%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n032.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 4.15s 4.37s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 45 ( 38 unt; 0 nHn; 14 RR)
% Number of literals : 68 ( 14 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 : 78 ( 4 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_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(18,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(19,plain,
additive_identity = add(additive_inverse(X),X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,left_inverse,closure_of_addition]) ).
cnf(20,plain,
add(additive_inverse(X),add(X,Y)) = add(additive_identity,Y),
inference('EMBED',[status(thm)],[19]) ).
cnf(22,plain,
X = multiply(X,X),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,x_squared_is_x,closure_of_multiplication]) ).
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(85,plain,
sum(X,multiply(additive_inverse(X),X),multiply(additive_identity,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(96,plain,
product(add(X,X),X,add(X,X)),
inference('HYPERRESOLVE',[status(thm)],[distributivity4,x_squared_is_x,x_squared_is_x,closure_of_addition,closure_of_addition]) ).
cnf(261,plain,
sum(multiply(X,additive_identity),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,51,left_inverse,left_inverse]) ).
cnf(350,plain,
sum(multiply(additive_identity,X),additive_identity,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,80,left_inverse,left_inverse]) ).
cnf(419,plain,
X = additive_inverse(additive_inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,20,theory(equality)]),18,theory(equality)]) ).
cnf(421,plain,
additive_inverse(X) = add(Y,additive_inverse(add(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,20,theory(equality)]),18,theory(equality)]) ).
cnf(676,plain,
additive_identity = multiply(X,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,261,additive_identity1]) ).
cnf(685,plain,
sum(X,multiply(X,additive_inverse(X)),additive_identity),
inference('REWRITE',[status(thm)],[56,676,theory(equality)]) ).
cnf(722,plain,
additive_identity = multiply(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,350,additive_identity1]) ).
cnf(731,plain,
sum(X,multiply(additive_inverse(X),X),additive_identity),
inference('REWRITE',[status(thm)],[85,722,theory(equality)]) ).
cnf(779,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(1795,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(2083,plain,
product(add(X,X),additive_inverse(X),additive_identity),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity2,685,96,closure_of_multiplication,closure_of_addition]),421,theory(equality)]) ).
cnf(2533,plain,
sum(multiply(additive_inverse(X),X),additive_identity,additive_inverse(X)),
inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,731,left_inverse,additive_identity1]) ).
cnf(2535,plain,
additive_identity = add(X,multiply(additive_inverse(X),X)),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,731,closure_of_addition]) ).
cnf(2846,plain,
product(additive_inverse(X),X,X),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity4,2083,closure_of_multiplication,26,additive_identity1]),22,419,theory(equality)]) ).
cnf(2925,plain,
X = multiply(additive_inverse(X),X),
inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,2846,closure_of_multiplication]) ).
cnf(2997,plain,
sum(X,additive_identity,additive_inverse(X)),
inference('REWRITE',[status(thm)],[2533,2925,theory(equality)]) ).
cnf(2999,plain,
additive_identity = add(X,X),
inference('REWRITE',[status(thm)],[2535,2925,theory(equality)]) ).
cnf(3031,plain,
product(add(b,a),a,add(c,a)),
inference('REWRITE',[status(thm)],[1795,18,2999,theory(equality)]) ).
cnf(3250,plain,
additive_inverse(X) = X,
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,2997,additive_identity1]) ).
cnf(3473,plain,
$false,
inference('REWRITE',[status(thm)],[779,3031,3250,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : RNG008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11 % Command : run-snark %s %d
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon May 30 07:32:57 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.40 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.40 *
% 0.16/0.40 *
% 0.16/0.41 #<PACKAGE "SNARK-USER">
% 0.16/0.41 *
% 0.16/0.41 SNARK-TPTP-OPTIONS
% 0.16/0.41 *
% 0.16/0.41 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.16/0.41 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.16/0.41 (USE-FACTORING :POS)
% 0.16/0.41 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.16/0.41 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.16/0.41 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.16/0.41 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.16/0.41 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.16/0.41 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.16/0.41 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.16/0.41 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.16/0.41 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.16/0.41 (DECLARE-TPTP-SYMBOLS2))
% 0.16/0.41 *
% 0.16/0.41 "."
% 0.16/0.41 *
% 0.16/0.41 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T07:32:57
% 0.16/0.41 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-05-30T07:32:57
% 0.16/0.42
% 0.16/0.42 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.16/0.42 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.16/0.42 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.16/0.42 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.16/0.42 ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.16/0.42 ; Recognized possible right inverse assertion (|sum| ?X (|additive_inverse| ?X) |additive_identity|).
% 0.16/0.42 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?Z ?U ?W)) (|sum| ?X ?V ?W)).
% 0.16/0.42 ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?X ?V ?W)) (|sum| ?Z ?U ?W)).
% 0.16/0.42 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.16/0.42 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.16/0.42 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.16/0.42 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.16/0.42 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.16/0.42 ; Declaring sum to be commutative.
% 0.16/0.42 ; Declaring add to be commutative.
% 4.15/4.37 ; Declaring add to be associative-commutative.
% 4.15/4.37
% 4.15/4.37 #||
% 4.15/4.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.15/4.37 % SZS output start Refutation
% See solution above
% 4.15/4.38 ||#
% 4.15/4.38
% 4.15/4.38 ; Summary of computation:
% 4.15/4.38 ; 55161 formulas have been input or derived (from 77 formulas).
% 4.15/4.38 ; 3473 ( 6%) were retained. Of these,
% 4.15/4.38 ; 2787 (80%) were simplified or subsumed later,
% 4.15/4.38 ; 686 (20%) are still being kept.
% 4.15/4.38 ;
% 4.15/4.38 ; Run time in seconds excluding printing time:
% 4.15/4.38 ; 0.003 0% Read assertion file (1 call)
% 4.15/4.38 ; 0.001 0% Assert (20 calls)
% 4.15/4.38 ; 0.300 8% Process new row (34,321 calls)
% 4.15/4.38 ; 2.427 61% Resolution (152 calls)
% 4.15/4.38 ; 0.002 0% Paramodulation (76 calls)
% 4.15/4.38 ; 0.000 0% Embedding (18 calls)
% 4.15/4.38 ; 0.000 0% Condensing (10 calls)
% 4.15/4.38 ; 0.000 0% Forward subsumption (10 calls)
% 4.15/4.38 ; 0.001 0% Backward subsumption (9 calls)
% 4.15/4.38 ; 0.000 0% Clause clause subsumption (7 calls)
% 4.15/4.38 ; 0.932 23% Forward simplification (32,759 calls)
% 4.15/4.38 ; 0.187 5% Backward simplification (3,462 calls)
% 4.15/4.38 ; 0.000 0% Ordering (216 calls)
% 4.15/4.38 ; 0.000 0% Ordering ac (6 calls)
% 4.15/4.38 ; 0.000 0% Sortal reasoning (32 calls)
% 4.15/4.38 ; 0.000 0% Purity testing (1 call)
% 4.15/4.38 ; 0.113 3% Other
% 4.15/4.38 ; 3.966 Total
% 4.15/4.38 ; 3.969 Real time
% 4.15/4.38 ;
% 4.15/4.38 ; Term-hash-array has 6,120 terms in all.
% 4.15/4.38 ; Feature-vector-row-index has 9 entries (9 at peak, 9 added, 0 deleted).
% 4.15/4.38 ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 4.15/4.38 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 4.15/4.38 ; Retrieved 3 possibly backward subsumed rows in 9 calls.
% 4.15/4.38 ; Path-index has 1,111 entries (4,721 at peak, 6,152 added, 5,041 deleted).
% 4.15/4.38 ; Path-index has 1,497 nodes (2,981 at peak, 3,411 added, 1,914 deleted).
% 4.15/4.38 ; Trie-index has 1,111 entries (4,721 at peak, 6,152 added, 5,041 deleted).
% 4.15/4.38 ; Trie-index has 1,930 nodes (5,875 at peak, 8,078 added, 6,148 deleted).
% 4.15/4.38 ; Retrieved 390,896 generalization terms in 125,483 calls.
% 4.15/4.38 ; Retrieved 12,615 instance terms in 3,452 calls.
% 4.15/4.38 ; Retrieved 3,745,597 unifiable terms in 103,621 calls.
% 4.15/4.38 ;
% 4.15/4.38 ; The agenda of backward simplifiable rows to process has 662 entries:
% 4.15/4.38 ; 662 with value 0
% 4.15/4.38 ; The agenda of rows to process has 4912 entries:
% 4.15/4.38 ; 16 with value 9 577 with value 16 67 with value 22
% 4.15/4.38 ; 78 with value 10 430 with value 17 12 with value 23
% 4.15/4.38 ; 436 with value 11 354 with value 18 28 with value 24
% 4.15/4.38 ; 651 with value 12 240 with value 19 4 with value 25
% 4.15/4.38 ; 552 with value 13 96 with value 20 8 with value 26
% 4.15/4.38 ; 595 with value 14 79 with value 21 8 with value 27
% 4.15/4.38 ; 681 with value 15
% 4.15/4.38 ; The agenda of rows to give has 640 entries:
% 4.15/4.38 ; 4 with value (4 9) 37 with value (4 16) 63 with value (4 22)
% 4.15/4.38 ; 8 with value (4 10) 90 with value (4 17) 6 with value (4 24)
% 4.15/4.38 ; 22 with value (4 12) 69 with value (4 18) 8 with value (4 25)
% 4.15/4.38 ; 32 with value (4 13) 53 with value (4 19) 14 with value (4 26)
% 4.15/4.38 ; 45 with value (4 14) 64 with value (4 20) 16 with value (4 27)
% 4.15/4.38 ; 68 with value (4 15) 41 with value (4 21)
% 4.15/4.38 Evaluation took:
% 4.15/4.38 3.97 seconds of real time
% 4.15/4.38 3.803071 seconds of user run time
% 4.15/4.38 0.166901 seconds of system run time
% 4.15/4.38 [Run times include 0.195 seconds GC run time.]
% 4.15/4.38 0 calls to %EVAL
% 4.15/4.38 0 page faults and
% 4.15/4.38 238,104,432 bytes consed.
% 4.15/4.38 :PROOF-FOUND
% 4.15/4.38 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T07:33:01
% 4.15/4.38 :PROOF-FOUND
% 4.15/4.38 *
%------------------------------------------------------------------------------