TSTP Solution File: GRP040-3 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP040-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n016.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 : Sat Jul 16 11:35:26 EDT 2022
% Result : Unsatisfiable 1.02s 1.22s
% Output : Refutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 16
% Syntax : Number of clauses : 27 ( 21 unt; 2 nHn; 20 RR)
% Number of literals : 42 ( 3 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(associativity1,axiom,
( ~ product(X,Y,Z)
| ~ product(Y,U,V)
| ~ product(Z,U,W)
| product(X,V,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(associativity2,axiom,
( ~ product(X,Y,Z)
| ~ product(Y,U,V)
| ~ product(X,V,W)
| product(Z,U,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(closure_of_product_and_inverse,axiom,
( ~ subgroup_member(X)
| ~ subgroup_member(Y)
| ~ product(X,inverse(Y),Z)
| subgroup_member(Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X,Y))
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(property_of_O2,axiom,
( product(X,element_in_O2(X,Y),Y)
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
cnf(a_in_subgroup,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_subgroup) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(d_in_subgroup,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_in_subgroup) ).
cnf(b_times_a_inverse_is_c,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(a_times_c_is_d,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(prove_inverse_is_self_cancelling,negated_conjecture,
inverse(inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
cnf(19,plain,
subgroup_member(element_in_O2(a,d)),
inference('UR-RESOLVE',[status(thm)],[an_element_in_O2,d_in_subgroup,a_in_subgroup]) ).
cnf(39,plain,
subgroup_member(identity),
inference('HYPERRESOLVE',[status(thm)],[closure_of_product_and_inverse,b_is_in_subgroup,b_is_in_subgroup,right_inverse]) ).
cnf(51,plain,
product(inverse(a),d,c),
inference('HYPERRESOLVE',[status(thm)],[associativity1,left_inverse,a_times_c_is_d,left_identity]) ).
cnf(101,plain,
product(c,a,b),
inference('HYPERRESOLVE',[status(thm)],[associativity2,b_times_a_inverse_is_c,left_inverse,right_identity]) ).
cnf(145,plain,
subgroup_member(inverse(b)),
inference('HYPERRESOLVE',[status(thm)],[closure_of_product_and_inverse,39,b_is_in_subgroup,left_identity]) ).
cnf(155,plain,
product(inverse(c),b,a),
inference('HYPERRESOLVE',[status(thm)],[associativity1,101,left_inverse,left_identity]) ).
cnf(193,plain,
subgroup_member(inverse(element_in_O2(a,d))),
inference('HYPERRESOLVE',[status(thm)],[closure_of_product_and_inverse,19,39,left_identity]) ).
cnf(364,plain,
product(identity,element_in_O2(a,d),c),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[associativity2,51,left_inverse,property_of_O2]),a_in_subgroup,d_in_subgroup]) ).
cnf(1970,plain,
~ product(inverse(element_in_O2(a,d)),b,a),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[closure_of_product_and_inverse,193,145,a_in_subgroup]),prove_inverse_is_self_cancelling,theory(equality)]) ).
cnf(2847,plain,
c = element_in_O2(a,d),
inference('HYPERRESOLVE',[status(thm)],[total_function2,364,left_identity]) ).
cnf(2931,plain,
$false,
inference('REWRITE',[status(thm)],[1970,155,2847,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP040-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n016.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 07:24:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 *
% 0.20/0.48 *
% 0.20/0.49 #<PACKAGE "SNARK-USER">
% 0.20/0.49 *
% 0.20/0.49 SNARK-TPTP-OPTIONS
% 0.20/0.49 *
% 0.20/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.49 (USE-FACTORING :POS)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.49 *
% 0.20/0.49 "."
% 0.20/0.49 *
% 0.20/0.49 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T07:24:01
% 0.20/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n016.cluster.edu at 2022-06-14T07:24:01
% 0.20/0.50
% 0.20/0.50 ; Recognized possible left identity assertion (|product| |identity| ?X ?X).
% 0.20/0.50 ; Recognized possible right identity assertion (|product| ?X |identity| ?X).
% 0.20/0.50 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |identity|).
% 0.20/0.50 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |identity|).
% 0.20/0.50 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.20/0.50 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.50 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 1.02/1.22 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 1.02/1.22
% 1.02/1.22 #||
% 1.02/1.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.02/1.22 % SZS output start Refutation
% See solution above
% 1.02/1.22 ||#
% 1.02/1.22
% 1.02/1.22 ; Summary of computation:
% 1.02/1.22 ; 11081 formulas have been input or derived (from 131 formulas).
% 1.02/1.22 ; 2931 (26%) were retained. Of these,
% 1.02/1.22 ; 544 (19%) were simplified or subsumed later,
% 1.02/1.22 ; 2387 (81%) are still being kept.
% 1.02/1.22 ;
% 1.02/1.22 ; Run time in seconds excluding printing time:
% 1.02/1.22 ; 0.004 1% Read assertion file (1 call)
% 1.02/1.22 ; 0.001 0% Assert (17 calls)
% 1.02/1.22 ; 0.163 22% Process new row (9,724 calls)
% 1.06/1.22 ; 0.299 41% Resolution (260 calls)
% 1.06/1.22 ; 0.004 1% Paramodulation (130 calls)
% 1.06/1.22 ; 0.000 0% Factoring (4 calls)
% 1.06/1.22 ; 0.005 1% Condensing (392 calls)
% 1.06/1.22 ; 0.019 3% Forward subsumption (392 calls)
% 1.06/1.22 ; 0.010 1% Backward subsumption (256 calls)
% 1.06/1.22 ; 0.004 1% Clause clause subsumption (1,146 calls)
% 1.06/1.22 ; 0.100 14% Forward simplification (9,366 calls)
% 1.06/1.22 ; 0.066 9% Backward simplification (2,931 calls)
% 1.06/1.22 ; 0.001 0% Ordering (1,032 calls)
% 1.06/1.22 ; 0.000 0% Sortal reasoning (32 calls)
% 1.06/1.22 ; 0.000 0% Purity testing (1 call)
% 1.06/1.22 ; 0.055 8% Other
% 1.06/1.22 ; 0.731 Total
% 1.06/1.22 ; 0.733 Real time
% 1.06/1.22 ;
% 1.06/1.22 ; Term-hash-array has 3,646 terms in all.
% 1.06/1.22 ; Feature-vector-row-index has 185 entries (241 at peak, 256 added, 71 deleted).
% 1.06/1.22 ; Feature-vector-row-index has 995 nodes (1,310 at peak, 1,416 added, 421 deleted).
% 1.06/1.22 ; Retrieved 2,009 possibly forward subsuming rows in 392 calls.
% 1.06/1.22 ; Retrieved 175 possibly backward subsumed rows in 256 calls.
% 1.06/1.22 ; Path-index has 2,992 entries (3,422 at peak, 3,667 added, 675 deleted).
% 1.06/1.22 ; Path-index has 1,092 nodes (1,121 at peak, 1,158 added, 66 deleted).
% 1.06/1.22 ; Trie-index has 2,992 entries (3,422 at peak, 3,667 added, 675 deleted).
% 1.06/1.22 ; Trie-index has 7,143 nodes (8,044 at peak, 8,553 added, 1,410 deleted).
% 1.06/1.22 ; Retrieved 17,712 generalization terms in 26,041 calls.
% 1.06/1.22 ; Retrieved 3,663 instance terms in 2,674 calls.
% 1.06/1.22 ; Retrieved 256,609 unifiable terms in 10,910 calls.
% 1.06/1.22 ;
% 1.06/1.22 ; The agenda of backward simplifiable rows to process has 179 entries:
% 1.06/1.22 ; 179 with value 0
% 1.06/1.22 ; The agenda of rows to process has 276 entries:
% 1.06/1.22 ; 15 with value 10 27 with value 16 2 with value 24
% 1.06/1.22 ; 19 with value 11 8 with value 17 2 with value 25
% 1.06/1.22 ; 17 with value 12 1 with value 18 5 with value 26
% 1.06/1.22 ; 70 with value 13 2 with value 19 1 with value 27
% 1.06/1.22 ; 47 with value 14 4 with value 22 2 with value 31
% 1.06/1.22 ; 48 with value 15 4 with value 23 2 with value 34
% 1.06/1.22 ; The agenda of rows to give has 2270 entries:
% 1.06/1.22 ; 1 with value (4 4) 339 with value (4 14) 8 with value (4 22)
% 1.06/1.22 ; 2 with value (4 7) 414 with value (4 15) 11 with value (4 23)
% 1.06/1.22 ; 3 with value (4 8) 326 with value (4 16) 14 with value (4 24)
% 1.06/1.22 ; 5 with value (4 9) 228 with value (4 17) 11 with value (4 25)
% 1.06/1.22 ; 31 with value (4 10) 103 with value (4 18) 4 with value (4 26)
% 1.06/1.22 ; 115 with value (4 11) 42 with value (4 19) 4 with value (4 27)
% 1.06/1.22 ; 235 with value (4 12) 23 with value (4 20) 4 with value (4 29)
% 1.06/1.22 ; 329 with value (4 13) 18 with value (4 21)
% 1.06/1.22 Evaluation took:
% 1.06/1.22 0.734 seconds of real time
% 1.06/1.22 0.665629 seconds of user run time
% 1.06/1.22 0.067961 seconds of system run time
% 1.06/1.22 [Run times include 0.05 seconds GC run time.]
% 1.06/1.22 0 calls to %EVAL
% 1.06/1.22 0 page faults and
% 1.06/1.22 41,545,096 bytes consed.
% 1.06/1.22 :PROOF-FOUND
% 1.06/1.22 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T07:24:01
% 1.06/1.22 :PROOF-FOUND
% 1.06/1.22 *
%------------------------------------------------------------------------------