%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV200^5 : 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 : 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 08:36:59 AM UTC 2026
% Result : Theorem 4.01s 2.35s
% Output : Refutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 85 ( 70 equ; 0 cnn)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 370 ( 33 ~; 31 |; 63 &; 215 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 11 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 119 ( 2 ^; 82 !; 32 ?; 119 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(x_decl,type,
x: a ).
thf(cZ_decl,type,
cZ: a ).
thf(cP_decl,type,
cP: a > a > a ).
thf(sk1_decl,type,
sk1: ( a > $o ) > a ).
thf(sk2_decl,type,
sk2: ( a > $o ) > a ).
thf(sk3_decl,type,
sk3: a > a > a > $o ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > $o] :
@+[B: a] :
~ ! [C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: a > $o] :
@+[B: a] :
~ ( ( ( A @ ( sk1 @ A ) )
& ( A @ B ) )
=> ( A @ ( cP @ ( sk1 @ A ) @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > a > a > $o] :
~ ( ! [B: a,C: a,D: a] :
( ( ( ( B = cZ )
& ( C = D ) )
| ( ( C = cZ )
& ( 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 @ cZ @ x @ x ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: a,B: a] :
( ( cP @ A @ B )
!= cZ )
& ! [A: a,B: a,C: a,D: a] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: a > $o] :
( ( ( A @ cZ )
& ! [B: a,C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: a] : ( A @ B ) ) )
=> ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = cZ )
& ( C = D ) )
| ( ( C = cZ )
& ( 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 @ cZ @ x @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_LEM1C_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: a,B: a] :
( ( cP @ A @ B )
!= cZ )
& ! [A: a,B: a,C: a,D: a] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: a > $o] :
( ( ( A @ cZ )
& ! [B: a,C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: a] : ( A @ B ) ) )
=> ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = cZ )
& ( C = D ) )
| ( ( C = cZ )
& ( 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 @ cZ @ x @ x ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: a,B: a] :
( ( cP @ A @ B )
!= cZ )
& ! [A: a,B: a,C: a,D: a] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: a > $o] :
( ( ( A @ cZ )
& ! [B: a,C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: a] : ( A @ B ) ) )
=> ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = cZ )
& ( C = D ) )
| ( ( C = cZ )
& ( 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 @ cZ @ x @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ~ ? [A: a,B: a] :
( ( cP @ A @ B )
= cZ )
& ! [A: a,B: a,C: a,D: a] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: a > $o] :
( ( ( A @ cZ )
& ! [B: a,C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: a] : ( A @ B ) ) )
=> ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = cZ )
& ( C = D ) )
| ( ( C = cZ )
& ( 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 @ cZ @ x @ x ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [Q: a,P: a,O: a,N: a,M: a,L: a,K: a,J: a,I: a,H: a,G: a > $o,F: a,E: a,D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ B )
!= cZ )
& ( ( ( cP @ C @ E )
!= ( cP @ D @ F ) )
| ( C = D ) )
& ( ( ( cP @ C @ E )
!= ( cP @ D @ F ) )
| ( E = F ) )
& ( ~ ( G @ cZ )
| ( G @ ( sk1 @ G ) )
| ( G @ H ) )
& ( ~ ( G @ cZ )
| ( G @ ( sk2 @ G ) )
| ( G @ H ) )
& ( ~ ( G @ cZ )
| ~ ( G @ ( cP @ ( sk1 @ G ) @ ( sk2 @ G ) ) )
| ( G @ H ) )
& ( ( I != cZ )
| ( J != K )
| ( sk3 @ I @ J @ K ) )
& ( ( J != cZ )
| ( I != K )
| ( sk3 @ I @ J @ K ) )
& ( ( I
!= ( cP @ L @ M ) )
| ( J
!= ( cP @ N @ O ) )
| ( K
!= ( cP @ P @ Q ) )
| ~ ( sk3 @ L @ N @ P )
| ~ ( sk3 @ M @ O @ Q )
| ( sk3 @ I @ J @ K ) )
& ~ ( sk3 @ cZ @ x @ x ) ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
~ ( sk3 @ cZ @ x @ x ),
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
! [C: a,B: a,A: a] :
( ( A != cZ )
| ( B != C )
| ( sk3 @ A @ B @ C ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(29,plain,
! [C: a,B: a,A: a] :
( ( A != cZ )
| ( B != C )
| ( sk3 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(30,plain,
! [A: a] : ( sk3 @ cZ @ A @ A ),
inference(simp,[status(thm)],[29]) ).
thf(43,plain,
~ $true,
inference(rewrite,[status(thm)],[12,30]) ).
thf(44,plain,
$false,
inference(simp,[status(thm)],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV200^5 : 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
% 0.09/0.21 % Computer : n010.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 15:21:32 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (200ms).
% 1.22/1.02 % [INFO] Running in sequential loop mode.
% 2.01/1.43 % [INFO] eprover registered as external prover.
% 2.01/1.44 % [INFO] Scanning for conjecture ...
% 2.21/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.41/1.61 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.41/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.41/1.62 % [INFO] Type checking passed.
% 2.41/1.62 % [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 ...
% 4.01/2.34 % [INFO] Killing All external provers ...
% 4.01/2.35 % Time passed: 1993ms (effective reasoning time: 1314ms)
% 4.01/2.35 % 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)>
% 4.01/2.35 % Axioms used in derivation (0):
% 4.01/2.35 % No. of inferences in proof: 11
% 4.01/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1993 ms resp. 1314 ms w/o parsing
% 4.34/2.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.34/2.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------