TSTP Solution File: RNG004-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG004-1 : 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 20:40:31 EDT 2022
% Result : Unsatisfiable 1.15s 1.39s
% Output : Refutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 32 ( 27 unt; 0 nHn; 25 RR)
% Number of literals : 49 ( 5 equ; 23 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 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(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(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(a_times_b,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(a_inverse_times_b_inverse,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(17,plain,
~ sum(additive_identity,d,c),
inference('UR-RESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,prove_c_equals_d]) ).
cnf(28,plain,
sum(additive_inverse(X),add(X,Y),Y),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,left_inverse,closure_of_addition,additive_identity1]) ).
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(42,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(43,plain,
sum(d,multiply(additive_inverse(a),additive_identity),d),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,a_inverse_times_b_inverse,closure_of_multiplication,additive_identity1,a_inverse_times_b_inverse]) ).
cnf(66,plain,
sum(c,multiply(additive_identity,b),c),
inference('HYPERRESOLVE',[status(thm)],[distributivity3,a_times_b,closure_of_multiplication,additive_identity1,a_times_b]) ).
cnf(69,plain,
sum(c,multiply(additive_inverse(a),b),multiply(additive_identity,b)),
inference('HYPERRESOLVE',[status(thm)],[distributivity3,a_times_b,closure_of_multiplication,left_inverse,closure_of_multiplication]) ).
cnf(102,plain,
sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,42,left_inverse,left_inverse]) ).
cnf(119,plain,
sum(multiply(additive_identity,b),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,66,left_inverse,left_inverse]) ).
cnf(161,plain,
~ sum(d,X,add(c,X)),
inference('UR-RESOLVE',[status(thm)],[associativity_of_addition1,28,left_inverse,17]) ).
cnf(232,plain,
additive_identity = multiply(a,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,102,additive_identity1]) ).
cnf(234,plain,
additive_identity = multiply(additive_identity,b),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,119,additive_identity1]) ).
cnf(235,plain,
sum(c,multiply(additive_inverse(a),b),additive_identity),
inference('REWRITE',[status(thm)],[69,234,theory(equality)]) ).
cnf(251,plain,
~ product(additive_inverse(a),additive_identity,add(c,multiply(additive_inverse(a),b))),
inference('UR-RESOLVE',[status(thm)],[distributivity1,161,a_inverse_times_b_inverse,closure_of_multiplication,left_inverse]) ).
cnf(280,plain,
product(a,additive_identity,additive_identity),
inference('PARAMODULATE',[status(thm)],[closure_of_multiplication,232,theory(equality)]) ).
cnf(520,plain,
sum(multiply(additive_inverse(a),additive_identity),X,X),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,43,30,30]) ).
cnf(734,plain,
additive_identity = add(c,multiply(additive_inverse(a),b)),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,235,closure_of_addition]) ).
cnf(736,plain,
~ product(additive_inverse(a),additive_identity,additive_identity),
inference('REWRITE',[status(thm)],[251,734,theory(equality)]) ).
cnf(1007,plain,
~ product(additive_identity,additive_identity,additive_identity),
inference('UR-RESOLVE',[status(thm)],[distributivity4,520,closure_of_multiplication,additive_identity1,736]) ).
cnf(1008,plain,
$false,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity4,520,closure_of_multiplication,280,left_inverse]),1007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n026.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 14:01:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 0.18/0.47 #<PACKAGE "SNARK-USER">
% 0.18/0.47 *
% 0.18/0.47 SNARK-TPTP-OPTIONS
% 0.18/0.47 *
% 0.18/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.47 (USE-FACTORING :POS)
% 0.18/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.47 *
% 0.18/0.47 "."
% 0.18/0.47 *
% 0.18/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T14:01:25
% 0.18/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-05-30T14:01:25
% 0.18/0.48
% 0.18/0.48 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.18/0.48 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.18/0.48 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.18/0.48 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.18/0.48 ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.18/0.48 ; Recognized possible right inverse assertion (|sum| ?X (|additive_inverse| ?X) |additive_identity|).
% 0.18/0.48 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?Z ?U ?W)) (|sum| ?X ?V ?W)).
% 0.18/0.48 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?X ?V ?W)) (|sum| ?Z ?U ?W)).
% 0.18/0.48 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.18/0.48 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.18/0.48 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.18/0.48 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.18/0.48 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.18/0.48 ; Declaring sum to be commutative.
% 0.18/0.48 ; Declaring add to be commutative.
% 1.15/1.39 ; Declaring add to be associative-commutative.
% 1.15/1.39
% 1.15/1.39 #||
% 1.15/1.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/1.39 % SZS output start Refutation
% See solution above
% 1.22/1.39 ||#
% 1.22/1.39
% 1.22/1.39 ; Summary of computation:
% 1.22/1.39 ; 17766 formulas have been input or derived (from 69 formulas).
% 1.22/1.39 ; 1008 ( 6%) were retained. Of these,
% 1.22/1.39 ; 107 (11%) were simplified or subsumed later,
% 1.22/1.39 ; 901 (89%) are still being kept.
% 1.22/1.39 ;
% 1.22/1.39 ; Run time in seconds excluding printing time:
% 1.22/1.39 ; 0.005 1% Read assertion file (1 call)
% 1.22/1.39 ; 0.002 0% Assert (20 calls)
% 1.22/1.39 ; 0.080 9% Process new row (11,111 calls)
% 1.22/1.39 ; 0.459 50% Resolution (136 calls)
% 1.22/1.39 ; 0.001 0% Paramodulation (68 calls)
% 1.22/1.39 ; 0.000 0% Embedding (9 calls)
% 1.22/1.39 ; 0.002 0% Condensing (10 calls)
% 1.22/1.39 ; 0.000 0% Forward subsumption (10 calls)
% 1.22/1.39 ; 0.000 0% Backward subsumption (9 calls)
% 1.22/1.39 ; 0.002 0% Clause clause subsumption (7 calls)
% 1.22/1.39 ; 0.296 32% Forward simplification (10,147 calls)
% 1.22/1.39 ; 0.025 3% Backward simplification (1,002 calls)
% 1.22/1.39 ; 0.000 0% Ordering (145 calls)
% 1.22/1.39 ; 0.001 0% Ordering ac (6 calls)
% 1.22/1.39 ; 0.000 0% Sortal reasoning (32 calls)
% 1.22/1.39 ; 0.000 0% Purity testing (1 call)
% 1.22/1.39 ; 0.046 5% Other
% 1.22/1.39 ; 0.919 Total
% 1.22/1.39 ; 0.922 Real time
% 1.22/1.39 ;
% 1.22/1.39 ; Term-hash-array has 1,734 terms in all.
% 1.22/1.39 ; Feature-vector-row-index has 9 entries (9 at peak, 9 added, 0 deleted).
% 1.22/1.39 ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 1.22/1.39 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 1.22/1.39 ; Retrieved 3 possibly backward subsumed rows in 9 calls.
% 1.22/1.39 ; Path-index has 1,593 entries (1,593 at peak, 1,739 added, 146 deleted).
% 1.22/1.39 ; Path-index has 1,177 nodes (1,177 at peak, 1,279 added, 102 deleted).
% 1.22/1.39 ; Trie-index has 1,593 entries (1,593 at peak, 1,739 added, 146 deleted).
% 1.22/1.39 ; Trie-index has 2,118 nodes (2,118 at peak, 2,371 added, 253 deleted).
% 1.22/1.39 ; Retrieved 112,012 generalization terms in 42,595 calls.
% 1.22/1.39 ; Retrieved 1,505 instance terms in 992 calls.
% 1.22/1.39 ; Retrieved 511,678 unifiable terms in 22,350 calls.
% 1.22/1.39 ;
% 1.22/1.39 ; The agenda of rows to process has 2458 entries:
% 1.22/1.39 ; 24 with value 10 253 with value 16 299 with value 21
% 1.22/1.39 ; 36 with value 11 165 with value 17 106 with value 22
% 1.22/1.39 ; 49 with value 12 301 with value 18 36 with value 23
% 1.22/1.39 ; 226 with value 13 379 with value 19 52 with value 24
% 1.22/1.39 ; 49 with value 14 281 with value 20 16 with value 25
% 1.22/1.39 ; 186 with value 15
% 1.22/1.39 ; The agenda of rows to give has 840 entries:
% 1.22/1.39 ; 1 with value (4 9) 63 with value (4 16) 112 with value (4 21)
% 1.22/1.39 ; 9 with value (4 12) 93 with value (4 17) 55 with value (4 22)
% 1.22/1.39 ; 28 with value (4 13) 95 with value (4 18) 26 with value (4 23)
% 1.22/1.39 ; 46 with value (4 14) 101 with value (4 19) 16 with value (4 24)
% 1.22/1.39 ; 67 with value (4 15) 128 with value (4 20)
% 1.22/1.39 Evaluation took:
% 1.22/1.39 0.922 seconds of real time
% 1.22/1.39 0.879912 seconds of user run time
% 1.22/1.39 0.042206 seconds of system run time
% 1.22/1.39 [Run times include 0.026 seconds GC run time.]
% 1.22/1.39 0 calls to %EVAL
% 1.22/1.39 0 page faults and
% 1.22/1.39 62,034,040 bytes consed.
% 1.22/1.39 :PROOF-FOUND
% 1.22/1.39 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T14:01:26
% 1.22/1.39 :PROOF-FOUND
% 1.22/1.39 *
%------------------------------------------------------------------------------