TSTP Solution File: GRP299-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP299-1 : TPTP v8.1.0. Released v2.5.0.
% 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 11:37:48 EDT 2022
% Result : Unsatisfiable 112.85s 113.06s
% Output : Refutation 112.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 57 ( 24 unt; 21 nHn; 43 RR)
% Number of literals : 124 ( 123 equ; 52 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 : 40 ( 0 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_1,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_3,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_15,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_16,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_21,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| 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/sandbox/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(112,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c7
| 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_3,theory(equality)]),theory(equality)]) ).
cnf(125,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c6) != sk_c5
| multiply(X,sk_c7) != sk_c6
| inverse(X) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| 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_15,theory(equality)]),theory(equality)]) ).
cnf(156,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[32,left_inverse,theory(equality)]) ).
cnf(157,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[32,32,theory(equality)]) ).
cnf(158,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[156,157,theory(equality)]) ).
cnf(160,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[33,158,theory(equality)]) ).
cnf(161,plain,
( inverse(sk_c1) = sk_c7
| sk_c4 = multiply(inverse(sk_c3),sk_c6) ),
inference('PARAMODULATE',[status(thm)],[32,prove_this_16,theory(equality)]) ).
cnf(170,plain,
( inverse(sk_c2) = sk_c7
| sk_c7 = multiply(inverse(sk_c5),sk_c6) ),
inference('PARAMODULATE',[status(thm)],[32,prove_this_20,theory(equality)]) ).
cnf(186,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| sk_c7 = multiply(inverse(sk_c5),sk_c6) ),
inference('PARAMODULATE',[status(thm)],[32,prove_this_21,theory(equality)]) ).
cnf(189,plain,
inverse(identity) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,158,theory(equality)]) ).
cnf(193,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[160,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(204,plain,
multiply(X,inverse(X)) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,193,theory(equality)]) ).
cnf(205,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('PARAMODULATE',[status(thm)],[160,193,theory(equality)]) ).
cnf(214,plain,
inverse(X) = multiply(inverse(multiply(Y,X)),Y),
inference('PARAMODULATE',[status(thm)],[32,205,theory(equality)]) ).
cnf(253,plain,
( inverse(sk_c1) = sk_c7
| sk_c4 = multiply(sk_c4,sk_c6) ),
inference('PARAMODULATE',[status(thm)],[161,prove_this_17,theory(equality)]) ).
cnf(260,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[32,253,theory(equality)]),left_inverse,theory(equality)]) ).
cnf(266,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference('PARAMODULATE',[status(thm)],[204,260,theory(equality)]) ).
cnf(278,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference('PARAMODULATE',[status(thm)],[prove_this_11,266,theory(equality)]) ).
cnf(280,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
inference('PARAMODULATE',[status(thm)],[prove_this_10,266,theory(equality)]) ).
cnf(283,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c4) = identity ),
inference('PARAMODULATE',[status(thm)],[204,278,theory(equality)]) ).
cnf(352,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[160,214,theory(equality)]) ).
cnf(695,plain,
identity = sk_c6,
inference('PARAMODULATE',[status(thm)],[280,283,theory(equality)]) ).
cnf(696,plain,
sk_c5 = sk_c7,
inference('REWRITE',[status(thm)],[prove_this_1,left_identity,158,695,theory(equality)]) ).
cnf(810,plain,
( multiply(sk_c5,sk_c5) = identity
| sk_c2 = sk_c5 ),
inference('REWRITE',[status(thm)],[prove_this_21,158,696,695,theory(equality)]) ).
cnf(814,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,158,696,695,theory(equality)])]) ).
cnf(851,plain,
( sk_c2 = sk_c5
| multiply(sk_c5,sk_c5) != identity
| inverse(sk_c5) != sk_c5 ),
inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[112,left_identity,696,158,695,theory(equality)])]) ).
cnf(855,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)],[125,left_identity,158,696,695,theory(equality)])]) ).
cnf(865,plain,
( inverse(sk_c2) = sk_c5
| inverse(sk_c5) = sk_c5 ),
inference('REWRITE',[status(thm)],[170,left_identity,189,352,696,695,theory(equality)]) ).
cnf(869,plain,
( sk_c2 = sk_c5
| inverse(sk_c5) = sk_c5 ),
inference('REWRITE',[status(thm)],[186,left_identity,189,352,696,158,695,theory(equality)]) ).
cnf(941,plain,
( multiply(sk_c5,sk_c5) != identity
| inverse(X) != sk_c5
| X != sk_c5 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[814,left_inverse,theory(equality)]),193,theory(equality)]) ).
cnf(1440,plain,
sk_c2 = sk_c5,
inference('HYPERRESOLVE',[status(thm)],[851,810,869]) ).
cnf(1534,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)],[855,1440,theory(equality)])]) ).
cnf(1537,plain,
sk_c2 = inverse(sk_c2),
inference('REWRITE',[status(thm)],[865,1440,theory(equality)]) ).
cnf(1545,plain,
( inverse(sk_c1) = sk_c2
| multiply(sk_c2,sk_c2) != identity ),
inference('REWRITE',[status(thm)],[1534,1537,theory(equality)]) ).
cnf(1571,plain,
( multiply(sk_c2,sk_c2) != identity
| inverse(X) != sk_c2
| X != sk_c2 ),
inference('REWRITE',[status(thm)],[941,1440,theory(equality)]) ).
cnf(1740,plain,
multiply(sk_c2,sk_c2) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,1537,theory(equality)]) ).
cnf(1746,plain,
inverse(sk_c1) = sk_c2,
inference('REWRITE',[status(thm)],[1545,1740,theory(equality)]) ).
cnf(1751,plain,
( inverse(X) != sk_c2
| X != sk_c2 ),
inference('REWRITE',[status(thm)],[1571,1740,theory(equality)]) ).
cnf(1778,plain,
sk_c1 = sk_c2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[193,1746,theory(equality)]),1537,theory(equality)]) ).
cnf(1793,plain,
sk_c1 = inverse(sk_c1),
inference('REWRITE',[status(thm)],[1537,1778,theory(equality)]) ).
cnf(1806,plain,
( inverse(X) != sk_c1
| X != sk_c1 ),
inference('REWRITE',[status(thm)],[1751,1778,theory(equality)]) ).
cnf(1814,plain,
$false,
inference('HYPERRESOLVE',[status(thm)],[1806,1793,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP299-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : run-snark %s %d
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 08:17:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T08:17:22
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-06-13T08:17:22
% 0.20/0.49
% 0.20/0.49 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.20/0.49 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 112.85/113.06 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 112.85/113.06
% 112.85/113.06 #||
% 112.85/113.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 112.85/113.06 % SZS output start Refutation
% See solution above
% 112.85/113.06 ||#
% 112.85/113.06
% 112.85/113.06 ; Summary of computation:
% 112.85/113.06 ; 355509 formulas have been input or derived (from 253 formulas).
% 112.85/113.06 ; 1814 ( 1%) were retained. Of these,
% 112.85/113.06 ; 1768 (97%) were simplified or subsumed later,
% 112.85/113.06 ; 46 ( 3%) are still being kept.
% 112.85/113.06 ;
% 112.85/113.06 ; Run time in seconds excluding printing time:
% 112.85/113.06 ; 0.006 0% Read assertion file (1 call)
% 112.85/113.06 ; 0.002 0% Assert (28 calls)
% 112.85/113.07 ; 0.972 1% Process new row (155,929 calls)
% 112.85/113.07 ; 46.806 42% Resolution (504 calls)
% 112.85/113.07 ; 0.062 0% Paramodulation (252 calls)
% 112.85/113.07 ; 0.000 0% Factoring (216 calls)
% 112.85/113.07 ; 0.343 0% Condensing (153,951 calls)
% 112.85/113.07 ; 49.028 44% Forward subsumption (153,951 calls)
% 112.85/113.07 ; 0.041 0% Backward subsumption (1,732 calls)
% 112.85/113.07 ; 6.588 6% Clause clause subsumption (1,161,141 calls)
% 112.85/113.07 ; 7.771 7% Forward simplification (155,576 calls)
% 112.85/113.07 ; 0.056 0% Backward simplification (1,814 calls)
% 112.85/113.07 ; 0.303 0% Ordering (165,985 calls)
% 112.85/113.07 ; 0.001 0% Sortal reasoning (32 calls)
% 112.85/113.07 ; 0.000 0% Purity testing (1 call)
% 112.85/113.07 ; 0.600 1% Other
% 112.85/113.07 ; 112.579 Total
% 112.85/113.07 ; 112.591 Real time
% 112.85/113.07 ;
% 112.85/113.07 ; Term-hash-array has 1,151 terms in all.
% 112.85/113.07 ; Feature-vector-row-index has 2 entries (668 at peak, 1,732 added, 1,730 deleted).
% 112.85/113.07 ; Feature-vector-row-index has 12 nodes (4,455 at peak, 9,814 added, 9,802 deleted).
% 112.85/113.07 ; Retrieved 6,117,071 possibly forward subsuming rows in 153,951 calls.
% 112.85/113.07 ; Retrieved 1,334 possibly backward subsumed rows in 1,732 calls.
% 112.85/113.07 ; Path-index has 133 entries (599 at peak, 1,451 added, 1,318 deleted).
% 112.85/113.07 ; Path-index has 210 nodes (362 at peak, 607 added, 397 deleted).
% 112.85/113.07 ; Trie-index has 133 entries (599 at peak, 1,451 added, 1,318 deleted).
% 112.85/113.07 ; Trie-index has 389 nodes (1,469 at peak, 3,178 added, 2,789 deleted).
% 112.85/113.07 ; Retrieved 6,763 generalization terms in 1,795,599 calls.
% 112.85/113.07 ; Retrieved 185 instance terms in 104 calls.
% 112.85/113.07 ; Retrieved 37,310,752 unifiable terms in 1,254,221 calls.
% 112.85/113.07 ;
% 112.85/113.07 ; The agenda of rows to process has 19 entries:
% 112.85/113.07 ; 1 with value 7 3 with value 11 1 with value 16
% 112.85/113.07 ; 3 with value 8 2 with value 12 1 with value 17
% 112.85/113.07 ; 2 with value 9 2 with value 13 1 with value 18
% 112.85/113.07 ; 2 with value 10 1 with value 15
% 112.85/113.07 ; The agenda of rows to give has 23 entries:
% 112.85/113.07 ; 2 with value (4 13) 6 with value (4 20) 1 with value (4 23)
% 112.85/113.07 ; 1 with value (4 17) 2 with value (4 21) 4 with value (4 24)
% 112.85/113.07 ; 3 with value (4 18) 1 with value (4 22) 1 with value (4 26)
% 112.85/113.07 ; 2 with value (4 19)
% 112.85/113.07 Evaluation took:
% 112.85/113.07 112.591 seconds of real time
% 112.85/113.07 109.71429 seconds of user run time
% 112.85/113.07 2.868946 seconds of system run time
% 112.85/113.07 [Run times include 3.964 seconds GC run time.]
% 112.85/113.07 0 calls to %EVAL
% 112.85/113.07 0 page faults and
% 112.85/113.07 11,637,971,168 bytes consed.
% 112.85/113.07 :PROOF-FOUND
% 112.85/113.07 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T08:19:15
% 112.85/113.07 :PROOF-FOUND
% 112.85/113.07 *
%------------------------------------------------------------------------------