%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO007-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n020.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 4.21s 4.37s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of clauses : 34 ( 29 unt; 0 nHn; 21 RR)
% Number of literals : 50 ( 5 equ; 19 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 : 46 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(additive_inverse1,axiom,
sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/BOO002-0.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/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(y_times_z,hypothesis,
product(y,z,y_times_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',y_times_z) ).
cnf(x_times__y_times_z,hypothesis,
product(x,y_times_z,x_times__y_times_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times__y_times_z) ).
cnf(x_times_y,hypothesis,
product(x,y,x_times_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_y) ).
cnf(x_times_y__times_z,hypothesis,
product(x_times_y,z,x_times_y__times_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_y__times_z) ).
cnf(prove_equality,negated_conjecture,
x_times__y_times_z != x_times_y__times_z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality) ).
cnf(21,plain,
X = add(additive_identity,X),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).
cnf(24,plain,
~ product(x,y_times_z,x_times_y__times_z),
inference('UR-RESOLVE',[status(thm)],[multiplication_is_well_defined,x_times__y_times_z,prove_equality]) ).
cnf(42,plain,
sum(additive_identity,multiply(X,X),X),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,multiplicative_inverse1,closure_of_multiplication,additive_inverse1,multiplicative_identity1]) ).
cnf(43,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(199,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(598,plain,
product(X,X,X),
inference('HYPERRESOLVE',[status(thm)],[distributivity5,42,additive_identity1,additive_identity1,closure_of_multiplication]) ).
cnf(679,plain,
additive_identity = multiply(X,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,43,additive_identity1]) ).
cnf(680,plain,
product(X,add(X,Y),X),
inference('REWRITE',[status(thm)],[199,21,679,theory(equality)]) ).
cnf(695,plain,
sum(x_times_y,x,x),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,680,x_times_y,598,closure_of_addition]) ).
cnf(696,plain,
sum(x_times_y,y,y),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,680,x_times_y,598,closure_of_addition]) ).
cnf(699,plain,
sum(y_times_z,y,y),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,680,y_times_z,598,closure_of_addition]) ).
cnf(700,plain,
sum(y_times_z,z,z),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,680,y_times_z,598,closure_of_addition]) ).
cnf(836,plain,
sum(x,x_times_y__times_z,x),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,695,closure_of_addition,x_times_y__times_z,680]) ).
cnf(875,plain,
sum(x_times_y__times_z,y_times_z,y_times_z),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,696,x_times_y__times_z,y_times_z,y_times_z]) ).
cnf(974,plain,
sum(x_times__y_times_z,x_times_y,x_times_y),
inference('HYPERRESOLVE',[status(thm)],[distributivity1,699,x_times__y_times_z,x_times_y,x_times_y]) ).
cnf(1011,plain,
sum(z,x_times__y_times_z,z),
inference('HYPERRESOLVE',[status(thm)],[distributivity6,700,closure_of_addition,x_times__y_times_z,680]) ).
cnf(1277,plain,
~ sum(x_times_y__times_z,x_times__y_times_z,x_times_y__times_z),
inference('UR-RESOLVE',[status(thm)],[distributivity5,875,836,x_times__y_times_z,24]) ).
cnf(1501,plain,
$false,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity6,1011,974,x_times_y__times_z,x_times_y__times_z]),1277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO007-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n020.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 : Wed Jun 1 21:22:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 *
% 0.21/0.47 *
% 0.21/0.47 #<PACKAGE "SNARK-USER">
% 0.21/0.47 *
% 0.21/0.47 SNARK-TPTP-OPTIONS
% 0.21/0.47 *
% 0.21/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.47 (USE-FACTORING :POS)
% 0.21/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.47 *
% 0.21/0.47 "."
% 0.21/0.47 *
% 0.21/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T21:22:23
% 0.21/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-01T21:22:23
% 0.21/0.49
% 0.21/0.49 ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.21/0.49 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.21/0.49 ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.21/0.49 ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.21/0.49 ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.21/0.49 ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.21/0.49 ; Recognized possible left identity assertion (|product| |multiplicative_identity| ?X ?X).
% 0.21/0.49 ; Recognized possible right identity assertion (|product| ?X |multiplicative_identity| ?X).
% 0.21/0.49 ; Recognized possible left inverse assertion (|sum| (|inverse| ?X) ?X |multiplicative_identity|).
% 0.21/0.49 ; Recognized possible right inverse assertion (|sum| ?X (|inverse| ?X) |multiplicative_identity|).
% 0.21/0.49 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |additive_identity|).
% 0.21/0.49 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |additive_identity|).
% 0.21/0.49 ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.21/0.49 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.21/0.49 ; Declaring sum to be commutative.
% 0.21/0.49 ; Declaring add to be commutative.
% 0.21/0.49 ; Declaring product to be commutative.
% 4.21/4.37 ; Declaring multiply to be commutative.
% 4.21/4.37
% 4.21/4.37 #||
% 4.21/4.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.21/4.37 % SZS output start Refutation
% See solution above
% 4.21/4.37 ||#
% 4.21/4.37
% 4.21/4.37 ; Summary of computation:
% 4.21/4.37 ; 123753 formulas have been input or derived (from 84 formulas).
% 4.21/4.37 ; 1501 ( 1%) were retained. Of these,
% 4.21/4.37 ; 666 (44%) were simplified or subsumed later,
% 4.21/4.37 ; 835 (56%) are still being kept.
% 4.21/4.37 ;
% 4.21/4.37 ; Run time in seconds excluding printing time:
% 4.21/4.37 ; 0.006 0% Read assertion file (1 call)
% 4.21/4.37 ; 0.001 0% Assert (27 calls)
% 4.21/4.37 ; 0.183 5% Process new row (68,035 calls)
% 4.21/4.37 ; 2.778 71% Resolution (166 calls)
% 4.21/4.37 ; 0.002 0% Paramodulation (83 calls)
% 4.21/4.37 ; 0.002 0% Condensing (10 calls)
% 4.21/4.37 ; 0.000 0% Forward subsumption (10 calls)
% 4.21/4.37 ; 0.000 0% Backward subsumption (6 calls)
% 4.21/4.37 ; 0.003 0% Clause clause subsumption (4 calls)
% 4.21/4.37 ; 0.677 17% Forward simplification (63,414 calls)
% 4.21/4.37 ; 0.049 1% Backward simplification (1,501 calls)
% 4.21/4.37 ; 0.000 0% Ordering (127 calls)
% 4.21/4.37 ; 0.000 0% Sortal reasoning (32 calls)
% 4.21/4.37 ; 0.000 0% Purity testing (1 call)
% 4.21/4.37 ; 0.195 5% Other
% 4.21/4.37 ; 3.896 Total
% 4.21/4.37 ; 3.898 Real time
% 4.21/4.37 ;
% 4.21/4.37 ; Term-hash-array has 2,518 terms in all.
% 4.21/4.37 ; Feature-vector-row-index has 6 entries (6 at peak, 6 added, 0 deleted).
% 4.21/4.37 ; Feature-vector-row-index has 15 nodes (15 at peak, 15 added, 0 deleted).
% 4.21/4.37 ; Retrieved 4 possibly forward subsuming rows in 10 calls.
% 4.21/4.37 ; Retrieved 0 possibly backward subsumed rows in 6 calls.
% 4.21/4.37 ; Path-index has 1,484 entries (1,484 at peak, 2,535 added, 1,051 deleted).
% 4.21/4.37 ; Path-index has 623 nodes (623 at peak, 820 added, 197 deleted).
% 4.21/4.37 ; Trie-index has 1,484 entries (1,484 at peak, 2,535 added, 1,051 deleted).
% 4.21/4.37 ; Trie-index has 4,934 nodes (4,934 at peak, 8,502 added, 3,568 deleted).
% 4.21/4.37 ; Retrieved 218,719 generalization terms in 168,275 calls.
% 4.21/4.37 ; Retrieved 3,425 instance terms in 1,494 calls.
% 4.21/4.37 ; Retrieved 3,658,487 unifiable terms in 222,475 calls.
% 4.21/4.37 ;
% 4.21/4.37 ; The agenda of rows to process has 1451 entries:
% 4.21/4.37 ; 137 with value 10 250 with value 16 22 with value 19
% 4.21/4.37 ; 12 with value 12 48 with value 17 20 with value 20
% 4.21/4.37 ; 387 with value 13 152 with value 18 8 with value 21
% 4.21/4.37 ; 415 with value 15
% 4.21/4.37 ; The agenda of rows to give has 762 entries:
% 4.21/4.37 ; 3 with value (4 9) 80 with value (4 15) 24 with value (4 21)
% 4.21/4.37 ; 22 with value (4 10) 96 with value (4 16) 4 with value (4 22)
% 4.21/4.37 ; 33 with value (4 11) 93 with value (4 17) 2 with value (4 23)
% 4.21/4.37 ; 54 with value (4 12) 107 with value (4 18) 4 with value (4 24)
% 4.21/4.37 ; 59 with value (4 13) 40 with value (4 19) 2 with value (4 25)
% 4.21/4.37 ; 101 with value (4 14) 38 with value (4 20)
% 4.21/4.37 Evaluation took:
% 4.21/4.37 3.899 seconds of real time
% 4.21/4.37 3.679269 seconds of user run time
% 4.21/4.37 0.219931 seconds of system run time
% 4.21/4.37 [Run times include 0.173 seconds GC run time.]
% 4.21/4.37 0 calls to %EVAL
% 4.21/4.37 0 page faults and
% 4.21/4.37 317,795,944 bytes consed.
% 4.21/4.37 :PROOF-FOUND
% 4.21/4.37 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T21:22:27
% 4.21/4.37 :PROOF-FOUND
% 4.21/4.37 *
%------------------------------------------------------------------------------