%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 5.90s 3.41s
% Output : Refutation 5.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 342 ( 56 ~; 54 |; 0 &; 232 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 104 ( 0 ^; 104 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(domain_decl,type,
domain: $i > $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(defined_decl,type,
defined: $i > $i > $o ).
thf(identity_map_decl,type,
identity_map: $i > $o ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(18,axiom,
! [A: $i] : ( A @ ( A @ ( A @ codomain @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_codomain) ).
thf(52,plain,
! [A: $i] : ( A @ ( A @ ( A @ codomain @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ defined ) )
| ~ ( C @ ( D @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom3) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ defined ) )
| ~ ( C @ ( D @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [A: $i] : ( A @ domain @ ( A @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
thf(53,plain,
! [A: $i] : ( A @ domain @ ( A @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i] : ( A @ codomain @ identity_map ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).
thf(49,plain,
! [A: $i] : ( A @ codomain @ identity_map ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_is_well_defined) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( F @ product ) ) )
| ~ ( F @ ( A @ ( D @ product ) ) )
| ~ ( E @ ( C @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom5) ).
thf(35,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( F @ product ) ) )
| ~ ( F @ ( A @ ( D @ product ) ) )
| ~ ( E @ ( C @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i] : ( A @ ( A @ domain @ ( A @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_domain) ).
thf(48,plain,
! [A: $i] : ( A @ ( A @ domain @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) ) )
| ~ ( A @ identity_map )
| ~ ( B @ ( A @ defined ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity1) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ product ) ) )
| ~ ( A @ identity_map )
| ~ ( B @ ( A @ defined ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [A: $i] : ( A @ domain @ identity_map ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
thf(51,plain,
! [A: $i] : ( A @ domain @ identity_map ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ product ) ) )
| ~ ( E @ ( D @ ( C @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom2) ).
thf(42,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ product ) ) )
| ~ ( E @ ( D @ ( C @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ defined ) )
| ~ ( B @ identity_map )
| ~ ( C @ ( B @ defined ) )
| ~ ( B @ ( A @ defined ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom6) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ defined ) )
| ~ ( B @ identity_map )
| ~ ( C @ ( B @ defined ) )
| ~ ( B @ ( A @ defined ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property1) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( a @ codomain @ domain )
!= ( a @ codomain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_codomain_is_codomain) ).
thf(20,plain,
( ( a @ codomain @ domain )
!= ( a @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ defined ) )
| ~ ( D @ ( C @ defined ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom1) ).
thf(46,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ defined ) )
| ~ ( D @ ( C @ defined ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ product ) ) )
| ~ ( B @ identity_map )
| ~ ( B @ ( A @ defined ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity2) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ product ) ) )
| ~ ( B @ identity_map )
| ~ ( B @ ( A @ defined ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ defined ) )
| ~ ( D @ ( C @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property2) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ defined ) )
| ~ ( D @ ( C @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ ( B @ ( A @ product ) ) )
| ~ ( B @ ( A @ defined ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_composition) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ ( B @ ( A @ product ) ) )
| ~ ( B @ ( A @ defined ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] : ( A @ ( A @ codomain @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
thf(50,plain,
! [A: $i] : ( A @ ( A @ codomain @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ defined ) )
| ~ ( C @ ( D @ defined ) )
| ~ ( E @ ( A @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom4) ).
thf(31,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ defined ) )
| ~ ( C @ ( D @ defined ) )
| ~ ( E @ ( A @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(54,plain,
$false,
inference(e,[status(thm)],[52,33,53,49,39,35,48,23,51,42,37,25,20,46,29,44,27,50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.48 % Computer : n004.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sat Sep 26 22:49:39 UTC 2026
% 0.25/0.49 % CPUTime :
% 0.25/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.39/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.62 % [INFO] Parsing done (286ms).
% 1.96/1.64 % [INFO] Running in sequential loop mode.
% 2.97/2.25 % [INFO] eprover registered as external prover.
% 2.97/2.26 % [INFO] Scanning for conjecture ...
% 3.17/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.34/2.46 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.53/2.51 % [INFO] Problem is propositional (TPTP CNF).
% 3.53/2.53 % [INFO] Type checking passed.
% 3.53/2.54 % [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 ...
% 5.90/3.40 % External prover 'e' found a proof!
% 5.90/3.41 % [INFO] Killing All external provers ...
% 5.90/3.41 % Time passed: 2710ms (effective reasoning time: 1758ms)
% 5.90/3.41 % Axioms used in derivation (18): category_theory_axiom5, domain_is_an_identity_map, category_theory_axiom1, codomain_is_an_identity_map, identity2, category_theory_axiom4, closure_of_composition, mapping_from_x_to_its_domain, mapping_from_codomain_of_x_to_x, associative_property1, product_on_codomain, category_theory_axiom3, category_theory_axiom6, associative_property2, identity1, category_theory_axiom2, product_on_domain, composition_is_well_defined
% 5.90/3.41 % No. of inferences in proof: 39
% 5.90/3.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2710 ms resp. 1758 ms w/o parsing
% 5.90/3.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.90/3.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------