%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO148^5 : 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 08:45:18 AM UTC 2026
% Result : Theorem 3.97s 1.83s
% Output : Refutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 149 ( 49 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 159 ( 46 ~; 18 |; 1 &; 91 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 6 ^; 15 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cZ_decl,type,
cZ: a > $o ).
thf(cY_decl,type,
cY: a > $o ).
thf(cX_decl,type,
cX: a > $o ).
thf(sk1_decl,type,
sk1: a ).
thf(1,conjecture,
( ! [A: a] :
( ( ~ ( cX @ A ) )
= ( ( cY @ A )
= ( cZ @ A ) ) )
=> ( cX
= ( ^ [A: a] :
( ( cY @ A )
!= ( cZ @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL25) ).
thf(2,negated_conjecture,
~ ( ! [A: a] :
( ( ~ ( cX @ A ) )
= ( ( cY @ A )
= ( cZ @ A ) ) )
=> ( cX
= ( ^ [A: a] :
( ( cY @ A )
!= ( cZ @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a] :
( ( ~ ( cX @ A ) )
= ( ( cY @ A )
= ( cZ @ A ) ) )
=> ( cX
= ( ^ [A: a] :
( ( cY @ A )
!= ( cZ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: a] :
( ( ( ~ ( cX @ A ) )
= ( ( cY @ A )
= ( cZ @ A ) ) )
& ( cX
!= ( ^ [B: a] :
( ( cY @ B )
!= ( cZ @ B ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: a] :
( ( ~ ( cX @ A ) )
= ( ( cY @ A )
= ( cZ @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [A: a] :
( ( ~ ( cX @ A ) )
= ( ( cY @ A )
= ( cZ @ A ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(16,plain,
! [A: a] :
( ~ ~ ( cX @ A )
| ( ( cY @ A )
= ( cZ @ A ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(18,plain,
! [A: a] :
( ( ( cY @ A )
= ( cZ @ A ) )
| ~ ~ ( cX @ A ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(20,plain,
! [A: a] :
( ( ( cY @ A )
= ( cZ @ A ) )
| ( cX @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(6,plain,
( cX
!= ( ^ [A: a] :
( ( cY @ A )
!= ( cZ @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( cX
!= ( ^ [A: a] :
( ( cY @ A )
!= ( cZ @ A ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
( ( cX @ sk1 )
!= ( ( cY @ sk1 )
!= ( cZ @ sk1 ) ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(10,plain,
( ~ ( cX @ sk1 )
| ~ ( ( ( cY @ sk1 )
!= ( cZ @ sk1 ) ) ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(12,plain,
( ~ ( cX @ sk1 )
| ( ( cY @ sk1 )
= ( cZ @ sk1 ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(13,plain,
( ( ( cY @ sk1 )
= ( cZ @ sk1 ) )
| ~ ( cX @ sk1 ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(37,plain,
! [A: a] :
( ( ( cY @ A )
= ( cZ @ A ) )
| ( ( cY @ sk1 )
= ( cZ @ sk1 ) )
| ~ $true
| ( ( cX @ A )
!= ( cX @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[20,13]) ).
thf(38,plain,
! [A: a] :
( ( ( cY @ A )
= ( cZ @ A ) )
| ( ( cY @ sk1 )
= ( cZ @ sk1 ) )
| ( ( cX @ A )
!= ( cX @ sk1 ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
( ( ( cY @ sk1 )
= ( cZ @ sk1 ) )
| ( ( cY @ sk1 )
= ( cZ @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk1 ))]]) ).
thf(45,plain,
( ( cY @ sk1 )
= ( cZ @ sk1 ) ),
inference(simp,[status(thm)],[39]) ).
thf(17,plain,
! [A: a] :
( ~ ( cX @ A )
| ( ( cY @ A )
!= ( cZ @ A ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(19,plain,
! [A: a] :
( ( ( cY @ A )
!= ( cZ @ A ) )
| ~ ( cX @ A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(21,plain,
! [A: a] :
( ( ( cY @ A )
!= ( cZ @ A ) )
| ~ ( cX @ A ) ),
inference(cnf,[status(esa)],[19]) ).
thf(53,plain,
! [A: a] :
( ( ( cZ @ sk1 )
!= ( cZ @ A ) )
| ~ ( cX @ A )
| ( ( cY @ sk1 )
!= ( cY @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,21]) ).
thf(54,plain,
( ( ( cZ @ sk1 )
!= ( cZ @ sk1 ) )
| ~ ( cX @ sk1 ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( sk1 ))]]) ).
thf(58,plain,
~ ( cX @ sk1 ),
inference(simp,[status(thm)],[54]) ).
thf(47,plain,
( ( cX @ sk1 )
!= ( ( cZ @ sk1 )
!= ( cZ @ sk1 ) ) ),
inference(rewrite,[status(thm)],[9,45]) ).
thf(48,plain,
cX @ sk1,
inference(simp,[status(thm)],[47]) ).
thf(72,plain,
~ $true,
inference(rewrite,[status(thm)],[58,48]) ).
thf(73,plain,
$false,
inference(simp,[status(thm)],[72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO148^5 : 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
% 0.12/0.20 % Computer : n013.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Sep 29 16:34:51 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 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
% 0.69/0.54 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.09/0.66 % [INFO] Parsing done (116ms).
% 1.09/0.67 % [INFO] Running in sequential loop mode.
% 1.62/0.90 % [INFO] eprover registered as external prover.
% 1.62/0.91 % [INFO] Scanning for conjecture ...
% 1.62/0.96 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.62/0.98 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.62/0.99 % [INFO] Problem is higher-order (TPTP THF).
% 1.62/0.99 % [INFO] Type checking passed.
% 1.62/0.99 % [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 ...
% 3.97/1.82 % [INFO] Killing All external provers ...
% 3.97/1.83 % Time passed: 1535ms (effective reasoning time: 1155ms)
% 3.97/1.83 % 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)>
% 3.97/1.83 % Axioms used in derivation (0):
% 3.97/1.83 % No. of inferences in proof: 29
% 3.97/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1535 ms resp. 1155 ms w/o parsing
% 4.25/1.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.25/1.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------