%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n027.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 : Thu Jul 14 23:48:55 EDT 2022
% Result : Unsatisfiable 0.61s 0.81s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 13 ( 10 unt; 0 nHn; 11 RR)
% Number of literals : 23 ( 2 equ; 12 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(distributivity5,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ product(Y,U,W)
| ~ sum(X,W,X1)
| product(Z,V,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity5) ).
cnf(distributivity6,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ product(Y,U,W)
| ~ product(Z,V,X1)
| sum(X,W,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(sum_to_multiplicative_identity1,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
cnf(sum_to_multiplicative_identity2,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
cnf(product_to_additive_identity1,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity1) ).
cnf(product_to_additive_identity2,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity2) ).
cnf(prove_both_inverse_are_equal,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
cnf(18,plain,
~ sum(additive_identity,z,y),
inference('UR-RESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,prove_both_inverse_are_equal]) ).
cnf(136,plain,
product(multiplicative_identity,add(y,z),y),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,sum_to_multiplicative_identity1,closure_of_addition,product_to_additive_identity2,additive_identity1]) ).
cnf(243,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[distributivity6,18,sum_to_multiplicative_identity2,closure_of_addition,product_to_additive_identity1]),136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n027.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 : Wed Jun 1 16:22:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 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/sandbox/benchmark/theBenchmark.p 2022-06-01T16:22:19
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n027.cluster.edu at 2022-06-01T16:22:19
% 0.19/0.49
% 0.19/0.49 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.19/0.49 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.19/0.49 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.19/0.49 ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.19/0.49 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.19/0.49 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.19/0.49 ; Recognized possible left identity assertion (|product| |multiplicative_identity| ?X ?X).
% 0.19/0.49 ; Recognized possible right identity assertion (|product| ?X |multiplicative_identity| ?X).
% 0.19/0.49 ; Recognized possible left inverse assertion (|sum| (|inverse| ?X) ?X |multiplicative_identity|).
% 0.19/0.49 ; Recognized possible right inverse assertion (|sum| ?X (|inverse| ?X) |multiplicative_identity|).
% 0.19/0.49 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |additive_identity|).
% 0.19/0.49 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |additive_identity|).
% 0.19/0.49 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.49 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.49 ; Declaring sum to be commutative.
% 0.19/0.49 ; Declaring add to be commutative.
% 0.19/0.49 ; Declaring product to be commutative.
% 0.61/0.81 ; Declaring multiply to be commutative.
% 0.61/0.81
% 0.61/0.81 #||
% 0.61/0.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.81 % SZS output start Refutation
% See solution above
% 0.61/0.81 ||#
% 0.61/0.81
% 0.61/0.81 ; Summary of computation:
% 0.61/0.81 ; 8705 formulas have been input or derived (from 19 formulas).
% 0.61/0.81 ; 243 ( 3%) were retained. Of these,
% 0.61/0.81 ; 243 (100%) are still being kept.
% 0.61/0.81 ;
% 0.61/0.81 ; Run time in seconds excluding printing time:
% 0.61/0.81 ; 0.006 2% Read assertion file (1 call)
% 0.61/0.81 ; 0.001 0% Assert (27 calls)
% 0.61/0.81 ; 0.026 8% Process new row (5,684 calls)
% 0.61/0.81 ; 0.182 54% Resolution (36 calls)
% 0.61/0.81 ; 0.000 0% Paramodulation (18 calls)
% 0.61/0.81 ; 0.001 0% Condensing (10 calls)
% 0.61/0.81 ; 0.000 0% Forward subsumption (10 calls)
% 0.61/0.81 ; 0.000 0% Backward subsumption (6 calls)
% 0.61/0.81 ; 0.003 1% Clause clause subsumption (4 calls)
% 0.61/0.81 ; 0.070 21% Forward simplification (5,684 calls)
% 0.61/0.81 ; 0.002 1% Backward simplification (243 calls)
% 0.61/0.81 ; 0.000 0% Ordering (12 calls)
% 0.61/0.81 ; 0.000 0% Sortal reasoning (32 calls)
% 0.61/0.81 ; 0.000 0% Purity testing (1 call)
% 0.61/0.81 ; 0.047 14% Other
% 0.61/0.81 ; 0.338 Total
% 0.61/0.81 ; 0.339 Real time
% 0.61/0.81 ;
% 0.61/0.81 ; Term-hash-array has 397 terms in all.
% 0.61/0.81 ; Feature-vector-row-index has 6 entries (6 at peak, 6 added, 0 deleted).
% 0.61/0.81 ; Feature-vector-row-index has 15 nodes (15 at peak, 15 added, 0 deleted).
% 0.61/0.81 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 0.61/0.81 ; Retrieved 0 possibly backward subsumed rows in 6 calls.
% 0.61/0.81 ; Path-index has 402 entries (402 at peak, 402 added, 0 deleted).
% 0.61/0.81 ; Path-index has 268 nodes (268 at peak, 268 added, 0 deleted).
% 0.61/0.81 ; Trie-index has 402 entries (402 at peak, 402 added, 0 deleted).
% 0.61/0.81 ; Trie-index has 1,239 nodes (1,239 at peak, 1,239 added, 0 deleted).
% 0.61/0.81 ; Retrieved 15,860 generalization terms in 17,843 calls.
% 0.61/0.81 ; Retrieved 365 instance terms in 236 calls.
% 0.61/0.81 ; Retrieved 185,579 unifiable terms in 14,710 calls.
% 0.61/0.81 ;
% 0.61/0.81 ; The agenda of rows to process has 40 entries:
% 0.61/0.81 ; 13 with value 10 21 with value 12 4 with value 14
% 0.61/0.81 ; 2 with value 11
% 0.61/0.81 ; The agenda of rows to give has 224 entries:
% 0.61/0.81 ; 3 with value (4 6) 44 with value (4 11) 6 with value (4 15)
% 0.61/0.81 ; 6 with value (4 7) 42 with value (4 12) 10 with value (4 16)
% 0.61/0.81 ; 6 with value (4 8) 12 with value (4 13) 4 with value (4 17)
% 0.61/0.81 ; 46 with value (4 9) 36 with value (4 14) 2 with value (4 19)
% 0.61/0.81 ; 7 with value (4 10)
% 0.61/0.81 Evaluation took:
% 0.61/0.81 0.34 seconds of real time
% 0.61/0.81 0.308357 seconds of user run time
% 0.61/0.81 0.031025 seconds of system run time
% 0.61/0.81 [Run times include 0.007 seconds GC run time.]
% 0.61/0.81 0 calls to %EVAL
% 0.61/0.81 0 page faults and
% 0.61/0.81 24,031,496 bytes consed.
% 0.61/0.81 :PROOF-FOUND
% 0.61/0.81 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T16:22:19
% 0.61/0.81 :PROOF-FOUND
% 0.61/0.81 *
%------------------------------------------------------------------------------