%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP277-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Sat Jul 16 11:37:45 EDT 2022
% Result : Unsatisfiable 88.24s 88.40s
% Output : Refutation 88.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 55 ( 21 unt; 22 nHn; 43 RR)
% Number of literals : 122 ( 121 equ; 51 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(prove_this_4,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_9,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_10,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_19,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_25,negated_conjecture,
( multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(Y) != sk_c7
| multiply(Y,sk_c6) != sk_c7
| multiply(Z,U) != sk_c6
| inverse(Z) != U
| multiply(U,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
cnf(32,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(33,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).
cnf(89,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(Y,Z) != sk_c6
| inverse(Y) != Z
| multiply(Z,sk_c7) != sk_c6 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[prove_this_25,prove_this_21,theory(equality)]),theory(equality)]) ).
cnf(116,plain,
( inverse(sk_c1) = sk_c7
| multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c2) != sk_c7
| multiply(Y,Z) != sk_c6
| inverse(Y) != Z
| multiply(Z,sk_c7) != sk_c6 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[prove_this_25,prove_this_9,theory(equality)]),theory(equality)]) ).
cnf(146,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[32,left_inverse,theory(equality)]) ).
cnf(147,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[32,32,theory(equality)]) ).
cnf(148,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[146,147,theory(equality)]) ).
cnf(150,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[33,148,theory(equality)]) ).
cnf(151,plain,
( inverse(sk_c1) = sk_c7
| sk_c4 = multiply(inverse(sk_c3),sk_c6) ),
inference('PARAMODULATE',[status(thm)],[32,prove_this_10,theory(equality)]) ).
cnf(182,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[150,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(193,plain,
multiply(X,inverse(X)) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,182,theory(equality)]) ).
cnf(194,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('PARAMODULATE',[status(thm)],[150,182,theory(equality)]) ).
cnf(207,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,inverse(sk_c5)) = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[194,prove_this_14,theory(equality)]) ).
cnf(218,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c6,inverse(sk_c5)) = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[194,prove_this_15,theory(equality)]) ).
cnf(241,plain,
( inverse(sk_c1) = sk_c7
| sk_c4 = multiply(sk_c4,sk_c6) ),
inference('PARAMODULATE',[status(thm)],[151,prove_this_11,theory(equality)]) ).
cnf(248,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[32,241,theory(equality)]),left_inverse,theory(equality)]) ).
cnf(254,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference('PARAMODULATE',[status(thm)],[193,248,theory(equality)]) ).
cnf(266,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference('PARAMODULATE',[status(thm)],[prove_this_5,254,theory(equality)]) ).
cnf(268,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
inference('PARAMODULATE',[status(thm)],[prove_this_4,254,theory(equality)]) ).
cnf(271,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c4) = identity ),
inference('PARAMODULATE',[status(thm)],[193,266,theory(equality)]) ).
cnf(664,plain,
identity = sk_c6,
inference('PARAMODULATE',[status(thm)],[268,271,theory(equality)]) ).
cnf(673,plain,
( multiply(sk_c7,sk_c5) = identity
| sk_c2 = sk_c7 ),
inference('REWRITE',[status(thm)],[prove_this_15,148,664,theory(equality)]) ).
cnf(677,plain,
sk_c5 = sk_c7,
inference('REWRITE',[status(thm)],[prove_this_19,left_identity,148,664,theory(equality)]) ).
cnf(786,plain,
( multiply(sk_c5,sk_c5) = identity
| sk_c2 = sk_c5 ),
inference('REWRITE',[status(thm)],[673,677,theory(equality)]) ).
cnf(790,plain,
( multiply(X,sk_c5) != identity
| inverse(X) != sk_c5
| multiply(sk_c5,sk_c5) != identity
| inverse(Y) != sk_c5
| Y != sk_c5 ),
inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[prove_this_25,left_identity,148,677,664,theory(equality)])]) ).
cnf(814,plain,
( sk_c2 = sk_c5
| multiply(sk_c5,sk_c5) != identity
| inverse(sk_c5) != sk_c5 ),
inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[89,left_identity,677,148,664,theory(equality)])]) ).
cnf(823,plain,
( inverse(sk_c1) = sk_c5
| multiply(X,sk_c5) != identity
| inverse(X) != sk_c5
| multiply(sk_c5,sk_c5) != identity
| inverse(sk_c2) != sk_c5 ),
inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[116,left_identity,148,677,664,theory(equality)])]) ).
cnf(840,plain,
( inverse(sk_c2) = sk_c5
| inverse(sk_c5) = sk_c5 ),
inference('REWRITE',[status(thm)],[207,left_identity,677,664,theory(equality)]) ).
cnf(843,plain,
( sk_c2 = sk_c5
| inverse(sk_c5) = sk_c5 ),
inference('REWRITE',[status(thm)],[218,left_identity,677,148,664,theory(equality)]) ).
cnf(904,plain,
( multiply(sk_c5,sk_c5) != identity
| inverse(X) != sk_c5
| X != sk_c5 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[790,left_inverse,theory(equality)]),182,theory(equality)]) ).
cnf(1416,plain,
sk_c2 = sk_c5,
inference('HYPERRESOLVE',[status(thm)],[814,786,843]) ).
cnf(1507,plain,
( inverse(sk_c1) = sk_c2
| multiply(sk_c2,sk_c2) != identity
| sk_c2 != inverse(sk_c2) ),
inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[823,1416,theory(equality)])]) ).
cnf(1514,plain,
sk_c2 = inverse(sk_c2),
inference('REWRITE',[status(thm)],[840,1416,theory(equality)]) ).
cnf(1521,plain,
( inverse(sk_c1) = sk_c2
| multiply(sk_c2,sk_c2) != identity ),
inference('REWRITE',[status(thm)],[1507,1514,theory(equality)]) ).
cnf(1545,plain,
( multiply(sk_c2,sk_c2) != identity
| inverse(X) != sk_c2
| X != sk_c2 ),
inference('REWRITE',[status(thm)],[904,1416,theory(equality)]) ).
cnf(1712,plain,
multiply(sk_c2,sk_c2) = identity,
inference('PARAMODULATE',[status(thm)],[193,1514,theory(equality)]) ).
cnf(1718,plain,
inverse(sk_c1) = sk_c2,
inference('REWRITE',[status(thm)],[1521,1712,theory(equality)]) ).
cnf(1722,plain,
( inverse(X) != sk_c2
| X != sk_c2 ),
inference('REWRITE',[status(thm)],[1545,1712,theory(equality)]) ).
cnf(1748,plain,
sk_c1 = sk_c2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[182,1718,theory(equality)]),1514,theory(equality)]) ).
cnf(1764,plain,
inverse(sk_c1) = sk_c1,
inference('REWRITE',[status(thm)],[1514,1748,theory(equality)]) ).
cnf(1778,plain,
( inverse(X) != sk_c1
| X != sk_c1 ),
inference('REWRITE',[status(thm)],[1722,1748,theory(equality)]) ).
cnf(1787,plain,
$false,
inference('HYPERRESOLVE',[status(thm)],[1778,1764,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP277-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Tue Jun 14 06:34:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 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 2022-06-14T06:34:51
% 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 2022-06-14T06:34:51
% 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|).
% 88.24/88.40 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 88.24/88.40
% 88.24/88.40 #||
% 88.24/88.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 88.24/88.40 % SZS output start Refutation
% See solution above
% 88.24/88.41 ||#
% 88.24/88.41
% 88.24/88.41 ; Summary of computation:
% 88.24/88.41 ; 286933 formulas have been input or derived (from 249 formulas).
% 88.24/88.41 ; 1787 ( 1%) were retained. Of these,
% 88.24/88.41 ; 1727 (97%) were simplified or subsumed later,
% 88.24/88.41 ; 60 ( 3%) are still being kept.
% 88.24/88.41 ;
% 88.24/88.41 ; Run time in seconds excluding printing time:
% 88.24/88.41 ; 0.006 0% Read assertion file (1 call)
% 88.24/88.41 ; 0.002 0% Assert (28 calls)
% 88.24/88.41 ; 0.817 1% Process new row (136,301 calls)
% 88.24/88.41 ; 38.282 44% Resolution (496 calls)
% 88.24/88.41 ; 0.070 0% Paramodulation (248 calls)
% 88.24/88.41 ; 0.001 0% Factoring (214 calls)
% 88.24/88.41 ; 0.305 0% Condensing (134,380 calls)
% 88.24/88.41 ; 35.261 40% Forward subsumption (134,380 calls)
% 88.24/88.41 ; 0.045 0% Backward subsumption (1,706 calls)
% 88.24/88.41 ; 5.738 7% Clause clause subsumption (953,122 calls)
% 88.24/88.41 ; 6.817 8% Forward simplification (135,964 calls)
% 88.24/88.41 ; 0.056 0% Backward simplification (1,787 calls)
% 88.24/88.41 ; 0.037 0% Ordering (20,198 calls)
% 88.24/88.41 ; 0.000 0% Sortal reasoning (32 calls)
% 88.24/88.41 ; 0.000 0% Purity testing (1 call)
% 88.24/88.41 ; 0.500 1% Other
% 88.24/88.41 ; 87.937 Total
% 88.24/88.41 ; 87.945 Real time
% 88.24/88.41 ;
% 88.24/88.41 ; Term-hash-array has 1,174 terms in all.
% 88.24/88.41 ; Feature-vector-row-index has 4 entries (672 at peak, 1,706 added, 1,702 deleted).
% 88.24/88.41 ; Feature-vector-row-index has 29 nodes (4,171 at peak, 9,232 added, 9,203 deleted).
% 88.24/88.41 ; Retrieved 4,688,156 possibly forward subsuming rows in 134,380 calls.
% 88.24/88.41 ; Retrieved 1,321 possibly backward subsumed rows in 1,706 calls.
% 88.24/88.41 ; Path-index has 171 entries (606 at peak, 1,480 added, 1,309 deleted).
% 88.24/88.41 ; Path-index has 240 nodes (366 at peak, 618 added, 378 deleted).
% 88.24/88.41 ; Trie-index has 171 entries (606 at peak, 1,480 added, 1,309 deleted).
% 88.24/88.41 ; Trie-index has 486 nodes (1,517 at peak, 3,262 added, 2,776 deleted).
% 88.24/88.41 ; Retrieved 6,711 generalization terms in 1,525,813 calls.
% 88.24/88.41 ; Retrieved 184 instance terms in 103 calls.
% 88.24/88.41 ; Retrieved 29,256,479 unifiable terms in 987,651 calls.
% 88.24/88.41 ;
% 88.24/88.41 ; The agenda of rows to process has 19 entries:
% 88.24/88.41 ; 2 with value 8 4 with value 12 1 with value 16
% 88.24/88.41 ; 2 with value 9 4 with value 13 1 with value 17
% 88.24/88.41 ; 2 with value 10 1 with value 15 1 with value 18
% 88.24/88.41 ; 1 with value 11
% 88.24/88.41 ; The agenda of rows to give has 36 entries:
% 88.24/88.41 ; 3 with value (4 12) 8 with value (4 18) 1 with value (4 22)
% 88.24/88.41 ; 2 with value (4 14) 3 with value (4 19) 3 with value (4 23)
% 88.24/88.41 ; 2 with value (4 15) 6 with value (4 20) 4 with value (4 24)
% 88.24/88.41 ; 1 with value (4 17) 2 with value (4 21) 1 with value (4 26)
% 88.24/88.41 Evaluation took:
% 88.24/88.41 87.945 seconds of real time
% 88.24/88.41 85.79324 seconds of user run time
% 88.24/88.41 2.157881 seconds of system run time
% 88.24/88.41 [Run times include 3.275 seconds GC run time.]
% 88.24/88.41 0 calls to %EVAL
% 88.24/88.41 0 page faults and
% 88.24/88.41 8,467,118,712 bytes consed.
% 88.24/88.41 :PROOF-FOUND
% 88.24/88.41 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T06:36:19
% 88.24/88.41 :PROOF-FOUND
% 88.24/88.41 *
%------------------------------------------------------------------------------