TSTP Solution File: RNG008-6 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG008-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n026.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 4.83s 5.02s
% Output : Refutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 39 ( 32 unt; 0 nHn; 14 RR)
% Number of literals : 62 ( 12 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 : 72 ( 2 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(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(x_times_identity_x_is_identity,axiom,
product(X,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_identity_x_is_identity) ).
cnf(identity_times_x_is_identity,axiom,
product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_times_x_is_identity) ).
cnf(x_squared_is_x,hypothesis,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(20,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(21,plain,
additive_identity = add(additive_inverse(X),X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,left_inverse,closure_of_addition]) ).
cnf(22,plain,
add(additive_inverse(X),add(X,Y)) = add(additive_identity,Y),
inference('EMBED',[status(thm)],[21]) ).
cnf(26,plain,
X = multiply(X,X),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,x_squared_is_x,closure_of_multiplication]) ).
cnf(30,plain,
sum(X,add(additive_inverse(X),Y),Y),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,left_inverse,closure_of_addition,additive_identity1]) ).
cnf(55,plain,
sum(X,multiply(X,additive_inverse(X)),additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,x_squared_is_x,closure_of_multiplication,left_inverse,x_times_identity_x_is_identity]) ).
cnf(68,plain,
product(X,add(X,X),add(X,X)),
inference('HYPERRESOLVE',[status(thm)],[distributivity2,x_squared_is_x,x_squared_is_x,closure_of_addition,closure_of_addition]) ).
cnf(77,plain,
sum(X,multiply(additive_inverse(X),X),additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity3,x_squared_is_x,closure_of_multiplication,left_inverse,identity_times_x_is_identity]) ).
cnf(88,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(231,plain,
X = additive_inverse(additive_inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,22,theory(equality)]),20,theory(equality)]) ).
cnf(233,plain,
additive_inverse(X) = add(Y,additive_inverse(add(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,22,theory(equality)]),20,theory(equality)]) ).
cnf(455,plain,
~ product(add(b,additive_inverse(a)),a,add(additive_inverse(a),c)),
inference('UR-RESOLVE',[status(thm)],[distributivity4,30,x_squared_is_x,30,prove_b_times_a_is_c]) ).
cnf(1239,plain,
sum(multiply(X,additive_inverse(X)),additive_identity,additive_inverse(X)),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,55,left_inverse,additive_identity1]) ).
cnf(1243,plain,
additive_identity = add(X,multiply(X,additive_inverse(X))),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,55,closure_of_addition]) ).
cnf(1922,plain,
product(additive_inverse(X),add(X,X),additive_identity),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity4,77,68,closure_of_multiplication,closure_of_addition]),233,theory(equality)]) ).
cnf(2244,plain,
product(add(b,a),add(b,add(b,a)),add(c,add(b,add(b,a)))),
inference('HYPERRESOLVE',[status(thm)],[distributivity2,88,x_squared_is_x,closure_of_addition,closure_of_addition]) ).
cnf(2973,plain,
product(X,additive_inverse(X),X),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity2,1922,closure_of_multiplication,30,additive_identity1]),26,231,theory(equality)]) ).
cnf(3053,plain,
X = multiply(X,additive_inverse(X)),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,2973,closure_of_multiplication]) ).
cnf(3130,plain,
sum(X,additive_identity,additive_inverse(X)),
inference('REWRITE',[status(thm)],[1239,3053,theory(equality)]) ).
cnf(3132,plain,
additive_identity = add(X,X),
inference('REWRITE',[status(thm)],[1243,3053,theory(equality)]) ).
cnf(3173,plain,
product(add(b,a),a,add(c,a)),
inference('REWRITE',[status(thm)],[2244,20,3132,theory(equality)]) ).
cnf(3482,plain,
additive_inverse(X) = X,
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,3130,additive_identity1]) ).
cnf(3759,plain,
$false,
inference('REWRITE',[status(thm)],[455,3173,3482,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG008-6 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon May 30 16:13:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.47 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.48 *
% 0.21/0.48 *
% 0.21/0.48 #<PACKAGE "SNARK-USER">
% 0.21/0.48 *
% 0.21/0.48 SNARK-TPTP-OPTIONS
% 0.21/0.48 *
% 0.21/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.48 (USE-FACTORING :POS)
% 0.21/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.48 *
% 0.21/0.48 "."
% 0.21/0.48 *
% 0.21/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T16:13:10
% 0.21/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-05-30T16:13:10
% 0.21/0.50
% 0.21/0.50 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.21/0.50 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.21/0.50 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.21/0.50 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.21/0.50 ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.21/0.50 ; Recognized possible right inverse assertion (|sum| ?X (|additive_inverse| ?X) |additive_identity|).
% 0.21/0.50 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?Z ?U ?W)) (|sum| ?X ?V ?W)).
% 0.21/0.50 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?X ?V ?W)) (|sum| ?Z ?U ?W)).
% 0.21/0.50 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.21/0.50 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.21/0.50 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.21/0.50 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.21/0.50 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.21/0.50 ; Declaring sum to be commutative.
% 0.21/0.50 ; Declaring add to be commutative.
% 4.83/5.02 ; Declaring add to be associative-commutative.
% 4.83/5.02
% 4.83/5.02 #||
% 4.83/5.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.83/5.02 % SZS output start Refutation
% See solution above
% 4.83/5.03 ||#
% 4.83/5.03
% 4.83/5.03 ; Summary of computation:
% 4.83/5.03 ; 53342 formulas have been input or derived (from 80 formulas).
% 4.83/5.03 ; 3759 ( 7%) were retained. Of these,
% 4.83/5.03 ; 2983 (79%) were simplified or subsumed later,
% 4.83/5.03 ; 776 (21%) are still being kept.
% 4.83/5.03 ;
% 4.83/5.03 ; Run time in seconds excluding printing time:
% 4.83/5.03 ; 0.005 0% Read assertion file (1 call)
% 4.83/5.03 ; 0.000 0% Assert (22 calls)
% 4.83/5.03 ; 0.347 8% Process new row (33,354 calls)
% 4.83/5.03 ; 2.702 60% Resolution (158 calls)
% 4.83/5.03 ; 0.008 0% Paramodulation (79 calls)
% 4.83/5.03 ; 0.000 0% Embedding (14 calls)
% 4.83/5.03 ; 0.001 0% Condensing (10 calls)
% 4.83/5.03 ; 0.000 0% Forward subsumption (10 calls)
% 4.83/5.03 ; 0.000 0% Backward subsumption (9 calls)
% 4.83/5.03 ; 0.002 0% Clause clause subsumption (7 calls)
% 4.83/5.03 ; 1.079 24% Forward simplification (32,644 calls)
% 4.83/5.03 ; 0.269 6% Backward simplification (3,752 calls)
% 4.83/5.03 ; 0.001 0% Ordering (208 calls)
% 4.83/5.03 ; 0.000 0% Ordering ac (6 calls)
% 4.83/5.03 ; 0.000 0% Sortal reasoning (32 calls)
% 4.83/5.03 ; 0.000 0% Purity testing (1 call)
% 4.83/5.03 ; 0.125 3% Other
% 4.83/5.03 ; 4.539 Total
% 4.83/5.03 ; 4.543 Real time
% 4.83/5.03 ;
% 4.83/5.03 ; Term-hash-array has 6,437 terms in all.
% 4.83/5.03 ; Feature-vector-row-index has 9 entries (9 at peak, 9 added, 0 deleted).
% 4.83/5.03 ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 4.83/5.03 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 4.83/5.03 ; Retrieved 3 possibly backward subsumed rows in 9 calls.
% 4.83/5.03 ; Path-index has 1,223 entries (5,489 at peak, 6,470 added, 5,247 deleted).
% 4.83/5.03 ; Path-index has 1,508 nodes (3,069 at peak, 3,261 added, 1,753 deleted).
% 4.83/5.03 ; Trie-index has 1,223 entries (5,489 at peak, 6,470 added, 5,247 deleted).
% 4.83/5.03 ; Trie-index has 2,004 nodes (6,316 at peak, 7,516 added, 5,512 deleted).
% 4.83/5.03 ; Retrieved 485,625 generalization terms in 132,082 calls.
% 4.83/5.03 ; Retrieved 14,096 instance terms in 3,742 calls.
% 4.83/5.03 ; Retrieved 4,232,386 unifiable terms in 98,445 calls.
% 4.83/5.03 ;
% 4.83/5.03 ; The agenda of backward simplifiable rows to process has 949 entries:
% 4.83/5.03 ; 949 with value 0
% 4.83/5.03 ; The agenda of rows to process has 5254 entries:
% 4.83/5.03 ; 33 with value 9 459 with value 16 67 with value 22
% 4.83/5.03 ; 379 with value 10 454 with value 17 28 with value 23
% 4.83/5.03 ; 386 with value 11 344 with value 18 12 with value 24
% 4.83/5.03 ; 805 with value 12 140 with value 19 4 with value 25
% 4.83/5.03 ; 510 with value 13 82 with value 20 8 with value 26
% 4.83/5.03 ; 607 with value 14 77 with value 21 8 with value 27
% 4.83/5.03 ; 851 with value 15
% 4.83/5.03 ; The agenda of rows to give has 723 entries:
% 4.83/5.03 ; 3 with value (4 9) 62 with value (4 15) 53 with value (4 21)
% 4.83/5.03 ; 6 with value (4 10) 51 with value (4 16) 63 with value (4 22)
% 4.83/5.03 ; 2 with value (4 11) 94 with value (4 17) 6 with value (4 24)
% 4.83/5.03 ; 26 with value (4 12) 87 with value (4 18) 8 with value (4 25)
% 4.83/5.03 ; 34 with value (4 13) 75 with value (4 19) 14 with value (4 26)
% 4.83/5.03 ; 43 with value (4 14) 80 with value (4 20) 16 with value (4 27)
% 4.83/5.03 Evaluation took:
% 4.83/5.03 4.543 seconds of real time
% 4.83/5.03 4.374455 seconds of user run time
% 4.83/5.03 0.168962 seconds of system run time
% 4.83/5.03 [Run times include 0.236 seconds GC run time.]
% 4.83/5.03 0 calls to %EVAL
% 4.83/5.03 0 page faults and
% 4.83/5.03 250,632,392 bytes consed.
% 4.83/5.03 :PROOF-FOUND
% 4.83/5.03 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T16:13:15
% 4.83/5.03 :PROOF-FOUND
% 4.83/5.03 *
%------------------------------------------------------------------------------