TSTP Solution File: CAT006-3 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : CAT006-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 3.66s 1.84s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 51 ( 11 unt; 8 typ; 0 def)
% Number of atoms : 87 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 248 ( 40 ~; 44 |; 0 &; 164 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 0 ^ 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(codomain_type,type,
codomain: $i > $i ).
thf(a_type,type,
a: $i ).
thf(d_type,type,
d: $i ).
thf(equivalent_type,type,
equivalent: $i > $i > $o ).
thf(f1_type,type,
f1: $i > $i > $i ).
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(2,axiom,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( there_exists @ ( codomain @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_codomain) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( there_exists @ ( codomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( ( domain @ A )
!= ( codomain @ B ) )
| ( there_exists @ ( compose @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(60,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)],[15]) ).
thf(20,axiom,
! [A: $i] :
( ( compose @ ( codomain @ A ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
thf(72,plain,
! [A: $i] :
( ( compose @ ( codomain @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence3) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( ( domain @ A )
= ( codomain @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( ( domain @ A )
= ( codomain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( there_exists @ ( codomain @ A ) )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(70,plain,
! [A: $i] :
( ~ ( there_exists @ ( codomain @ A ) )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A
!= ( f1 @ A @ B ) )
| ( B
!= ( f1 @ A @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles3) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A
!= ( f1 @ A @ B ) )
| ( B
!= ( f1 @ A @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
thf(38,plain,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( there_exists @ ( domain @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( there_exists @ ( domain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( there_exists @ ( compose @ A @ d ) )
| ( ( compose @ A @ d )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xd_equals_x) ).
thf(64,plain,
! [A: $i] :
( ~ ( there_exists @ ( compose @ A @ d ) )
| ( ( compose @ A @ d )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,negated_conjecture,
( ( codomain @ a )
!= d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_a_is_d) ).
thf(22,plain,
( ( codomain @ a )
!= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( there_exists @ ( f1 @ A @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles1) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( there_exists @ ( f1 @ A @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
there_exists @ ( compose @ d @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',da_exists) ).
thf(63,plain,
there_exists @ ( compose @ d @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( there_exists @ ( compose @ d @ A ) )
| ( ( compose @ d @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dx_equals_x) ).
thf(67,plain,
! [A: $i] :
( ~ ( there_exists @ ( compose @ d @ A ) )
| ( ( compose @ d @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A
= ( f1 @ A @ B ) )
| ( B
= ( f1 @ A @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles2) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A
= ( f1 @ A @ B ) )
| ( B
= ( f1 @ A @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ A )
| ( A != B )
| ( equivalent @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ A )
| ( A != B )
| ( equivalent @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
thf(55,plain,
! [A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( compose @ A @ ( compose @ B @ C ) )
= ( compose @ ( compose @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
thf(36,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)],[6]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( there_exists @ A )
| ~ ( there_exists @ B )
| ( A != B )
| ( equivalent @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence2) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ A )
| ~ ( there_exists @ B )
| ( A != B )
| ( equivalent @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(76,plain,
$false,
inference(e,[status(thm)],[25,74,60,72,46,57,70,28,38,34,64,22,44,48,63,67,31,40,55,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n005.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 13:50:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.00/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/1.00 % [INFO] Parsing done (126ms).
% 1.15/1.01 % [INFO] Running in sequential loop mode.
% 1.84/1.24 % [INFO] eprover registered as external prover.
% 1.84/1.25 % [INFO] cvc4 registered as external prover.
% 1.84/1.25 % [INFO] Scanning for conjecture ...
% 2.01/1.31 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 2.01/1.35 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.18/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 2.18/1.38 % [INFO] Type checking passed.
% 2.18/1.38 % [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 ...
% 3.66/1.83 % External prover 'e' found a proof!
% 3.66/1.84 % [INFO] Killing All external provers ...
% 3.66/1.84 % Time passed: 1298ms (effective reasoning time: 820ms)
% 3.66/1.84 % 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)>
% 3.66/1.84 % Axioms used in derivation (20): equivalence_implies_existence3, existence_and_equality_implies_equivalence2, compose_codomain, indiscernibles3, domain_codomain_composition2, compose_domain, composition_implies_codomain, xd_equals_x, equivalence_implies_existence1, indiscernibles1, dx_equals_x, equivalence_implies_existence2, codomain_has_elements, da_exists, associativity_of_compose, domain_codomain_composition1, composition_implies_domain, domain_has_elements, existence_and_equality_implies_equivalence1, indiscernibles2
% 3.66/1.84 % No. of inferences in proof: 43
% 3.66/1.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1298 ms resp. 820 ms w/o parsing
% 3.66/1.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.66/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------