TSTP Solution File: FLD054-4 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : FLD054-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n024.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 : 600s
% DateTime : Sat Jul 16 02:27:14 EDT 2022
% Result : Unsatisfiable 23.29s 23.51s
% Output : Refutation 23.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of clauses : 35 ( 26 unt; 2 nHn; 35 RR)
% Number of literals : 55 ( 0 equ; 25 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
( sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ sum(U,W,Y)
| ~ sum(V,W,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(associativity_multiplication_1,axiom,
( product(X,Y,Z)
| ~ product(X,U,V)
| ~ product(U,W,Y)
| ~ product(V,W,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(distributivity_1,axiom,
( sum(X,Y,Z)
| ~ sum(U,V,W)
| ~ product(W,X1,Z)
| ~ product(U,X1,X)
| ~ product(V,X1,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(distributivity_2,axiom,
( product(X,Y,Z)
| ~ sum(U,V,X)
| ~ product(U,Y,W)
| ~ product(V,Y,X1)
| ~ sum(W,X1,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
cnf(l_is_defined,hypothesis,
defined(l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_is_defined) ).
cnf(not_sum_6,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_6) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
cnf(sum_8,negated_conjecture,
sum(multiplicative_inverse(a),multiplicative_inverse(b),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_8) ).
cnf(sum_9,negated_conjecture,
sum(a,b,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_9) ).
cnf(product_10,negated_conjecture,
product(a,b,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
cnf(not_product_11,negated_conjecture,
~ product(k,multiplicative_inverse(l),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_11) ).
cnf(38,plain,
sum(additive_identity,a,a),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,a_is_defined]) ).
cnf(43,plain,
product(multiplicative_identity,u,u),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,u_is_defined]) ).
cnf(44,plain,
product(multiplicative_identity,b,b),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,b_is_defined]) ).
cnf(45,plain,
product(multiplicative_identity,a,a),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,a_is_defined]) ).
cnf(60,plain,
sum(additive_inverse(multiplicative_identity),multiplicative_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_addition,well_definedness_of_multiplicative_identity]) ).
cnf(292,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_6,a_is_defined]) ).
cnf(293,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_7,b_is_defined]) ).
cnf(294,plain,
( product(multiplicative_inverse(l),l,multiplicative_identity)
| sum(additive_identity,l,additive_identity) ),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_multiplication,l_is_defined]) ).
cnf(60396,plain,
~ sum(b,multiplicative_identity,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,60,not_sum_7,60]) ).
cnf(60444,plain,
product(multiplicative_inverse(a),l,b),
inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,292,product_10,44]) ).
cnf(60452,plain,
product(multiplicative_inverse(b),l,a),
inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,293,product_10,45]) ).
cnf(78766,plain,
~ sum(l,a,a),
inference('UR-RESOLVE',[status(thm)],[distributivity_1,60444,60396,292,292]) ).
cnf(78814,plain,
~ sum(additive_identity,l,additive_identity),
inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,78766,38,38]) ).
cnf(78816,plain,
product(multiplicative_inverse(l),l,multiplicative_identity),
inference('REWRITE',[status(thm)],[294,78814]) ).
cnf(80006,plain,
~ product(l,u,k),
inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,78816,not_product_11,43]) ).
cnf(80068,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[distributivity_2,80006,sum_8,60444,sum_9]),60452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD054-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 6 16:01:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 *
% 0.19/0.47 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-06T16:01:35
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n024.cluster.edu at 2022-06-06T16:01:35
% 0.19/0.49
% 0.19/0.49 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.19/0.49 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.19/0.49 ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.19/0.49 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.19/0.49 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.19/0.49 ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.19/0.49 ; Declaring sum to be commutative.
% 23.29/23.51 ; Declaring product to be commutative.
% 23.29/23.51
% 23.29/23.51 #||
% 23.29/23.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.29/23.51 % SZS output start Refutation
% See solution above
% 23.29/23.51 ||#
% 23.29/23.51
% 23.29/23.51 ; Summary of computation:
% 23.29/23.51 ; 166626 formulas have been input or derived (from 411 formulas).
% 23.29/23.51 ; 80068 (48%) were retained. Of these,
% 23.29/23.51 ; 112 ( 0%) were simplified or subsumed later,
% 23.29/23.51 ; 79956 (100%) are still being kept.
% 23.29/23.51 ;
% 23.29/23.51 ; Run time in seconds excluding printing time:
% 23.29/23.51 ; 0.007 0% Read assertion file (1 call)
% 23.29/23.51 ; 0.001 0% Assert (37 calls)
% 23.29/23.51 ; 5.291 23% Process new row (164,254 calls)
% 23.29/23.51 ; 13.173 57% Resolution (820 calls)
% 23.29/23.51 ; 0.008 0% Paramodulation (410 calls)
% 23.29/23.51 ; 0.000 0% Factoring (21 calls)
% 23.29/23.51 ; 0.023 0% Condensing (18,599 calls)
% 23.29/23.51 ; 0.869 4% Forward subsumption (18,599 calls)
% 23.29/23.51 ; 0.430 2% Backward subsumption (9,988 calls)
% 23.29/23.51 ; 0.098 0% Clause clause subsumption (86,845 calls)
% 23.29/23.51 ; 1.521 7% Forward simplification (164,254 calls)
% 23.29/23.51 ; 1.003 4% Backward simplification (80,068 calls)
% 23.29/23.51 ; 0.018 0% Ordering (9,894 calls)
% 23.29/23.51 ; 0.000 0% Sortal reasoning (32 calls)
% 23.29/23.51 ; 0.000 0% Purity testing (1 call)
% 23.29/23.51 ; 0.592 3% Other
% 23.29/23.51 ; 23.034 Total
% 23.29/23.51 ; 23.039 Real time
% 23.29/23.52 ;
% 23.29/23.52 ; Term-hash-array has 120,421 terms in all.
% 23.29/23.52 ; Feature-vector-row-index has 9,909 entries (9,909 at peak, 9,988 added, 79 deleted).
% 23.29/23.52 ; Feature-vector-row-index has 8,414 nodes (8,414 at peak, 8,480 added, 66 deleted).
% 23.29/23.52 ; Retrieved 161,439 possibly forward subsuming rows in 18,599 calls.
% 23.29/23.52 ; Retrieved 69,019 possibly backward subsumed rows in 9,988 calls.
% 23.29/23.52 ; Path-index has 120,382 entries (120,382 at peak, 120,514 added, 132 deleted).
% 23.29/23.52 ; Path-index has 1,685 nodes (1,685 at peak, 1,701 added, 16 deleted).
% 23.29/23.52 ; Trie-index has 120,382 entries (120,382 at peak, 120,514 added, 132 deleted).
% 23.29/23.52 ; Trie-index has 333,518 nodes (333,518 at peak, 333,710 added, 192 deleted).
% 23.29/23.52 ; Retrieved 75,598 generalization terms in 183,359 calls.
% 23.29/23.52 ; Retrieved 70,384 instance terms in 70,079 calls.
% 23.29/23.52 ; Retrieved 33,518,905 unifiable terms in 135,142 calls.
% 23.29/23.52 ;
% 23.29/23.52 ; The agenda of rows to process has 29 entries:
% 23.29/23.52 ; 1 with value 10 12 with value 11 16 with value 13
% 23.29/23.52 ; The agenda of rows to give has 79559 entries:
% 23.29/23.52 ; 53 with value (4 9) 9428 with value (4 15) 4732 with value (4 20)
% 23.29/23.52 ; 669 with value (4 10) 744 with value (4 16) 5590 with value (4 21)
% 23.29/23.52 ; 3587 with value (4 11) 4706 with value (4 17) 83 with value (4 22)
% 23.29/23.52 ; 5491 with value (4 12) 1161 with value (4 18) 1352 with value (4 23)
% 23.29/23.52 ; 20702 with value (4 13) 19877 with value (4 19) 13 with value (4 25)
% 23.29/23.52 ; 1371 with value (4 14)
% 23.29/23.52 Evaluation took:
% 23.29/23.52 23.042 seconds of real time
% 23.29/23.52 21.844057 seconds of user run time
% 23.29/23.52 1.195871 seconds of system run time
% 23.29/23.52 [Run times include 3.53 seconds GC run time.]
% 23.29/23.52 0 calls to %EVAL
% 23.29/23.52 0 page faults and
% 23.29/23.52 1,142,155,864 bytes consed.
% 23.29/23.52 :PROOF-FOUND
% 23.29/23.52 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-06T16:01:58
% 23.29/23.52 :PROOF-FOUND
% 23.29/23.52 *
%------------------------------------------------------------------------------