TSTP Solution File: CAT004-4 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : CAT004-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 07:28:54 EDT 2024
% Result : Unsatisfiable 2.89s 1.67s
% Output : Refutation 2.89s
% 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(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(domain_type,type,
domain: $i > $i ).
thf(codomain_type,type,
codomain: $i > $i ).
thf(b_type,type,
b: $i ).
thf(14,axiom,
! [A: $i] :
( ( compose @ ( codomain @ A ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
thf(53,plain,
! [A: $i] :
( ( compose @ ( codomain @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
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(32,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( ( domain @ A )
= ( codomain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( equivalent @ A @ B )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/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)],[10]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ A @ b )
!= B )
| ( ( compose @ C @ b )
!= B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product2) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ A @ b )
!= B )
| ( ( compose @ C @ b )
!= B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
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(35,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(1,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
thf(18,plain,
h != g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(17,axiom,
( ( compose @ h @ ( compose @ a @ b ) )
= ( compose @ g @ ( compose @ a @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_ab_equals_g_ab) ).
thf(58,plain,
( ( compose @ h @ ( compose @ a @ b ) )
= ( compose @ g @ ( compose @ a @ b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( there_exists @ ( codomain @ A ) )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(47,plain,
! [A: $i] :
( ~ ( there_exists @ ( codomain @ A ) )
| ( there_exists @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
thf(42,plain,
! [A: $i] :
( ( compose @ A @ ( domain @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,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(24,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ A )
| ( A != B )
| ( equivalent @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
there_exists @ ( compose @ a @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
thf(46,plain,
there_exists @ ( compose @ a @ b ),
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(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(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ A @ a )
!= B )
| ( ( compose @ C @ a )
!= B )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product1) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( ( compose @ A @ a )
!= B )
| ( ( compose @ C @ a )
!= B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(38,plain,
! [B: $i,A: $i] :
( ~ ( there_exists @ ( compose @ A @ B ) )
| ( there_exists @ ( domain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(40,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(15,axiom,
! [A: $i] :
( ~ ( there_exists @ ( domain @ A ) )
| ( there_exists @ A ) ),
file('/export/starexec/sandbox2/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)],[15]) ).
thf(60,plain,
$false,
inference(cvc4,[status(thm)],[53,32,44,49,35,18,58,47,42,24,46,57,21,28,38,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT004-4 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n002.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 : Mon May 6 13:51:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (118ms).
% 1.23/0.98 % [INFO] Running in sequential loop mode.
% 1.66/1.18 % [INFO] eprover registered as external prover.
% 1.66/1.18 % [INFO] cvc4 registered as external prover.
% 1.66/1.19 % [INFO] Scanning for conjecture ...
% 1.84/1.24 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.84/1.27 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.84/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.29 % [INFO] Type checking passed.
% 1.84/1.30 % [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 ...
% 2.89/1.67 % External prover 'cvc4' found a proof!
% 2.89/1.67 % [INFO] Killing All external provers ...
% 2.89/1.67 % Time passed: 1140ms (effective reasoning time: 683ms)
% 2.89/1.67 % 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)>
% 2.89/1.67 % Axioms used in derivation (16): assume_ab_exists, compose_codomain, domain_codomain_composition2, compose_domain, cancellation_for_product1, equivalence_implies_existence1, h_ab_equals_g_ab, assume_h_exists, equivalence_implies_existence2, codomain_has_elements, existence_and_equality_implies_equivalence1, associativity_of_compose, cancellation_for_product2, domain_codomain_composition1, composition_implies_domain, domain_has_elements
% 2.89/1.67 % No. of inferences in proof: 35
% 2.89/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1140 ms resp. 683 ms w/o parsing
% 2.89/1.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.89/1.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------