%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV236^5 : 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 : n013.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 08:37:03 AM UTC 2026
% Result : Theorem 6.18s 2.94s
% Output : Refutation 6.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 121 ( 15 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 324 ( 53 ~; 40 |; 19 &; 180 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 13 ^; 44 !; 13 ?; 74 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cS_decl,type,
cS: a > $o ).
thf(cK_decl,type,
cK: ( a > $o ) > a > $o ).
thf(sk1_decl,type,
sk1: ( a > $o ) > ( a > $o ) > a ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: ( a > $o ) > a ).
thf(sk5_decl,type,
sk5: a > $o ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > $o,B: a > $o] :
@+[C: a] :
~ ( ( B @ C )
=> ( A @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a] :
~ ( ( cK @ cS @ A )
=> ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cS @ D ) )
& ( C @ B ) )
@ A ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: a > $o] :
@+[B: a] :
~ ( ( A @ B )
=> ( cS @ B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cS @ B ) )
& ( A @ sk3 ) ) ) ) ).
thf(1,conjecture,
( ! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: a] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) )
=> ! [A: a] :
( ( cK @ cS @ A )
=> ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cS @ D ) )
& ( C @ B ) )
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM91_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: a] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) )
=> ! [A: a] :
( ( cK @ cS @ A )
=> ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cS @ D ) )
& ( C @ B ) )
@ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ! [C: a] :
( ( cK @ A @ C )
=> ( cK @ B @ C ) ) )
=> ! [A: a] :
( ( cK @ cS @ A )
=> ( cK
@ ^ [B: a] :
? [C: a > $o] :
( ! [D: a] :
( ( C @ D )
=> ( cS @ D ) )
& ( C @ B ) )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: a,B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( cK @ B @ C ) )
& ( ~ ( B @ ( sk1 @ B @ A ) )
| ~ ( cK @ A @ C )
| ( cK @ B @ C ) )
& ( cK @ cS @ sk2 )
& ~ ( cK
@ ^ [D: a] :
? [E: a > $o] :
( ! [F: a] :
( ( E @ F )
=> ( cS @ F ) )
& ( E @ D ) )
@ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
cK @ cS @ sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
~ ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cS @ C ) )
& ( B @ A ) )
@ sk2 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ~ $true
| ( ( cK @ cS @ sk2 )
!= ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cS @ C ) )
& ( B @ A ) )
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(10,plain,
( ( cK @ cS @ sk2 )
!= ( cK
@ ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cS @ C ) )
& ( B @ A ) )
@ sk2 ) ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
( ( cS
!= ( ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cS @ C ) )
& ( B @ A ) ) ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
( cS
!= ( ^ [A: a] :
? [B: a > $o] :
( ! [C: a] :
( ( B @ C )
=> ( cS @ C ) )
& ( B @ A ) ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
( ( cS @ sk3 )
!= ( ? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cS @ B ) )
& ( A @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[12]) ).
thf(14,plain,
( ~ ( cS @ sk3 )
| ~ ? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cS @ B ) )
& ( A @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[13]) ).
thf(16,plain,
! [A: a > $o] :
( ( ~ ( cS @ sk3 )
| ( A @ ( sk4 @ A ) )
| ~ ( A @ sk3 ) )
& ( ~ ( cS @ sk3 )
| ~ ( cS @ ( sk4 @ A ) )
| ~ ( A @ sk3 ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(17,plain,
! [A: a > $o] :
( ~ ( cS @ sk3 )
| ( A @ ( sk4 @ A ) )
| ~ ( A @ sk3 ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(15,plain,
( ( cS @ sk3 )
| ? [A: a > $o] :
( ! [B: a] :
( ( A @ B )
=> ( cS @ B ) )
& ( A @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[13]) ).
thf(19,plain,
! [A: a] :
( ( ( cS @ sk3 )
| ~ ( sk5 @ A )
| ( cS @ A ) )
& ( ( cS @ sk3 )
| ( sk5 @ sk3 ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(21,plain,
( ( cS @ sk3 )
| ( sk5 @ sk3 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(20,plain,
! [A: a] :
( ( cS @ sk3 )
| ~ ( sk5 @ A )
| ( cS @ A ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(266,plain,
! [A: a] :
( ( cS @ sk3 )
| ( cS @ sk3 )
| ~ $true
| ( cS @ A )
| ( ( sk5 @ sk3 )
!= ( sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,20]) ).
thf(267,plain,
! [A: a] :
( ( cS @ sk3 )
| ( cS @ A )
| ( ( sk5 @ sk3 )
!= ( sk5 @ A ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(268,plain,
( ( cS @ sk3 )
| ( cS @ sk3 ) ),
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( sk3 ))]]) ).
thf(270,plain,
cS @ sk3,
inference(simp,[status(thm)],[268]) ).
thf(424,plain,
! [A: a > $o] :
( ~ $true
| ( A @ ( sk4 @ A ) )
| ~ ( A @ sk3 ) ),
inference(rewrite,[status(thm)],[17,270]) ).
thf(425,plain,
! [A: a > $o] :
( ( A @ ( sk4 @ A ) )
| ~ ( A @ sk3 ) ),
inference(simp,[status(thm)],[424]) ).
thf(18,plain,
! [A: a > $o] :
( ~ ( cS @ sk3 )
| ~ ( cS @ ( sk4 @ A ) )
| ~ ( A @ sk3 ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(25,plain,
! [A: a > $o] :
( ~ ( cS @ sk3 )
| ~ ( cS @ ( sk4 @ A ) )
| ( ( A @ sk3 )
!= ( cS @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[18]) ).
thf(37,plain,
( ~ ( cS @ sk3 )
| ~ ( cS @ ( sk4 @ cS ) ) ),
inference(pre_uni,[status(thm)],[25:[bind(A,$thf( cS ))]]) ).
thf(361,plain,
( ~ $true
| ~ ( cS @ ( sk4 @ cS ) ) ),
inference(rewrite,[status(thm)],[37,270]) ).
thf(362,plain,
~ ( cS @ ( sk4 @ cS ) ),
inference(simp,[status(thm)],[361]) ).
thf(454,plain,
! [A: a > $o] :
( ~ ( A @ sk3 )
| ~ $true
| ( ( A @ ( sk4 @ A ) )
!= ( cS @ ( sk4 @ cS ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,362]) ).
thf(455,plain,
! [A: a > $o] :
( ~ ( A @ sk3 )
| ( ( A @ ( sk4 @ A ) )
!= ( cS @ ( sk4 @ cS ) ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(481,plain,
~ ( cS @ sk3 ),
inference(pre_uni,[status(thm)],[455:[bind(A,$thf( cS ))]]) ).
thf(504,plain,
~ $true,
inference(rewrite,[status(thm)],[481,270]) ).
thf(505,plain,
$false,
inference(simp,[status(thm)],[504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV236^5 : 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
% 0.11/0.22 % Computer : n013.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 15:26:10 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.97 % [INFO] Parsing done (174ms).
% 1.16/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.38 % [INFO] eprover registered as external prover.
% 1.72/1.39 % [INFO] Scanning for conjecture ...
% 1.91/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.05/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.05/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.53 % [INFO] Type checking passed.
% 2.05/1.53 % [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 ...
% 6.18/2.94 % [INFO] Killing All external provers ...
% 6.18/2.94 % Time passed: 2573ms (effective reasoning time: 1949ms)
% 6.18/2.94 % 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)>
% 6.18/2.94 % Axioms used in derivation (0):
% 6.18/2.94 % No. of inferences in proof: 34
% 6.18/2.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2573 ms resp. 1949 ms w/o parsing
% 6.18/2.97 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.18/2.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------