%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV195^5 : 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 : n004.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 98.94s 26.72s
% Output : Refutation 98.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 92 ( 88 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 350 ( 75 ~; 38 |; 29 &; 190 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 117 ( 26 ^; 76 !; 12 ?; 117 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cP_decl,type,
cP: a > a > a ).
thf(cZ_decl,type,
cZ: a ).
thf(sk1_decl,type,
sk1: ( a > $o ) > a ).
thf(sk2_decl,type,
sk2: ( a > $o ) > a ).
thf(sk3_decl,type,
sk3: a ).
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 = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ) ) ).
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 = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_LEM1D_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 = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ),
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 = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ),
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 = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [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 ) )
& ( sk3 != cZ )
& ( sk3
!= ( cP @ I @ J ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(24,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(47,plain,
! [B: a > $o,A: a] :
( ~ ~ ( B @ cZ )
| ~ ~ ( B
@ ( cP
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[24:[bind(A,$thf( ^ [D: a] : ~ ( C @ D ) ))]]) ).
thf(71,plain,
! [B: a > $o,A: a] :
( ( B @ cZ )
| ( B
@ ( cP
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[47]) ).
thf(72,plain,
! [B: a > $o,A: a] :
( ( B @ cZ )
| ( B
@ ( cP
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[71]) ).
thf(11150,plain,
! [B: a > $o,A: a] :
( ( B @ cZ )
| ~ ( B @ A )
| ( ( B
@ ( cP
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) ) )
!= ( B @ cZ ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[72]) ).
thf(11270,plain,
! [A: a] :
( ( A = cZ )
| ( A != A )
| ( ( A
= ( cP
@ ( sk1
@ ^ [B: a] : ( A != B ) )
@ ( sk2
@ ^ [B: a] : ( A != B ) ) ) )
!= ( A = cZ ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[11150:[bind(A,$thf( A )),bind(B,$thf( (=) @ a @ A ))]]) ).
thf(11324,plain,
! [A: a] :
( ( A = cZ )
| ( A != A )
| ( ( A
= ( cP
@ ( sk1
@ ^ [B: a] : ( A != B ) )
@ ( sk2
@ ^ [B: a] : ( A != B ) ) ) )
!= ( A = cZ ) )
| ~ $true ),
inference(lifteq,[status(thm)],[11270]) ).
thf(11681,plain,
! [A: a] :
( ( A = cZ )
| ( ( A
= ( cP
@ ( sk1
@ ^ [B: a] : ( A != B ) )
@ ( sk2
@ ^ [B: a] : ( A != B ) ) ) )
!= ( A = cZ ) ) ),
inference(simp,[status(thm)],[11324]) ).
thf(13,plain,
sk3 != cZ,
inference(cnfConj,[status(thm)],[5]) ).
thf(25,plain,
sk3 != cZ,
inference(lifteq,[status(thm)],[13]) ).
thf(17476,plain,
! [A: a] :
( ( ( A
= ( cP
@ ( sk1
@ ^ [B: a] : ( A != B ) )
@ ( sk2
@ ^ [B: a] : ( A != B ) ) ) )
!= ( A = cZ ) )
| ( cZ != cZ )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[11681,25]) ).
thf(17477,plain,
! [A: a] :
( ( ( A
= ( cP
@ ( sk1
@ ^ [B: a] : ( A != B ) )
@ ( sk2
@ ^ [B: a] : ( A != B ) ) ) )
!= ( A = cZ ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[17476]) ).
thf(17478,plain,
( ( sk3
= ( cP
@ ( sk1
@ ^ [A: a] : ( sk3 != A ) )
@ ( sk2
@ ^ [A: a] : ( sk3 != A ) ) ) )
!= ( sk3 = cZ ) ),
inference(pattern_uni,[status(thm)],[17477:[bind(A,$thf( sk3 ))]]) ).
thf(18269,plain,
( ( sk3
= ( cP
@ ( sk1
@ ^ [A: a] : ( sk3 != A ) )
@ ( sk2
@ ^ [A: a] : ( sk3 != A ) ) ) )
| ( sk3 = cZ ) ),
inference(bool_ext,[status(thm)],[17478]) ).
thf(18316,plain,
( ( ( cP
@ ( sk1
@ ^ [A: a] : ( sk3 != A ) )
@ ( sk2
@ ^ [A: a] : ( sk3 != A ) ) )
= sk3 )
| ( sk3 = cZ ) ),
inference(lifteq,[status(thm)],[18269]) ).
thf(8,plain,
! [B: a,A: a] :
( sk3
!= ( cP @ A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(34,plain,
! [B: a,A: a] :
( ( cP @ A @ B )
!= sk3 ),
inference(lifteq,[status(thm)],[8]) ).
thf(35,plain,
! [B: a,A: a] :
( ( cP @ A @ B )
!= sk3 ),
inference(simp,[status(thm)],[34]) ).
thf(18384,plain,
$false,
inference(simplifyReflect,[status(thm)],[18316,35,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV195^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:20:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.87/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.99 % [INFO] Parsing done (193ms).
% 1.21/1.01 % [INFO] Running in sequential loop mode.
% 1.99/1.41 % [INFO] eprover registered as external prover.
% 1.99/1.42 % [INFO] Scanning for conjecture ...
% 2.18/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.18/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.18/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.18/1.57 % [INFO] Type checking passed.
% 2.18/1.57 % [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 ...
% 98.94/26.71 % [INFO] Killing All external provers ...
% 98.94/26.72 % Time passed: 26375ms (effective reasoning time: 25700ms)
% 98.94/26.72 % 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)>
% 98.94/26.72 % Axioms used in derivation (0):
% 98.94/26.72 % No. of inferences in proof: 25
% 98.94/26.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 26375 ms resp. 25700 ms w/o parsing
% 98.94/26.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 98.94/26.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------