%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG254^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : 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 07:45:03 AM UTC 2026
% Result : Theorem 5.40s 2.54s
% Output : Refutation 5.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 5 def)
% Number of atoms : 29 ( 17 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 60 ( 2 ~; 0 |; 4 &; 48 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(id_decl,type,
id: subst ).
thf(comp_decl,type,
comp: subst > subst > subst ).
thf(axassoc_decl,type,
axassoc: $o ).
thf(axidr_decl,type,
axidr: $o ).
thf(axidl_decl,type,
axidl: $o ).
thf(substmonoid_lthm_decl,type,
substmonoid_lthm: $o ).
thf(substmonoid_decl,type,
substmonoid: $o ).
thf(axassoc_def,definition,
( axassoc
= ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) ) ) ) ).
thf(axidr_def,definition,
( axidr
= ( ! [A: subst] :
( ( comp @ A @ id )
= A ) ) ) ).
thf(axidl_def,definition,
( axidl
= ( ! [A: subst] :
( ( comp @ id @ A )
= A ) ) ) ).
thf(substmonoid_lthm_def,definition,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ) ).
thf(substmonoid_def,definition,
( substmonoid
= ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
& ! [A: subst] :
( ( comp @ id @ A )
= A )
& ! [A: subst] :
( ( comp @ A @ id )
= A ) ) ) ).
thf(1,conjecture,
substmonoid_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ substmonoid_lthm,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: subst] :
( ( comp @ id @ A )
= A )
=> ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
=> ( ! [A: subst] :
( ( comp @ A @ id )
= A )
=> ( ! [A: subst,B: subst,C: subst] :
( ( comp @ ( comp @ A @ B ) @ C )
= ( comp @ A @ ( comp @ B @ C ) ) )
& ! [A: subst] :
( ( comp @ id @ A )
= A )
& ! [A: subst] :
( ( comp @ A @ id )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG254^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.07 % 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 : n004.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 17:33:52 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.21 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
% 0.83/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.08 % [INFO] Parsing done (312ms).
% 1.59/1.10 % [INFO] Running in sequential loop mode.
% 2.57/1.47 % [INFO] eprover registered as external prover.
% 2.57/1.48 % [INFO] Scanning for conjecture ...
% 3.87/1.93 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.87/1.96 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.87/1.96 % [INFO] Problem is higher-order (TPTP THF).
% 3.87/1.96 % [INFO] Type checking passed.
% 3.87/1.97 % [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 ...
% 5.40/2.54 % External prover 'e' found a proof!
% 5.40/2.54 % [INFO] Killing All external provers ...
% 5.40/2.54 % Time passed: 2202ms (effective reasoning time: 1439ms)
% 5.40/2.54 % 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)>
% 5.40/2.54 % Axioms used in derivation (0):
% 5.40/2.54 % No. of inferences in proof: 4
% 5.40/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2202 ms resp. 1439 ms w/o parsing
% 5.40/2.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.40/2.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------