TSTP Solution File: RNG008-5 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG008-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n021.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 1.37s 1.56s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 16
% Syntax : Number of clauses : 27 ( 21 unt; 0 nHn; 11 RR)
% Number of literals : 46 ( 6 equ; 21 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; 4 con; 0-2 aty)
% Number of variables : 55 ( 1 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(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
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(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(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/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
cnf(distributivity4,axiom,
( ~ product(X,Y,Z)
| ~ product(U,Y,V)
| ~ sum(X,U,W)
| ~ sum(Z,V,X1)
| product(W,Y,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
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(multiplication_is_well_defined,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(additive_inverse_additive_inverse,axiom,
sum(additive_inverse(additive_inverse(X)),additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
cnf(multiply_additive_id2,axiom,
product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id2) ).
cnf(multiply_additive_inverse,axiom,
product(X,additive_inverse(Y),additive_inverse(multiply(X,Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse) ).
cnf(x_squared_is_x,hypothesis,
product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_squared_is_x) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(23,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(24,plain,
additive_inverse(additive_inverse(X)) = X,
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,additive_inverse_additive_inverse]) ).
cnf(32,plain,
X = multiply(X,X),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,x_squared_is_x,closure_of_multiplication]) ).
cnf(35,plain,
sum(additive_inverse(X),add(X,Y),Y),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,left_inverse,closure_of_addition,additive_identity1]) ).
cnf(98,plain,
product(a,add(b,a),add(c,a)),
inference('HYPERRESOLVE',[status(thm)],[distributivity2,a_times_b_is_c,x_squared_is_x,closure_of_addition,closure_of_addition]) ).
cnf(115,plain,
sum(additive_inverse(X),additive_inverse(X),additive_identity),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity3,x_squared_is_x,multiply_additive_inverse,left_inverse,multiply_additive_id2]),32,theory(equality)]) ).
cnf(207,plain,
product(X,additive_inverse(X),additive_inverse(X)),
inference('PARAMODULATE',[status(thm)],[multiply_additive_inverse,32,theory(equality)]) ).
cnf(288,plain,
sum(X,X,additive_identity),
inference('PARAMODULATE',[status(thm)],[115,24,theory(equality)]) ).
cnf(290,plain,
additive_identity = add(X,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,288,closure_of_addition]) ).
cnf(562,plain,
~ product(b,add(b,a),add(c,b)),
inference('UR-RESOLVE',[status(thm)],[distributivity2,207,35,35,prove_b_times_a_is_c]) ).
cnf(1067,plain,
$false,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity4,98,x_squared_is_x,closure_of_addition,closure_of_addition]),562,23,290,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG008-5 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n021.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 May 30 17:42:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.46 #<PACKAGE "SNARK-USER">
% 0.20/0.46 *
% 0.20/0.46 SNARK-TPTP-OPTIONS
% 0.20/0.46 *
% 0.20/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.46 (USE-FACTORING :POS)
% 0.20/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.46 *
% 0.20/0.46 "."
% 0.20/0.46 *
% 0.20/0.46 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T17:42:44
% 0.20/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n021.cluster.edu at 2022-05-30T17:42:44
% 0.20/0.48
% 0.20/0.48 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.20/0.48 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.20/0.48 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.20/0.48 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.20/0.48 ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.20/0.48 ; Recognized possible right inverse assertion (|sum| ?X (|additive_inverse| ?X) |additive_identity|).
% 0.20/0.48 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?Z ?U ?W)) (|sum| ?X ?V ?W)).
% 0.20/0.48 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?X ?V ?W)) (|sum| ?Z ?U ?W)).
% 0.20/0.48 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.20/0.48 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.20/0.48 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.20/0.48 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.48 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.48 ; Declaring sum to be commutative.
% 0.20/0.48 ; Declaring add to be commutative.
% 1.37/1.56 ; Declaring add to be associative-commutative.
% 1.37/1.56
% 1.37/1.56 #||
% 1.37/1.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.37/1.56 % SZS output start Refutation
% See solution above
% 1.37/1.57 ||#
% 1.37/1.57
% 1.37/1.57 ; Summary of computation:
% 1.37/1.57 ; 25636 formulas have been input or derived (from 71 formulas).
% 1.37/1.57 ; 1067 ( 4%) were retained. Of these,
% 1.37/1.57 ; 477 (45%) were simplified or subsumed later,
% 1.37/1.57 ; 590 (55%) are still being kept.
% 1.37/1.57 ;
% 1.37/1.57 ; Run time in seconds excluding printing time:
% 1.37/1.57 ; 0.005 0% Read assertion file (1 call)
% 1.37/1.57 ; 0.000 0% Assert (26 calls)
% 1.37/1.57 ; 0.098 9% Process new row (17,166 calls)
% 1.37/1.57 ; 0.655 60% Resolution (140 calls)
% 1.37/1.57 ; 0.004 0% Paramodulation (70 calls)
% 1.37/1.57 ; 0.000 0% Embedding (6 calls)
% 1.37/1.57 ; 0.002 0% Condensing (10 calls)
% 1.37/1.57 ; 0.000 0% Forward subsumption (10 calls)
% 1.37/1.57 ; 0.000 0% Backward subsumption (9 calls)
% 1.37/1.57 ; 0.001 0% Clause clause subsumption (7 calls)
% 1.37/1.57 ; 0.231 21% Forward simplification (16,733 calls)
% 1.37/1.57 ; 0.029 3% Backward simplification (1,063 calls)
% 1.37/1.57 ; 0.001 0% Ordering (179 calls)
% 1.37/1.57 ; 0.000 0% Ordering ac (16 calls)
% 1.37/1.57 ; 0.001 0% Sortal reasoning (32 calls)
% 1.37/1.57 ; 0.000 0% Purity testing (1 call)
% 1.37/1.57 ; 0.073 7% Other
% 1.37/1.57 ; 1.100 Total
% 1.37/1.57 ; 1.102 Real time
% 1.37/1.57 ;
% 1.37/1.57 ; Term-hash-array has 1,711 terms in all.
% 1.37/1.57 ; Feature-vector-row-index has 9 entries (9 at peak, 9 added, 0 deleted).
% 1.37/1.57 ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 1.37/1.57 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 1.37/1.57 ; Retrieved 3 possibly backward subsumed rows in 9 calls.
% 1.37/1.57 ; Path-index has 975 entries (1,040 at peak, 1,731 added, 756 deleted).
% 1.37/1.57 ; Path-index has 793 nodes (914 at peak, 1,118 added, 325 deleted).
% 1.37/1.57 ; Trie-index has 975 entries (1,040 at peak, 1,731 added, 756 deleted).
% 1.37/1.57 ; Trie-index has 1,774 nodes (2,016 at peak, 3,253 added, 1,479 deleted).
% 1.37/1.57 ; Retrieved 103,928 generalization terms in 69,086 calls.
% 1.37/1.57 ; Retrieved 1,862 instance terms in 1,053 calls.
% 1.37/1.57 ; Retrieved 827,557 unifiable terms in 53,129 calls.
% 1.37/1.57 ;
% 1.37/1.57 ; The agenda of rows to process has 75 entries:
% 1.37/1.57 ; 22 with value 20 23 with value 22 1 with value 27
% 1.37/1.57 ; 28 with value 21 1 with value 26
% 1.37/1.57 ; The agenda of rows to give has 533 entries:
% 1.37/1.57 ; 9 with value (4 11) 77 with value (4 17) 4 with value (4 23)
% 1.37/1.57 ; 17 with value (4 12) 73 with value (4 18) 2 with value (4 24)
% 1.37/1.57 ; 38 with value (4 13) 38 with value (4 19) 4 with value (4 25)
% 1.37/1.57 ; 54 with value (4 14) 36 with value (4 20) 12 with value (4 26)
% 1.37/1.57 ; 53 with value (4 15) 31 with value (4 21) 4 with value (4 27)
% 1.37/1.57 ; 55 with value (4 16) 26 with value (4 22)
% 1.37/1.57 Evaluation took:
% 1.37/1.57 1.102 seconds of real time
% 1.37/1.57 1.01048 seconds of user run time
% 1.37/1.57 0.091623 seconds of system run time
% 1.37/1.57 [Run times include 0.038 seconds GC run time.]
% 1.37/1.57 0 calls to %EVAL
% 1.37/1.57 0 page faults and
% 1.37/1.57 83,966,880 bytes consed.
% 1.37/1.57 :PROOF-FOUND
% 1.37/1.57 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T17:42:45
% 1.37/1.57 :PROOF-FOUND
% 1.37/1.57 *
%------------------------------------------------------------------------------