%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP214-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n015.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 11:37:34 EDT 2022
% Result : Unsatisfiable 4.73s 4.97s
% Output : Refutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 13 unt; 11 nHn; 17 RR)
% Number of literals : 56 ( 55 equ; 21 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_7,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
cnf(prove_this_8,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_13,negated_conjecture,
( multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c7,Y) != sk_c6
| multiply(Z,sk_c7) != U
| inverse(Z) != sk_c7
| multiply(V,U) != sk_c6
| inverse(V) != U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(20,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(21,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).
cnf(52,plain,
( multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c7,Y) != sk_c6
| multiply(Z,sk_c7) != U
| inverse(Z) != sk_c7
| identity != sk_c6
| inverse(inverse(U)) != U ),
inference('PARAMODULATE',[status(thm)],[prove_this_13,left_inverse,theory(equality)]) ).
cnf(84,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[20,left_inverse,theory(equality)]) ).
cnf(85,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[20,20,theory(equality)]) ).
cnf(86,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[84,85,theory(equality)]) ).
cnf(87,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[21,86,theory(equality)]) ).
cnf(90,plain,
( inverse(sk_c1) = sk_c7
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference('PARAMODULATE',[status(thm)],[20,prove_this_7,theory(equality)]) ).
cnf(109,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[87,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(110,plain,
( multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c7,Y) != sk_c6
| identity != sk_c6 ),
inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[52,109,theory(equality)])]) ).
cnf(120,plain,
multiply(X,inverse(X)) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,109,theory(equality)]) ).
cnf(157,plain,
( inverse(sk_c1) = sk_c7
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference('PARAMODULATE',[status(thm)],[90,prove_this_8,theory(equality)]) ).
cnf(162,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,157,theory(equality)]),left_inverse,theory(equality)]) ).
cnf(166,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference('PARAMODULATE',[status(thm)],[120,162,theory(equality)]) ).
cnf(174,plain,
( identity = sk_c6
| inverse(sk_c4) = sk_c5 ),
inference('PARAMODULATE',[status(thm)],[prove_this_4,166,theory(equality)]) ).
cnf(176,plain,
( identity = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference('PARAMODULATE',[status(thm)],[prove_this_3,166,theory(equality)]) ).
cnf(178,plain,
( identity = sk_c6
| multiply(sk_c4,sk_c5) = identity ),
inference('PARAMODULATE',[status(thm)],[120,174,theory(equality)]) ).
cnf(345,plain,
identity = sk_c6,
inference('PARAMODULATE',[status(thm)],[176,178,theory(equality)]) ).
cnf(401,plain,
( multiply(X,sk_c7) != identity
| inverse(X) != sk_c7
| multiply(sk_c7,Y) != identity ),
inference('REWRITE',[status(thm)],[110,345,theory(equality)]) ).
cnf(5451,plain,
$false,
inference('HYPERRESOLVE',[status(thm)],[401,left_inverse,109,120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP214-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n015.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 : Mon Jun 13 08:08:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.46 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T08:08:22
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-06-13T08:08:22
% 0.19/0.48
% 0.19/0.48 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.19/0.48 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 4.73/4.97 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 4.73/4.97
% 4.73/4.97 #||
% 4.73/4.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.73/4.97 % SZS output start Refutation
% See solution above
% 4.73/4.97 ||#
% 4.73/4.97
% 4.73/4.97 ; Summary of computation:
% 4.73/4.97 ; 19321 formulas have been input or derived (from 355 formulas).
% 4.73/4.97 ; 5451 (28%) were retained. Of these,
% 4.73/4.97 ; 372 ( 7%) were simplified or subsumed later,
% 4.73/4.97 ; 5079 (93%) are still being kept.
% 4.73/4.97 ;
% 4.73/4.97 ; Run time in seconds excluding printing time:
% 4.73/4.97 ; 0.003 0% Read assertion file (1 call)
% 4.73/4.97 ; 0.001 0% Assert (16 calls)
% 4.73/4.97 ; 0.484 11% Process new row (17,935 calls)
% 4.73/4.97 ; 0.071 2% Resolution (708 calls)
% 4.73/4.97 ; 0.256 6% Paramodulation (354 calls)
% 4.73/4.97 ; 0.004 0% Factoring (325 calls)
% 4.73/4.97 ; 0.081 2% Condensing (14,701 calls)
% 4.73/4.97 ; 1.498 33% Forward subsumption (14,701 calls)
% 4.73/4.97 ; 0.260 6% Backward subsumption (5,027 calls)
% 4.73/4.97 ; 0.391 9% Clause clause subsumption (122,791 calls)
% 4.73/4.97 ; 0.726 16% Forward simplification (17,765 calls)
% 4.73/4.97 ; 0.045 1% Backward simplification (5,451 calls)
% 4.73/4.97 ; 0.582 13% Ordering (151,315 calls)
% 4.73/4.97 ; 0.001 0% Sortal reasoning (32 calls)
% 4.73/4.97 ; 0.000 0% Purity testing (1 call)
% 4.73/4.97 ; 0.099 2% Other
% 4.73/4.97 ; 4.502 Total
% 4.73/4.97 ; 4.505 Real time
% 4.73/4.97 ;
% 4.73/4.97 ; Term-hash-array has 5,208 terms in all.
% 4.73/4.97 ; Feature-vector-row-index has 4,697 entries (4,697 at peak, 5,027 added, 330 deleted).
% 4.73/4.97 ; Feature-vector-row-index has 11,911 nodes (11,911 at peak, 14,439 added, 2,528 deleted).
% 4.73/4.97 ; Retrieved 174,083 possibly forward subsuming rows in 14,701 calls.
% 4.73/4.97 ; Retrieved 23,469 possibly backward subsumed rows in 5,027 calls.
% 4.73/4.97 ; Path-index has 4,922 entries (4,922 at peak, 5,341 added, 419 deleted).
% 4.73/4.97 ; Path-index has 1,785 nodes (1,785 at peak, 1,856 added, 71 deleted).
% 4.73/4.97 ; Trie-index has 4,922 entries (4,922 at peak, 5,341 added, 419 deleted).
% 4.73/4.97 ; Trie-index has 17,995 nodes (17,995 at peak, 18,891 added, 896 deleted).
% 4.73/4.97 ; Retrieved 80,134 generalization terms in 133,659 calls.
% 4.73/4.97 ; Retrieved 2,722 instance terms in 1,069 calls.
% 4.73/4.97 ; Retrieved 62,040 unifiable terms in 2,705 calls.
% 4.73/4.97 ;
% 4.73/4.97 ; The agenda of rows to process has 990 entries:
% 4.73/4.97 ; 6 with value 9 30 with value 18 44 with value 27
% 4.73/4.97 ; 6 with value 10 25 with value 19 52 with value 28
% 4.73/4.97 ; 9 with value 11 44 with value 20 28 with value 29
% 4.73/4.97 ; 6 with value 12 68 with value 21 36 with value 30
% 4.73/4.97 ; 4 with value 13 106 with value 22 39 with value 31
% 4.73/4.97 ; 2 with value 14 119 with value 23 37 with value 32
% 4.73/4.97 ; 15 with value 15 102 with value 24 15 with value 33
% 4.73/4.97 ; 21 with value 16 63 with value 25 7 with value 34
% 4.73/4.97 ; 59 with value 17 47 with value 26
% 4.73/4.97 ; The agenda of rows to give has 4764 entries:
% 4.73/4.97 ; 170 with value (4 21) 402 with value (4 26) 585 with value (4 31)
% 4.73/4.97 ; 167 with value (4 22) 314 with value (4 27) 88 with value (4 32)
% 4.73/4.97 ; 185 with value (4 23) 526 with value (4 28) 18 with value (4 33)
% 4.73/4.97 ; 243 with value (4 24) 680 with value (4 29) 1 with value (4 34)
% 4.73/4.97 ; 381 with value (4 25) 1003 with value (4 30) 1 with value (4 43)
% 4.73/4.97 Evaluation took:
% 4.73/4.97 4.507 seconds of real time
% 4.73/4.97 4.018697 seconds of user run time
% 4.73/4.97 0.488047 seconds of system run time
% 4.73/4.97 [Run times include 0.321 seconds GC run time.]
% 4.73/4.97 0 calls to %EVAL
% 4.73/4.97 0 page faults and
% 4.73/4.97 384,289,112 bytes consed.
% 4.73/4.97 :PROOF-FOUND
% 4.73/4.97 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T08:08:27
% 4.73/4.97 :PROOF-FOUND
% 4.73/4.97 *
%------------------------------------------------------------------------------