%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO362^5 : 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 : n010.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 08:45:39 AM UTC 2026
% Result : Theorem 7.87s 3.17s
% Output : Refutation 7.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 13 unt; 0 typ; 3 def)
% Number of atoms : 138 ( 31 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 329 ( 54 ~; 55 |; 5 &; 196 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 23 ^; 67 !; 0 ?; 93 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cK_decl,type,
cK: ( $i > $o ) > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk6_decl,type,
sk6: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ! [B: $i > $o] :
( ! [C: $i] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: $i] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ( ! [B: $i] :
( ( sk1 @ B )
=> ( A @ B ) )
=> ! [B: $i] :
( ( cK @ sk1 @ B )
=> ( cK @ A @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( cK @ sk1 @ A )
=> ( cK @ sk2 @ A ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i > $o,B: $i > $o] :
( ( cK
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: $i] :
( ( cK @ A @ C )
| ( cK @ B @ C ) ) ) )
=> ! [A: $i > $o,B: $i > $o] :
( ! [C: $i] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: $i] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM631A_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: $i > $o,B: $i > $o] :
( ( cK
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: $i] :
( ( cK @ A @ C )
| ( cK @ B @ C ) ) ) )
=> ! [A: $i > $o,B: $i > $o] :
( ! [C: $i] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: $i] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o,B: $i > $o] :
( ( cK
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: $i] :
( ( cK @ A @ C )
| ( cK @ B @ C ) ) ) )
=> ! [A: $i > $o,B: $i > $o] :
( ! [C: $i] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: $i] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( ( cK
@ ^ [D: $i] :
( ( A @ D )
| ( B @ D ) ) )
= ( ^ [D: $i] :
( ( cK @ A @ D )
| ( cK @ B @ D ) ) ) )
& ( ~ ( sk1 @ C )
| ( sk2 @ C ) )
& ( cK @ sk1 @ sk3 )
& ~ ( cK @ sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
cK @ sk1 @ sk3,
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [B: $i > $o,A: $i > $o] :
( ( cK
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: $i] :
( ( cK @ A @ C )
| ( cK @ B @ C ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [B: $i > $o,A: $i > $o] :
( ( cK
@ ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) )
= ( ^ [C: $i] :
( ( cK @ A @ C )
| ( cK @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(34,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( cK
@ ^ [D: $i] :
( ( A @ D )
| ( B @ D ) )
@ C )
= ( ( cK @ A @ C )
| ( cK @ B @ C ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(8,plain,
~ ( cK @ sk2 @ sk3 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(42,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( ( cK @ A @ C )
| ( cK @ B @ C ) )
| ( ( cK
@ ^ [D: $i] :
( ( A @ D )
| ( B @ D ) )
@ C )
!= ( cK @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[34,8]) ).
thf(43,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( ( cK @ A @ C )
| ( cK @ B @ C ) )
| ( ( ^ [D: $i] :
( ( A @ D )
| ( B @ D ) ) )
!= sk2 )
| ( C != sk3 ) ),
inference(simp,[status(thm)],[42]) ).
thf(50,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( ~ ( cK @ A @ C )
| ( ( ^ [D: $i] :
( ( A @ D )
| ( B @ D ) ) )
!= sk2 )
| ( C != sk3 ) )
& ( ~ ( cK @ B @ C )
| ( ( ^ [D: $i] :
( ( A @ D )
| ( B @ D ) ) )
!= sk2 )
| ( C != sk3 ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(51,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ~ ( cK @ A @ C )
| ( ( ^ [D: $i] :
( ( A @ D )
| ( B @ D ) ) )
!= sk2 )
| ( C != sk3 ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(53,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( cK @ A @ sk3 )
| ( ( ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) )
!= sk2 ) ),
inference(simp,[status(thm)],[51]) ).
thf(62,plain,
! [B: $i > $o,A: $i > $o] :
( ~ $true
| ( ( ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) )
!= sk2 )
| ( ( cK @ sk1 @ sk3 )
!= ( cK @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[7,53]) ).
thf(63,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( ^ [C: $i] :
( ( A @ C )
| ( B @ C ) ) )
!= sk2 )
| ( ( cK @ sk1 @ sk3 )
!= ( cK @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
! [A: $i > $o] :
( ( ^ [B: $i] :
( ( sk1 @ B )
| ( A @ B ) ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(65,plain,
! [A: $i > $o] :
( ( ^ [B: $i] :
( ( sk1 @ B )
| ( A @ B ) ) )
!= sk2 ),
inference(simp,[status(thm)],[64]) ).
thf(71,plain,
! [A: $i > $o] :
( ( ( sk1 @ ( sk6 @ A ) )
| ( A @ ( sk6 @ A ) ) )
!= ( sk2 @ ( sk6 @ A ) ) ),
inference(func_ext,[status(esa)],[65]) ).
thf(6,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(149,plain,
! [A: $i > $o] :
( ~ ( ( sk1 @ ( sk6 @ A ) )
| ( A @ ( sk6 @ A ) ) )
| ~ ( sk2 @ ( sk6 @ A ) ) ),
inference(bool_ext,[status(thm)],[71]) ).
thf(171,plain,
! [A: $i > $o] :
( ( ~ ( sk1 @ ( sk6 @ A ) )
| ~ ( sk2 @ ( sk6 @ A ) ) )
& ( ~ ( A @ ( sk6 @ A ) )
| ~ ( sk2 @ ( sk6 @ A ) ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(172,plain,
! [A: $i > $o] :
( ~ ( sk1 @ ( sk6 @ A ) )
| ~ ( sk2 @ ( sk6 @ A ) ) ),
inference(cnfConj,[status(thm)],[171]) ).
thf(190,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk1 @ A )
| ~ ( sk1 @ ( sk6 @ B ) )
| ~ $true
| ( ( sk2 @ A )
!= ( sk2 @ ( sk6 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,172]) ).
thf(191,plain,
! [B: $i > $o,A: $i] :
( ~ ( sk1 @ A )
| ~ ( sk1 @ ( sk6 @ B ) )
| ( ( sk2 @ A )
!= ( sk2 @ ( sk6 @ B ) ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
! [A: $i > $o] :
( ~ ( sk1 @ ( sk6 @ A ) )
| ~ ( sk1 @ ( sk6 @ A ) ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( sk6 @ C )),bind(B,$thf( C ))]]) ).
thf(194,plain,
! [A: $i > $o] :
~ ( sk1 @ ( sk6 @ A ) ),
inference(simp,[status(thm)],[192]) ).
thf(222,plain,
! [A: $i > $o] :
( ( $false
| ( A @ ( sk6 @ A ) ) )
!= ( sk2 @ ( sk6 @ A ) ) ),
inference(rewrite,[status(thm)],[71,194]) ).
thf(223,plain,
! [A: $i > $o] :
( ( A @ ( sk6 @ A ) )
!= ( sk2 @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(253,plain,
$false,
inference(pre_uni,[status(thm)],[223:[bind(A,$thf( sk2 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO362^5 : 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
% 0.10/0.20 % Computer : n010.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:49:18 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.97 % [INFO] Parsing done (190ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 2.05/1.40 % [INFO] eprover registered as external prover.
% 2.05/1.41 % [INFO] Scanning for conjecture ...
% 2.23/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.54 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.55 % [INFO] Type checking passed.
% 2.23/1.55 % [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 ...
% 7.87/3.16 % [INFO] Killing All external provers ...
% 7.87/3.17 % Time passed: 2816ms (effective reasoning time: 2171ms)
% 7.87/3.17 % 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)>
% 7.87/3.17 % Axioms used in derivation (0):
% 7.87/3.17 % No. of inferences in proof: 31
% 7.87/3.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2816 ms resp. 2171 ms w/o parsing
% 7.04/3.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.04/3.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------