%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV194^5 : 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 : n018.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 08:36:59 AM UTC 2026
% Result : Theorem 3.53s 2.18s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 62 ( 47 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 214 ( 20 ~; 23 |; 35 &; 126 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 11 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 66 ( 0 ^; 35 !; 30 ?; 66 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(x_decl,type,
x: a ).
thf(c0_decl,type,
c0: a ).
thf(cP_decl,type,
cP: a > a > a ).
thf(sk1_decl,type,
sk1: a > a > a > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > a > a > $o] :
~ ( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a] :
( ( B
= ( cP @ E @ F ) )
& ? [G: a,H: a] :
( ( C
= ( cP @ G @ H ) )
& ? [I: a,J: a] :
( ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ c0 @ x @ x ) ) ) ) ).
thf(1,conjecture,
! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) ) )
=> ( A @ c0 @ x @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_INCL_LEM2_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) ) )
=> ( A @ c0 @ x @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ c0 @ x @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a] :
( ( B
= ( cP @ E @ F ) )
& ? [G: a,H: a] :
( ( C
= ( cP @ G @ H ) )
& ? [I: a,J: a] :
( ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ c0 @ x @ x ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [I: a,H: a,G: a,F: a,E: a,D: a,C: a,B: a,A: a] :
( ( ( A != c0 )
| ( B != C )
| ( sk1 @ A @ B @ C ) )
& ( ( B != c0 )
| ( A != C )
| ( sk1 @ A @ B @ C ) )
& ( ( A
!= ( cP @ D @ E ) )
| ( B
!= ( cP @ F @ G ) )
| ( C
!= ( cP @ H @ I ) )
| ~ ( sk1 @ D @ F @ H )
| ~ ( sk1 @ E @ G @ I )
| ( sk1 @ A @ B @ C ) )
& ~ ( sk1 @ c0 @ x @ x ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
~ ( sk1 @ c0 @ x @ x ),
inference(cnfConj,[status(thm)],[5]) ).
thf(6,plain,
! [C: a,B: a,A: a] :
( ( A != c0 )
| ( B != C )
| ( sk1 @ A @ B @ C ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [C: a,B: a,A: a] :
( ( A != c0 )
| ( B != C )
| ( sk1 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: a] : ( sk1 @ c0 @ A @ A ),
inference(simp,[status(thm)],[10]) ).
thf(16,plain,
~ $true,
inference(rewrite,[status(thm)],[9,11]) ).
thf(17,plain,
$false,
inference(simp,[status(thm)],[16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV194^5 : 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
% 0.11/0.21 % Computer : n018.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 15:22:11 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (179ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 2.04/1.40 % [INFO] eprover registered as external prover.
% 2.04/1.41 % [INFO] Scanning for conjecture ...
% 2.23/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.58 % [INFO] Type checking passed.
% 2.23/1.59 % [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 ...
% 3.53/2.17 % [INFO] Killing All external provers ...
% 3.53/2.18 % Time passed: 1814ms (effective reasoning time: 1174ms)
% 3.53/2.18 % 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)>
% 3.53/2.18 % Axioms used in derivation (0):
% 3.53/2.18 % No. of inferences in proof: 11
% 3.53/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1814 ms resp. 1174 ms w/o parsing
% 3.73/2.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.73/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------