%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO008-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n027.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 : Thu Jul 14 23:48:53 EDT 2022
% Result : Unsatisfiable 0.70s 0.87s
% Output : Refutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 2 RR)
% Number of literals : 51 ( 50 equ; 1 neg)
% Maximal clause size : 1 ( 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; 5 con; 0-2 aty)
% Number of variables : 105 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(distributivity3,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(prove_associativity,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
cnf(8,plain,
add(multiply(X,Y),Z) = add(add(multiply(X,Y),multiply(X,Z)),add(multiply(Y,Z),multiply(Z,Z))),
inference('REWRITE',[status(thm)],[distributivity1,distributivity3,theory(equality)]) ).
cnf(11,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(additive_identity,Y)),
inference('PARAMODULATE',[status(thm)],[distributivity3,additive_id1,theory(equality)]) ).
cnf(12,plain,
X = add(multiply(X,Y),multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[distributivity3,additive_inverse1,theory(equality)]),multiplicative_id1,theory(equality)]) ).
cnf(13,plain,
add(multiply(X,inverse(add(X,Y))),multiply(Y,inverse(add(X,Y)))) = additive_identity,
inference('PARAMODULATE',[status(thm)],[multiplicative_inverse1,distributivity3,theory(equality)]) ).
cnf(15,plain,
add(multiply(X,X),Y) = add(multiply(Y,Y),X),
inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]) ).
cnf(17,plain,
add(X,Y) = add(add(X,Y),add(multiply(X,Y),multiply(Y,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,multiplicative_id1,theory(equality)]),multiplicative_id1,theory(equality)]) ).
cnf(18,plain,
X = add(multiply(X,Y),add(multiply(inverse(Y),X),multiply(X,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(22,plain,
add(multiply(inverse(Y),X),Y) = add(multiply(Y,Y),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,multiplicative_inverse1,theory(equality)]),additive_id1,12,theory(equality)]) ).
cnf(25,plain,
add(multiply(X,Y),inverse(Y)) = add(X,add(multiply(additive_identity,additive_identity),inverse(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,multiplicative_inverse1,theory(equality)]),15,12,theory(equality)]) ).
cnf(31,plain,
additive_identity = multiply(additive_identity,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(32,plain,
add(multiply(X,Y),inverse(Y)) = add(X,inverse(Y)),
inference('REWRITE',[status(thm)],[25,additive_id1,31,theory(equality)]) ).
cnf(34,plain,
X = add(multiply(X,Y),multiply(X,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,31,theory(equality)]),31,additive_id1,theory(equality)]) ).
cnf(37,plain,
X = add(X,multiply(X,Y)),
inference('REWRITE',[status(thm)],[18,34,theory(equality)]) ).
cnf(39,plain,
add(X,Y) = add(add(X,Y),Y),
inference('REWRITE',[status(thm)],[17,34,theory(equality)]) ).
cnf(40,plain,
add(multiply(X,Y),Z) = add(add(multiply(X,Y),multiply(X,Z)),Z),
inference('REWRITE',[status(thm)],[8,34,theory(equality)]) ).
cnf(50,plain,
multiply(X,Y) = add(multiply(X,Y),multiply(multiply(X,Z),Y)),
inference('PARAMODULATE',[status(thm)],[distributivity3,37,theory(equality)]) ).
cnf(53,plain,
X = multiply(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(54,plain,
add(multiply(inverse(X),Y),X) = add(X,Y),
inference('REWRITE',[status(thm)],[22,53,theory(equality)]) ).
cnf(55,plain,
X = multiply(inverse(inverse(X)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(56,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,multiplicative_inverse1,theory(equality)]),additive_id1,55,theory(equality)]) ).
cnf(89,plain,
additive_identity = multiply(multiply(X,Y),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(90,plain,
additive_identity = multiply(multiply(inverse(X),Y),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(92,plain,
multiply(X,multiply(X,Y)) = multiply(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,53,theory(equality)]),37,theory(equality)]) ).
cnf(98,plain,
inverse(X) = multiply(inverse(multiply(X,Y)),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,89,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(101,plain,
X = multiply(inverse(multiply(inverse(X),Y)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,90,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(127,plain,
add(X,Y) = add(add(X,multiply(inverse(multiply(inverse(X),Z)),Y)),Y),
inference('PARAMODULATE',[status(thm)],[40,101,theory(equality)]) ).
cnf(166,plain,
additive_identity = multiply(X,inverse(add(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[39,13,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(169,plain,
inverse(X) = add(inverse(add(X,Y)),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[32,166,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(172,plain,
additive_identity = multiply(multiply(X,Y),inverse(add(X,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,166,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(173,plain,
additive_identity = multiply(X,multiply(inverse(add(X,Y)),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,166,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(174,plain,
inverse(add(X,Y)) = multiply(inverse(X),inverse(add(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,166,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(227,plain,
additive_identity = multiply(X,inverse(add(add(X,Y),Z))),
inference('PARAMODULATE',[status(thm)],[173,174,theory(equality)]) ).
cnf(230,plain,
inverse(X) = add(multiply(inverse(X),Y),inverse(add(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,174,theory(equality)]),additive_id1,multiplicative_inverse1,distributivity3,theory(equality)]) ).
cnf(245,plain,
add(add(X,Y),Z) = add(add(add(X,Y),Z),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[54,227,theory(equality)]),additive_id1,theory(equality)]) ).
cnf(280,plain,
inverse(multiply(X,Y)) = add(inverse(X),inverse(add(inverse(X),Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[230,98,theory(equality)]),32,theory(equality)]) ).
cnf(287,plain,
add(X,Y) = add(add(multiply(inverse(add(X,Z)),Y),X),Y),
inference('REWRITE',[status(thm)],[127,40,distributivity3,56,280,theory(equality)]) ).
cnf(311,plain,
add(X,inverse(add(X,Y))) = add(X,inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[230,12,theory(equality)]),32,additive_id1,172,92,distributivity3,56,280,theory(equality)]) ).
cnf(317,plain,
inverse(multiply(X,Y)) = add(inverse(X),inverse(Y)),
inference('REWRITE',[status(thm)],[280,311,theory(equality)]) ).
cnf(332,plain,
inverse(add(inverse(X),inverse(Y))) = multiply(X,Y),
inference('PARAMODULATE',[status(thm)],[56,317,theory(equality)]) ).
cnf(337,plain,
add(X,Y) = add(add(inverse(add(add(X,Z),inverse(Y))),X),Y),
inference('REWRITE',[status(thm)],[287,56,332,theory(equality)]) ).
cnf(466,plain,
add(X,Y) = add(add(X,inverse(add(inverse(Y),Z))),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[337,245,theory(equality)]),311,theory(equality)]) ).
cnf(469,plain,
add(X,add(Y,Z)) = add(add(X,Y),add(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[466,169,theory(equality)]),56,theory(equality)]) ).
cnf(491,plain,
add(X,add(Y,Z)) = add(add(X,Y),Z),
inference('PARAMODULATE',[status(thm)],[469,469,theory(equality)]) ).
cnf(492,plain,
$false,
inference('REWRITE',[status(thm)],[prove_associativity,491,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO008-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n027.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 : Wed Jun 1 17:21:04 EDT 2022
% 0.19/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.45 *
% 0.19/0.45 #<PACKAGE "SNARK-USER">
% 0.19/0.45 *
% 0.19/0.45 SNARK-TPTP-OPTIONS
% 0.19/0.45 *
% 0.19/0.45 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.45 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.45 (USE-FACTORING :POS)
% 0.19/0.45 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.45 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.45 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.45 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.45 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.45 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.45 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.45 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.45 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.45 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.45 *
% 0.19/0.45 "."
% 0.19/0.45 *
% 0.19/0.45 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T17:21:04
% 0.19/0.45 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n027.cluster.edu at 2022-06-01T17:21:04
% 0.19/0.46
% 0.19/0.46 ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.19/0.46 ; Recognized commutativity assertion (= (|multiply| ?X ?Y) (|multiply| ?Y ?X)).
% 0.19/0.46 ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |multiplicative_identity|).
% 0.19/0.46 ; Recognized possible left inverse assertion (= (|add| (|inverse| ?X) ?X) |multiplicative_identity|).
% 0.19/0.46 ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |additive_identity|).
% 0.19/0.46 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |additive_identity|).
% 0.19/0.46 ; Recognized right identity assertion (= (|multiply| ?X |multiplicative_identity|) ?X).
% 0.19/0.46 ; Recognized left identity assertion (= (|multiply| |multiplicative_identity| ?X) ?X).
% 0.19/0.46 ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.19/0.46 ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.19/0.46 ; Declaring add to be commutative.
% 0.70/0.87 ; Declaring multiply to be commutative.
% 0.70/0.87
% 0.70/0.87 #||
% 0.70/0.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.70/0.87 % SZS output start Refutation
% See solution above
% 0.70/0.88 ||#
% 0.70/0.88
% 0.70/0.88 ; Summary of computation:
% 0.70/0.88 ; 5884 formulas have been input or derived (from 79 formulas).
% 0.70/0.88 ; 492 ( 8%) were retained. Of these,
% 0.70/0.88 ; 403 (82%) were simplified or subsumed later,
% 0.70/0.88 ; 89 (18%) are still being kept.
% 0.70/0.88 ;
% 0.70/0.88 ; Run time in seconds excluding printing time:
% 0.70/0.88 ; 0.001 0% Read assertion file (1 call)
% 0.70/0.88 ; 0.000 0% Assert (15 calls)
% 0.70/0.88 ; 0.056 13% Process new row (4,807 calls)
% 0.70/0.88 ; 0.003 1% Resolution (156 calls)
% 0.70/0.88 ; 0.070 17% Paramodulation (78 calls)
% 0.70/0.88 ; 0.203 48% Forward simplification (4,449 calls)
% 0.70/0.88 ; 0.037 9% Backward simplification (492 calls)
% 0.70/0.88 ; 0.023 5% Ordering (5,731 calls)
% 0.70/0.88 ; 0.000 0% Sortal reasoning (32 calls)
% 0.70/0.88 ; 0.000 0% Purity testing (1 call)
% 0.70/0.88 ; 0.028 7% Other
% 0.70/0.88 ; 0.421 Total
% 0.70/0.88 ; 0.425 Real time
% 0.70/0.88 ;
% 0.70/0.88 ; Term-hash-array has 1,538 terms in all.
% 0.70/0.88 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.70/0.88 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.70/0.88 ; Path-index has 357 entries (630 at peak, 1,614 added, 1,257 deleted).
% 0.70/0.88 ; Path-index has 554 nodes (655 at peak, 988 added, 434 deleted).
% 0.70/0.88 ; Trie-index has 357 entries (630 at peak, 1,614 added, 1,257 deleted).
% 0.70/0.88 ; Trie-index has 2,198 nodes (3,238 at peak, 10,275 added, 8,077 deleted).
% 0.70/0.88 ; Retrieved 38,545 generalization terms in 32,209 calls.
% 0.70/0.88 ; Retrieved 3,267 instance terms in 505 calls.
% 0.70/0.88 ; Retrieved 7,721 unifiable terms in 540 calls.
% 0.70/0.88 ;
% 0.70/0.88 ; The agenda of backward simplifiable rows to process has 27 entries:
% 0.70/0.88 ; 27 with value 0
% 0.70/0.88 ; The agenda of rows to process has 160 entries:
% 0.70/0.88 ; 7 with value 22 14 with value 29 5 with value 35
% 0.70/0.88 ; 9 with value 23 6 with value 30 3 with value 36
% 0.70/0.88 ; 14 with value 24 14 with value 31 3 with value 37
% 0.70/0.88 ; 20 with value 25 11 with value 32 2 with value 38
% 0.70/0.88 ; 17 with value 26 11 with value 33 1 with value 39
% 0.70/0.88 ; 12 with value 27 5 with value 34 2 with value 40
% 0.70/0.88 ; 4 with value 28
% 0.70/0.88 ; The agenda of rows to give has 66 entries:
% 0.70/0.88 ; 1 with value (4 22) 5 with value (4 33) 2 with value (4 43)
% 0.70/0.88 ; 2 with value (4 26) 3 with value (4 34) 2 with value (4 45)
% 0.70/0.88 ; 6 with value (4 27) 1 with value (4 35) 3 with value (4 46)
% 0.70/0.88 ; 5 with value (4 28) 8 with value (4 36) 1 with value (4 48)
% 0.70/0.88 ; 4 with value (4 29) 3 with value (4 37) 1 with value (4 51)
% 0.70/0.88 ; 2 with value (4 30) 6 with value (4 38) 2 with value (4 57)
% 0.70/0.88 ; 2 with value (4 31) 1 with value (4 40) 1 with value (4 59)
% 0.70/0.88 ; 2 with value (4 32) 2 with value (4 42) 1 with value (4 62)
% 0.70/0.88 Evaluation took:
% 0.70/0.88 0.425 seconds of real time
% 0.70/0.88 0.395043 seconds of user run time
% 0.70/0.88 0.030202 seconds of system run time
% 0.70/0.88 [Run times include 0.012 seconds GC run time.]
% 0.70/0.88 0 calls to %EVAL
% 0.70/0.88 0 page faults and
% 0.70/0.88 46,845,296 bytes consed.
% 0.70/0.88 :PROOF-FOUND
% 0.70/0.88 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-01T17:21:04
% 0.70/0.88 :PROOF-FOUND
% 0.70/0.88 *
%------------------------------------------------------------------------------