%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV087^5 : 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 : n019.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 4.97s 2.51s
% Output : Refutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 163 ( 41 equ; 16 cnn)
% Maximal formula atoms : 69 ( 10 avg)
% Number of connectives : 352 ( 33 ~; 37 |; 28 &; 243 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 36 ^; 24 !; 3 ?; 69 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% 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(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 ) )
=> ( B = C ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: ( $i > $o ) > ( $i > $o ) > $o] :
@+[B: $i > $o] :
~ ( ( ( A @ ( sk5 @ A ) @ B )
& ( A @ B @ ( sk5 @ A ) ) )
=> ( ( sk5 @ A )
= B ) ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [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 ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120H_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [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 ) )
=> ( B = C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [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 ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
& ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) )
& ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( ( sk5 @ A )
!= ( sk6 @ A ) ) )
& ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
& ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) )
& ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
| ( ( sk5 @ A )
!= ( sk6 @ A ) ) )
& ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk5 @ A ) @ ( sk6 @ A ) ) )
& ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) )
& ( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( ( sk5 @ A )
!= ( sk6 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( ( sk5 @ A )
!= ( sk6 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk5 @ ( (=) @ ( $i > $o ) ) )
!= ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(24,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(25,plain,
( ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
!= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(54,plain,
$false,
inference(e,[status(thm)],[3,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV087^5 : 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
% 0.11/0.21 % Computer : n019.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % 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 15:07:17 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (192ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 2.05/1.40 % [INFO] eprover registered as external prover.
% 2.05/1.41 % [INFO] Scanning for conjecture ...
% 2.22/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.55 % [INFO] Type checking passed.
% 2.22/1.56 % [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 ...
% 4.97/2.50 % External prover 'e' found a proof!
% 4.97/2.51 % [INFO] Killing All external provers ...
% 4.97/2.51 % Time passed: 2162ms (effective reasoning time: 1504ms)
% 4.97/2.51 % 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)>
% 4.97/2.51 % Axioms used in derivation (0):
% 4.97/2.51 % No. of inferences in proof: 9
% 4.97/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2162 ms resp. 1504 ms w/o parsing
% 5.24/2.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.24/2.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------