%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO223^5 : 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 : 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 08:45:25 AM UTC 2026
% Result : Theorem 9.46s 3.81s
% Output : Refutation 9.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 2
% Syntax : Number of formulae : 45 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 141 ( 49 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 285 ( 54 ~; 42 |; 16 &; 167 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 74 ( 6 ^; 50 !; 17 ?; 74 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cJ_decl,type,
cJ: $i ).
thf(cLIKE_decl,type,
cLIKE: $i > $i > $o ).
thf(cUNIQUE_decl,type,
cUNIQUE: $i > $o ).
thf(cS_decl,type,
cS: $i ).
thf(cP_decl,type,
cP: $i ).
thf(sk2_decl,type,
sk2: ( $i > $o ) > $i ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $o] :
@+[B: $i] : ( cLIKE @ cJ @ B ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( cUNIQUE @ A )
=> ! [B: $i] : ( A = B ) )
& ( cUNIQUE @ cS ) )
=> ? [A: $i > $o] :
( ( ( A @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( A @ cJ )
= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cLING2) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( cUNIQUE @ A )
=> ! [B: $i] : ( A = B ) )
& ( cUNIQUE @ cS ) )
=> ? [A: $i > $o] :
( ( ( A @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( A @ cJ )
= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] :
( ( cUNIQUE @ A )
=> ! [B: $i] : ( A = B ) )
& ( cUNIQUE @ cS ) )
=> ? [A: $i > $o] :
( ( ( A @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( A @ cJ )
= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i > $o,B: $i,A: $i] :
( ( ~ ( cUNIQUE @ A )
| ( A = B ) )
& ( cUNIQUE @ cS )
& ( ( ( C @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( C @ cJ )
!= ( ? [D: $i] :
( ( cUNIQUE @ D )
& ( cLIKE @ cJ @ D ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [A: $i > $o] :
( ( ( A @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( A @ cJ )
!= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i > $o] :
( ( ( A @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( A @ cJ )
!= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(10,plain,
! [A: $i > $o] :
( ( ( A @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( A @ cJ )
!= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(6,plain,
cUNIQUE @ cS,
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ~ ( cUNIQUE @ A )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( cUNIQUE @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ $true
| ( ( cUNIQUE @ cS )
!= ( cUNIQUE @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,8]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( cUNIQUE @ cS )
!= ( cUNIQUE @ A ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(17,plain,
! [A: $i] : ( cS = A ),
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( cS ))]]) ).
thf(18,plain,
! [A: $i] : ( cS = A ),
inference(simp,[status(thm)],[17]) ).
thf(20,plain,
! [A: $i] :
( ( cUNIQUE @ A )
| ( cS != cS ) ),
inference(paramod_ordered,[status(thm)],[18,6]) ).
thf(21,plain,
! [A: $i] : ( cUNIQUE @ A ),
inference(pattern_uni,[status(thm)],[20:[]]) ).
thf(33,plain,
! [A: $i > $o] :
( ( ( A @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( A @ cJ )
!= ( ? [B: $i] :
( $true
& ( cLIKE @ cJ @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[10,21]) ).
thf(34,plain,
! [A: $i > $o] :
( ( ( A @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( A @ cJ )
!= ( ? [B: $i] : ( cLIKE @ cJ @ B ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(38,plain,
! [A: $i > $o] :
( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ? [B: $i] : ( cLIKE @ cJ @ B ) ),
inference(bool_ext,[status(thm)],[34]) ).
thf(63,plain,
! [A: $i > $o] :
( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ( cLIKE @ cJ @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ $true ),
inference(rewrite,[status(thm)],[8,21]) ).
thf(32,plain,
! [B: $i,A: $i] : ( A = B ),
inference(simp,[status(thm)],[31]) ).
thf(49,plain,
! [B: $i > $o,A: $i] :
( ~ ( cLIKE @ cP @ cS )
| ( ( B @ cJ )
!= ( ? [C: $i] : ( cLIKE @ cJ @ C ) ) )
| ( ( cUNIQUE @ A )
!= ( B @ cP ) ) ),
inference(paramod_ordered,[status(thm)],[21,34]) ).
thf(58,plain,
! [A: $i > $i] :
( ~ ( cLIKE @ cP @ cS )
| ( ( cUNIQUE @ ( A @ cJ ) )
!= ( ? [B: $i] : ( cLIKE @ cJ @ B ) ) ) ),
inference(pre_uni,[status(thm)],[49:[bind(A,$thf( C @ cP )),bind(B,$thf( ^ [D: $i] : ( cUNIQUE @ ( C @ D ) ) ))]]) ).
thf(70,plain,
! [A: $i > $i] :
( ~ ( cLIKE @ cP @ cS )
| ( ( cUNIQUE @ ( A @ cJ ) )
!= ( ? [B: $i] : ( cLIKE @ cJ @ B ) ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(72,plain,
( ~ ( cLIKE @ cP @ cS )
| ~ ? [A: $i] : ( cLIKE @ cJ @ A ) ),
inference(rewrite,[status(thm)],[70,21]) ).
thf(73,plain,
! [A: $i] :
( ~ ( cLIKE @ cP @ cS )
| ~ ( cLIKE @ cJ @ A ) ),
inference(cnf,[status(esa)],[72]) ).
thf(189,plain,
! [A: $i] :
( ~ ( cLIKE @ cP @ cS )
| ( ( cLIKE @ cJ @ A )
!= ( cLIKE @ cP @ cS ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[73]) ).
thf(191,plain,
! [A: $i] :
( ~ ( cLIKE @ cP @ cS )
| ( cP != cJ )
| ( A != cS ) ),
inference(simp,[status(thm)],[189]) ).
thf(200,plain,
( ~ ( cLIKE @ cP @ cS )
| ( cP != cJ ) ),
inference(simp,[status(thm)],[191]) ).
thf(201,plain,
~ ( cLIKE @ cP @ cS ),
inference(simplifyReflect,[status(thm)],[200,32]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( cLIKE @ A @ cS )
| ( B != cP ) ),
inference(paramod_ordered,[status(thm)],[32,201]) ).
thf(208,plain,
! [A: $i] :
~ ( cLIKE @ A @ cS ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( A )),bind(B,$thf( cP ))]]) ).
thf(262,plain,
! [A: $i > $o] :
( ( A @ cP )
| $false
| ( A @ cJ )
| ( cLIKE @ cJ @ ( sk2 @ A ) ) ),
inference(rewrite,[status(thm)],[63,208]) ).
thf(263,plain,
! [A: $i > $o] :
( ( A @ cP )
| ( A @ cJ )
| ( cLIKE @ cJ @ ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(298,plain,
( $false
| $false
| ( cLIKE @ cJ
@ ( sk2
@ ^ [A: $i] : $false ) ) ),
inference(prim_subst,[status(thm)],[263:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(319,plain,
( cLIKE @ cJ
@ ( sk2
@ ^ [A: $i] : $false ) ),
inference(simp,[status(thm)],[298]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ~ ( cLIKE @ cP @ A )
| ( B != cS ) ),
inference(paramod_ordered,[status(thm)],[32,201]) ).
thf(210,plain,
! [A: $i] :
~ ( cLIKE @ cP @ A ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( cS ))]]) ).
thf(344,plain,
! [A: $i] :
( ~ $true
| ( ( cLIKE @ cP @ A )
!= ( cLIKE @ cJ
@ ( sk2
@ ^ [B: $i] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[319,210]) ).
thf(345,plain,
! [A: $i] :
( ( cLIKE @ cP @ A )
!= ( cLIKE @ cJ
@ ( sk2
@ ^ [B: $i] : $false ) ) ),
inference(simp,[status(thm)],[344]) ).
thf(352,plain,
! [A: $i] :
( ( cP != cJ )
| ( A
!= ( sk2
@ ^ [B: $i] : $false ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(353,plain,
cP != cJ,
inference(simp,[status(thm)],[352]) ).
thf(358,plain,
$false,
inference(simplifyReflect,[status(thm)],[353,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO223^5 : 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
% 0.10/0.26 % Computer : n010.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:40:18 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 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
% 1.13/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.60/1.20 % [INFO] Parsing done (201ms).
% 1.72/1.21 % [INFO] Running in sequential loop mode.
% 2.34/1.68 % [INFO] eprover registered as external prover.
% 2.34/1.68 % [INFO] Scanning for conjecture ...
% 2.56/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.75/1.83 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.75/1.83 % [INFO] Problem is higher-order (TPTP THF).
% 2.75/1.83 % [INFO] Type checking passed.
% 2.75/1.84 % [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 ...
% 8.95/3.80 % [INFO] Killing All external provers ...
% 9.46/3.80 % Time passed: 3327ms (effective reasoning time: 2578ms)
% 9.46/3.80 % 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)>
% 9.46/3.81 % Axioms used in derivation (0):
% 9.46/3.81 % No. of inferences in proof: 44
% 9.46/3.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3327 ms resp. 2578 ms w/o parsing
% 9.46/3.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.46/3.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------