%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT009-4 : 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 : n001.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 06:55:20 AM UTC 2026
% Result : Unsatisfiable 5.57s 8.37s
% Output : Refutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 16 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 146 ( 22 ~; 20 |; 0 &; 104 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
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(equivalent_decl,type,
equivalent: $i > $i > $o ).
thf(there_exists_decl,type,
there_exists: $i > $o ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ compose ) @ domain )
!= ( b @ domain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
thf(14,plain,
( ( b @ ( a @ compose ) @ domain )
!= ( b @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ there_exists )
| ( ( A @ domain )
!= ( B @ codomain ) )
| ~ ( A @ domain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ there_exists )
| ( ( A @ domain )
!= ( B @ codomain ) )
| ~ ( A @ domain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ codomain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(28,plain,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ codomain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ compose ) @ ( A @ compose ) )
= ( C @ ( B @ ( A @ compose ) @ compose ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ compose ) @ ( A @ compose ) )
= ( C @ ( B @ ( A @ compose ) @ compose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( A @ domain )
= ( B @ codomain ) )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( ( A @ domain )
= ( B @ codomain ) )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( A @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( A @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( A @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
b @ ( a @ compose ) @ there_exists,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
thf(44,plain,
b @ ( a @ compose ) @ there_exists,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
thf(40,plain,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ domain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
thf(26,plain,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ domain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A @ domain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A @ domain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equivalent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(59,plain,
$false,
inference(e,[status(thm)],[42,14,35,28,38,32,17,22,44,40,26,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT009-4 : 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
% 0.25/5.51 % Computer : n001.cluster.edu
% 0.25/5.51 % Model : x86_64 x86_64
% 0.25/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/5.51 % Memory : 8046.5625MB
% 0.25/5.51 % OS : Linux 6.8.0-71-generic
% 0.25/5.51 % CPULimit : 300
% 0.25/5.51 % WCLimit : 300
% 0.25/5.51 % DateTime : Sat Sep 26 22:55:04 UTC 2026
% 0.25/5.51 % CPUTime :
% 0.25/5.51 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
% 1.40/6.40 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.91/6.69 % [INFO] Parsing done (283ms).
% 2.15/6.71 % [INFO] Running in sequential loop mode.
% 3.26/7.35 % [INFO] eprover registered as external prover.
% 3.26/7.36 % [INFO] Scanning for conjecture ...
% 3.47/7.50 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 3.63/7.54 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 3.63/7.57 % [INFO] Problem is propositional (TPTP CNF).
% 3.63/7.58 % [INFO] Type checking passed.
% 3.63/7.59 % [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 ...
% 5.57/8.36 % External prover 'e' found a proof!
% 5.57/8.36 % [INFO] Killing All external provers ...
% 5.57/8.36 % Time passed: 2634ms (effective reasoning time: 1641ms)
% 5.57/8.36 % Axioms used in derivation (12): ab_exists, compose_codomain, domain_codomain_composition2, compose_domain, equivalence_implies_existence1, equivalence_implies_existence2, codomain_has_elements, existence_and_equality_implies_equivalence1, associativity_of_compose, domain_codomain_composition1, composition_implies_domain, domain_has_elements
% 5.57/8.36 % No. of inferences in proof: 27
% 5.57/8.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2634 ms resp. 1641 ms w/o parsing
% 5.79/8.41 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.79/8.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------