%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG008-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n018.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 2.50s 2.71s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 36 ( 29 unt; 0 nHn; 14 RR)
% Number of literals : 59 ( 10 equ; 25 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 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 : 67 ( 2 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(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(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(cancellation1,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,U,Z)
| Y = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
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(19,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(20,plain,
additive_identity = add(additive_inverse(X),X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,left_inverse,closure_of_addition]) ).
cnf(24,plain,
X = additive_inverse(additive_inverse(X)),
inference('HYPERRESOLVE',[status(thm)],[cancellation1,left_inverse,left_inverse]) ).
cnf(26,plain,
sum(X,add(additive_inverse(X),Y),Y),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,left_inverse,closure_of_addition,additive_identity1]) ).
cnf(51,plain,
sum(X,multiply(X,additive_identity),X),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,x_squared_is_x,closure_of_multiplication,additive_identity1,x_squared_is_x]) ).
cnf(56,plain,
sum(X,multiply(X,additive_inverse(X)),multiply(X,additive_identity)),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,x_squared_is_x,closure_of_multiplication,left_inverse,closure_of_multiplication]) ).
cnf(80,plain,
sum(X,multiply(additive_identity,X),X),
inference('HYPERRESOLVE',[status(thm)],[distributivity3,x_squared_is_x,closure_of_multiplication,additive_identity1,x_squared_is_x]) ).
cnf(90,plain,
sum(additive_inverse(X),multiply(X,additive_inverse(X)),multiply(additive_identity,additive_inverse(X))),
inference('HYPERRESOLVE',[status(thm)],[distributivity3,x_squared_is_x,closure_of_multiplication,left_inverse,closure_of_multiplication]) ).
cnf(95,plain,
product(add(b,a),b,add(c,b)),
inference('HYPERRESOLVE',[status(thm)],[distributivity4,a_times_b_is_c,x_squared_is_x,closure_of_addition,closure_of_addition]) ).
cnf(247,plain,
multiply(X,additive_identity) = additive_identity,
inference('HYPERRESOLVE',[status(thm)],[cancellation1,51,additive_identity1]) ).
cnf(254,plain,
sum(X,multiply(X,additive_inverse(X)),additive_identity),
inference('REWRITE',[status(thm)],[56,247,theory(equality)]) ).
cnf(260,plain,
multiply(additive_identity,X) = additive_identity,
inference('HYPERRESOLVE',[status(thm)],[cancellation1,80,additive_identity1]) ).
cnf(265,plain,
sum(additive_inverse(X),multiply(X,additive_inverse(X)),additive_identity),
inference('REWRITE',[status(thm)],[90,260,theory(equality)]) ).
cnf(483,plain,
~ product(add(additive_inverse(a),b),a,add(additive_inverse(a),c)),
inference('UR-RESOLVE',[status(thm)],[distributivity4,26,x_squared_is_x,26,prove_b_times_a_is_c]) ).
cnf(1502,plain,
product(add(b,a),add(b,add(b,a)),add(c,add(b,add(b,a)))),
inference('HYPERRESOLVE',[status(thm)],[distributivity2,95,x_squared_is_x,closure_of_addition,closure_of_addition]) ).
cnf(1725,plain,
multiply(X,additive_inverse(X)) = additive_inverse(X),
inference('HYPERRESOLVE',[status(thm)],[cancellation1,254,left_inverse]) ).
cnf(1727,plain,
sum(additive_inverse(X),additive_inverse(X),additive_identity),
inference('REWRITE',[status(thm)],[265,1725,theory(equality)]) ).
cnf(1730,plain,
sum(X,X,additive_identity),
inference('PARAMODULATE',[status(thm)],[1727,24,theory(equality)]) ).
cnf(1732,plain,
additive_inverse(X) = X,
inference('HYPERRESOLVE',[status(thm)],[cancellation1,1730,left_inverse]) ).
cnf(2011,plain,
additive_identity = add(X,X),
inference('REWRITE',[status(thm)],[20,1732,theory(equality)]) ).
cnf(2017,plain,
product(add(b,a),a,add(c,a)),
inference('REWRITE',[status(thm)],[1502,19,2011,theory(equality)]) ).
cnf(2121,plain,
$false,
inference('REWRITE',[status(thm)],[483,2017,1732,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG008-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 10:31:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T10:31:57
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-05-30T10:31:57
% 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|).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?Z ?U ?W)) (|sum| ?X ?V ?W)).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?X ?V ?W)) (|sum| ?Z ?U ?W)).
% 0.19/0.48 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.19/0.48 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.48 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.48 ; Declaring sum to be commutative.
% 0.19/0.48 ; Declaring add to be commutative.
% 2.50/2.71 ; Declaring add to be associative-commutative.
% 2.50/2.71
% 2.50/2.71 #||
% 2.50/2.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.50/2.71 % SZS output start Refutation
% See solution above
% 2.50/2.71 ||#
% 2.50/2.71
% 2.50/2.71 ; Summary of computation:
% 2.50/2.71 ; 35165 formulas have been input or derived (from 67 formulas).
% 2.50/2.71 ; 2121 ( 6%) were retained. Of these,
% 2.50/2.71 ; 1442 (68%) were simplified or subsumed later,
% 2.50/2.71 ; 679 (32%) are still being kept.
% 2.50/2.71 ;
% 2.50/2.71 ; Run time in seconds excluding printing time:
% 2.50/2.71 ; 0.005 0% Read assertion file (1 call)
% 2.50/2.71 ; 0.001 0% Assert (22 calls)
% 2.50/2.71 ; 0.186 8% Process new row (22,744 calls)
% 2.50/2.71 ; 1.406 63% Resolution (132 calls)
% 2.50/2.71 ; 0.005 0% Paramodulation (66 calls)
% 2.50/2.71 ; 0.000 0% Embedding (10 calls)
% 2.50/2.71 ; 0.003 0% Condensing (12 calls)
% 2.50/2.71 ; 0.000 0% Forward subsumption (12 calls)
% 2.50/2.71 ; 0.000 0% Backward subsumption (10 calls)
% 2.50/2.71 ; 0.001 0% Clause clause subsumption (10 calls)
% 2.50/2.71 ; 0.456 20% Forward simplification (17,985 calls)
% 2.50/2.71 ; 0.090 4% Backward simplification (2,118 calls)
% 2.50/2.71 ; 0.000 0% Ordering (184 calls)
% 2.50/2.71 ; 0.000 0% Ordering ac (5 calls)
% 2.50/2.71 ; 0.001 0% Sortal reasoning (32 calls)
% 2.50/2.71 ; 0.001 0% Purity testing (1 call)
% 2.50/2.71 ; 0.087 4% Other
% 2.50/2.71 ; 2.242 Total
% 2.50/2.71 ; 2.246 Real time
% 2.50/2.71 ;
% 2.50/2.71 ; Term-hash-array has 3,919 terms in all.
% 2.50/2.71 ; Feature-vector-row-index has 10 entries (10 at peak, 10 added, 0 deleted).
% 2.50/2.71 ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 2.50/2.71 ; Retrieved 7 possibly forward subsuming rows in 12 calls.
% 2.50/2.71 ; Retrieved 4 possibly backward subsumed rows in 10 calls.
% 2.50/2.71 ; Path-index has 1,104 entries (3,305 at peak, 3,952 added, 2,848 deleted).
% 2.50/2.71 ; Path-index has 1,017 nodes (1,556 at peak, 1,662 added, 645 deleted).
% 2.50/2.71 ; Trie-index has 1,104 entries (3,305 at peak, 3,952 added, 2,848 deleted).
% 2.50/2.71 ; Trie-index has 1,925 nodes (3,263 at peak, 4,204 added, 2,279 deleted).
% 2.50/2.71 ; Retrieved 184,541 generalization terms in 65,336 calls.
% 2.50/2.71 ; Retrieved 7,475 instance terms in 2,107 calls.
% 2.50/2.71 ; Retrieved 2,070,916 unifiable terms in 71,447 calls.
% 2.50/2.71 ;
% 2.50/2.71 ; The agenda of backward simplifiable rows to process has 238 entries:
% 2.50/2.71 ; 238 with value 0
% 2.50/2.71 ; The agenda of rows to process has 2005 entries:
% 2.50/2.71 ; 46 with value 9 273 with value 15 40 with value 21
% 2.50/2.71 ; 119 with value 10 140 with value 16 1 with value 23
% 2.50/2.71 ; 254 with value 11 118 with value 17 4 with value 24
% 2.50/2.71 ; 171 with value 12 174 with value 18 16 with value 25
% 2.50/2.71 ; 332 with value 13 56 with value 19 4 with value 28
% 2.50/2.71 ; 181 with value 14 72 with value 20 4 with value 29
% 2.50/2.71 ; The agenda of rows to give has 632 entries:
% 2.50/2.71 ; 3 with value (4 8) 63 with value (4 15) 42 with value (4 21)
% 2.50/2.71 ; 1 with value (4 9) 35 with value (4 16) 62 with value (4 22)
% 2.50/2.71 ; 8 with value (4 10) 90 with value (4 17) 4 with value (4 24)
% 2.50/2.71 ; 4 with value (4 11) 66 with value (4 18) 8 with value (4 25)
% 2.50/2.71 ; 24 with value (4 12) 52 with value (4 19) 14 with value (4 26)
% 2.50/2.71 ; 33 with value (4 13) 64 with value (4 20) 16 with value (4 27)
% 2.50/2.71 ; 43 with value (4 14)
% 2.50/2.71 Evaluation took:
% 2.50/2.71 2.246 seconds of real time
% 2.50/2.71 2.146496 seconds of user run time
% 2.50/2.71 0.099033 seconds of system run time
% 2.50/2.71 [Run times include 0.102 seconds GC run time.]
% 2.50/2.71 0 calls to %EVAL
% 2.50/2.71 0 page faults and
% 2.50/2.71 143,739,936 bytes consed.
% 2.50/2.71 :PROOF-FOUND
% 2.50/2.71 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T10:31:59
% 2.50/2.71 :PROOF-FOUND
% 2.50/2.71 *
%------------------------------------------------------------------------------