @ ( f @ ( sk1 @ A ) ) )
!= ( sk1 @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [A: $i > $i] :
( ( A @ ( f @ ( sk1 @ A ) ) )
!= ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(13,plain,
! [B: $i > $i,A: $i] :
( ( A
!= ( sk1 @ B ) )
| ( ( sk2 @ ( f @ A ) )
!= ( B @ ( f @ ( sk1 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,6]) ).
thf(15,plain,
( ( sk1 @ sk2 )
!= ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[13:[bind(A,$thf( sk1 @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(16,plain,
$false,
inference(pattern_uni,[status(thm)],[15:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV429^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.09/0.21 % Computer : n006.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 15:46:39 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.02/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.03 % [INFO] Parsing done (208ms).
% 1.20/1.05 % [INFO] Running in sequential loop mode.
% 2.14/1.51 % [INFO] eprover registered as external prover.
% 2.14/1.52 % [INFO] Scanning for conjecture ...
% 2.33/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.33/1.66 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.33/1.66 % [INFO] Problem is higher-order (TPTP THF).
% 2.33/1.67 % [INFO] Type checking passed.
% 2.33/1.67 % [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 ...
% 4.21/2.33 % [INFO] Killing All external provers ...
% 4.21/2.33 % Time passed: 1976ms (effective reasoning time: 1269ms)
% 4.21/2.33 % 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)>
% 4.21/2.33 % Axioms used in derivation (1): finj
% 4.21/2.33 % No. of inferences in proof: 15
% 4.21/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1976 ms resp. 1269 ms w/o parsing
% 4.21/2.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.21/2.38 % [INFO] Killing All external provers ...
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