%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU974^5 : 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 : n018.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 08:29:40 AM UTC 2026
% Result : Theorem 5.59s 3.25s
% Output : Refutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 45 equ; 0 cnn)
% Maximal formula atoms : 11 ( 11 avg)
% Number of connectives : 257 ( 5 ~; 0 |; 39 &; 186 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 13 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 48 !; 6 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cR_decl,type,
cR: a > a ).
thf(cP_decl,type,
cP: a > a > a ).
thf(cL_decl,type,
cL: a > a ).
thf(cZ_decl,type,
cZ: a ).
thf(1,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [A: a,B: a] :
( ( cL @ ( cP @ A @ B ) )
= A )
& ! [A: a,B: a] :
( ( cR @ ( cP @ A @ B ) )
= B )
& ! [A: a] :
( ( A != cZ )
= ( A
= ( cP @ ( cL @ A ) @ ( cR @ A ) ) ) )
& ! [A: a > $o] :
( ! [B: a,C: a] :
( ( A @ ( cP @ B @ C ) )
=> ( ( ( B = cZ )
= ( C = cZ ) )
& ( A @ ( cP @ ( cL @ B ) @ ( cL @ C ) ) )
& ( A @ ( cP @ ( cR @ B ) @ ( cR @ C ) ) ) ) )
=> ! [B: a,C: a] :
( ( A @ ( cP @ B @ C ) )
=> ( B = C ) ) ) )
=> ! [A: a,B: a] :
( ? [C: a > $o] :
( ( C @ ( cP @ A @ B ) )
& ! [D: a,E: a] :
( ( C @ ( cP @ D @ E ) )
=> ( ( ( E = cZ )
=> ( D = cZ ) )
& ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
& ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) )
=> ? [C: a > $o] :
( ( C @ ( cP @ ( cR @ A ) @ ( cR @ B ) ) )
& ! [D: a,E: a] :
( ( C @ ( cP @ D @ E ) )
=> ( ( ( E = cZ )
=> ( D = cZ ) )
& ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
& ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPU_LEM2C_pme) ).
thf(2,negated_conjecture,
~ ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [A: a,B: a] :
( ( cL @ ( cP @ A @ B ) )
= A )
& ! [A: a,B: a] :
( ( cR @ ( cP @ A @ B ) )
= B )
& ! [A: a] :
( ( A != cZ )
= ( A
= ( cP @ ( cL @ A ) @ ( cR @ A ) ) ) )
& ! [A: a > $o] :
( ! [B: a,C: a] :
( ( A @ ( cP @ B @ C ) )
=> ( ( ( B = cZ )
= ( C = cZ ) )
& ( A @ ( cP @ ( cL @ B ) @ ( cL @ C ) ) )
& ( A @ ( cP @ ( cR @ B ) @ ( cR @ C ) ) ) ) )
=> ! [B: a,C: a] :
( ( A @ ( cP @ B @ C ) )
=> ( B = C ) ) ) )
=> ! [A: a,B: a] :
( ? [C: a > $o] :
( ( C @ ( cP @ A @ B ) )
& ! [D: a,E: a] :
( ( C @ ( cP @ D @ E ) )
=> ( ( ( E = cZ )
=> ( D = cZ ) )
& ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
& ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) )
=> ? [C: a > $o] :
( ( C @ ( cP @ ( cR @ A ) @ ( cR @ B ) ) )
& ! [D: a,E: a] :
( ( C @ ( cP @ D @ E ) )
=> ( ( ( E = cZ )
=> ( D = cZ ) )
& ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
& ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [A: a,B: a] :
( ( cL @ ( cP @ A @ B ) )
= A )
& ! [A: a,B: a] :
( ( cR @ ( cP @ A @ B ) )
= B )
& ! [A: a] :
( ( A != cZ )
= ( A
= ( cP @ ( cL @ A ) @ ( cR @ A ) ) ) )
& ! [A: a > $o] :
( ! [B: a,C: a] :
( ( A @ ( cP @ B @ C ) )
=> ( ( ( B = cZ )
= ( C = cZ ) )
& ( A @ ( cP @ ( cL @ B ) @ ( cL @ C ) ) )
& ( A @ ( cP @ ( cR @ B ) @ ( cR @ C ) ) ) ) )
=> ! [B: a,C: a] :
( ( A @ ( cP @ B @ C ) )
=> ( B = C ) ) ) )
=> ! [A: a,B: a] :
( ? [C: a > $o] :
( ( C @ ( cP @ A @ B ) )
& ! [D: a,E: a] :
( ( C @ ( cP @ D @ E ) )
=> ( ( ( E = cZ )
=> ( D = cZ ) )
& ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
& ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) )
=> ? [C: a > $o] :
( ( C @ ( cP @ ( cR @ A ) @ ( cR @ B ) ) )
& ! [D: a,E: a] :
( ( C @ ( cP @ D @ E ) )
=> ( ( ( E = cZ )
=> ( D = cZ ) )
& ( C @ ( cP @ ( cL @ D ) @ ( cL @ E ) ) )
& ( C @ ( cP @ ( cR @ D ) @ ( cR @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU974^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.11/0.28 % Computer : n018.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 14:56:56 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 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
% 1.16/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.66/1.25 % [INFO] Parsing done (282ms).
% 1.66/1.27 % [INFO] Running in sequential loop mode.
% 2.60/1.85 % [INFO] eprover registered as external prover.
% 2.60/1.87 % [INFO] Scanning for conjecture ...
% 2.79/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.05/2.10 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.05/2.10 % [INFO] Problem is higher-order (TPTP THF).
% 3.05/2.11 % [INFO] Type checking passed.
% 3.05/2.12 % [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 ...
% 5.59/3.24 % External prover 'e' found a proof!
% 5.59/3.24 % [INFO] Killing All external provers ...
% 5.59/3.24 % Time passed: 2754ms (effective reasoning time: 1964ms)
% 5.59/3.25 % 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)>
% 5.59/3.25 % Axioms used in derivation (0):
% 5.59/3.25 % No. of inferences in proof: 4
% 5.59/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2754 ms resp. 1964 ms w/o parsing
% 5.82/3.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.82/3.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------