%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO361^5 : 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 : n009.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 5.54s 2.59s
% Output : Refutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 66 ( 51 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 319 ( 45 ~; 56 |; 2 &; 204 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 90 ( 37 ^; 49 !; 0 ?; 90 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $o ).
thf(sk4_decl,type,
sk4: ( $i > $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( A = B )
= ( ! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( sk1 = A )
!= ( ! [B: $i > $i > $o] :
( ! [C: $i] : ( B @ C @ C )
=> ( B @ sk1 @ A ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i > $o] :
~ ( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i > $i > $o] :
@+[B: $i] :
~ ( A @ B @ B ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A = B )
= ( ! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM47) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( A = B )
= ( ! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i] :
( ( A = B )
= ( ! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk1 = sk2 )
!= ( ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( sk1 = sk2 )
!= ( ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( sk1 = sk2 )
| ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( sk2 = sk1 )
| ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
! [A: $i > $i > $o] :
( ( sk2 = sk1 )
| ~ ( A @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(6,plain,
( ( sk1 != sk2 )
| ~ ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( sk2 != sk1 )
| ~ ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
! [A: $i] :
( ( ( sk2 != sk1 )
| ( sk3 @ A @ A ) )
& ( ( sk2 != sk1 )
| ~ ( sk3 @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( sk3 @ A @ A ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(12,plain,
( ( sk2 != sk1 )
| ~ ( sk3 @ sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(14,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( sk2 != sk1 )
| ~ $true
| ( ( sk3 @ A @ A )
!= ( sk3 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(15,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( ( sk3 @ A @ A )
!= ( sk3 @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(16,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( A != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[15]) ).
thf(17,plain,
sk2 != sk1,
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [A: $i > $i > $o] :
( ~ ( A @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 ) ),
inference(simplifyReflect,[status(thm)],[13,17]) ).
thf(23,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( B
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ) )
| ( A @ sk1 @ sk2 )
| ( B @ sk1 @ sk2 ) ),
inference(prim_subst,[status(thm)],[18:[bind(A,$thf( ^ [D: $i] : ^ [E: $i] : ( ( B @ D @ E ) | ( C @ D @ E ) ) ))]]) ).
thf(27,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( ~ ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( A @ sk1 @ sk2 )
| ( B @ sk1 @ sk2 ) )
& ( ~ ( B
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( A @ sk1 @ sk2 )
| ( B @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(28,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( A @ sk1 @ sk2 )
| ( B @ sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(30,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( A @ sk1 @ sk2 )
| ( B @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[28]) ).
thf(74,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( A @ sk1 @ sk2 )
| ( ( B @ sk1 @ sk2 )
!= ( A @ sk1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[30]) ).
thf(85,plain,
! [A: $i > $i > $o] :
( ( ( sk4
@ ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) )
!= ( sk4
@ ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) )
| ( sk1 = sk2 )
| ( ( A @ sk1 @ sk2 )
!= ( sk1 = sk2 ) )
| ~ $true ),
inference(replace_andrewseq,[status(thm)],[74:[bind(A,$thf( (=) @ $i ))]]) ).
thf(97,plain,
! [A: $i > $i > $o] :
( ( ( sk4
@ ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) )
!= ( sk4
@ ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) )
| ( sk2 = sk1 )
| ( ( A @ sk1 @ sk2 )
!= ( sk1 = sk2 ) )
| ~ $true ),
inference(lifteq,[status(thm)],[85]) ).
thf(128,plain,
( ~ $true
| ( sk2 = sk1 ) ),
inference(pre_uni,[status(thm)],[97:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( B = sk2 ) ))]]) ).
thf(140,plain,
sk2 = sk1,
inference(simp,[status(thm)],[128]) ).
thf(190,plain,
$false,
inference(simplifyReflect,[status(thm)],[140,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO361^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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 : n009.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 16:49:00 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
% 0.63/0.52 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.94/0.68 % [INFO] Parsing done (163ms).
% 1.07/0.70 % [INFO] Running in sequential loop mode.
% 1.51/1.09 % [INFO] eprover registered as external prover.
% 1.51/1.09 % [INFO] Scanning for conjecture ...
% 1.69/1.18 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.80/1.21 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.80/1.21 % [INFO] Problem is higher-order (TPTP THF).
% 1.80/1.22 % [INFO] Type checking passed.
% 1.80/1.22 % [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 ...
% 5.54/2.58 % [INFO] Killing All external provers ...
% 5.54/2.58 % Time passed: 2271ms (effective reasoning time: 1876ms)
% 5.54/2.58 % 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)>
% 5.54/2.59 % Axioms used in derivation (0):
% 5.54/2.59 % No. of inferences in proof: 28
% 5.54/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2271 ms resp. 1876 ms w/o parsing
% 5.97/2.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.97/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------