%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT014-3 : 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 : n016.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 2.73s 6.44s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 32 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 222 ( 36 ~; 40 |; 0 &; 146 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(codomain_decl,type,
codomain: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(equivalent_decl,type,
equivalent: $i > $i > $o ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(there_exists_decl,type,
there_exists: $i > $o ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
a @ codomain @ there_exists,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_codomain_exists) ).
thf(61,plain,
a @ codomain @ there_exists,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,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(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( A @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ domain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
thf(53,plain,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ domain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence3) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( B @ there_exists )
| ~ ( A @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence2) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( B @ there_exists )
| ~ ( A @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A @ codomain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_codomain) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( A @ codomain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,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(58,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)],[15]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
thf(36,plain,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ codomain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(62,plain,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ codomain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,negated_conjecture,
( ( a @ codomain @ codomain )
!= ( a @ codomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_is_idempotent) ).
thf(20,plain,
( ( a @ codomain @ codomain )
!= ( a @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles1) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B
= ( B @ ( A @ f1 ) ) )
| ( A
= ( B @ ( A @ f1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles2) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B
= ( B @ ( A @ f1 ) ) )
| ( A
= ( B @ ( A @ f1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,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(32,plain,
! [B: $i,A: $i] :
( ( A @ domain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,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(34,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)],[6]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B
!= ( B @ ( A @ f1 ) ) )
| ( A
!= ( B @ ( A @ f1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles3) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B
!= ( B @ ( A @ f1 ) ) )
| ( A
!= ( B @ ( A @ f1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,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(55,plain,
! [B: $i,A: $i] :
( ( ( A @ domain )
= ( B @ codomain ) )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equivalent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(69,plain,
$false,
inference(e,[status(thm)],[42,61,38,53,44,49,66,58,36,62,20,46,29,64,32,34,26,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT014-3 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.14/5.41 % Computer : n016.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 22:54:39 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 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
% 0.18/5.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/5.81 % [INFO] Parsing done (99ms).
% 0.18/5.81 % [INFO] Running in sequential loop mode.
% 0.18/6.00 % [INFO] eprover registered as external prover.
% 0.18/6.00 % [INFO] Scanning for conjecture ...
% 1.53/6.05 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 1.53/6.08 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.53/6.09 % [INFO] Problem is propositional (TPTP CNF).
% 1.53/6.09 % [INFO] Type checking passed.
% 1.53/6.10 % [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 ...
% 2.73/6.44 % External prover 'e' found a proof!
% 2.73/6.44 % [INFO] Killing All external provers ...
% 2.73/6.44 % Time passed: 940ms (effective reasoning time: 626ms)
% 2.73/6.44 % Axioms used in derivation (18): equivalence_implies_existence3, existence_and_equality_implies_equivalence2, assume_codomain_exists, compose_codomain, indiscernibles3, domain_codomain_composition2, compose_domain, composition_implies_codomain, equivalence_implies_existence1, indiscernibles1, equivalence_implies_existence2, codomain_has_elements, associativity_of_compose, domain_codomain_composition1, composition_implies_domain, domain_has_elements, existence_and_equality_implies_equivalence1, indiscernibles2
% 2.73/6.44 % No. of inferences in proof: 39
% 2.73/6.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 940 ms resp. 626 ms w/o parsing
% 2.73/6.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.73/6.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------