%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 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 : n003.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 3.72s 2.48s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 32 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 204 ( 2 ~; 0 |; 0 &; 202 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(codomain_decl,type,
codomain: $i > $i ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(equivalent_decl,type,
equivalent: $i > $i > $i ).
thf(true_decl,type,
true: $i ).
thf(there_exists_decl,type,
there_exists: $i > $i ).
thf(ifeq3_decl,type,
ifeq3: $i > $i > $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
thf(48,plain,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( true @ ( A @ there_exists @ ( true @ ( A @ codomain @ there_exists @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(42,plain,
! [A: $i] :
( ( true @ ( A @ there_exists @ ( true @ ( A @ codomain @ there_exists @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( true @ ( A @ there_exists @ ( true @ ( B @ ( A @ equivalent ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ there_exists @ ( true @ ( B @ ( A @ equivalent ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( true @ ( A @ domain @ there_exists @ ( true @ ( B @ ( A @ compose ) @ there_exists @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ domain @ there_exists @ ( true @ ( B @ ( A @ compose ) @ there_exists @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i] :
( ( true @ ( A @ ( A @ equivalent ) @ ( true @ ( A @ there_exists @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
thf(28,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ equivalent ) @ ( true @ ( A @ there_exists @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,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)],[11]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ compose ) @ codomain )
!= ( a @ codomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
thf(17,plain,
( ( b @ ( a @ compose ) @ codomain )
!= ( a @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( true @ ( A @ there_exists @ ( true @ ( A @ domain @ there_exists @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
thf(32,plain,
! [A: $i] :
( ( true @ ( A @ there_exists @ ( true @ ( A @ domain @ there_exists @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
thf(34,plain,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ codomain @ ( A @ domain @ ( true @ ( B @ ( A @ compose ) @ there_exists @ ifeq2 ) ) ) )
= ( B @ codomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ codomain @ ( A @ domain @ ( true @ ( B @ ( A @ compose ) @ there_exists @ ifeq2 ) ) ) )
= ( B @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
( ( b @ ( a @ compose ) @ there_exists )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
thf(40,plain,
( ( b @ ( a @ compose ) @ there_exists )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( true @ ( B @ ( A @ equivalent ) @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( true @ ( B @ ( A @ equivalent ) @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ compose ) @ there_exists @ ( B @ codomain @ ( A @ domain @ ifeq3 ) ) ) @ ( true @ ( A @ domain @ there_exists @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ compose ) @ there_exists @ ( B @ codomain @ ( A @ domain @ ifeq3 ) ) ) @ ( true @ ( A @ domain @ there_exists @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq3 ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq3 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(65,plain,
$false,
inference(e,[status(thm)],[48,42,24,20,46,28,38,17,32,34,22,44,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n003.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 22:50:55 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.86/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.19 % [INFO] Parsing done (180ms).
% 1.40/1.20 % [INFO] Running in sequential loop mode.
% 1.80/1.60 % [INFO] eprover registered as external prover.
% 2.00/1.60 % [INFO] Scanning for conjecture ...
% 2.00/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.18/1.75 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.18/1.78 % [INFO] Problem is propositional (TPTP CNF).
% 2.18/1.79 % [INFO] Type checking passed.
% 2.18/1.79 % [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 ...
% 3.72/2.47 % External prover 'e' found a proof!
% 3.72/2.47 % [INFO] Killing All external provers ...
% 3.72/2.47 % Time passed: 1899ms (effective reasoning time: 1266ms)
% 3.72/2.48 % Axioms used in derivation (15): ifeq_axiom_001, ifeq_axiom, ab_exists, compose_codomain, domain_codomain_composition2, compose_domain, equivalence_implies_existence1, equivalence_implies_existence2, codomain_has_elements, associativity_of_compose, domain_codomain_composition1, composition_implies_domain, domain_has_elements, existence_and_equality_implies_equivalence1, ifeq_axiom_002
% 3.72/2.48 % No. of inferences in proof: 33
% 3.72/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1899 ms resp. 1266 ms w/o parsing
% 4.11/2.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.11/2.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------