%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : RNG034-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n023.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 20:40:38 EDT 2022
% Result : Unsatisfiable 16.63s 16.85s
% Output : Refutation 16.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 20 unt; 0 nHn; 9 RR)
% Number of literals : 32 ( 31 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_additive_identity,axiom,
add(additive_identity,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',left_additive_identity) ).
cnf(add_inverse,axiom,
add(additive_inverse(X),X) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',add_inverse) ).
cnf(5,plain,
add(additive_inverse(X),add(X,Y)) = add(additive_identity,Y),
inference('EMBED',[status(thm)],[add_inverse]) ).
cnf(sum_of_inverses,axiom,
additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',sum_of_inverses) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',additive_inverse_additive_inverse) ).
cnf(multiply_over_add1,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',multiply_over_add1) ).
cnf(multiply_over_add2,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',multiply_over_add2) ).
cnf(left_alternative,axiom,
multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',left_alternative) ).
cnf(left_cancellation_for_addition,axiom,
( add(X,Y) != add(Y,Z)
| X = Z ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',left_cancellation_for_addition) ).
cnf(associator,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
cnf(prove_skew_symmetry,negated_conjecture,
associator(cy,cx,cz) != additive_inverse(associator(cx,cy,cz)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_skew_symmetry) ).
cnf(19,plain,
add(multiply(multiply(cy,cx),cz),additive_inverse(multiply(cy,multiply(cx,cz)))) != additive_inverse(add(multiply(multiply(cx,cy),cz),additive_inverse(multiply(cx,multiply(cy,cz))))),
inference('REWRITE',[status(thm)],[prove_skew_symmetry,associator,theory(equality)]) ).
cnf(20,plain,
additive_inverse(X) = add(additive_inverse(add(X,Y)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]),left_additive_identity,theory(equality)]) ).
cnf(21,plain,
add(additive_inverse(add(X,Y)),add(Y,Z)) = add(additive_inverse(X),Z),
inference('EMBED',[status(thm)],[20]) ).
cnf(22,plain,
additive_inverse(add(additive_inverse(X),Y)) = add(X,additive_inverse(Y)),
inference('PARAMODULATE',[status(thm)],[sum_of_inverses,additive_inverse_additive_inverse,theory(equality)]) ).
cnf(24,plain,
( X != add(X,Y)
| additive_identity = Y ),
inference('PARAMODULATE',[status(thm)],[left_cancellation_for_addition,left_additive_identity,theory(equality)]) ).
cnf(27,plain,
( X != add(X,add(additive_inverse(Y),Z))
| Y = Z ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[left_cancellation_for_addition,5,theory(equality)]),left_additive_identity,theory(equality)]) ).
cnf(28,plain,
( X != add(Y,add(X,Z))
| additive_inverse(Y) = Z ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[left_cancellation_for_addition,5,theory(equality)]),left_additive_identity,theory(equality)]) ).
cnf(62,plain,
( X != Y
| additive_identity = add(additive_inverse(X),Y) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[24,5,theory(equality)]),left_additive_identity,theory(equality)]) ).
cnf(76,plain,
additive_inverse(add(additive_inverse(add(Y,Z)),X)) = add(additive_inverse(add(X,additive_inverse(Y))),Z),
inference('PARAMODULATE',[status(thm)],[20,21,theory(equality)]) ).
cnf(148,plain,
additive_identity = add(additive_inverse(multiply(X,multiply(X,Y))),multiply(multiply(X,X),Y)),
inference('HYPERRESOLVE',[status(thm)],[62,left_alternative]) ).
cnf(203,plain,
X != add(additive_inverse(add(multiply(cy,multiply(cx,cz)),multiply(cx,multiply(cy,cz)))),add(X,add(multiply(multiply(cx,cy),cz),multiply(multiply(cy,cx),cz)))),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[27,19]),76,22,additive_inverse_additive_inverse,theory(equality)]) ).
cnf(220,plain,
( X != Y
| additive_inverse(Z) = add(Y,additive_inverse(add(Z,X))) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,5,theory(equality)]),left_additive_identity,theory(equality)]) ).
cnf(698,plain,
additive_inverse(X) = add(multiply(multiply(Y,Y),Z),additive_inverse(add(multiply(Y,multiply(Y,Z)),X))),
inference('HYPERRESOLVE',[status(thm)],[220,left_alternative]) ).
cnf(2429,plain,
additive_identity = add(multiply(multiply(X,Y),Z),add(multiply(multiply(Y,X),Z),additive_inverse(add(multiply(X,multiply(Y,Z)),multiply(Y,multiply(X,Z)))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[148,multiply_over_add2,theory(equality)]),698,multiply_over_add1,multiply_over_add2,theory(equality)]) ).
cnf(2431,plain,
$false,
inference('REWRITE',[status(thm)],[203,left_additive_identity,2429,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG034-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n023.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 22:11:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T22:11:27
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n023.cluster.edu at 2022-05-30T22:11:27
% 0.20/0.49
% 0.20/0.49 ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.20/0.49 ; Recognized possible left inverse assertion (= (|add| (|additive_inverse| ?X) ?X) |additive_identity|).
% 0.20/0.49 ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.20/0.49 ; Recognized associativity assertion (= (|add| ?X (|add| ?Y ?Z)) (|add| (|add| ?X ?Y) ?Z)).
% 0.20/0.49 ; Declaring add to be commutative.
% 16.63/16.85 ; Declaring add to be associative-commutative.
% 16.63/16.85
% 16.63/16.85 #||
% 16.63/16.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.63/16.85 % SZS output start Refutation
% See solution above
% 16.63/16.85 ||#
% 16.63/16.85
% 16.63/16.85 ; Summary of computation:
% 16.63/16.85 ; 34702 formulas have been input or derived (from 138 formulas).
% 16.63/16.85 ; 2431 ( 7%) were retained. Of these,
% 16.63/16.85 ; 34 ( 1%) were simplified or subsumed later,
% 16.63/16.85 ; 2397 (99%) are still being kept.
% 16.63/16.85 ;
% 16.63/16.85 ; Run time in seconds excluding printing time:
% 16.63/16.85 ; 0.003 0% Read assertion file (1 call)
% 16.63/16.85 ; 0.001 0% Assert (19 calls)
% 16.63/16.85 ; 0.340 2% Process new row (32,997 calls)
% 16.63/16.85 ; 1.830 11% Resolution (274 calls)
% 16.63/16.85 ; 0.209 1% Paramodulation (137 calls)
% 16.63/16.85 ; 0.002 0% Embedding (85 calls)
% 16.63/16.85 ; 2.650 16% Condensing (11,573 calls)
% 16.63/16.85 ; 0.834 5% Forward subsumption (11,573 calls)
% 16.63/16.85 ; 0.160 1% Backward subsumption (2,157 calls)
% 16.63/16.85 ; 1.341 8% Clause clause subsumption (80,942 calls)
% 16.63/16.85 ; 6.916 42% Forward simplification (32,922 calls)
% 16.63/16.85 ; 0.015 0% Backward simplification (2,355 calls)
% 16.63/16.85 ; 0.519 3% Ordering (183,040 calls)
% 16.63/16.85 ; 1.404 9% Ordering ac (158,066 calls)
% 16.63/16.85 ; 0.001 0% Sortal reasoning (32 calls)
% 16.63/16.85 ; 0.000 0% Purity testing (1 call)
% 16.63/16.85 ; 0.145 1% Other
% 16.63/16.85 ; 16.370 Total
% 16.63/16.85 ; 16.373 Real time
% 16.63/16.85 ;
% 16.63/16.85 ; Term-hash-array has 3,699 terms in all.
% 16.63/16.85 ; Feature-vector-row-index has 2,141 entries (2,141 at peak, 2,157 added, 16 deleted).
% 16.63/16.85 ; Feature-vector-row-index has 4,595 nodes (4,607 at peak, 4,639 added, 44 deleted).
% 16.63/16.85 ; Retrieved 349,817 possibly forward subsuming rows in 11,573 calls.
% 16.63/16.85 ; Retrieved 9,091 possibly backward subsumed rows in 2,157 calls.
% 16.63/16.85 ; Path-index has 3,659 entries (3,665 at peak, 3,706 added, 47 deleted).
% 16.63/16.85 ; Path-index has 1,088 nodes (1,088 at peak, 1,112 added, 24 deleted).
% 16.63/16.85 ; Trie-index has 3,659 entries (3,665 at peak, 3,706 added, 47 deleted).
% 16.63/16.85 ; Trie-index has 1,476 nodes (1,476 at peak, 1,604 added, 128 deleted).
% 16.63/16.85 ; Retrieved 12,680,385 generalization terms in 472,273 calls.
% 16.63/16.85 ; Retrieved 1,313 instance terms in 367 calls.
% 16.63/16.85 ; Retrieved 3,643,701 unifiable terms in 14,590 calls.
% 16.63/16.85 ;
% 16.63/16.85 ; The agenda of backward simplifiable rows to process has 3 entries:
% 16.63/16.85 ; 3 with value 0
% 16.63/16.85 ; The agenda of rows to process has 22 entries:
% 16.63/16.85 ; 12 with value 35 1 with value 38 1 with value 41
% 16.63/16.85 ; 3 with value 36 1 with value 39 1 with value 42
% 16.63/16.85 ; 1 with value 37 2 with value 40
% 16.63/16.85 ; The agenda of rows to give has 2259 entries:
% 16.63/16.85 ; 22 with value (4 22) 178 with value (4 31) 28 with value (4 40)
% 16.63/16.85 ; 39 with value (4 23) 209 with value (4 32) 60 with value (4 41)
% 16.63/16.85 ; 49 with value (4 24) 173 with value (4 33) 28 with value (4 42)
% 16.63/16.85 ; 81 with value (4 25) 163 with value (4 34) 6 with value (4 43)
% 16.63/16.85 ; 102 with value (4 26) 136 with value (4 35) 3 with value (4 44)
% 16.63/16.85 ; 105 with value (4 27) 103 with value (4 36) 4 with value (4 52)
% 16.63/16.85 ; 146 with value (4 28) 129 with value (4 37) 2 with value (4 56)
% 16.63/16.85 ; 123 with value (4 29) 66 with value (4 38) 12 with value (4 70)
% 16.63/16.85 ; 188 with value (4 30) 100 with value (4 39) 4 with value (4 134)
% 16.63/16.85 Evaluation took:
% 16.63/16.85 16.374 seconds of real time
% 16.63/16.85 15.673097 seconds of user run time
% 16.63/16.85 0.70001 seconds of system run time
% 16.63/16.85 [Run times include 0.597 seconds GC run time.]
% 16.63/16.85 0 calls to %EVAL
% 16.63/16.85 0 page faults and
% 16.63/16.85 2,098,608,192 bytes consed.
% 16.63/16.85 :PROOF-FOUND
% 16.63/16.85 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T22:11:43
% 16.63/16.85 :PROOF-FOUND
% 16.63/16.85 *
%------------------------------------------------------------------------------