%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV085^5 : 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 : n006.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 08:36:49 AM UTC 2026
% Result : Theorem 34.33s 8.62s
% Output : Refutation 29.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 203 ( 99 equ; 46 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 531 ( 66 ~; 57 |; 21 &; 380 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 257 ( 257 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 170 ( 43 ^; 105 !; 18 ?; 170 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk2_decl,type,
sk2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk3_decl,type,
sk3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk4_decl,type,
sk4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ( A @ B @ B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ! [C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ! [C: $i > $o] :
( ( ( A @ ( sk2 @ A ) @ B )
& ( A @ B @ C ) )
=> ( A @ ( sk2 @ A ) @ C ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ( ( ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
& ( A @ ( sk3 @ A ) @ B ) )
=> ( A @ ( sk2 @ A ) @ B ) ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ? [B: $i > $o,C: $i > $o] :
~ ( A @ B @ C )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_2_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ? [B: $i > $o,C: $i > $o] :
~ ( A @ B @ C )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ? [B: $i > $o,C: $i > $o] :
~ ( A @ B @ C )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ~ ! [B: $i > $o,C: $i > $o] : ( A @ B @ C )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) ) )
& ( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) ) )
& ( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(49,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( ( A @ D @ E )
!= ( ~ ( A @ B @ C ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(125,plain,
! [E: $i > $o,D: ( $i > $o ) > ( $i > $o ) > $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( A @ ( D @ A @ B ) )
| ~ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk4
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ( ( E
@ ( D
@ ^ [F: $i] :
~ ( E @ F )
@ C ) )
!= ( A @ ( D @ A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[49:[bind(A,$thf( ^ [G: $i > $o] : ^ [H: $i > $o] : ( G @ ( G @ G @ H ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ^ [G: $i] : ~ ( L @ G ) ))]]) ).
thf(129,plain,
! [E: $i > $o,D: ( $i > $o ) > ( $i > $o ) > $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk4
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( A @ ( D @ A @ B ) )
| ( ( E
@ ( D
@ ^ [F: $i] :
~ ( E @ F )
@ C ) )
!= ( A @ ( D @ A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[125:[]]) ).
thf(135,plain,
! [E: $i > $o,D: ( $i > $o ) > ( $i > $o ) > $i,C: $i > $o,B: $i > $o,A: $i > $o] :
( ~ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk2
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk4
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) )
@ ( D
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) )
@ ( sk1
@ ^ [F: $i > $o,G: $i > $o] : ( F @ ( D @ F @ G ) ) ) ) )
| ~ ( A @ ( D @ A @ B ) )
| ( ( E
@ ( D
@ ^ [F: $i] :
~ ( E @ F )
@ C ) )
!= ( A @ ( D @ A @ B ) ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(11,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk4 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[8:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(16,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(17,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(7,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk4 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[7:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(12,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(13,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(24,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= B )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
!= A ) ),
inference(eqfactor_ordered,[status(thm)],[13]) ).
thf(25,plain,
( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk3 @ ( (=) @ ( $i > $o ) ) )),bind(B,$thf( sk4 @ ( (=) @ ( $i > $o ) ) ))]]) ).
thf(29,plain,
! [A: $i] :
( ( sk4 @ ( (=) @ ( $i > $o ) ) @ A )
= ( sk3 @ ( (=) @ ( $i > $o ) ) @ A ) ),
inference(func_ext,[status(esa)],[25]) ).
thf(6,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i > $o,A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ B @ C )
| ( A @ D @ E )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(14,plain,
! [D: $i > $o,C: $i > $o,B: $i > $o,A: $i > $o] :
( ( A != B )
| ( C = D )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(15,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(317,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
!= B )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= A ) ),
inference(eqfactor_ordered,[status(thm)],[15]) ).
thf(326,plain,
( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( sk2 @ ( (=) @ ( $i > $o ) ) )),bind(B,$thf( sk3 @ ( (=) @ ( $i > $o ) ) ))]]) ).
thf(354,plain,
! [A: $i] :
( ( sk3 @ ( (=) @ ( $i > $o ) ) @ A )
= ( sk2 @ ( (=) @ ( $i > $o ) ) @ A ) ),
inference(func_ext,[status(esa)],[326]) ).
thf(643,plain,
! [A: $i] :
( ( sk4 @ ( (=) @ ( $i > $o ) ) @ A )
= ( sk2 @ ( (=) @ ( $i > $o ) ) @ A ) ),
inference(rewrite,[status(thm)],[29,354]) ).
thf(826,plain,
! [B: $i > $o,A: $i > $o] :
( ( A = B )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(rewrite,[status(thm)],[17,643]) ).
thf(827,plain,
! [B: $i > $o,A: $i > $o] : ( A = B ),
inference(simp,[status(thm)],[826]) ).
thf(828,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ C )
= ( B @ C ) ),
inference(func_ext,[status(esa)],[827]) ).
thf(935,plain,
$false,
inference(simplifyReflect,[status(thm)],[135,828]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV085^5 : 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
% 0.10/0.22 % Computer : n006.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 15:09:27 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.22/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.10 % [INFO] Parsing done (175ms).
% 1.48/1.11 % [INFO] Running in sequential loop mode.
% 2.29/1.53 % [INFO] eprover registered as external prover.
% 2.29/1.54 % [INFO] Scanning for conjecture ...
% 2.54/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.54/1.67 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.54/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 2.54/1.68 % [INFO] Type checking passed.
% 2.54/1.68 % [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 ...
% 34.33/8.61 % [INFO] Killing All external provers ...
% 34.33/8.61 % Time passed: 8233ms (effective reasoning time: 7496ms)
% 34.33/8.61 % 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)>
% 34.33/8.62 % Axioms used in derivation (0):
% 34.33/8.62 % No. of inferences in proof: 32
% 34.33/8.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8233 ms resp. 7496 ms w/o parsing
% 29.04/8.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.04/8.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------