%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV167^5 : 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 : n020.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 11.09s 3.78s
% Output : Refutation 9.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 65 ( 49 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 203 ( 28 ~; 13 |; 10 &; 136 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-4 aty)
% Number of variables : 125 ( 74 ^; 46 !; 0 ?; 125 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > a > a > a > $o ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > a > a > a > $o] :
~ ( ! [B: ( a > a > a ) > a,C: ( a > a > a ) > a] :
( ( A
@ ( B
@ ^ [D: a,E: a] : D )
@ ( B
@ ^ [D: a,E: a] : E )
@ ( C
@ ^ [D: a,E: a] : D )
@ ( C
@ ^ [D: a,E: a] : E ) )
=> ( B = C ) )
=> ! [B: a,C: a,D: a,E: a] :
( ( A @ B @ C @ D @ E )
=> ( ( B = D )
& ( C = E ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a] :
~ ! [B: a,C: a,D: a] :
( ( sk1 @ A @ B @ C @ D )
=> ( ( A = C )
& ( B = D ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a] :
~ ! [B: a,C: a] :
( ( sk1 @ sk2 @ A @ B @ C )
=> ( ( sk2 = B )
& ( A = C ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a] :
~ ! [B: a] :
( ( sk1 @ sk2 @ sk3 @ A @ B )
=> ( ( sk2 = A )
& ( sk3 = B ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: a] :
~ ( ( sk1 @ sk2 @ sk3 @ sk4 @ A )
=> ( ( sk2 = sk4 )
& ( sk3 = A ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > a > a > a > $o] :
( ! [B: ( a > a > a ) > a,C: ( a > a > a ) > a] :
( ( A
@ ( B
@ ^ [D: a,E: a] : D )
@ ( B
@ ^ [D: a,E: a] : E )
@ ( C
@ ^ [D: a,E: a] : D )
@ ( C
@ ^ [D: a,E: a] : E ) )
=> ( B = C ) )
=> ! [B: a,C: a,D: a,E: a] :
( ( A @ B @ C @ D @ E )
=> ( ( B = D )
& ( C = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM189_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > a > a > $o] :
( ! [B: ( a > a > a ) > a,C: ( a > a > a ) > a] :
( ( A
@ ( B
@ ^ [D: a,E: a] : D )
@ ( B
@ ^ [D: a,E: a] : E )
@ ( C
@ ^ [D: a,E: a] : D )
@ ( C
@ ^ [D: a,E: a] : E ) )
=> ( B = C ) )
=> ! [B: a,C: a,D: a,E: a] :
( ( A @ B @ C @ D @ E )
=> ( ( B = D )
& ( C = E ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > a > a > $o] :
( ! [B: ( a > a > a ) > a,C: ( a > a > a ) > a] :
( ( A
@ ( B
@ ^ [D: a,E: a] : D )
@ ( B
@ ^ [D: a,E: a] : E )
@ ( C
@ ^ [D: a,E: a] : D )
@ ( C
@ ^ [D: a,E: a] : E ) )
=> ( B = C ) )
=> ! [B: a,C: a,D: a,E: a] :
( ( A @ B @ C @ D @ E )
=> ( ( B = D )
& ( C = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: ( a > a > a ) > a,A: ( a > a > a ) > a] :
( ( ~ ( sk1
@ ( A
@ ^ [C: a,D: a] : C )
@ ( A
@ ^ [C: a,D: a] : D )
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) )
| ( A = B ) )
& ( sk1 @ sk2 @ sk3 @ sk4 @ sk5 )
& ( ( sk2 != sk4 )
| ( sk3 != sk5 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
sk1 @ sk2 @ sk3 @ sk4 @ sk5,
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [B: ( a > a > a ) > a,A: ( a > a > a ) > a] :
( ~ ( sk1
@ ( A
@ ^ [C: a,D: a] : C )
@ ( A
@ ^ [C: a,D: a] : D )
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [B: ( a > a > a ) > a,A: ( a > a > a ) > a] :
( ( A = B )
| ~ ( sk1
@ ( A
@ ^ [C: a,D: a] : C )
@ ( A
@ ^ [C: a,D: a] : D )
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(11,plain,
! [B: ( a > a > a ) > a,A: ( a > a > a ) > a] :
( ( A = B )
| ~ $true
| ( ( sk1 @ sk2 @ sk3 @ sk4 @ sk5 )
!= ( sk1
@ ( A
@ ^ [C: a,D: a] : C )
@ ( A
@ ^ [C: a,D: a] : D )
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,8]) ).
thf(12,plain,
! [B: ( a > a > a ) > a,A: ( a > a > a ) > a] :
( ( A = B )
| ( ( sk1 @ sk2 @ sk3 @ sk4 @ sk5 )
!= ( sk1
@ ( A
@ ^ [C: a,D: a] : C )
@ ( A
@ ^ [C: a,D: a] : D )
@ ( B
@ ^ [C: a,D: a] : C )
@ ( B
@ ^ [C: a,D: a] : D ) ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
( ( ^ [A: a > a > a] : ( A @ sk4 @ sk5 ) )
= ( ^ [A: a > a > a] : ( A @ sk2 @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[12:[bind(A,$thf( ^ [C: a > a > a] : ( C @ sk2 @ sk3 ) )),bind(B,$thf( ^ [C: a > a > a] : ( C @ sk4 @ sk5 ) ))]]) ).
thf(20,plain,
! [A: a > a > a] :
( ( A @ sk4 @ sk5 )
= ( A @ sk2 @ sk3 ) ),
inference(func_ext,[status(esa)],[13]) ).
thf(7,plain,
( ( sk2 != sk4 )
| ( sk3 != sk5 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ( sk4 != sk2 )
| ( sk5 != sk3 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(685,plain,
! [A: a > a > a] :
( ( ( A @ sk2 @ sk3 )
!= sk2 )
| ( sk5 != sk3 )
| ( ( A @ sk4 @ sk5 )
!= sk4 ) ),
inference(paramod_ordered,[status(thm)],[20,9]) ).
thf(771,plain,
( ( sk2 != sk2 )
| ( sk5 != sk3 ) ),
inference(pre_uni,[status(thm)],[685:[bind(A,$thf( ^ [B: a] : ^ [C: a] : B ))]]) ).
thf(799,plain,
sk5 != sk3,
inference(simp,[status(thm)],[771]) ).
thf(843,plain,
! [A: a > a > a] :
( ( ( A @ sk2 @ sk3 )
!= sk3 )
| ( ( A @ sk4 @ sk5 )
!= sk5 ) ),
inference(paramod_ordered,[status(thm)],[20,799]) ).
thf(879,plain,
sk3 != sk3,
inference(pre_uni,[status(thm)],[843:[bind(A,$thf( ^ [B: a] : ^ [C: a] : C ))]]) ).
thf(880,plain,
$false,
inference(pattern_uni,[status(thm)],[879:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV167^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:19:04 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 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
% 0.88/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.95 % [INFO] Parsing done (180ms).
% 1.19/0.96 % [INFO] Running in sequential loop mode.
% 1.76/1.35 % [INFO] eprover registered as external prover.
% 1.76/1.36 % [INFO] Scanning for conjecture ...
% 1.95/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.95/1.49 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.95/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.50 % [INFO] Type checking passed.
% 2.10/1.51 % [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 ...
% 11.09/3.77 % [INFO] Killing All external provers ...
% 11.09/3.78 % Time passed: 3455ms (effective reasoning time: 2804ms)
% 11.09/3.78 % 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)>
% 11.09/3.78 % Axioms used in derivation (0):
% 11.09/3.78 % No. of inferences in proof: 19
% 11.09/3.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3455 ms resp. 2804 ms w/o parsing
% 9.87/3.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.87/3.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------