%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV165^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 08:36:56 AM UTC 2026
% Result : Theorem 9.18s 3.52s
% Output : Refutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 34 ( 13 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 108 ( 8 ~; 0 |; 9 &; 91 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 99 ( 99 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 13 ^; 20 !; 3 ?; 40 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: ( ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o ) > $i > $o ).
thf(sk2_decl,type,
sk2: ( ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o ) > $i > $o ).
thf(sk3_decl,type,
sk3: ( ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o ) > $i ).
thf(sk4_decl,type,
sk4: ( ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
@+[B: $i > $o] :
~ ! [C: $i > $o,D: $i,E: $i] :
( ( A @ B @ C
@ ^ [F: $i > $i > $i] : ( F @ D @ E ) )
= ( ( B @ D )
& ( C @ E ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
@+[B: $i > $o] :
~ ! [C: $i,D: $i] :
( ( A @ ( sk1 @ A ) @ B
@ ^ [E: $i > $i > $i] : ( E @ C @ D ) )
= ( ( sk1 @ A @ C )
& ( B @ D ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
@+[B: $i] :
~ ! [C: $i] :
( ( A @ ( sk1 @ A ) @ ( sk2 @ A )
@ ^ [D: $i > $i > $i] : ( D @ B @ C ) )
= ( ( sk1 @ A @ B )
& ( sk2 @ A @ C ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
@+[B: $i] :
( ( A @ ( sk1 @ A ) @ ( sk2 @ A )
@ ^ [C: $i > $i > $i] : ( C @ ( sk3 @ A ) @ B ) )
!= ( ( sk1 @ A @ ( sk3 @ A ) )
& ( sk2 @ A @ B ) ) ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
! [B: $i > $o,C: $i > $o,D: $i,E: $i] :
( ( A @ B @ C
@ ^ [F: $i > $i > $i] : ( F @ D @ E ) )
= ( ( B @ D )
& ( C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXISTS_CART_SET_PROD_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
! [B: $i > $o,C: $i > $o,D: $i,E: $i] :
( ( A @ B @ C
@ ^ [F: $i > $i > $i] : ( F @ D @ E ) )
= ( ( B @ D )
& ( C @ E ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
! [B: $i > $o,C: $i > $o,D: $i,E: $i] :
( ( A @ B @ C
@ ^ [F: $i > $i > $i] : ( F @ D @ E ) )
= ( ( B @ D )
& ( C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
( ( A @ ( sk1 @ A ) @ ( sk2 @ A )
@ ^ [B: $i > $i > $i] : ( B @ ( sk3 @ A ) @ ( sk4 @ A ) ) )
!= ( ( sk1 @ A @ ( sk3 @ A ) )
& ( sk2 @ A @ ( sk4 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
( ( A @ ( sk1 @ A ) @ ( sk2 @ A )
@ ^ [B: $i > $i > $i] : ( B @ ( sk3 @ A ) @ ( sk4 @ A ) ) )
!= ( ( sk1 @ A @ ( sk3 @ A ) )
& ( sk2 @ A @ ( sk4 @ A ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
$false,
inference(pre_uni,[status(thm)],[5:[bind(A,$thf( ^ [B: $i > $o] : ^ [C: $i > $o] : ^ [D: ( $i > $i > $i ) > $i] : ( ( B @ ( D @ ^ [E: $i] : ^ [F: $i] : E ) ) & ( C @ ( D @ ^ [E: $i] : ^ [F: $i] : F ) ) ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV165^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.20 % Computer : n008.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % 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 15:18:54 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.71/0.53 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.92/0.62 % [INFO] Parsing done (94ms).
% 1.03/0.63 % [INFO] Running in sequential loop mode.
% 1.33/0.82 % [INFO] eprover registered as external prover.
% 1.33/0.82 % [INFO] Scanning for conjecture ...
% 1.33/0.86 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.33/0.88 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.33/0.88 % [INFO] Problem is higher-order (TPTP THF).
% 1.33/0.89 % [INFO] Type checking passed.
% 1.33/0.89 % [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 ...
% 9.18/3.51 % [INFO] Killing All external provers ...
% 9.18/3.52 % Time passed: 3225ms (effective reasoning time: 2885ms)
% 9.18/3.52 % 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)>
% 9.18/3.52 % Axioms used in derivation (0):
% 9.18/3.52 % No. of inferences in proof: 6
% 9.18/3.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3225 ms resp. 2885 ms w/o parsing
% 9.61/3.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.61/3.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------