%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT014-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 : Sun Sep 27 06:55:22 AM UTC 2026
% Result : Unsatisfiable 3.27s 2.70s
% Output : Refutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 96 ( 10 ~; 8 |; 0 &; 78 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(codomain_decl,type,
codomain: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(3,axiom,
! [A: $i] :
( ( A @ codomain @ domain )
= ( A @ codomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_codomain_is_codomain) ).
thf(14,plain,
! [A: $i] :
( ( A @ codomain @ domain )
= ( A @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ compose ) @ domain )
= ( A @ domain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_domain1) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ compose ) @ domain )
= ( A @ domain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( a @ codomain @ codomain )
!= ( a @ codomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_is_idempotent) ).
thf(9,plain,
( ( a @ codomain @ codomain )
!= ( a @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ domain @ codomain )
= ( A @ domain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_domain_is_domain) ).
thf(12,plain,
! [A: $i] :
( ( A @ domain @ codomain )
= ( A @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ codomain @ ( A @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_composition) ).
thf(18,plain,
! [A: $i] :
( ( A @ codomain @ ( A @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ domain @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_composition) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ domain @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ compose ) @ ( A @ compose ) )
= ( C @ ( B @ ( A @ compose ) @ compose ) ) )
| ( ( B @ codomain )
!= ( C @ domain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_property) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ compose ) @ ( A @ compose ) )
= ( C @ ( B @ ( A @ compose ) @ compose ) ) )
| ( ( B @ codomain )
!= ( C @ domain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ compose ) @ codomain )
= ( B @ codomain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_domain2) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ compose ) @ codomain )
= ( B @ codomain ) )
| ( ( A @ codomain )
!= ( B @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,plain,
$false,
inference(e,[status(thm)],[14,20,9,12,18,16,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT014-2 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.12/0.57 % Computer : n018.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Sat Sep 26 22:51:54 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 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
% 0.92/1.26 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.48 % [INFO] Parsing done (222ms).
% 1.33/1.50 % [INFO] Running in sequential loop mode.
% 1.86/1.92 % [INFO] eprover registered as external prover.
% 1.86/1.93 % [INFO] Scanning for conjecture ...
% 1.86/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.02/2.08 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.02/2.10 % [INFO] Problem is propositional (TPTP CNF).
% 2.02/2.11 % [INFO] Type checking passed.
% 2.02/2.11 % [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 ...
% 3.27/2.70 % External prover 'e' found a proof!
% 3.27/2.70 % [INFO] Killing All external provers ...
% 3.27/2.70 % Time passed: 1977ms (effective reasoning time: 1190ms)
% 3.27/2.70 % Axioms used in derivation (7): domain_of_codomain_is_codomain, codomain_composition, codomain_of_domain_is_domain, codomain_domain1, star_property, domain_composition, codomain_domain2
% 3.27/2.70 % No. of inferences in proof: 17
% 3.27/2.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1977 ms resp. 1190 ms w/o parsing
% 3.27/2.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.27/2.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------