TSTP Solution File: RNG006-3 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %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 : 600s
% DateTime : Mon Jul 18 20:40:32 EDT 2022
% Result : Unsatisfiable 0.59s 0.77s
% Output : Refutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 20 ( 16 unt; 0 nHn; 17 RR)
% Number of literals : 33 ( 2 equ; 15 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(associativity_of_addition1,axiom,
( ~ sum(X,Y,Z)
| ~ sum(Y,U,V)
| ~ sum(Z,U,W)
| sum(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
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/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(distributivity2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,V)
| ~ sum(Y,U,W)
| ~ sum(Z,V,X1)
| product(X,W,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(b_plus_inverse_c,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).
cnf(a_times_b,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(a_times_c,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).
cnf(aPb_plus_IaPc,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
cnf(30,plain,
sum(c,bS_Ic,b),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,left_inverse,b_plus_inverse_c,additive_identity1]) ).
cnf(64,plain,
sum(aPc,multiply(a,additive_identity),aPc),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,a_times_c,closure_of_multiplication,additive_identity1,a_times_c]) ).
cnf(84,plain,
~ sum(multiply(a,additive_identity),multiply(a,bS_Ic),aPb_S_IaPc),
inference('UR-RESOLVE',[status(thm)],[distributivity2,closure_of_multiplication,closure_of_multiplication,additive_identity1,prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(139,plain,
sum(aPc,multiply(a,bS_Ic),aPb),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,30,a_times_c,closure_of_multiplication,a_times_b]) ).
cnf(178,plain,
sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,64,left_inverse,left_inverse]) ).
cnf(361,plain,
sum(multiply(a,bS_Ic),additive_identity,aPb_S_IaPc),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,139,left_inverse,aPb_plus_IaPc]) ).
cnf(389,plain,
additive_identity = multiply(a,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,178,additive_identity1]) ).
cnf(392,plain,
$false,
inference('REWRITE',[status(thm)],[84,361,389,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n025.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 19:07:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.46 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 *
% 0.19/0.47 *
% 0.19/0.48 #<PACKAGE "SNARK-USER">
% 0.19/0.48 *
% 0.19/0.48 SNARK-TPTP-OPTIONS
% 0.19/0.48 *
% 0.19/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48 (USE-FACTORING :POS)
% 0.19/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48 *
% 0.19/0.48 "."
% 0.19/0.48 *
% 0.19/0.48 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T19:07:42
% 0.19/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-05-30T19:07:42
% 0.19/0.49
% 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 relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.19/0.49 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.19/0.49 ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.19/0.49 ; 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)).
% 0.19/0.50 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.19/0.50 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.50 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.50 ; Declaring sum to be commutative.
% 0.19/0.50 ; Declaring add to be commutative.
% 0.59/0.77 ; Declaring add to be associative-commutative.
% 0.59/0.77
% 0.59/0.77 #||
% 0.59/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.77 % SZS output start Refutation
% See solution above
% 0.59/0.78 ||#
% 0.59/0.78
% 0.59/0.78 ; Summary of computation:
% 0.59/0.78 ; 5786 formulas have been input or derived (from 47 formulas).
% 0.59/0.78 ; 392 ( 7%) were retained. Of these,
% 0.59/0.78 ; 88 (22%) were simplified or subsumed later,
% 0.59/0.78 ; 304 (78%) are still being kept.
% 0.59/0.78 ;
% 0.59/0.78 ; Run time in seconds excluding printing time:
% 0.59/0.78 ; 0.005 2% Read assertion file (1 call)
% 0.59/0.78 ; 0.001 0% Assert (22 calls)
% 0.59/0.78 ; 0.040 14% Process new row (3,410 calls)
% 0.59/0.78 ; 0.123 42% Resolution (92 calls)
% 0.59/0.78 ; 0.014 5% Paramodulation (46 calls)
% 0.59/0.78 ; 0.001 0% Embedding (20 calls)
% 0.59/0.78 ; 0.003 1% Condensing (10 calls)
% 0.59/0.78 ; 0.000 0% Forward subsumption (10 calls)
% 0.59/0.78 ; 0.000 0% Backward subsumption (9 calls)
% 0.59/0.78 ; 0.000 0% Clause clause subsumption (7 calls)
% 0.59/0.78 ; 0.065 22% Forward simplification (3,391 calls)
% 0.59/0.78 ; 0.006 2% Backward simplification (373 calls)
% 0.59/0.78 ; 0.000 0% Ordering (196 calls)
% 0.59/0.78 ; 0.000 0% Ordering ac (65 calls)
% 0.59/0.78 ; 0.000 0% Sortal reasoning (32 calls)
% 0.59/0.78 ; 0.000 0% Purity testing (1 call)
% 0.59/0.78 ; 0.037 13% Other
% 0.59/0.78 ; 0.295 Total
% 0.59/0.78 ; 0.298 Real time
% 0.59/0.78 ;
% 0.59/0.78 ; Term-hash-array has 707 terms in all.
% 0.59/0.78 ; Feature-vector-row-index has 9 entries (9 at peak, 9 added, 0 deleted).
% 0.59/0.78 ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 0.59/0.78 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 0.59/0.78 ; Retrieved 3 possibly backward subsumed rows in 9 calls.
% 0.59/0.78 ; Path-index has 584 entries (650 at peak, 717 added, 133 deleted).
% 0.59/0.78 ; Path-index has 599 nodes (614 at peak, 657 added, 58 deleted).
% 0.59/0.78 ; Trie-index has 584 entries (650 at peak, 717 added, 133 deleted).
% 0.59/0.78 ; Trie-index has 915 nodes (960 at peak, 1,025 added, 110 deleted).
% 0.59/0.78 ; Retrieved 30,256 generalization terms in 9,546 calls.
% 0.59/0.78 ; Retrieved 550 instance terms in 363 calls.
% 0.59/0.78 ; Retrieved 97,955 unifiable terms in 9,471 calls.
% 0.59/0.78 ;
% 0.59/0.78 ; The agenda of backward simplifiable rows to process has 38 entries:
% 0.59/0.78 ; 38 with value 0
% 0.59/0.78 ; The agenda of rows to process has 176 entries:
% 0.59/0.78 ; 10 with value 10 18 with value 14 8 with value 17
% 0.59/0.78 ; 30 with value 11 30 with value 15 4 with value 18
% 0.59/0.78 ; 7 with value 12 32 with value 16 4 with value 19
% 0.59/0.78 ; 33 with value 13
% 0.59/0.78 ; The agenda of rows to give has 260 entries:
% 0.59/0.78 ; 6 with value (4 10) 43 with value (4 14) 19 with value (4 18)
% 0.59/0.78 ; 22 with value (4 11) 47 with value (4 15) 12 with value (4 19)
% 0.59/0.78 ; 34 with value (4 12) 39 with value (4 16) 2 with value (4 20)
% 0.59/0.78 ; 17 with value (4 13) 19 with value (4 17)
% 0.59/0.78 Evaluation took:
% 0.59/0.78 0.298 seconds of real time
% 0.59/0.78 0.277735 seconds of user run time
% 0.59/0.78 0.020066 seconds of system run time
% 0.59/0.78 [Run times include 0.008 seconds GC run time.]
% 0.59/0.78 0 calls to %EVAL
% 0.59/0.78 0 page faults and
% 0.59/0.78 17,433,256 bytes consed.
% 0.59/0.78 :PROOF-FOUND
% 0.59/0.78 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T19:07:43
% 0.59/0.78 :PROOF-FOUND
% 0.59/0.78 *
%------------------------------------------------------------------------------