TSTP Solution File: BOO008-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO008-1 : 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 : Thu Jul 14 23:48:53 EDT 2022
% Result : Unsatisfiable 4.71s 4.90s
% Output : Refutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 42 ( 38 unt; 0 nHn; 32 RR)
% Number of literals : 56 ( 4 equ; 17 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 39 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
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/BOO002-0.ax',distributivity1) ).
cnf(distributivity5,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ product(Y,U,W)
| ~ sum(X,W,X1)
| product(Z,V,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity5) ).
cnf(distributivity6,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ product(Y,U,W)
| ~ product(Z,V,X1)
| sum(X,W,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X,Y,Z)
| ~ sum(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(y_plus_z,hypothesis,
sum(y,z,y_plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',y_plus_z) ).
cnf(x_plus__y_plus_z,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus__y_plus_z) ).
cnf(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
cnf(x_plus_y__plus_z,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y__plus_z) ).
cnf(prove_equality,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality) ).
cnf(19,plain,
~ sum(x,y_plus_z,x_plus_y__plus_z),
inference('UR-RESOLVE',[status(thm)],[addition_is_well_defined,x_plus__y_plus_z,prove_equality]) ).
cnf(27,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(35,plain,
sum(additive_identity,multiply(X,additive_identity),additive_identity),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,multiplicative_inverse1,closure_of_multiplication,additive_identity1,multiplicative_inverse1]) ).
cnf(102,plain,
product(x_plus_y__plus_z,add(x_plus_y,multiplicative_identity),x_plus_y__plus_z),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus_y__plus_z,closure_of_addition,multiplicative_identity1,x_plus_y__plus_z]) ).
cnf(107,plain,
product(x__plus_y_plus_z,add(y_plus_z,multiplicative_identity),x__plus_y_plus_z),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus__y_plus_z,closure_of_addition,multiplicative_identity1,x_plus__y_plus_z]) ).
cnf(122,plain,
product(x_plus_y__plus_z,x_plus_y,add(x_plus_y,multiply(z,additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus_y__plus_z,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(128,plain,
product(x_plus_y,x,add(x,multiply(y,additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus_y,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(131,plain,
product(x_plus_y,y,add(y,multiply(x,additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus_y,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(135,plain,
product(x__plus_y_plus_z,y_plus_z,add(y_plus_z,multiply(x,additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus__y_plus_z,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(137,plain,
product(y_plus_z,y,add(y,multiply(z,additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,y_plus_z,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(139,plain,
product(y_plus_z,z,add(z,multiply(y,additive_identity))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,y_plus_z,additive_identity1,closure_of_multiplication,closure_of_addition]) ).
cnf(164,plain,
product(X,add(X,Y),add(X,multiply(additive_identity,Y))),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,additive_identity1,closure_of_addition,closure_of_multiplication,closure_of_addition]) ).
cnf(331,plain,
additive_identity = multiply(X,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,35,additive_identity1]) ).
cnf(332,plain,
product(X,add(X,Y),X),
inference('REWRITE',[status(thm)],[164,27,331,theory(equality)]) ).
cnf(336,plain,
product(x_plus_y,y,y),
inference('REWRITE',[status(thm)],[131,27,331,theory(equality)]) ).
cnf(337,plain,
product(x__plus_y_plus_z,y_plus_z,y_plus_z),
inference('REWRITE',[status(thm)],[135,27,331,theory(equality)]) ).
cnf(340,plain,
product(x_plus_y,x,x),
inference('REWRITE',[status(thm)],[128,27,331,theory(equality)]) ).
cnf(341,plain,
product(y_plus_z,z,z),
inference('REWRITE',[status(thm)],[139,27,331,theory(equality)]) ).
cnf(346,plain,
product(x_plus_y__plus_z,x_plus_y,x_plus_y),
inference('REWRITE',[status(thm)],[122,27,331,theory(equality)]) ).
cnf(347,plain,
product(y_plus_z,y,y),
inference('REWRITE',[status(thm)],[137,27,331,theory(equality)]) ).
cnf(391,plain,
product(x_plus_y__plus_z,y_plus_z,y_plus_z),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,336,x_plus_y__plus_z,y_plus_z,y_plus_z]) ).
cnf(630,plain,
product(x__plus_y_plus_z,x_plus_y,x_plus_y),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,347,x_plus__y_plus_z,x_plus_y,x_plus_y]) ).
cnf(769,plain,
sum(x_plus_y,x_plus_y__plus_z,x_plus_y__plus_z),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,102,346,multiplicative_identity1,closure_of_addition]) ).
cnf(1170,plain,
sum(y_plus_z,x__plus_y_plus_z,x__plus_y_plus_z),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,107,337,multiplicative_identity1,closure_of_addition]) ).
cnf(1411,plain,
sum(x_plus_y__plus_z,x,x_plus_y__plus_z),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,332,769,closure_of_addition,340]) ).
cnf(1412,plain,
sum(x__plus_y_plus_z,z,x__plus_y_plus_z),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,332,1170,closure_of_addition,341]) ).
cnf(1672,plain,
~ product(x_plus_y__plus_z,x__plus_y_plus_z,x_plus_y__plus_z),
inference('UR-RESOLVE',[status(thm)],[distributivity6,1411,x_plus__y_plus_z,391,19]) ).
cnf(1716,plain,
$false,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity5,1412,x_plus_y__plus_z,630,x_plus_y__plus_z]),1672]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : BOO008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 2 00:14:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.46 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 *
% 0.19/0.47 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-02T00:14:27
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-06-02T00:14:27
% 0.19/0.49
% 0.19/0.49 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.19/0.49 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.19/0.49 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.19/0.49 ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.19/0.49 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.19/0.49 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.19/0.49 ; Recognized possible left identity assertion (|product| |multiplicative_identity| ?X ?X).
% 0.19/0.49 ; Recognized possible right identity assertion (|product| ?X |multiplicative_identity| ?X).
% 0.19/0.49 ; Recognized possible left inverse assertion (|sum| (|inverse| ?X) ?X |multiplicative_identity|).
% 0.19/0.49 ; Recognized possible right inverse assertion (|sum| ?X (|inverse| ?X) |multiplicative_identity|).
% 0.19/0.49 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |additive_identity|).
% 0.19/0.49 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |additive_identity|).
% 0.19/0.49 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.49 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.49 ; Declaring sum to be commutative.
% 0.19/0.49 ; Declaring add to be commutative.
% 0.19/0.49 ; Declaring product to be commutative.
% 4.71/4.90 ; Declaring multiply to be commutative.
% 4.71/4.90
% 4.71/4.90 #||
% 4.71/4.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.71/4.90 % SZS output start Refutation
% See solution above
% 4.71/4.90 ||#
% 4.71/4.90
% 4.71/4.90 ; Summary of computation:
% 4.71/4.90 ; 130725 formulas have been input or derived (from 84 formulas).
% 4.71/4.90 ; 1716 ( 1%) were retained. Of these,
% 4.71/4.90 ; 908 (53%) were simplified or subsumed later,
% 4.71/4.90 ; 808 (47%) are still being kept.
% 4.71/4.90 ;
% 4.71/4.90 ; Run time in seconds excluding printing time:
% 4.71/4.90 ; 0.005 0% Read assertion file (1 call)
% 4.71/4.90 ; 0.001 0% Assert (27 calls)
% 4.71/4.90 ; 0.193 4% Process new row (70,106 calls)
% 4.71/4.90 ; 3.287 74% Resolution (166 calls)
% 4.71/4.90 ; 0.004 0% Paramodulation (83 calls)
% 4.71/4.90 ; 0.003 0% Condensing (10 calls)
% 4.71/4.90 ; 0.000 0% Forward subsumption (10 calls)
% 4.71/4.90 ; 0.000 0% Backward subsumption (6 calls)
% 4.71/4.90 ; 0.002 0% Clause clause subsumption (4 calls)
% 4.71/4.90 ; 0.654 15% Forward simplification (63,714 calls)
% 4.71/4.90 ; 0.050 1% Backward simplification (1,716 calls)
% 4.71/4.90 ; 0.000 0% Ordering (113 calls)
% 4.71/4.90 ; 0.001 0% Sortal reasoning (32 calls)
% 4.71/4.90 ; 0.000 0% Purity testing (1 call)
% 4.71/4.90 ; 0.221 5% Other
% 4.71/4.90 ; 4.421 Total
% 4.71/4.90 ; 4.424 Real time
% 4.71/4.90 ;
% 4.71/4.90 ; Term-hash-array has 2,725 terms in all.
% 4.71/4.90 ; Feature-vector-row-index has 6 entries (6 at peak, 6 added, 0 deleted).
% 4.71/4.90 ; Feature-vector-row-index has 15 nodes (15 at peak, 15 added, 0 deleted).
% 4.71/4.90 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 4.71/4.90 ; Retrieved 0 possibly backward subsumed rows in 6 calls.
% 4.71/4.90 ; Path-index has 1,352 entries (1,891 at peak, 2,739 added, 1,387 deleted).
% 4.71/4.90 ; Path-index has 504 nodes (542 at peak, 658 added, 154 deleted).
% 4.71/4.90 ; Trie-index has 1,352 entries (1,891 at peak, 2,739 added, 1,387 deleted).
% 4.71/4.90 ; Trie-index has 4,103 nodes (5,676 at peak, 8,110 added, 4,007 deleted).
% 4.71/4.90 ; Retrieved 201,401 generalization terms in 165,933 calls.
% 4.71/4.90 ; Retrieved 4,235 instance terms in 1,709 calls.
% 4.71/4.90 ; Retrieved 4,699,779 unifiable terms in 245,359 calls.
% 4.71/4.90 ;
% 4.71/4.90 ; The agenda of rows to process has 1541 entries:
% 4.71/4.90 ; 198 with value 9 250 with value 15 14 with value 18
% 4.71/4.90 ; 16 with value 11 48 with value 16 20 with value 19
% 4.71/4.90 ; 428 with value 12 144 with value 17 8 with value 20
% 4.71/4.90 ; 415 with value 14
% 4.71/4.90 ; The agenda of rows to give has 738 entries:
% 4.71/4.90 ; 7 with value (4 8) 152 with value (4 14) 24 with value (4 19)
% 4.71/4.90 ; 31 with value (4 9) 111 with value (4 15) 15 with value (4 20)
% 4.71/4.90 ; 27 with value (4 10) 82 with value (4 16) 2 with value (4 22)
% 4.71/4.90 ; 52 with value (4 11) 48 with value (4 17) 1 with value (4 23)
% 4.71/4.90 ; 79 with value (4 12) 21 with value (4 18) 1 with value (4 24)
% 4.71/4.90 ; 85 with value (4 13)
% 4.71/4.90 Evaluation took:
% 4.71/4.90 4.424 seconds of real time
% 4.71/4.90 4.179604 seconds of user run time
% 4.71/4.90 0.245127 seconds of system run time
% 4.71/4.90 [Run times include 0.2 seconds GC run time.]
% 4.71/4.90 0 calls to %EVAL
% 4.71/4.90 0 page faults and
% 4.71/4.90 335,125,280 bytes consed.
% 4.71/4.90 :PROOF-FOUND
% 4.71/4.90 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-02T00:14:31
% 4.71/4.90 :PROOF-FOUND
% 4.71/4.90 *
%------------------------------------------------------------------------------