%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV164^5 : 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 : n016.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 5.16s 2.44s
% Output : Refutation 5.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 51 ( 15 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 148 ( 20 ~; 10 |; 0 &; 118 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 124 ( 80 ^; 15 !; 25 ?; 124 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > a > $o ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: ( a > a > a ) > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > a > $o] :
( ( ? [B: a,C: a] : ( A @ B @ C ) )
!= ( ? [B: ( a > a > a ) > a] :
( A
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a] :
? [B: a] : ( sk1 @ A @ B ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a] : ( sk1 @ sk2 @ A ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: ( a > a > a ) > a] :
( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ) ) ).
thf(1,conjecture,
! [A: a > a > $o] :
( ( ? [B: a,C: a] : ( A @ B @ C ) )
= ( ? [B: ( a > a > a ) > a] :
( A
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM185_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o] :
( ( ? [B: a,C: a] : ( A @ B @ C ) )
= ( ? [B: ( a > a > a ) > a] :
( A
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > $o] :
( ( ? [B: a,C: a] : ( A @ B @ C ) )
= ( ? [B: ( a > a > a ) > a] :
( A
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [A: a,B: a] : ( sk1 @ A @ B ) )
!= ( ? [A: ( a > a > a ) > a] :
( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ? [A: a,B: a] : ( sk1 @ A @ B ) )
!= ( ? [A: ( a > a > a ) > a] :
( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ? [A: a,B: a] : ( sk1 @ A @ B )
| ? [A: ( a > a > a ) > a] :
( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( sk1 @ sk2 @ sk3 )
| ( sk1
@ ( sk4
@ ^ [A: a,B: a] : A )
@ ( sk4
@ ^ [A: a,B: a] : B ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(6,plain,
( ~ ? [A: a,B: a] : ( sk1 @ A @ B )
| ~ ? [A: ( a > a > a ) > a] :
( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
! [C: ( a > a > a ) > a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1
@ ( C
@ ^ [D: a,E: a] : D )
@ ( C
@ ^ [D: a,E: a] : E ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(22,plain,
! [C: ( a > a > a ) > a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk1
@ ( C
@ ^ [D: a,E: a] : D )
@ ( C
@ ^ [D: a,E: a] : E ) )
!= ( sk1 @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(27,plain,
! [A: ( a > a > a ) > a] :
~ ( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ),
inference(pre_uni,[status(thm)],[22:[bind(A,$thf( C @ ^ [D: a] : ^ [E: a] : D )),bind(B,$thf( C @ ^ [D: a] : ^ [E: a] : E ))]]) ).
thf(29,plain,
! [A: ( a > a > a ) > a] :
~ ( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ),
inference(simp,[status(thm)],[27]) ).
thf(30,plain,
! [A: ( a > a > a ) > a] :
( ( sk1 @ sk2 @ sk3 )
| ~ $true
| ( ( sk1
@ ( sk4
@ ^ [B: a,C: a] : B )
@ ( sk4
@ ^ [B: a,C: a] : C ) )
!= ( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,29]) ).
thf(31,plain,
! [A: ( a > a > a ) > a] :
( ( sk1 @ sk2 @ sk3 )
| ( ( sk1
@ ( sk4
@ ^ [B: a,C: a] : B )
@ ( sk4
@ ^ [B: a,C: a] : C ) )
!= ( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
sk1 @ sk2 @ sk3,
inference(pre_uni,[status(thm)],[31:[bind(A,$thf( sk4 ))]]) ).
thf(58,plain,
! [A: ( a > a > a ) > a] :
( ~ $true
| ( ( sk1 @ sk2 @ sk3 )
!= ( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,29]) ).
thf(59,plain,
! [A: ( a > a > a ) > a] :
( ( sk1 @ sk2 @ sk3 )
!= ( sk1
@ ( A
@ ^ [B: a,C: a] : B )
@ ( A
@ ^ [B: a,C: a] : C ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(65,plain,
$false,
inference(pre_uni,[status(thm)],[59:[bind(A,$thf( ^ [C: a > a > a] : ( C @ sk2 @ ( C @ ( F @ C ) @ sk3 ) ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV164^5 : 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
% 0.09/0.23 % Computer : n016.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 15:22:49 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 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
% 0.62/0.52 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.08/0.70 % [INFO] Parsing done (172ms).
% 1.08/0.71 % [INFO] Running in sequential loop mode.
% 1.54/1.12 % [INFO] eprover registered as external prover.
% 1.74/1.13 % [INFO] Scanning for conjecture ...
% 1.85/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.85/1.25 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.85/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.85/1.26 % [INFO] Type checking passed.
% 1.85/1.26 % [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 ...
% 5.16/2.43 % [INFO] Killing All external provers ...
% 5.16/2.43 % Time passed: 2119ms (effective reasoning time: 1712ms)
% 5.16/2.43 % 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)>
% 5.16/2.44 % Axioms used in derivation (0):
% 5.16/2.44 % No. of inferences in proof: 18
% 5.16/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2119 ms resp. 1712 ms w/o parsing
% 5.16/2.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.16/2.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------