TSTP Solution File: GRP114-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP114-1 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 : Fri May 19 11:13:11 EDT 2023
% Result : Unsatisfiable 4.78s 2.05s
% Output : Refutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 29
% Syntax : Number of formulae : 51 ( 43 unt; 8 typ; 0 def)
% Number of atoms : 43 ( 42 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 220 ( 2 ~; 0 |; 0 &; 218 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 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 : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(positive_part_type,type,
positive_part: $i > $i ).
thf(a_type,type,
a: $i ).
thf(negative_part_type,type,
negative_part: $i > $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(20,axiom,
! [A: $i] :
( ( negative_part @ A )
= ( intersection @ A @ identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',negative_part) ).
thf(61,plain,
! [A: $i] :
( ( negative_part @ A )
= ( intersection @ A @ identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( intersection @ ( union @ A @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( intersection @ ( union @ A @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [A: $i] :
( ( positive_part @ A )
= ( union @ A @ identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',positive_part) ).
thf(53,plain,
! [A: $i] :
( ( positive_part @ A )
= ( union @ A @ identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [A: $i] :
( ( intersection @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_idempotent) ).
thf(41,plain,
! [A: $i] :
( ( intersection @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( inverse @ ( multiply @ A @ B ) )
= ( multiply @ ( inverse @ B ) @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product_lemma) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( inverse @ ( multiply @ A @ B ) )
= ( multiply @ ( inverse @ B ) @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( union @ A @ B ) @ C )
= ( union @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_union2) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( union @ A @ B ) @ C )
= ( union @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_commutative) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( union @ A @ ( union @ B @ C ) )
= ( union @ ( union @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_associative) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( union @ A @ ( union @ B @ C ) )
= ( union @ ( union @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( intersection @ A @ ( intersection @ B @ C ) )
= ( intersection @ ( intersection @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_associative) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( intersection @ A @ ( intersection @ B @ C ) )
= ( intersection @ ( intersection @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_involution) ).
thf(43,plain,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(55,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(51,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( union @ B @ C ) )
= ( union @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_union1) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( union @ B @ C ) )
= ( union @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_commutative) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( intersection @ A @ B )
= ( intersection @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
( ( inverse @ identity )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_of_identity) ).
thf(25,plain,
( ( inverse @ identity )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( intersection @ A @ B ) @ C )
= ( intersection @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_intersection2) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( intersection @ A @ B ) @ C )
= ( intersection @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( union @ ( intersection @ A @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( union @ ( intersection @ A @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
( ( multiply @ ( positive_part @ a ) @ ( negative_part @ a ) )
!= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product) ).
thf(22,plain,
( ( multiply @ ( positive_part @ a ) @ ( negative_part @ a ) )
!= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( intersection @ B @ C ) )
= ( intersection @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_intersection1) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( intersection @ B @ C ) )
= ( intersection @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i] :
( ( union @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_idempotent) ).
thf(27,plain,
! [A: $i] :
( ( union @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(184,plain,
$false,
inference(e,[status(thm)],[61,33,53,41,45,49,39,35,63,31,43,55,51,47,37,25,57,29,22,59,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP114-1 : TPTP v8.1.2. Released v1.2.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 02:08:34 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (120ms).
% 1.23/0.98 % [INFO] Running in sequential loop mode.
% 1.56/1.17 % [INFO] eprover registered as external prover.
% 1.74/1.17 % [INFO] cvc4 registered as external prover.
% 1.74/1.17 % [INFO] Scanning for conjecture ...
% 1.83/1.22 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 1.91/1.26 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 1.91/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.28 % [INFO] Type checking passed.
% 1.91/1.28 % [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 ...
% 4.78/2.05 % External prover 'e' found a proof!
% 4.78/2.05 % [INFO] Killing All external provers ...
% 4.78/2.05 % Time passed: 1527ms (effective reasoning time: 1071ms)
% 4.78/2.05 % 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)>
% 4.78/2.05 % Axioms used in derivation (20): multiply_intersection1, intersection_associative, left_identity, multiply_union1, union_commutative, intersection_commutative, union_idempotent, multiply_intersection2, multiply_union2, associativity, intersection_idempotent, union_intersection_absorbtion, negative_part, inverse_product_lemma, positive_part, inverse_of_identity, intersection_union_absorbtion, left_inverse, union_associative, inverse_involution
% 4.78/2.05 % No. of inferences in proof: 43
% 4.78/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1527 ms resp. 1071 ms w/o parsing
% 4.79/2.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.79/2.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------