TSTP Solution File: RNG004-2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG004-2 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:40:31 EDT 2022
% Result : Unsatisfiable 0.91s 1.09s
% Output : Refutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 30 ( 5 equ; 12 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(distributivity1,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,V)
| ~ sum(Y,U,W)
| ~ product(X,W,X1)
| sum(Z,V,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(distributivity3,axiom,
( ~ product(X,Y,Z)
| ~ product(U,Y,V)
| ~ sum(X,U,W)
| ~ product(W,Y,X1)
| sum(Z,V,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
cnf(cancellation1,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,U,Z)
| Y = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation1) ).
cnf(a_times_b,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(a_inverse_times_b_inverse,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(29,plain,
~ sum(additive_inverse(c),d,additive_identity),
inference('UR-RESOLVE',[status(thm)],[cancellation1,left_inverse,prove_c_equals_d]) ).
cnf(46,plain,
sum(c,multiply(a,additive_identity),c),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,a_times_b,closure_of_multiplication,additive_identity1,a_times_b]) ).
cnf(49,plain,
sum(c,multiply(a,additive_inverse(b)),multiply(a,additive_identity)),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,a_times_b,closure_of_multiplication,left_inverse,closure_of_multiplication]) ).
cnf(69,plain,
sum(d,multiply(additive_identity,additive_inverse(b)),d),
inference('HYPERRESOLVE',[status(thm)],[distributivity3,a_inverse_times_b_inverse,closure_of_multiplication,additive_identity1,a_inverse_times_b_inverse]) ).
cnf(73,plain,
sum(d,multiply(a,additive_inverse(b)),multiply(additive_identity,additive_inverse(b))),
inference('HYPERRESOLVE',[status(thm)],[distributivity3,a_inverse_times_b_inverse,closure_of_multiplication,left_inverse,closure_of_multiplication]) ).
cnf(132,plain,
multiply(a,additive_identity) = additive_identity,
inference('HYPERRESOLVE',[status(thm)],[cancellation1,46,additive_identity1]) ).
cnf(133,plain,
sum(c,multiply(a,additive_inverse(b)),additive_identity),
inference('REWRITE',[status(thm)],[49,132,theory(equality)]) ).
cnf(516,plain,
multiply(additive_identity,additive_inverse(b)) = additive_identity,
inference('HYPERRESOLVE',[status(thm)],[cancellation1,69,additive_identity1]) ).
cnf(517,plain,
sum(d,multiply(a,additive_inverse(b)),additive_identity),
inference('REWRITE',[status(thm)],[73,516,theory(equality)]) ).
cnf(612,plain,
multiply(a,additive_inverse(b)) = additive_inverse(c),
inference('HYPERRESOLVE',[status(thm)],[cancellation1,133,left_inverse]) ).
cnf(615,plain,
$false,
inference('REWRITE',[status(thm)],[517,29,612,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 22:19:36 EDT 2022
% 0.12/0.34 % 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 2022-05-30T22:19:36
% 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 2022-05-30T22:19:36
% 0.19/0.48
% 0.19/0.48 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.19/0.48 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.19/0.48 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.19/0.48 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.19/0.48 ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.19/0.48 ; Recognized possible right inverse assertion (|sum| ?X (|additive_inverse| ?X) |additive_identity|).
% 0.19/0.49 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?Z ?U ?W)) (|sum| ?X ?V ?W)).
% 0.19/0.49 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?X ?V ?W)) (|sum| ?Z ?U ?W)).
% 0.19/0.49 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.19/0.49 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.19/0.49 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 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.
% 0.91/1.09 ; Declaring add to be associative-commutative.
% 0.91/1.09
% 0.91/1.09 #||
% 0.91/1.09 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.91/1.09 % SZS output start Refutation
% See solution above
% 0.91/1.09 ||#
% 0.91/1.09
% 0.91/1.09 ; Summary of computation:
% 0.91/1.09 ; 11636 formulas have been input or derived (from 55 formulas).
% 0.91/1.09 ; 615 ( 5%) were retained. Of these,
% 0.91/1.09 ; 49 ( 8%) were simplified or subsumed later,
% 0.91/1.09 ; 566 (92%) are still being kept.
% 0.91/1.09 ;
% 0.91/1.09 ; Run time in seconds excluding printing time:
% 0.91/1.09 ; 0.005 1% Read assertion file (1 call)
% 0.91/1.09 ; 0.001 0% Assert (22 calls)
% 0.91/1.09 ; 0.059 10% Process new row (8,527 calls)
% 0.91/1.09 ; 0.295 48% Resolution (108 calls)
% 0.91/1.09 ; 0.002 0% Paramodulation (54 calls)
% 0.91/1.09 ; 0.000 0% Embedding (5 calls)
% 0.91/1.09 ; 0.000 0% Condensing (12 calls)
% 0.91/1.09 ; 0.000 0% Forward subsumption (12 calls)
% 0.91/1.09 ; 0.000 0% Backward subsumption (10 calls)
% 0.91/1.09 ; 0.001 0% Clause clause subsumption (10 calls)
% 0.91/1.09 ; 0.185 30% Forward simplification (7,629 calls)
% 0.91/1.09 ; 0.018 3% Backward simplification (613 calls)
% 0.91/1.09 ; 0.000 0% Ordering (110 calls)
% 0.91/1.09 ; 0.000 0% Ordering ac (5 calls)
% 0.91/1.09 ; 0.000 0% Sortal reasoning (32 calls)
% 0.91/1.09 ; 0.000 0% Purity testing (1 call)
% 0.91/1.09 ; 0.053 9% Other
% 0.91/1.09 ; 0.619 Total
% 0.91/1.09 ; 0.621 Real time
% 0.91/1.09 ;
% 0.91/1.09 ; Term-hash-array has 1,149 terms in all.
% 0.91/1.09 ; Feature-vector-row-index has 10 entries (10 at peak, 10 added, 0 deleted).
% 0.91/1.09 ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 0.91/1.09 ; Retrieved 7 possibly forward subsuming rows in 12 calls.
% 0.91/1.09 ; Retrieved 4 possibly backward subsumed rows in 10 calls.
% 0.91/1.09 ; Path-index has 1,088 entries (1,098 at peak, 1,154 added, 66 deleted).
% 0.91/1.09 ; Path-index has 816 nodes (816 at peak, 829 added, 13 deleted).
% 0.91/1.09 ; Trie-index has 1,088 entries (1,098 at peak, 1,154 added, 66 deleted).
% 0.91/1.09 ; Trie-index has 1,412 nodes (1,423 at peak, 1,535 added, 123 deleted).
% 0.91/1.09 ; Retrieved 65,034 generalization terms in 30,344 calls.
% 0.91/1.09 ; Retrieved 996 instance terms in 602 calls.
% 0.91/1.09 ; Retrieved 306,439 unifiable terms in 16,314 calls.
% 0.91/1.09 ;
% 0.91/1.09 ; The agenda of rows to process has 334 entries:
% 0.91/1.09 ; 17 with value 12 35 with value 16 30 with value 20
% 0.91/1.09 ; 10 with value 13 53 with value 17 6 with value 21
% 0.91/1.09 ; 42 with value 14 57 with value 18 1 with value 22
% 0.91/1.09 ; 45 with value 15 38 with value 19
% 0.91/1.09 ; The agenda of rows to give has 516 entries:
% 0.91/1.09 ; 1 with value (4 9) 48 with value (4 15) 76 with value (4 20)
% 0.91/1.09 ; 4 with value (4 11) 46 with value (4 16) 42 with value (4 21)
% 0.91/1.09 ; 23 with value (4 12) 77 with value (4 17) 25 with value (4 22)
% 0.91/1.09 ; 13 with value (4 13) 45 with value (4 18) 16 with value (4 23)
% 0.91/1.09 ; 41 with value (4 14) 49 with value (4 19) 10 with value (4 24)
% 0.91/1.09 Evaluation took:
% 0.91/1.09 0.621 seconds of real time
% 0.91/1.09 0.575921 seconds of user run time
% 0.91/1.09 0.044776 seconds of system run time
% 0.91/1.09 [Run times include 0.018 seconds GC run time.]
% 0.91/1.09 0 calls to %EVAL
% 0.91/1.09 0 page faults and
% 0.91/1.09 40,284,072 bytes consed.
% 0.91/1.09 :PROOF-FOUND
% 0.91/1.09 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T22:19:37
% 0.91/1.09 :PROOF-FOUND
% 0.91/1.09 *
%------------------------------------------------------------------------------