%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO374^5 : 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 : n017.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 08:45:40 AM UTC 2026
% Result : Theorem 4.03s 2.32s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 30 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 71 ( 10 ~; 3 |; 1 &; 54 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 20 !; 0 ?; 21 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cN_decl,type,
cN: $i > $i ).
thf(cM_decl,type,
cM: $i > $i ).
thf(sk1_decl,type,
sk1: ( $i > $i ) > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( $i > $i ) > $o] :
( ( A @ cM )
!= ( A @ cN ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i,B: $i > $o] :
( ( B @ ( cM @ A ) )
= ( B @ ( cN @ A ) ) )
=> ! [A: ( $i > $i ) > $o] :
( ( A @ cM )
= ( A @ cN ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT_A_LEIB2) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i > $o] :
( ( B @ ( cM @ A ) )
= ( B @ ( cN @ A ) ) )
=> ! [A: ( $i > $i ) > $o] :
( ( A @ cM )
= ( A @ cN ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o] :
( ( B @ ( cM @ A ) )
= ( B @ ( cN @ A ) ) )
=> ! [A: ( $i > $i ) > $o] :
( ( A @ cM )
= ( A @ cN ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i] :
( ( ( B @ ( cM @ A ) )
= ( B @ ( cN @ A ) ) )
& ( ( sk1 @ cM )
!= ( sk1 @ cN ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( ( sk1 @ cM )
!= ( sk1 @ cN ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( sk1 @ cM )
!= ( sk1 @ cN ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(5,plain,
! [B: $i > $o,A: $i] :
( ( B @ ( cM @ A ) )
= ( B @ ( cN @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i > $o,A: $i] :
( ( B @ ( cM @ A ) )
= ( B @ ( cN @ A ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(14,plain,
! [B: $i > $o,A: $i] :
( ( B @ ( cM @ A ) )
| ~ ( B @ ( cN @ A ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(17,plain,
! [A: $i] :
( ( ( cN @ A )
= ( cM @ A ) )
| ( ( cN @ A )
!= ( cN @ A ) ) ),
inference(replace_leibeq,[status(thm)],[14:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ ( cN @ A ) ))]]) ).
thf(18,plain,
! [A: $i] :
( ( ( cM @ A )
= ( cN @ A ) )
| ( ( cN @ A )
!= ( cN @ A ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(20,plain,
! [A: $i] :
( ( cM @ A )
= ( cN @ A ) ),
inference(pattern_uni,[status(thm)],[18:[]]) ).
thf(55,plain,
( ( sk1 @ cN )
!= ( sk1 @ cN ) ),
inference(rewrite,[status(thm)],[8,20]) ).
thf(56,plain,
$false,
inference(simp,[status(thm)],[55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO374^5 : 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
% 0.10/0.20 % Computer : n017.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 16:44:52 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.86/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.95 % [INFO] Parsing done (176ms).
% 1.18/0.96 % [INFO] Running in sequential loop mode.
% 1.74/1.35 % [INFO] eprover registered as external prover.
% 1.74/1.36 % [INFO] Scanning for conjecture ...
% 1.92/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.92/1.48 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.92/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 1.92/1.48 % [INFO] Type checking passed.
% 1.92/1.49 % [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 ...
% 4.03/2.31 % [INFO] Killing All external provers ...
% 4.03/2.32 % Time passed: 1980ms (effective reasoning time: 1346ms)
% 4.03/2.32 % 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)>
% 4.03/2.32 % Axioms used in derivation (0):
% 4.03/2.32 % No. of inferences in proof: 14
% 4.03/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1980 ms resp. 1346 ms w/o parsing
% 4.03/2.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.03/2.36 % [INFO] Killing All external provers ...
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