TSTP Solution File: GRP039-3 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP039-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n014.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 11:35:25 EDT 2022
% Result : Unsatisfiable 152.88s 153.12s
% Output : Refutation 153.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of clauses : 47 ( 33 unt; 7 nHn; 32 RR)
% Number of literals : 72 ( 12 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,Z)
| U = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_left_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(U,Y,Z)
| U = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(inverse_is_self_cancelling,axiom,
inverse(inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
cnf(identity_is_in_subgroup,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
cnf(subgroup_member_inverse_are_in_subgroup,axiom,
( ~ subgroup_member(X)
| subgroup_member(inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_inverse_are_in_subgroup) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X,Y))
| subgroup_member(Y)
| subgroup_member(X) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(21,plain,
subgroup_member(inverse(b)),
inference('HYPERRESOLVE',[status(thm)],[subgroup_member_inverse_are_in_subgroup,b_is_in_subgroup]) ).
cnf(30,plain,
X = multiply(X,identity),
inference('HYPERRESOLVE',[status(thm)],[total_function2,right_identity,total_function1]) ).
cnf(37,plain,
( subgroup_member(a)
| c = element_in_O2(a,d) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,property_of_O2,a_times_c_is_d]),prove_d_is_in_subgroup]) ).
cnf(54,plain,
product(inverse(a),d,c),
inference('HYPERRESOLVE',[status(thm)],[associativity1,left_inverse,a_times_c_is_d,left_identity]) ).
cnf(56,plain,
product(inverse(b),c,inverse(a)),
inference('HYPERRESOLVE',[status(thm)],[associativity1,left_inverse,b_times_a_inverse_is_c,left_identity]) ).
cnf(61,plain,
product(X,multiply(inverse(X),Y),Y),
inference('HYPERRESOLVE',[status(thm)],[associativity1,right_inverse,total_function1,left_identity]) ).
cnf(104,plain,
product(c,a,b),
inference('HYPERRESOLVE',[status(thm)],[associativity2,b_times_a_inverse_is_c,left_inverse,right_identity]) ).
cnf(107,plain,
product(multiply(X,Y),inverse(Y),X),
inference('HYPERRESOLVE',[status(thm)],[associativity2,total_function1,right_inverse,right_identity]) ).
cnf(111,plain,
product(multiply(X,inverse(Y)),Y,X),
inference('HYPERRESOLVE',[status(thm)],[associativity2,total_function1,left_inverse,right_identity]) ).
cnf(174,plain,
product(inverse(c),b,a),
inference('HYPERRESOLVE',[status(thm)],[associativity1,104,left_inverse,left_identity]) ).
cnf(262,plain,
product(c,inverse(d),inverse(a)),
inference('HYPERRESOLVE',[status(thm)],[associativity2,54,right_inverse,right_identity]) ).
cnf(399,plain,
inverse(a) = multiply(inverse(b),c),
inference('HYPERRESOLVE',[status(thm)],[total_function2,56,total_function1]) ).
cnf(473,plain,
product(a,inverse(b),inverse(c)),
inference('HYPERRESOLVE',[status(thm)],[associativity2,174,right_inverse,right_identity]) ).
cnf(753,plain,
product(inverse(multiply(X,Y)),X,inverse(Y)),
inference('HYPERRESOLVE',[status(thm)],[associativity1,107,left_inverse,left_identity]) ).
cnf(1195,plain,
product(inverse(c),inverse(a),inverse(d)),
inference('HYPERRESOLVE',[status(thm)],[associativity1,262,left_inverse,left_identity]) ).
cnf(1608,plain,
( c = element_in_O2(a,d)
| subgroup_member(multiply(a,inverse(b))) ),
inference('HYPERRESOLVE',[status(thm)],[closure_of_product_and_inverse,37,b_is_in_subgroup,total_function1]) ).
cnf(1692,plain,
product(X,inverse(multiply(inverse(Y),X)),Y),
inference('HYPERRESOLVE',[status(thm)],[associativity2,61,right_inverse,right_identity]) ).
cnf(2442,plain,
inverse(c) = multiply(a,inverse(b)),
inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,111,174]) ).
cnf(2443,plain,
( c = element_in_O2(a,d)
| subgroup_member(inverse(c)) ),
inference('REWRITE',[status(thm)],[1608,2442,theory(equality)]) ).
cnf(23365,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,753,107]) ).
cnf(56794,plain,
~ subgroup_member(inverse(d)),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[closure_of_product_and_inverse,1692,identity_is_in_subgroup,prove_d_is_in_subgroup]),30,theory(equality)]) ).
cnf(65910,plain,
c = element_in_O2(a,d),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[closure_of_product_and_inverse,2443,37,1195]),56794]) ).
cnf(65911,plain,
( subgroup_member(c)
| subgroup_member(a) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[an_element_in_O2,65910,theory(equality)]),prove_d_is_in_subgroup]) ).
cnf(65912,plain,
( subgroup_member(a)
| subgroup_member(inverse(c)) ),
inference('HYPERRESOLVE',[status(thm)],[subgroup_member_inverse_are_in_subgroup,65911]) ).
cnf(94654,plain,
subgroup_member(a),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[closure_of_product_and_inverse,65912,21,total_function1]),399,23365,inverse_is_self_cancelling,theory(equality)]) ).
cnf(94657,plain,
subgroup_member(inverse(c)),
inference('HYPERRESOLVE',[status(thm)],[closure_of_product_and_inverse,94654,b_is_in_subgroup,473]) ).
cnf(94659,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[closure_of_product_and_inverse,94654,1195,56794]),94657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP039-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n014.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 Jun 13 18:57:52 EDT 2022
% 0.13/0.34 % 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 2022-06-13T18:57:52
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-06-13T18:57:52
% 0.19/0.49
% 0.19/0.49 ; Recognized possible left identity assertion (|product| |identity| ?X ?X).
% 0.19/0.49 ; Recognized possible right identity assertion (|product| ?X |identity| ?X).
% 0.19/0.49 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |identity|).
% 0.19/0.49 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |identity|).
% 0.19/0.49 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 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 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 152.88/153.12 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 152.88/153.12
% 152.88/153.12 #||
% 152.88/153.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 152.88/153.12 % SZS output start Refutation
% See solution above
% 153.00/153.21 ||#
% 153.00/153.21
% 153.00/153.21 ; Summary of computation:
% 153.00/153.21 ; 596114 formulas have been input or derived (from 1333 formulas).
% 153.00/153.21 ; 94659 (16%) were retained. Of these,
% 153.00/153.21 ; 13737 (15%) were simplified or subsumed later,
% 153.00/153.21 ; 80922 (85%) are still being kept.
% 153.00/153.21 ;
% 153.00/153.21 ; Run time in seconds excluding printing time:
% 153.00/153.21 ; 0.004 0% Read assertion file (1 call)
% 153.00/153.21 ; 0.001 0% Assert (20 calls)
% 153.00/153.21 ; 10.522 7% Process new row (587,015 calls)
% 153.00/153.21 ; 109.987 72% Resolution (2,664 calls)
% 153.00/153.21 ; 0.236 0% Paramodulation (1,332 calls)
% 153.00/153.21 ; 0.000 0% Factoring (27 calls)
% 153.00/153.21 ; 0.170 0% Condensing (8,499 calls)
% 153.00/153.21 ; 0.862 1% Forward subsumption (8,499 calls)
% 153.00/153.21 ; 0.630 0% Backward subsumption (3,687 calls)
% 153.00/153.21 ; 0.225 0% Clause clause subsumption (78,404 calls)
% 153.00/153.21 ; 19.377 13% Forward simplification (569,144 calls)
% 153.00/153.21 ; 4.875 3% Backward simplification (94,659 calls)
% 153.00/153.21 ; 3.859 3% Ordering (927,761 calls)
% 153.00/153.21 ; 0.000 0% Sortal reasoning (32 calls)
% 153.00/153.21 ; 0.000 0% Purity testing (1 call)
% 153.00/153.21 ; 1.895 1% Other
% 153.00/153.21 ; 152.643 Total
% 153.00/153.21 ; 152.736 Real time
% 153.00/153.22 ;
% 153.00/153.22 ; Term-hash-array has 116,842 terms in all.
% 153.00/153.22 ; Feature-vector-row-index has 2,456 entries (3,128 at peak, 3,687 added, 1,231 deleted).
% 153.00/153.22 ; Feature-vector-row-index has 10,017 nodes (14,250 at peak, 18,091 added, 8,074 deleted).
% 153.00/153.22 ; Retrieved 97,958 possibly forward subsuming rows in 8,499 calls.
% 153.00/153.22 ; Retrieved 19,942 possibly backward subsumed rows in 3,687 calls.
% 153.00/153.22 ; Path-index has 99,862 entries (100,862 at peak, 117,102 added, 17,240 deleted).
% 153.00/153.22 ; Path-index has 9,183 nodes (9,390 at peak, 10,061 added, 878 deleted).
% 153.00/153.22 ; Trie-index has 99,862 entries (100,862 at peak, 117,102 added, 17,240 deleted).
% 153.00/153.22 ; Trie-index has 314,793 nodes (318,484 at peak, 363,336 added, 48,543 deleted).
% 153.00/153.22 ; Retrieved 3,036,779 generalization terms in 3,875,457 calls.
% 153.00/153.22 ; Retrieved 151,384 instance terms in 90,979 calls.
% 153.00/153.22 ; Retrieved 55,217,297 unifiable terms in 227,511 calls.
% 153.00/153.22 ;
% 153.00/153.22 ; The agenda of rows to process has 883 entries:
% 153.00/153.22 ; 1 with value 13 63 with value 20 85 with value 26
% 153.00/153.22 ; 7 with value 14 107 with value 21 39 with value 27
% 153.00/153.22 ; 7 with value 15 99 with value 22 15 with value 28
% 153.00/153.22 ; 24 with value 16 108 with value 23 3 with value 29
% 153.00/153.22 ; 23 with value 17 116 with value 24 1 with value 30
% 153.00/153.22 ; 19 with value 18 114 with value 25 3 with value 31
% 153.00/153.22 ; 49 with value 19
% 153.00/153.22 ; The agenda of rows to give has 79634 entries:
% 153.00/153.22 ; 1 with value (4 11) 10136 with value (4 23) 57 with value (4 34)
% 153.00/153.22 ; 3 with value (4 13) 8250 with value (4 24) 66 with value (4 35)
% 153.00/153.22 ; 34 with value (4 14) 7597 with value (4 25) 38 with value (4 36)
% 153.00/153.22 ; 937 with value (4 15) 4072 with value (4 26) 47 with value (4 37)
% 153.00/153.22 ; 1513 with value (4 16) 2883 with value (4 27) 35 with value (4 38)
% 153.00/153.22 ; 2707 with value (4 17) 1551 with value (4 28) 17 with value (4 39)
% 153.00/153.22 ; 4274 with value (4 18) 818 with value (4 29) 14 with value (4 40)
% 153.00/153.22 ; 5909 with value (4 19) 249 with value (4 30) 11 with value (4 41)
% 153.00/153.22 ; 7966 with value (4 20) 137 with value (4 31) 13 with value (4 42)
% 153.00/153.22 ; 9751 with value (4 21) 58 with value (4 32) 12 with value (4 43)
% 153.00/153.22 ; 10385 with value (4 22) 89 with value (4 33) 4 with value (4 44)
% 153.00/153.22 Evaluation took:
% 153.00/153.22 152.743 seconds of real time
% 153.00/153.22 147.79292 seconds of user run time
% 153.00/153.22 4.950883 seconds of system run time
% 153.00/153.22 [Run times include 16.494 seconds GC run time.]
% 153.00/153.22 0 calls to %EVAL
% 153.00/153.22 0 page faults and
% 153.00/153.22 2,987,048,152 bytes consed.
% 153.00/153.22 :PROOF-FOUND
% 153.00/153.22 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T19:00:25
% 153.00/153.22 :PROOF-FOUND
% 153.00/153.22 *
%------------------------------------------------------------------------------