TSTP Solution File: CAT001-4 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : CAT001-4 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 18:59:46 EDT 2024
% Result : Unsatisfiable 2.90s 1.73s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 42 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 57 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 176 ( 26 ~; 24 |; 0 &; 126 @)
% ( 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 : 44 ( 0 ^ 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(h_type,type,
h: $i ).
thf(g_type,type,
g: $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(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(codomain_type,type,
codomain: $i > $i ).
thf(15,axiom,
there_exists @ ( compose @ b @ h ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_bh_exists) ).
thf(52,plain,
there_exists @ ( compose @ b @ h ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
( ( compose @ b @ h )
= ( compose @ b @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bh_equals_bg) ).
thf(53,plain,
( ( compose @ b @ h )
= ( compose @ b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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(41,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ A )
| ( A != B )
| ( equivalent @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
thf(39,plain,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(35,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( there_exists @ ( domain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,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)],[13]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
thf(50,plain,
! [A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(37,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(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ ( compose @ a @ b ) @ A )
!= B )
| ( ( compose @ ( compose @ a @ b ) @ C )
!= B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monomorphism) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ ( compose @ a @ b ) @ A )
!= B )
| ( ( compose @ ( compose @ a @ b ) @ C )
!= B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( there_exists @ ( codomain @ A ) )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(46,plain,
! [A: $i] :
( ~ ( there_exists @ ( codomain @ A ) )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,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(29,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( ( domain @ A )
= ( codomain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,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(32,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)],[6]) ).
thf(11,axiom,
there_exists @ ( compose @ a @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
thf(45,plain,
there_exists @ ( compose @ a @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
thf(17,plain,
h != g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(55,plain,
$false,
inference(e,[status(thm)],[52,53,41,39,35,48,50,23,37,25,20,46,29,32,45,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : CAT001-4 : TPTP v8.2.0. Released v1.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat May 18 11:34:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.92/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.09/0.97 % [INFO] Parsing done (101ms).
% 1.09/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.24 % [INFO] eprover registered as external prover.
% 1.72/1.24 % [INFO] cvc4 registered as external prover.
% 1.72/1.25 % [INFO] Scanning for conjecture ...
% 1.86/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 1.86/1.34 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.04/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 2.04/1.37 % [INFO] Type checking passed.
% 2.11/1.37 % [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 ...
% 2.90/1.73 % External prover 'e' found a proof!
% 2.90/1.73 % [INFO] Killing All external provers ...
% 2.90/1.73 % Time passed: 1202ms (effective reasoning time: 746ms)
% 2.90/1.73 % Axioms used in derivation (15): assume_ab_exists, assume_bh_exists, bh_equals_bg, compose_codomain, compose_domain, equivalence_implies_existence1, equivalence_implies_existence2, codomain_has_elements, existence_and_equality_implies_equivalence1, associativity_of_compose, domain_codomain_composition1, composition_implies_domain, domain_has_elements, monomorphism, domain_codomain_composition2
% 2.90/1.73 % No. of inferences in proof: 33
% 2.90/1.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1202 ms resp. 746 ms w/o parsing
% 3.14/1.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.14/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------