TSTP Solution File: GRP353-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP353-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n020.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 11:37:58 EDT 2022
% Result : Unsatisfiable 81.45s 81.64s
% Output : Refutation 81.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 21 unt; 20 nHn; 39 RR)
% Number of literals : 106 ( 105 equ; 41 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 : 33 ( 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_1,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_10,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_10) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c4 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_20,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_21,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_21) ).
cnf(prove_this_25,negated_conjecture,
( multiply(sk_c6,sk_c5) != 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(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(112,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c5) != 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_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(142,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[32,left_inverse,theory(equality)]) ).
cnf(143,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[32,32,theory(equality)]) ).
cnf(144,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[142,143,theory(equality)]) ).
cnf(146,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[33,144,theory(equality)]) ).
cnf(147,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(178,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[146,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(189,plain,
multiply(X,inverse(X)) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,178,theory(equality)]) ).
cnf(190,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('PARAMODULATE',[status(thm)],[146,178,theory(equality)]) ).
cnf(209,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,inverse(sk_c5)) = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[190,prove_this_20,theory(equality)]) ).
cnf(223,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c6,inverse(sk_c5)) = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[190,prove_this_21,theory(equality)]) ).
cnf(237,plain,
( inverse(sk_c1) = sk_c7
| sk_c4 = multiply(sk_c4,sk_c6) ),
inference('PARAMODULATE',[status(thm)],[147,prove_this_17,theory(equality)]) ).
cnf(244,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[32,237,theory(equality)]),left_inverse,theory(equality)]) ).
cnf(250,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference('PARAMODULATE',[status(thm)],[189,244,theory(equality)]) ).
cnf(262,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference('PARAMODULATE',[status(thm)],[prove_this_11,250,theory(equality)]) ).
cnf(264,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c4) = sk_c6 ),
inference('PARAMODULATE',[status(thm)],[prove_this_10,250,theory(equality)]) ).
cnf(267,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c4) = identity ),
inference('PARAMODULATE',[status(thm)],[189,262,theory(equality)]) ).
cnf(663,plain,
identity = sk_c6,
inference('PARAMODULATE',[status(thm)],[264,267,theory(equality)]) ).
cnf(664,plain,
sk_c5 = sk_c7,
inference('REWRITE',[status(thm)],[prove_this_1,left_identity,663,theory(equality)]) ).
cnf(773,plain,
( multiply(sk_c5,sk_c5) = identity
| sk_c2 = sk_c5 ),
inference('REWRITE',[status(thm)],[prove_this_21,144,664,663,theory(equality)]) ).
cnf(777,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_25,144,664,left_identity,663,theory(equality)])]) ).
cnf(810,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)],[112,left_identity,664,663,theory(equality)])]) ).
cnf(827,plain,
( inverse(sk_c2) = sk_c5
| inverse(sk_c5) = sk_c5 ),
inference('REWRITE',[status(thm)],[209,left_identity,664,663,theory(equality)]) ).
cnf(830,plain,
( sk_c2 = sk_c5
| inverse(sk_c5) = sk_c5 ),
inference('REWRITE',[status(thm)],[223,left_identity,664,144,663,theory(equality)]) ).
cnf(893,plain,
( multiply(sk_c5,sk_c5) != identity
| inverse(X) != sk_c5
| X != sk_c5 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[777,left_inverse,theory(equality)]),178,theory(equality)]) ).
cnf(1440,plain,
sk_c2 = sk_c5,
inference('HYPERRESOLVE',[status(thm)],[893,773,830,theory(equality)]) ).
cnf(1529,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)],[810,1440,theory(equality)])]) ).
cnf(1536,plain,
sk_c2 = inverse(sk_c2),
inference('REWRITE',[status(thm)],[827,1440,theory(equality)]) ).
cnf(1541,plain,
( inverse(sk_c1) = sk_c2
| multiply(sk_c2,sk_c2) != identity ),
inference('REWRITE',[status(thm)],[1529,1536,theory(equality)]) ).
cnf(1567,plain,
( multiply(sk_c2,sk_c2) != identity
| inverse(X) != sk_c2
| X != sk_c2 ),
inference('REWRITE',[status(thm)],[893,1440,theory(equality)]) ).
cnf(1734,plain,
multiply(sk_c2,sk_c2) = identity,
inference('PARAMODULATE',[status(thm)],[189,1536,theory(equality)]) ).
cnf(1736,plain,
inverse(sk_c1) = sk_c2,
inference('REWRITE',[status(thm)],[1541,1734,theory(equality)]) ).
cnf(1743,plain,
( inverse(X) != sk_c2
| X != sk_c2 ),
inference('REWRITE',[status(thm)],[1567,1734,theory(equality)]) ).
cnf(1755,plain,
sk_c1 = sk_c2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[178,1736,theory(equality)]),1536,theory(equality)]) ).
cnf(1777,plain,
inverse(sk_c1) = sk_c1,
inference('REWRITE',[status(thm)],[1536,1755,theory(equality)]) ).
cnf(1818,plain,
( inverse(X) != sk_c1
| X != sk_c1 ),
inference('REWRITE',[status(thm)],[1743,1755,theory(equality)]) ).
cnf(1824,plain,
$false,
inference('HYPERRESOLVE',[status(thm)],[1818,1777,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GRP353-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.11 % Command : run-snark %s %d
% 0.11/0.31 % Computer : n020.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jun 13 18:01:20 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.42 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 *
% 0.16/0.42 *
% 0.16/0.43 #<PACKAGE "SNARK-USER">
% 0.16/0.43 *
% 0.16/0.43 SNARK-TPTP-OPTIONS
% 0.16/0.43 *
% 0.16/0.43 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.16/0.43 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.16/0.43 (USE-FACTORING :POS)
% 0.16/0.43 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.16/0.43 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.16/0.43 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.16/0.43 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.16/0.43 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.16/0.43 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.16/0.43 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.16/0.43 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.16/0.43 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.16/0.43 (DECLARE-TPTP-SYMBOLS2))
% 0.16/0.43 *
% 0.16/0.43 "."
% 0.16/0.43 *
% 0.16/0.43 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T18:01:20
% 0.16/0.43 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-13T18:01:20
% 0.16/0.44
% 0.16/0.44 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.16/0.44 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 81.45/81.64 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 81.45/81.64
% 81.45/81.64 #||
% 81.45/81.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.45/81.64 % SZS output start Refutation
% See solution above
% 81.45/81.64 ||#
% 81.45/81.64
% 81.45/81.64 ; Summary of computation:
% 81.45/81.64 ; 287203 formulas have been input or derived (from 249 formulas).
% 81.45/81.64 ; 1824 ( 1%) were retained. Of these,
% 81.45/81.64 ; 1776 (97%) were simplified or subsumed later,
% 81.45/81.64 ; 48 ( 3%) are still being kept.
% 81.45/81.64 ;
% 81.45/81.64 ; Run time in seconds excluding printing time:
% 81.45/81.64 ; 0.003 0% Read assertion file (1 call)
% 81.45/81.64 ; 0.002 0% Assert (28 calls)
% 81.45/81.64 ; 0.769 1% Process new row (137,741 calls)
% 81.45/81.64 ; 32.376 40% Resolution (496 calls)
% 81.45/81.64 ; 0.079 0% Paramodulation (248 calls)
% 81.45/81.64 ; 0.000 0% Factoring (218 calls)
% 81.45/81.64 ; 0.250 0% Condensing (135,710 calls)
% 81.45/81.64 ; 37.439 46% Forward subsumption (135,710 calls)
% 81.45/81.64 ; 0.050 0% Backward subsumption (1,757 calls)
% 81.45/81.64 ; 3.191 4% Clause clause subsumption (583,087 calls)
% 81.45/81.64 ; 6.476 8% Forward simplification (137,295 calls)
% 81.45/81.64 ; 0.053 0% Backward simplification (1,824 calls)
% 81.45/81.64 ; 0.044 0% Ordering (21,795 calls)
% 81.45/81.64 ; 0.000 0% Sortal reasoning (32 calls)
% 81.45/81.64 ; 0.000 0% Purity testing (1 call)
% 81.45/81.64 ; 0.474 1% Other
% 81.45/81.64 ; 81.206 Total
% 81.45/81.64 ; 81.209 Real time
% 81.45/81.64 ;
% 81.45/81.64 ; Term-hash-array has 1,207 terms in all.
% 81.45/81.64 ; Feature-vector-row-index has 6 entries (699 at peak, 1,757 added, 1,751 deleted).
% 81.45/81.64 ; Feature-vector-row-index has 47 nodes (4,270 at peak, 9,808 added, 9,761 deleted).
% 81.45/81.64 ; Retrieved 4,563,256 possibly forward subsuming rows in 135,710 calls.
% 81.45/81.64 ; Retrieved 1,455 possibly backward subsumed rows in 1,757 calls.
% 81.45/81.64 ; Path-index has 137 entries (643 at peak, 1,518 added, 1,381 deleted).
% 81.45/81.64 ; Path-index has 218 nodes (372 at peak, 644 added, 426 deleted).
% 81.45/81.64 ; Trie-index has 137 entries (643 at peak, 1,518 added, 1,381 deleted).
% 81.45/81.64 ; Trie-index has 397 nodes (1,609 at peak, 3,355 added, 2,958 deleted).
% 81.45/81.64 ; Retrieved 6,986 generalization terms in 1,537,443 calls.
% 81.45/81.64 ; Retrieved 170 instance terms in 89 calls.
% 81.45/81.64 ; Retrieved 26,040,804 unifiable terms in 878,504 calls.
% 81.45/81.64 ;
% 81.45/81.64 ; The agenda of rows to process has 17 entries:
% 81.45/81.64 ; 2 with value 8 3 with value 12 1 with value 16
% 81.45/81.64 ; 2 with value 9 4 with value 13 1 with value 17
% 81.45/81.64 ; 1 with value 10 1 with value 15 1 with value 18
% 81.45/81.64 ; 1 with value 11
% 81.45/81.64 ; The agenda of rows to give has 28 entries:
% 81.45/81.64 ; 1 with value (4 12) 6 with value (4 20) 4 with value (4 23)
% 81.45/81.64 ; 2 with value (4 15) 2 with value (4 21) 4 with value (4 24)
% 81.45/81.64 ; 3 with value (4 18) 2 with value (4 22) 1 with value (4 26)
% 81.45/81.64 ; 3 with value (4 19)
% 81.45/81.64 Evaluation took:
% 81.45/81.64 81.21 seconds of real time
% 81.45/81.64 79.450195 seconds of user run time
% 81.45/81.64 1.759526 seconds of system run time
% 81.45/81.64 [Run times include 2.963 seconds GC run time.]
% 81.45/81.64 0 calls to %EVAL
% 81.45/81.64 0 page faults and
% 81.45/81.64 8,672,478,240 bytes consed.
% 81.45/81.64 :PROOF-FOUND
% 81.45/81.64 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T18:02:41
% 81.45/81.64 :PROOF-FOUND
% 81.45/81.64 *
%------------------------------------------------------------------------------