%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT002-1 : 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 : n020.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 06:55:17 AM UTC 2026
% Result : Unsatisfiable 47.10s 9.92s
% Output : Refutation 47.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 320 ( 50 ~; 48 |; 0 &; 222 @)
% ( 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 : 13 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 98 ( 0 ^; 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(h_decl,type,
h: $i ).
thf(g_decl,type,
g: $i ).
thf(defined_decl,type,
defined: $i > $i > $o ).
thf(domain_decl,type,
domain: $i > $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(d_decl,type,
d: $i ).
thf(18,axiom,
d @ ( g @ ( c @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cg_equals_d) ).
thf(53,plain,
d @ ( g @ ( c @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
c @ ( b @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).
thf(27,plain,
c @ ( b @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( A @ ( A @ codomain @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_codomain) ).
thf(35,plain,
! [A: $i] : ( A @ ( A @ ( A @ codomain @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_well_defined) ).
thf(43,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)],[13]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',category_theory_axiom2) ).
thf(47,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)],[15]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ codomain @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
thf(24,plain,
! [A: $i] : ( A @ ( A @ codomain @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ ( B @ ( A @ product ) ) )
| ~ ( B @ ( A @ defined ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_composition) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ ( B @ ( A @ product ) ) )
| ~ ( B @ ( A @ defined ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
thf(20,plain,
h != g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [A: $i] : ( A @ ( A @ domain @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_domain) ).
thf(46,plain,
! [A: $i] : ( A @ ( A @ domain @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',category_theory_axiom4) ).
thf(33,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)],[8]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property1) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',category_theory_axiom5) ).
thf(38,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)],[11]) ).
thf(19,axiom,
d @ ( h @ ( c @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ch_equals_d) ).
thf(54,plain,
d @ ( h @ ( c @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ defined ) )
| ~ ( D @ ( C @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property2) ).
thf(49,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)],[16]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ( C @ ( a @ product ) ) )
| ~ ( B @ ( A @ ( a @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product1) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ( C @ ( a @ product ) ) )
| ~ ( B @ ( A @ ( a @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,axiom,
! [A: $i] : ( A @ domain @ ( A @ defined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
thf(23,plain,
! [A: $i] : ( A @ domain @ ( A @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ defined ) )
| ~ ( C @ ( D @ defined ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom3) ).
thf(36,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)],[10]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ( C @ ( b @ product ) ) )
| ~ ( B @ ( A @ ( b @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product2) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( B @ ( C @ ( b @ product ) ) )
| ~ ( B @ ( A @ ( b @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',category_theory_axiom1) ).
thf(51,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)],[17]) ).
thf(25160,plain,
$false,
inference(e,[status(thm)],[53,27,35,43,47,24,25,20,46,33,28,38,54,49,40,23,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT002-1 : 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
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 22:48:48 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.70/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.93/0.81 % [INFO] Parsing done (103ms).
% 0.93/0.82 % [INFO] Running in sequential loop mode.
% 1.17/1.00 % [INFO] eprover registered as external prover.
% 1.17/1.00 % [INFO] Scanning for conjecture ...
% 1.49/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 1.49/1.10 % [INFO] Axiom selection finished. Selected 18 axioms (removed 5 axioms).
% 1.71/1.14 % [INFO] Problem is propositional (TPTP CNF).
% 1.71/1.15 % [INFO] Type checking passed.
% 1.71/1.15 % [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 ...
% 47.10/9.91 % External prover 'e' found a proof!
% 47.10/9.91 % [INFO] Killing All external provers ...
% 47.10/9.92 % Time passed: 9413ms (effective reasoning time: 9094ms)
% 47.10/9.92 % Axioms used in derivation (18): category_theory_axiom5, category_theory_axiom1, cg_equals_d, category_theory_axiom4, ch_equals_d, closure_of_composition, mapping_from_x_to_its_domain, mapping_from_codomain_of_x_to_x, associative_property1, cancellation_for_product1, product_on_codomain, category_theory_axiom3, associative_property2, cancellation_for_product2, product_on_domain, composition_is_well_defined, category_theory_axiom2, ab_equals_c
% 47.10/9.92 % No. of inferences in proof: 39
% 47.10/9.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 9413 ms resp. 9094 ms w/o parsing
% 47.10/9.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.10/9.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------