TSTP Solution File: CAT006-1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : CAT006-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:28:55 EDT 2024
% Result : Unsatisfiable 3.38s 1.84s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 51 ( 19 unt; 8 typ; 0 def)
% Number of atoms : 97 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 344 ( 56 ~; 54 |; 0 &; 234 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 104 ( 0 ^ 104 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(codomain_type,type,
codomain: $i > $i ).
thf(a_type,type,
a: $i ).
thf(h_type,type,
h: $i ).
thf(defined_type,type,
defined: $i > $i > $o ).
thf(domain_type,type,
domain: $i > $i ).
thf(identity_map_type,type,
identity_map: $i > $o ).
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(20,axiom,
! [A: $i] : ( identity_map @ ( codomain @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).
thf(56,plain,
! [A: $i] : ( identity_map @ ( codomain @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,axiom,
! [A: $i] : ( identity_map @ ( domain @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
thf(52,plain,
! [A: $i] : ( identity_map @ ( domain @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
defined @ h @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ha_defined) ).
thf(53,plain,
defined @ h @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,negated_conjecture,
( ( codomain @ a )
!= h ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_a_is_h) ).
thf(22,plain,
( ( codomain @ a )
!= h ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(18,axiom,
identity_map @ h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_is_the_identity_map) ).
thf(54,plain,
identity_map @ h,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( defined @ C @ D )
| ( defined @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property2) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( defined @ C @ D )
| ( defined @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( defined @ C @ D )
| ( defined @ A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom1) ).
thf(50,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( defined @ C @ D )
| ( defined @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_is_well_defined) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] : ( defined @ A @ ( domain @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
thf(25,plain,
! [A: $i] : ( defined @ A @ ( domain @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ C @ D @ E )
| ~ ( product @ B @ D @ F )
| ( product @ A @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom2) ).
thf(46,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ C @ D @ E )
| ~ ( product @ B @ D @ F )
| ( product @ A @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: $i] : ( defined @ ( codomain @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
thf(57,plain,
! [A: $i] : ( defined @ ( codomain @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( defined @ A @ B )
| ~ ( identity_map @ A )
| ( product @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity1) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( defined @ A @ B )
| ~ ( identity_map @ A )
| ( product @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( defined @ D @ C )
| ( defined @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom3) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( defined @ D @ C )
| ( defined @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [A: $i] : ( product @ A @ ( domain @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_domain) ).
thf(45,plain,
! [A: $i] : ( product @ A @ ( domain @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( defined @ A @ B )
| ( product @ A @ B @ ( compose @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_composition) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( defined @ A @ B )
| ( product @ A @ B @ ( compose @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( defined @ A @ B )
| ~ ( identity_map @ B )
| ( product @ A @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity2) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( defined @ A @ B )
| ~ ( identity_map @ B )
| ( product @ A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ C @ E )
| ~ ( product @ D @ A @ F )
| ( product @ F @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom5) ).
thf(40,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ C @ E )
| ~ ( product @ D @ A @ F )
| ( product @ F @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( defined @ A @ B )
| ~ ( defined @ B @ C )
| ~ ( identity_map @ B )
| ( defined @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom6) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( defined @ A @ B )
| ~ ( defined @ B @ C )
| ~ ( identity_map @ B )
| ( defined @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
! [A: $i] : ( product @ ( codomain @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_codomain) ).
thf(55,plain,
! [A: $i] : ( product @ ( codomain @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ A @ E )
| ~ ( defined @ D @ C )
| ( defined @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom4) ).
thf(36,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ A @ E )
| ~ ( defined @ D @ C )
| ( defined @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ( defined @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property1) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ( defined @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(58,plain,
$false,
inference(e,[status(thm)],[56,52,53,22,54,48,50,42,25,46,57,28,38,45,32,34,40,26,55,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : CAT006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.17 % Command : run_Leo-III %s %d
% 0.17/0.39 % Computer : n014.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Mon May 6 13:50:54 EDT 2024
% 0.17/0.39 % CPUTime :
% 0.94/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/1.00 % [INFO] Parsing done (123ms).
% 1.18/1.01 % [INFO] Running in sequential loop mode.
% 1.64/1.24 % [INFO] eprover registered as external prover.
% 1.76/1.24 % [INFO] cvc4 registered as external prover.
% 1.77/1.25 % [INFO] Scanning for conjecture ...
% 1.77/1.30 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 1.89/1.34 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.04/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 2.04/1.37 % [INFO] Type checking passed.
% 2.04/1.37 % [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 ...
% 3.38/1.84 % External prover 'e' found a proof!
% 3.38/1.84 % [INFO] Killing All external provers ...
% 3.38/1.84 % Time passed: 1299ms (effective reasoning time: 825ms)
% 3.38/1.84 % Solved by 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)>
% 3.38/1.84 % Axioms used in derivation (20): category_theory_axiom5, domain_is_an_identity_map, category_theory_axiom1, codomain_is_an_identity_map, identity2, ha_defined, h_is_the_identity_map, 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
% 3.38/1.84 % No. of inferences in proof: 43
% 3.38/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1299 ms resp. 825 ms w/o parsing
% 3.38/1.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.38/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------