TSTP Solution File: CAT002-4 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : CAT002-4 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 18:59:47 EDT 2024
% Result : Unsatisfiable 3.49s 2.13s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 44 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 63 ( 30 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 188 ( 30 ~; 28 |; 0 &; 130 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 0 ^ 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $i ).
thf(h_type,type,
h: $i ).
thf(equivalent_type,type,
equivalent: $i > $i > $o ).
thf(there_exists_type,type,
there_exists: $i > $o ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(codomain_type,type,
codomain: $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(13,axiom,
there_exists @ ( compose @ a @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
thf(52,plain,
there_exists @ ( compose @ a @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( there_exists @ ( codomain @ A ) )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(53,plain,
! [A: $i] :
( ~ ( there_exists @ ( codomain @ A ) )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
thf(34,plain,
! [A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( ( domain @ A )
!= ( codomain @ B ) )
| ( there_exists @ ( compose @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( ( domain @ A )
!= ( codomain @ B ) )
| ( there_exists @ ( compose @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
( ( compose @ ( compose @ a @ b ) @ h )
= ( compose @ ( compose @ a @ b ) @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
thf(58,plain,
( ( compose @ ( compose @ a @ b ) @ h )
= ( compose @ ( compose @ a @ b ) @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ A )
| ( A != B )
| ( equivalent @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ A )
| ( A != B )
| ( equivalent @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( ( domain @ A )
= ( codomain @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( ( domain @ A )
= ( codomain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
there_exists @ h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_h_exists) ).
thf(57,plain,
there_exists @ h,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,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)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ b @ A )
!= B )
| ( ( compose @ b @ C )
!= B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_compose2) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ b @ A )
!= B )
| ( ( compose @ b @ C )
!= B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
g != h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_g_equals_h) ).
thf(18,plain,
g != h,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
thf(40,plain,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i] :
( ( compose @ ( codomain @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
thf(55,plain,
! [A: $i] :
( ( compose @ ( codomain @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( there_exists @ ( domain @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( there_exists @ ( domain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ a @ A )
!= B )
| ( ( compose @ a @ C )
!= B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_compose1) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ a @ A )
!= B )
| ( ( compose @ a @ C )
!= B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[52,53,34,27,58,42,24,46,57,38,21,48,18,40,55,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : CAT002-4 : TPTP v8.2.0. Released v1.0.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n008.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat May 18 11:34:24 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.88/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.06 % [INFO] Parsing done (155ms).
% 1.32/1.07 % [INFO] Running in sequential loop mode.
% 1.89/1.42 % [INFO] eprover registered as external prover.
% 1.89/1.42 % [INFO] cvc4 registered as external prover.
% 1.89/1.43 % [INFO] Scanning for conjecture ...
% 1.98/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.10/1.55 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.24/1.58 % [INFO] Problem is propositional (TPTP CNF).
% 2.24/1.58 % [INFO] Type checking passed.
% 2.24/1.59 % [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 ...
% 3.49/2.12 % External prover 'e' found a proof!
% 3.49/2.12 % [INFO] Killing All external provers ...
% 3.49/2.12 % Time passed: 1666ms (effective reasoning time: 1038ms)
% 3.49/2.12 % Axioms used in derivation (16): assume_ab_exists, cancellation_for_compose2, compose_codomain, domain_codomain_composition2, compose_domain, equivalence_implies_existence1, ab_h_equals_ab_g, assume_h_exists, equivalence_implies_existence2, codomain_has_elements, associativity_of_compose, domain_codomain_composition1, composition_implies_domain, domain_has_elements, existence_and_equality_implies_equivalence1, cancellation_for_compose1
% 3.49/2.12 % No. of inferences in proof: 35
% 3.49/2.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1666 ms resp. 1038 ms w/o parsing
% 3.49/2.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.49/2.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------