%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT004-2 : 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 06:55:18 AM UTC 2026
% Result : Unsatisfiable 11.04s 4.55s
% Output : Refutation 11.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 52 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 190 ( 26 ~; 24 |; 0 &; 140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(h_decl,type,
h: $i ).
thf(g_decl,type,
g: $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(5,axiom,
! [A: $i] :
( ( A @ codomain @ ( A @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_composition) ).
thf(24,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(22,plain,
! [A: $i] :
( ( A @ ( A @ domain @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
( ( h @ ( b @ ( a @ compose ) @ compose ) )
= ( g @ ( b @ ( a @ compose ) @ compose ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
thf(49,plain,
( ( h @ ( b @ ( a @ compose ) @ compose ) )
= ( g @ ( b @ ( a @ compose ) @ compose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( C @ ( b @ compose ) )
!= B )
| ( ( b @ codomain )
!= ( C @ domain ) )
| ( ( A @ ( b @ compose ) )
!= B )
| ( ( b @ codomain )
!= ( A @ domain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism2) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( C @ ( b @ compose ) )
!= B )
| ( ( b @ codomain )
!= ( C @ domain ) )
| ( ( A @ ( b @ compose ) )
!= B )
| ( ( b @ codomain )
!= ( A @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( C @ ( a @ compose ) )
!= B )
| ( ( a @ codomain )
!= ( C @ domain ) )
| ( ( A @ ( a @ compose ) )
!= B )
| ( ( a @ codomain )
!= ( A @ domain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism1) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( C @ ( a @ compose ) )
!= B )
| ( ( a @ codomain )
!= ( C @ domain ) )
| ( ( A @ ( a @ compose ) )
!= B )
| ( ( a @ codomain )
!= ( A @ domain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ domain @ codomain )
= ( A @ domain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_domain_is_domain) ).
thf(18,plain,
! [A: $i] :
( ( A @ domain @ codomain )
= ( A @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
( ( a @ codomain )
= ( b @ domain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
thf(43,plain,
( ( a @ codomain )
= ( b @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(26,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(3,axiom,
! [A: $i] :
( ( A @ codomain @ domain )
= ( A @ codomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_codomain_is_codomain) ).
thf(20,plain,
! [A: $i] :
( ( A @ codomain @ domain )
= ( A @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(29,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(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(32,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(12,axiom,
( ( b @ ( a @ compose ) @ codomain )
= ( h @ domain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_h) ).
thf(45,plain,
( ( b @ ( a @ compose ) @ codomain )
= ( h @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
( ( b @ ( a @ compose ) @ codomain )
= ( g @ domain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_g) ).
thf(47,plain,
( ( b @ ( a @ compose ) @ codomain )
= ( g @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
thf(15,plain,
h != g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(625,plain,
$false,
inference(e,[status(thm)],[24,22,49,39,35,18,43,26,20,29,32,45,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.13 % 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
% 0.26/0.51 % Computer : n018.cluster.edu
% 0.26/0.51 % Model : x86_64 x86_64
% 0.26/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.51 % Memory : 8046.5625MB
% 0.26/0.51 % OS : Linux 6.8.0-71-generic
% 0.26/0.51 % CPULimit : 300
% 0.26/0.51 % WCLimit : 300
% 0.26/0.51 % DateTime : Sat Sep 26 22:50:39 UTC 2026
% 0.26/0.52 % CPUTime :
% 0.26/0.52 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
% 1.19/1.09 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.38 % [INFO] Parsing done (280ms).
% 1.86/1.40 % [INFO] Running in sequential loop mode.
% 2.62/2.02 % [INFO] eprover registered as external prover.
% 2.62/2.04 % [INFO] Scanning for conjecture ...
% 3.12/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 3.23/2.21 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 3.23/2.26 % [INFO] Problem is propositional (TPTP CNF).
% 3.23/2.27 % [INFO] Type checking passed.
% 3.23/2.28 % [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 ...
% 11.04/4.54 % External prover 'e' found a proof!
% 11.04/4.55 % [INFO] Killing All external provers ...
% 11.04/4.55 % Time passed: 3888ms (effective reasoning time: 3139ms)
% 11.04/4.55 % Axioms used in derivation (13): codomain_of_a_equals_domain_of_b, codomain_composition, codomain_of_domain_is_domain, epimorphism1, codomain_domain1, codomain_of_ab_equals_domain_of_h, star_property, domain_composition, codomain_domain2, epimorphism2, domain_of_codomain_is_codomain, ab_h_equals_ab_g, codomain_of_ab_equals_domain_of_g
% 11.04/4.55 % No. of inferences in proof: 29
% 11.04/4.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3888 ms resp. 3139 ms w/o parsing
% 11.52/4.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.52/4.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------