%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO266^5 : 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 : n009.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 08:45:30 AM UTC 2026
% Result : Theorem 5.53s 2.77s
% Output : Refutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 89 ( 8 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 278 ( 62 ~; 57 |; 13 &; 146 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 6 ^; 18 !; 5 ?; 31 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cQ_decl,type,
cQ: $i > $o ).
thf(cP_decl,type,
cP: $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( ( A @ B )
| ( cP @ B ) )
& ( ~ ( A @ B )
| ( cQ @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( cP @ B )
| ( cQ @ B ) ) ) ) ).
thf(1,conjecture,
( ( ? [A: $i > $o] :
! [B: $i] :
( ( ( A @ B )
| ( cP @ B ) )
& ( ~ ( A @ B )
| ( cQ @ B ) ) ) )
= ( ! [A: $i] :
( ( cP @ A )
| ( cQ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM44) ).
thf(2,negated_conjecture,
( ( ? [A: $i > $o] :
! [B: $i] :
( ( ( A @ B )
| ( cP @ B ) )
& ( ~ ( A @ B )
| ( cQ @ B ) ) ) )
!= ( ! [A: $i] :
( ( cP @ A )
| ( cQ @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [A: $i > $o] :
! [B: $i] :
( ( ( A @ B )
| ( cP @ B ) )
& ( ~ ( A @ B )
| ( cQ @ B ) ) ) )
!= ( ! [A: $i] :
( ( cP @ A )
| ( cQ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [A: $i > $o] :
! [B: $i] :
( ( ( A @ B )
| ( cP @ B ) )
& ( ~ ( A @ B )
| ( cQ @ B ) ) ) )
!= ( ! [A: $i] :
( ( cP @ A )
| ( cQ @ A ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ~ ? [A: $i > $o] :
! [B: $i] :
( ( ( A @ B )
| ( cP @ B ) )
& ( ~ ( A @ B )
| ( cQ @ B ) ) )
| ~ ! [A: $i] :
( ( cP @ A )
| ( cQ @ A ) ) ),
inference(bool_ext,[status(thm)],[4]) ).
thf(7,plain,
! [A: $i > $o] :
( ( ~ ( A @ ( sk1 @ A ) )
| ( A @ ( sk1 @ A ) )
| ~ ( cP @ ( sk2 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) )
| ( A @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk2 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk1 @ A ) )
| ~ ( cP @ ( sk2 @ A ) ) )
& ( ~ ( A @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk2 @ A ) ) )
& ( ~ ( cP @ ( sk1 @ A ) )
| ( A @ ( sk1 @ A ) )
| ~ ( cP @ ( sk2 @ A ) ) )
& ( ~ ( cP @ ( sk1 @ A ) )
| ( A @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk2 @ A ) ) )
& ( ~ ( cP @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk1 @ A ) )
| ~ ( cP @ ( sk2 @ A ) ) )
& ( ~ ( cP @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(14,plain,
! [A: $i > $o] :
( ~ ( cP @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk1 @ A ) )
| ~ ( cP @ ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(8,plain,
! [A: $i > $o] :
( ~ ( cP @ ( sk1 @ A ) )
| ( A @ ( sk1 @ A ) )
| ~ ( cP @ ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(33,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( cP @ ( sk1 @ A ) )
| ~ ( cP @ ( sk2 @ A ) )
| ~ ( cP @ ( sk1 @ B ) )
| ~ $true
| ~ ( cP @ ( sk2 @ B ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cQ @ ( sk1 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,14]) ).
thf(34,plain,
! [B: $i > $o,A: $i > $o] :
( ~ ( cP @ ( sk1 @ A ) )
| ~ ( cP @ ( sk2 @ A ) )
| ~ ( cP @ ( sk1 @ B ) )
| ~ ( cP @ ( sk2 @ B ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cQ @ ( sk1 @ B ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(64,plain,
( ~ ( cP @ ( sk1 @ cQ ) )
| ~ ( cP @ ( sk2 @ cQ ) )
| ~ ( cP @ ( sk1 @ cQ ) )
| ~ ( cP @ ( sk2 @ cQ ) ) ),
inference(pre_uni,[status(thm)],[34:[bind(A,$thf( cQ )),bind(B,$thf( cQ ))]]) ).
thf(70,plain,
( ~ ( cP @ ( sk1 @ cQ ) )
| ~ ( cP @ ( sk2 @ cQ ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(52,plain,
( ~ ( cP
@ ( sk1
@ ^ [A: $i] : $false ) )
| $false
| ~ ( cP
@ ( sk2
@ ^ [A: $i] : $false ) ) ),
inference(prim_subst,[status(thm)],[8:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(86,plain,
( ~ ( cP
@ ( sk1
@ ^ [A: $i] : $false ) )
| ~ ( cP
@ ( sk2
@ ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(15,plain,
! [A: $i > $o] :
( ~ ( cP @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk1 @ A ) )
| ~ ( cQ @ ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(209,plain,
$false,
inference(e,[status(thm)],[14,70,86,3,8,4,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO266^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:42:30 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.97 % [INFO] Parsing done (186ms).
% 1.25/0.98 % [INFO] Running in sequential loop mode.
% 1.85/1.39 % [INFO] eprover registered as external prover.
% 2.04/1.40 % [INFO] Scanning for conjecture ...
% 2.04/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.53 % [INFO] Type checking passed.
% 2.22/1.54 % [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 ...
% 5.53/2.77 % External prover 'e' found a proof!
% 5.53/2.77 % [INFO] Killing All external provers ...
% 5.53/2.77 % Time passed: 2432ms (effective reasoning time: 1781ms)
% 5.53/2.77 % 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)>
% 5.53/2.77 % Axioms used in derivation (0):
% 5.53/2.77 % No. of inferences in proof: 16
% 5.53/2.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2432 ms resp. 1781 ms w/o parsing
% 5.53/2.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.97/2.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------