%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO276^5 : 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 : n004.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 08:45:31 AM UTC 2026
% Result : Theorem 5.19s 2.74s
% Output : Refutation 5.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 38 ( 22 equ; 8 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 162 ( 18 ~; 14 |; 9 &; 110 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 2 ^; 13 !; 0 ?; 17 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(m_decl,type,
m: $i ).
thf(cP_decl,type,
cP: $i > $o ).
thf(n_decl,type,
n: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(cO_decl,type,
cO: $i ).
thf(sk1_decl,type,
sk1: ( $i > $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: ( $i > $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $i > $o] :
@+[B: $i] :
~ ! [C: $i] :
( ( A @ B @ C )
=> ( A @ ( s @ B ) @ ( s @ C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $i > $o] :
@+[B: $i] :
~ ( ( A @ ( sk1 @ A ) @ B )
=> ( A @ ( s @ ( sk1 @ A ) ) @ ( s @ B ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i > $i > $o] :
( ( ( A @ cO @ cO )
& ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ ( s @ B ) @ ( s @ C ) ) ) )
=> ( A @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE_FENG_SV_I2) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i > $i > $o] :
( ( ( A @ cO @ cO )
& ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ ( s @ B ) @ ( s @ C ) ) ) )
=> ( A @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i > $i > $o] :
( ( ( A @ cO @ cO )
& ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ ( s @ B ) @ ( s @ C ) ) ) )
=> ( A @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i > $i > $o] :
( ( ~ ( A @ cO @ cO )
| ( A @ ( sk1 @ A ) @ ( sk2 @ A ) )
| ( A @ n @ m ) )
& ( ~ ( A @ cO @ cO )
| ~ ( A @ ( s @ ( sk1 @ A ) ) @ ( s @ ( sk2 @ A ) ) )
| ( A @ n @ m ) )
& ( cP @ n )
& ~ ( cP @ m ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [A: $i > $i > $o] :
( ~ ( A @ cO @ cO )
| ~ ( A @ ( s @ ( sk1 @ A ) ) @ ( s @ ( sk2 @ A ) ) )
| ( A @ n @ m ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
cP @ n,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
~ ( cP @ m ),
inference(cnfConj,[status(thm)],[4]) ).
thf(15,plain,
( ~ $true
| ( ( cP @ n )
!= ( cP @ m ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(16,plain,
( ( cP @ n )
!= ( cP @ m ) ),
inference(simp,[status(thm)],[15]) ).
thf(17,plain,
n != m,
inference(simp,[status(thm)],[16]) ).
thf(5,plain,
! [A: $i > $i > $o] :
( ~ ( A @ cO @ cO )
| ( A @ ( sk1 @ A ) @ ( sk2 @ A ) )
| ( A @ n @ m ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ( cO != cO )
| ( ( sk1 @ ( (=) @ $i ) )
= ( sk2 @ ( (=) @ $i ) ) )
| ( n = m ) ),
inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ $i ))]]) ).
thf(13,plain,
( ( cO != cO )
| ( ( sk2 @ ( (=) @ $i ) )
= ( sk1 @ ( (=) @ $i ) ) )
| ( n = m ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
( ( ( sk2 @ ( (=) @ $i ) )
= ( sk1 @ ( (=) @ $i ) ) )
| ( n = m ) ),
inference(simp,[status(thm)],[13]) ).
thf(18,plain,
( ( sk2 @ ( (=) @ $i ) )
= ( sk1 @ ( (=) @ $i ) ) ),
inference(simplifyReflect,[status(thm)],[14,17]) ).
thf(81,plain,
$false,
inference(e,[status(thm)],[6,17,7,3,18,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO276^5 : 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
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:42:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 1.02/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.08 % [INFO] Parsing done (227ms).
% 1.42/1.10 % [INFO] Running in sequential loop mode.
% 2.11/1.56 % [INFO] eprover registered as external prover.
% 2.11/1.57 % [INFO] Scanning for conjecture ...
% 2.31/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.50/1.71 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.50/1.71 % [INFO] Problem is higher-order (TPTP THF).
% 2.50/1.72 % [INFO] Type checking passed.
% 2.50/1.72 % [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 ...
% 5.19/2.74 % External prover 'e' found a proof!
% 5.19/2.74 % [INFO] Killing All external provers ...
% 5.19/2.74 % Time passed: 2402ms (effective reasoning time: 1635ms)
% 5.19/2.74 % 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)>
% 5.19/2.74 % Axioms used in derivation (0):
% 5.19/2.74 % No. of inferences in proof: 16
% 5.19/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2402 ms resp. 1635 ms w/o parsing
% 5.59/2.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.59/2.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------