%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV000^5 : 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 : n026.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 08:36:41 AM UTC 2026
% Result : Theorem 9.80s 4.09s
% Output : Refutation 9.80s
% 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 : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 203 ( 2 ~; 0 |; 21 &; 174 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 11 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% Number of variables : 72 ( 0 ^; 72 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(1,conjecture,
! [A: a > a > a,B: a > a > a] :
( ( ! [C: a] :
( ( A @ C @ C )
= C )
& ! [C: a] :
( ( B @ C @ C )
= C )
& ! [C: a,D: a,E: a] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: a,D: a,E: a] :
( ( B @ ( B @ C @ D ) @ E )
= ( B @ C @ ( B @ D @ E ) ) )
& ! [C: a,D: a] :
( ( A @ C @ D )
= ( A @ D @ C ) )
& ! [C: a,D: a] :
( ( B @ C @ D )
= ( B @ D @ C ) )
& ! [C: a,D: a] :
( ( A @ ( B @ C @ D ) @ D )
= D )
& ! [C: a,D: a] :
( ( B @ ( A @ C @ D ) @ D )
= D ) )
=> ( ( ! [C: a,D: a,E: a] :
( ( ( A @ C @ E )
= E )
=> ( ( A @ C @ ( B @ D @ E ) )
= ( B @ ( A @ C @ D ) @ E ) ) ) )
= ( ! [C: a,D: a,E: a] :
( ( A @ C @ ( B @ D @ ( A @ C @ E ) ) )
= ( B @ ( A @ C @ D ) @ ( A @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cMODULAR_EQUIV_THM_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > a,B: a > a > a] :
( ( ! [C: a] :
( ( A @ C @ C )
= C )
& ! [C: a] :
( ( B @ C @ C )
= C )
& ! [C: a,D: a,E: a] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: a,D: a,E: a] :
( ( B @ ( B @ C @ D ) @ E )
= ( B @ C @ ( B @ D @ E ) ) )
& ! [C: a,D: a] :
( ( A @ C @ D )
= ( A @ D @ C ) )
& ! [C: a,D: a] :
( ( B @ C @ D )
= ( B @ D @ C ) )
& ! [C: a,D: a] :
( ( A @ ( B @ C @ D ) @ D )
= D )
& ! [C: a,D: a] :
( ( B @ ( A @ C @ D ) @ D )
= D ) )
=> ( ( ! [C: a,D: a,E: a] :
( ( ( A @ C @ E )
= E )
=> ( ( A @ C @ ( B @ D @ E ) )
= ( B @ ( A @ C @ D ) @ E ) ) ) )
= ( ! [C: a,D: a,E: a] :
( ( A @ C @ ( B @ D @ ( A @ C @ E ) ) )
= ( B @ ( A @ C @ D ) @ ( A @ C @ E ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > a,B: a > a > a] :
( ( ! [C: a] :
( ( A @ C @ C )
= C )
& ! [C: a] :
( ( B @ C @ C )
= C )
& ! [C: a,D: a,E: a] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: a,D: a,E: a] :
( ( B @ ( B @ C @ D ) @ E )
= ( B @ C @ ( B @ D @ E ) ) )
& ! [C: a,D: a] :
( ( A @ C @ D )
= ( A @ D @ C ) )
& ! [C: a,D: a] :
( ( B @ C @ D )
= ( B @ D @ C ) )
& ! [C: a,D: a] :
( ( A @ ( B @ C @ D ) @ D )
= D )
& ! [C: a,D: a] :
( ( B @ ( A @ C @ D ) @ D )
= D ) )
=> ( ( ! [C: a,D: a,E: a] :
( ( ( A @ C @ E )
= E )
=> ( ( A @ C @ ( B @ D @ E ) )
= ( B @ ( A @ C @ D ) @ E ) ) ) )
= ( ! [C: a,D: a,E: a] :
( ( A @ C @ ( B @ D @ ( A @ C @ E ) ) )
= ( B @ ( A @ C @ D ) @ ( A @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1225,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV000^5 : 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 : n026.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 15:00:12 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.21 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
% 0.88/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (202ms).
% 1.22/1.02 % [INFO] Running in sequential loop mode.
% 2.02/1.43 % [INFO] eprover registered as external prover.
% 2.02/1.44 % [INFO] Scanning for conjecture ...
% 2.23/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.41/1.60 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.41/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.41/1.61 % [INFO] Type checking passed.
% 2.41/1.61 % [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 ...
% 9.80/4.09 % External prover 'e' found a proof!
% 9.80/4.09 % [INFO] Killing All external provers ...
% 9.80/4.09 % Time passed: 3737ms (effective reasoning time: 3066ms)
% 9.80/4.09 % 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)>
% 9.80/4.09 % Axioms used in derivation (0):
% 9.80/4.09 % No. of inferences in proof: 4
% 9.80/4.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3737 ms resp. 3066 ms w/o parsing
% 9.80/4.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.80/4.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------