%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV086^5 : 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 4.69s 2.49s
% Output : Refutation 5.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 16 ( 11 unt; 0 typ; 7 def)
% Number of atoms : 134 ( 40 equ; 16 cnn)
% Maximal formula atoms : 51 ( 8 avg)
% Number of connectives : 337 ( 31 ~; 25 |; 25 &; 245 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 7 ^; 29 !; 3 ?; 46 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% 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(sk5_decl,type,
sk5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk6_decl,type,
sk6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk7_decl,type,
sk7: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i ).
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(sk5_def,definition,
( sk5
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ! [C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ! [D: $i] :
( ( B @ D )
= ( C @ D ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ( ( ( A @ ( sk5 @ A ) @ B )
& ( A @ B @ ( sk5 @ A ) ) )
=> ! [C: $i] :
( ( sk5 @ A @ C )
= ( B @ C ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i] :
( ( sk5 @ A @ B )
!= ( sk6 @ A @ B ) ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ! [D: $i] :
( ( B @ D )
= ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120I_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ! [D: $i] :
( ( B @ D )
= ( C @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ! [D: $i] :
( ( B @ D )
= ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( ( sk5 @ A @ ( sk7 @ A ) )
!= ( sk6 @ A @ ( sk7 @ A ) ) ) )
& ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( sk5 @ A @ ( sk7 @ A ) )
!= ( sk6 @ A @ ( sk7 @ A ) ) ) )
& ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( ( sk5 @ A @ ( sk7 @ A ) )
!= ( sk6 @ A @ ( sk7 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
( ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk5 @ ( (=) @ ( $i > $o ) ) )
= ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(23,plain,
( ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(24,plain,
( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[3,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV086^5 : 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
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:06:39 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 0.93/0.74 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/0.93 % [INFO] Parsing done (187ms).
% 1.28/0.95 % [INFO] Running in sequential loop mode.
% 1.88/1.36 % [INFO] eprover registered as external prover.
% 1.88/1.37 % [INFO] Scanning for conjecture ...
% 2.09/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.26/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.26/1.50 % [INFO] Type checking passed.
% 2.26/1.51 % [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 ...
% 4.69/2.48 % External prover 'e' found a proof!
% 4.69/2.48 % [INFO] Killing All external provers ...
% 4.69/2.48 % Time passed: 2187ms (effective reasoning time: 1529ms)
% 4.69/2.48 % 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)>
% 4.69/2.49 % Axioms used in derivation (0):
% 4.69/2.49 % No. of inferences in proof: 9
% 4.69/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2187 ms resp. 1529 ms w/o parsing
% 5.37/2.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.37/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------