TSTP Solution File: CAT010-10 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : CAT010-10 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 : Mon May 20 18:59:51 EDT 2024
% Result : Unsatisfiable 3.10s 1.62s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of formulae : 44 ( 33 unt; 11 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 : 19 ( 19 >; 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_type,type,
codomain: $i > $i ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(ifeq2_type,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(equivalent_type,type,
equivalent: $i > $i > $i ).
thf(true_type,type,
true: $i ).
thf(there_exists_type,type,
there_exists: $i > $i ).
thf(ifeq3_type,type,
ifeq3: $i > $i > $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(16,axiom,
! [A: $i] :
( ( compose @ ( codomain @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
thf(48,plain,
! [A: $i] :
( ( compose @ ( codomain @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( ifeq @ ( there_exists @ ( codomain @ A ) ) @ true @ ( there_exists @ A ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(42,plain,
! [A: $i] :
( ( ifeq @ ( there_exists @ ( codomain @ A ) ) @ true @ ( there_exists @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( equivalent @ A @ B ) @ true @ ( there_exists @ A ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( equivalent @ A @ B ) @ true @ ( there_exists @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( there_exists @ ( compose @ A @ B ) ) @ true @ ( there_exists @ ( domain @ A ) ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( there_exists @ ( compose @ A @ B ) ) @ true @ ( there_exists @ ( domain @ A ) ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i] :
( ( ifeq @ ( there_exists @ A ) @ true @ ( equivalent @ A @ A ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
thf(28,plain,
! [A: $i] :
( ( ifeq @ ( there_exists @ A ) @ true @ ( equivalent @ A @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( compose @ A @ ( compose @ B @ C ) )
= ( compose @ ( compose @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( compose @ A @ ( compose @ B @ C ) )
= ( compose @ ( compose @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
( ( codomain @ ( compose @ a @ b ) )
!= ( codomain @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
thf(17,plain,
( ( codomain @ ( compose @ a @ b ) )
!= ( codomain @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( ifeq @ ( there_exists @ ( domain @ A ) ) @ true @ ( there_exists @ A ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
thf(32,plain,
! [A: $i] :
( ( ifeq @ ( there_exists @ ( domain @ A ) ) @ true @ ( there_exists @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
thf(34,plain,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( ifeq2 @ ( there_exists @ ( compose @ A @ B ) ) @ true @ ( domain @ A ) @ ( codomain @ B ) )
= ( codomain @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( ifeq2 @ ( there_exists @ ( compose @ A @ B ) ) @ true @ ( domain @ A ) @ ( codomain @ B ) )
= ( codomain @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
( ( there_exists @ ( compose @ a @ b ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).
thf(40,plain,
( ( there_exists @ ( compose @ a @ b ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ifeq2 @ ( equivalent @ A @ B ) @ true @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( ifeq2 @ ( equivalent @ A @ B ) @ true @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( there_exists @ ( domain @ A ) ) @ true @ ( ifeq3 @ ( domain @ A ) @ ( codomain @ B ) @ ( there_exists @ ( compose @ A @ B ) ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( there_exists @ ( domain @ A ) ) @ true @ ( ifeq3 @ ( domain @ A ) @ ( codomain @ B ) @ ( there_exists @ ( compose @ A @ B ) ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq3 @ A @ A @ B @ C )
= 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
% 0.12/0.12 % Problem : CAT010-10 : TPTP v8.2.0. Released v7.3.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 11:45:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.81/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.07/0.88 % [INFO] Parsing done (99ms).
% 1.07/0.89 % [INFO] Running in sequential loop mode.
% 1.39/1.10 % [INFO] eprover registered as external prover.
% 1.54/1.10 % [INFO] cvc4 registered as external prover.
% 1.54/1.10 % [INFO] Scanning for conjecture ...
% 1.54/1.15 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 1.77/1.19 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 1.77/1.21 % [INFO] Problem is propositional (TPTP CNF).
% 1.77/1.21 % [INFO] Type checking passed.
% 1.77/1.21 % [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 ...
% 3.10/1.62 % External prover 'e' found a proof!
% 3.10/1.62 % [INFO] Killing All external provers ...
% 3.10/1.62 % Time passed: 1117ms (effective reasoning time: 727ms)
% 3.10/1.62 % 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
% 3.10/1.62 % No. of inferences in proof: 33
% 3.10/1.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1117 ms resp. 727 ms w/o parsing
% 3.10/1.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.10/1.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------