%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV177^5 : 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 : n020.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 08:36:57 AM UTC 2026
% Result : Theorem 5.63s 2.79s
% Output : Refutation 6.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 49 ( 25 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 119 ( 22 ~; 9 |; 11 &; 72 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 8 ^; 16 !; 10 ?; 36 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( $i > $o ) > $i] :
~ ! [B: $i > $o] :
( ( B
= ( ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) ) )
=> ( B @ ( A @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ( ( A
= ( ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( sk1 @ C ) )
& ( B
= ( sk1 @ C ) ) ) ) )
=> ( A @ ( sk1 @ A ) ) ) ) ) ).
thf(1,conjecture,
! [A: ( $i > $o ) > $i,B: $i > $o] :
( ( B
= ( ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) ) )
=> ( B @ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM144_pme) ).
thf(2,negated_conjecture,
~ ! [A: ( $i > $o ) > $i,B: $i > $o] :
( ( B
= ( ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) ) )
=> ( B @ ( A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( $i > $o ) > $i,B: $i > $o] :
( ( B
= ( ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) ) )
=> ( B @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk2
= ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) )
& ~ ( sk2 @ ( sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( sk2
= ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( sk2
= ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(8,plain,
! [A: $i] :
( ( sk2 @ A )
= ( ? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(14,plain,
! [A: $i] :
( ( sk2 @ A )
| ~ ? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ),
inference(bool_ext,[status(thm)],[8]) ).
thf(27,plain,
! [B: $i > $o,A: $i] :
( ( sk2 @ A )
| ( B @ ( sk1 @ B ) )
| ( A
!= ( sk1 @ B ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(28,plain,
! [B: $i > $o,A: $i] :
( ( A
!= ( sk1 @ B ) )
| ( sk2 @ A )
| ( B @ ( sk1 @ B ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(29,plain,
! [A: $i > $o] :
( ( sk2 @ ( sk1 @ A ) )
| ( A @ ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(6,plain,
~ ( sk2 @ ( sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(66,plain,
! [A: $i > $o] :
( ( A @ ( sk1 @ A ) )
| ~ $true
| ( ( sk2 @ ( sk1 @ A ) )
!= ( sk2 @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,6]) ).
thf(67,plain,
! [A: $i > $o] :
( ( A @ ( sk1 @ A ) )
| ( ( sk2 @ ( sk1 @ A ) )
!= ( sk2 @ ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
sk2 @ ( sk1 @ sk2 ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( sk2 ))]]) ).
thf(147,plain,
$false,
inference(rewrite,[status(thm)],[68,6]) ).
thf(148,plain,
$false,
inference(simp,[status(thm)],[147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV177^5 : 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
% 0.09/0.20 % Computer : n020.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:19:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.94/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/0.97 % [INFO] Parsing done (182ms).
% 1.29/0.98 % [INFO] Running in sequential loop mode.
% 1.87/1.37 % [INFO] eprover registered as external prover.
% 1.87/1.38 % [INFO] Scanning for conjecture ...
% 2.05/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.05/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.19/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.50 % [INFO] Type checking passed.
% 2.19/1.51 % [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 ...
% 5.63/2.78 % [INFO] Killing All external provers ...
% 5.63/2.79 % Time passed: 2449ms (effective reasoning time: 1796ms)
% 5.63/2.79 % 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)>
% 5.63/2.79 % Axioms used in derivation (0):
% 5.63/2.79 % No. of inferences in proof: 17
% 5.63/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2449 ms resp. 1796 ms w/o parsing
% 6.11/2.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.11/2.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------