%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV088^5 : 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 08:36:50 AM UTC 2026
% Result : Theorem 13.17s 5.49s
% Output : Refutation 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 8 unt; 0 typ; 6 def)
% Number of atoms : 80 ( 8 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 381 ( 26 ~; 37 |; 14 &; 298 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 101 ( 36 ^; 53 !; 6 ?; 101 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $o ).
thf(sk2_decl,type,
sk2: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(sk3_decl,type,
sk3: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(sk4_decl,type,
sk4: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(sk5_decl,type,
sk5: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(sk6_decl,type,
sk6: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(sk7_decl,type,
sk7: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
@+[C: $i > $o] :
~ ! [D: $i > $o,E: $i > $o] :
( ( ! [F: $i] :
( ( A @ C @ D @ F )
| ( B @ C @ D @ F ) )
& ! [F: $i] :
( ( A @ D @ E @ F )
| ( B @ D @ E @ F ) ) )
=> ! [F: $i] :
( ( A @ C @ E @ F )
| ( B @ C @ E @ F ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
@+[C: $i > $o] :
~ ! [D: $i > $o] :
( ( ! [E: $i] :
( ( A @ ( sk2 @ A @ B ) @ C @ E )
| ( B @ ( sk2 @ A @ B ) @ C @ E ) )
& ! [E: $i] :
( ( A @ C @ D @ E )
| ( B @ C @ D @ E ) ) )
=> ! [E: $i] :
( ( A @ ( sk2 @ A @ B ) @ D @ E )
| ( B @ ( sk2 @ A @ B ) @ D @ E ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
@+[C: $i > $o] :
~ ( ( ! [D: $i] :
( ( A @ ( sk2 @ A @ B ) @ ( sk3 @ A @ B ) @ D )
| ( B @ ( sk2 @ A @ B ) @ ( sk3 @ A @ B ) @ D ) )
& ! [D: $i] :
( ( A @ ( sk3 @ A @ B ) @ C @ D )
| ( B @ ( sk3 @ A @ B ) @ C @ D ) ) )
=> ! [D: $i] :
( ( A @ ( sk2 @ A @ B ) @ C @ D )
| ( B @ ( sk2 @ A @ B ) @ C @ D ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
@+[C: $i] :
~ ( ( A @ ( sk2 @ A @ B ) @ ( sk4 @ A @ B ) @ C )
| ( B @ ( sk2 @ A @ B ) @ ( sk4 @ A @ B ) @ C ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
@+[C: $i > $o] :
~ ! [D: $i] :
( ( A @ C @ C @ D )
| ( B @ C @ C @ D ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
@+[C: $i] :
~ ( ( A @ ( sk6 @ A @ B ) @ ( sk6 @ A @ B ) @ C )
| ( B @ ( sk6 @ A @ B ) @ ( sk6 @ A @ B ) @ C ) ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [C: $i > $o,D: $i > $o,E: $i > $o] :
( ( ! [F: $i] :
( ( B @ C @ D @ F )
| ( A @ C @ D @ F ) )
& ! [F: $i] :
( ( B @ D @ E @ F )
| ( A @ D @ E @ F ) ) )
=> ! [F: $i] :
( ( B @ C @ E @ F )
| ( A @ C @ E @ F ) ) )
& ! [C: $i > $o,D: $i] :
( ( B @ C @ C @ D )
| ( A @ C @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120G_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [C: $i > $o,D: $i > $o,E: $i > $o] :
( ( ! [F: $i] :
( ( B @ C @ D @ F )
| ( A @ C @ D @ F ) )
& ! [F: $i] :
( ( B @ D @ E @ F )
| ( A @ D @ E @ F ) ) )
=> ! [F: $i] :
( ( B @ C @ E @ F )
| ( A @ C @ E @ F ) ) )
& ! [C: $i > $o,D: $i] :
( ( B @ C @ C @ D )
| ( A @ C @ C @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $i > $o,B: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [C: $i > $o,D: $i > $o,E: $i > $o] :
( ( ! [F: $i] :
( ( B @ C @ D @ F )
| ( A @ C @ D @ F ) )
& ! [F: $i] :
( ( B @ D @ E @ F )
| ( A @ D @ E @ F ) ) )
=> ! [F: $i] :
( ( B @ C @ E @ F )
| ( A @ C @ E @ F ) ) )
& ! [C: $i > $o,D: $i] :
( ( B @ C @ C @ D )
| ( A @ C @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [D: $i,C: $i,B: ( $i > $o ) > ( $i > $o ) > $i > $o,A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( B @ ( sk2 @ B @ A ) @ ( sk3 @ B @ A ) @ C )
| ( A @ ( sk2 @ B @ A ) @ ( sk3 @ B @ A ) @ C )
| ~ ( sk1 @ B @ A ) )
& ( ( B @ ( sk3 @ B @ A ) @ ( sk4 @ B @ A ) @ D )
| ( A @ ( sk3 @ B @ A ) @ ( sk4 @ B @ A ) @ D )
| ~ ( sk1 @ B @ A ) )
& ( ~ ( B @ ( sk2 @ B @ A ) @ ( sk4 @ B @ A ) @ ( sk5 @ B @ A ) )
| ~ ( sk1 @ B @ A ) )
& ( ~ ( A @ ( sk2 @ B @ A ) @ ( sk4 @ B @ A ) @ ( sk5 @ B @ A ) )
| ~ ( sk1 @ B @ A ) )
& ( ( sk1 @ B @ A )
| ~ ( B @ ( sk6 @ B @ A ) @ ( sk6 @ B @ A ) @ ( sk7 @ B @ A ) ) )
& ( ( sk1 @ B @ A )
| ~ ( A @ ( sk6 @ B @ A ) @ ( sk6 @ B @ A ) @ ( sk7 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [B: ( $i > $o ) > ( $i > $o ) > $i > $o,A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( sk1 @ B @ A )
| ~ ( B @ ( sk6 @ B @ A ) @ ( sk6 @ B @ A ) @ ( sk7 @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(42,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( sk1
@ ^ [B: $i > $o,C: $i > $o,D: $i] : $true
@ A )
| ~ $true ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i > $o] : ^ [D: $i > $o] : ^ [E: $i] : $true ))]]) ).
thf(54,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( sk1
@ ^ [B: $i > $o,C: $i > $o,D: $i] : $true
@ A ),
inference(simp,[status(thm)],[42]) ).
thf(5,plain,
! [B: ( $i > $o ) > ( $i > $o ) > $i > $o,A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( A @ ( sk2 @ B @ A ) @ ( sk4 @ B @ A ) @ ( sk5 @ B @ A ) )
| ~ ( sk1 @ B @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ $true
| ~ ( sk1 @ A
@ ^ [B: $i > $o,C: $i > $o,D: $i] : $true ) ),
inference(prim_subst,[status(thm)],[5:[bind(A,$thf( ^ [C: $i > $o] : ^ [D: $i > $o] : ^ [E: $i] : $true ))]]) ).
thf(27,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
~ ( sk1 @ A
@ ^ [B: $i > $o,C: $i > $o,D: $i] : $true ),
inference(simp,[status(thm)],[14]) ).
thf(66,plain,
! [B: ( $i > $o ) > ( $i > $o ) > $i > $o,A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ $true
| ( ( sk1
@ ^ [C: $i > $o,D: $i > $o,E: $i] : $true
@ A )
!= ( sk1 @ B
@ ^ [C: $i > $o,D: $i > $o,E: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[54,27]) ).
thf(67,plain,
! [B: ( $i > $o ) > ( $i > $o ) > $i > $o,A: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( sk1
@ ^ [C: $i > $o,D: $i > $o,E: $i] : $true
@ A )
!= ( sk1 @ B
@ ^ [C: $i > $o,D: $i > $o,E: $i] : $true ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
$false,
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( ^ [C: $i > $o] : ^ [D: $i > $o] : ^ [E: $i] : $true )),bind(B,$thf( ^ [C: $i > $o] : ^ [D: $i > $o] : ^ [E: $i] : $true ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV088^5 : 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 15:07:33 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
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (183ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.74/1.38 % [INFO] eprover registered as external prover.
% 1.74/1.39 % [INFO] Scanning for conjecture ...
% 1.91/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.09/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.53 % [INFO] Type checking passed.
% 2.09/1.54 % [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 ...
% 13.17/5.48 % [INFO] Killing All external provers ...
% 13.17/5.49 % Time passed: 5127ms (effective reasoning time: 4495ms)
% 13.17/5.49 % 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)>
% 13.17/5.49 % Axioms used in derivation (0):
% 13.17/5.49 % No. of inferences in proof: 13
% 13.17/5.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5127 ms resp. 4495 ms w/o parsing
% 13.58/5.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.58/5.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------