TSTP Solution File: COL002-4 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% 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 : Fri Jul 15 00:41:33 EDT 2022
% Result : Unsatisfiable 3.44s 3.64s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 2 RR)
% Number of literals : 12 ( 11 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(i_definition,axiom,
apply(i,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
cnf(weak_fixed_point,axiom,
weak_fixed_point(X) = apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
cnf(prove_weak_fixed_point,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
cnf(29,plain,
apply(apply(apply(s,i),X),Y) = apply(Y,apply(X,Y)),
inference('PARAMODULATE',[status(thm)],[s_definition,i_definition,theory(equality)]) ).
cnf(30,plain,
apply(apply(apply(s,X),i),Y) = apply(apply(X,Y),Y),
inference('PARAMODULATE',[status(thm)],[s_definition,i_definition,theory(equality)]) ).
cnf(85,plain,
apply(apply(apply(s,i),i),X) = apply(X,X),
inference('PARAMODULATE',[status(thm)],[29,i_definition,theory(equality)]) ).
cnf(87,plain,
weak_fixed_point(X) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i)),
inference('REWRITE',[status(thm)],[weak_fixed_point,85,theory(equality)]) ).
cnf(145,plain,
apply(apply(apply(s,apply(b,X)),i),Y) = apply(X,apply(Y,Y)),
inference('PARAMODULATE',[status(thm)],[b_definition,30,theory(equality)]) ).
cnf(776,plain,
weak_fixed_point(X) = apply(X,weak_fixed_point(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[85,145,theory(equality)]),85,87,theory(equality)]) ).
cnf(777,plain,
$false,
inference('REWRITE',[status(thm)],[prove_weak_fixed_point,776,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.10/0.12 % Command : run-snark %s %d
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Tue May 31 08:12:56 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.43 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 *
% 0.18/0.44 *
% 0.18/0.44 #<PACKAGE "SNARK-USER">
% 0.18/0.44 *
% 0.18/0.44 SNARK-TPTP-OPTIONS
% 0.18/0.44 *
% 0.18/0.44 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.44 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.44 (USE-FACTORING :POS)
% 0.18/0.44 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.44 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.44 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.44 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.44 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.44 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.44 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.44 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.44 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.44 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.44 *
% 0.18/0.44 "."
% 0.18/0.44 *
% 0.18/0.44 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T08:12:56
% 0.18/0.44 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-05-31T08:12:56
% 0.18/0.45
% 3.44/3.64 ; Recognized left identity assertion (= (|apply| |i| ?X) ?X).
% 3.44/3.64
% 3.44/3.64 #||
% 3.44/3.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/3.64 % SZS output start Refutation
% See solution above
% 3.44/3.64 ||#
% 3.44/3.64
% 3.44/3.64 ; Summary of computation:
% 3.44/3.64 ; 1498 formulas have been input or derived (from 28 formulas).
% 3.44/3.64 ; 777 (52%) were retained. Of these,
% 3.44/3.64 ; 23 ( 3%) were simplified or subsumed later,
% 3.44/3.64 ; 754 (97%) are still being kept.
% 3.44/3.64 ;
% 3.44/3.64 ; Run time in seconds excluding printing time:
% 3.44/3.64 ; 0.002 0% Read assertion file (1 call)
% 3.44/3.64 ; 0.000 0% Assert (6 calls)
% 3.44/3.64 ; 0.109 3% Process new row (1,492 calls)
% 3.44/3.64 ; 0.000 0% Resolution (54 calls)
% 3.44/3.64 ; 0.026 1% Paramodulation (27 calls)
% 3.44/3.64 ; 0.704 22% Forward simplification (1,287 calls)
% 3.44/3.64 ; 0.318 10% Backward simplification (777 calls)
% 3.44/3.64 ; 2.002 63% Ordering (348,532 calls)
% 3.44/3.64 ; 0.001 0% Sortal reasoning (32 calls)
% 3.44/3.64 ; 0.000 0% Purity testing (1 call)
% 3.44/3.64 ; 0.027 1% Other
% 3.44/3.64 ; 3.189 Total
% 3.44/3.64 ; 3.195 Real time
% 3.44/3.64 ;
% 3.44/3.64 ; Term-hash-array has 3,183 terms in all.
% 3.44/3.64 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 3.44/3.64 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 3.44/3.64 ; Path-index has 3,129 entries (3,132 at peak, 3,203 added, 74 deleted).
% 3.44/3.64 ; Path-index has 779 nodes (785 at peak, 804 added, 25 deleted).
% 3.44/3.64 ; Trie-index has 3,129 entries (3,132 at peak, 3,203 added, 74 deleted).
% 3.44/3.64 ; Trie-index has 15,254 nodes (15,263 at peak, 15,642 added, 388 deleted).
% 3.44/3.64 ; Retrieved 278,020 generalization terms in 15,169 calls.
% 3.44/3.64 ; Retrieved 189,512 instance terms in 2,102 calls.
% 3.44/3.64 ; Retrieved 17,932 unifiable terms in 267 calls.
% 3.44/3.64 ;
% 3.44/3.64 ; The agenda of rows to process has 6 entries:
% 3.44/3.64 ; 1 with value 40 3 with value 45 2 with value 47
% 3.44/3.64 ; The agenda of rows to give has 731 entries:
% 3.44/3.64 ; 1 with value (4 13) 77 with value (4 31) 8 with value (4 41)
% 3.44/3.64 ; 3 with value (4 22) 75 with value (4 32) 11 with value (4 42)
% 3.44/3.64 ; 10 with value (4 23) 44 with value (4 33) 1 with value (4 43)
% 3.44/3.64 ; 18 with value (4 24) 27 with value (4 34) 7 with value (4 44)
% 3.44/3.64 ; 37 with value (4 25) 25 with value (4 35) 1 with value (4 45)
% 3.44/3.64 ; 52 with value (4 26) 17 with value (4 36) 1 with value (4 47)
% 3.44/3.64 ; 56 with value (4 27) 14 with value (4 37) 4 with value (4 49)
% 3.44/3.64 ; 57 with value (4 28) 26 with value (4 38) 1 with value (4 50)
% 3.44/3.64 ; 59 with value (4 29) 14 with value (4 39) 1 with value (4 53)
% 3.44/3.64 ; 73 with value (4 30) 11 with value (4 40)
% 3.44/3.64 Evaluation took:
% 3.44/3.64 3.195 seconds of real time
% 3.44/3.64 2.753725 seconds of user run time
% 3.44/3.64 0.43708 seconds of system run time
% 3.44/3.64 [Run times include 0.098 seconds GC run time.]
% 3.44/3.64 0 calls to %EVAL
% 3.44/3.64 0 page faults and
% 3.44/3.64 242,306,920 bytes consed.
% 3.44/3.64 :PROOF-FOUND
% 3.44/3.64 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T08:12:59
% 3.44/3.64 :PROOF-FOUND
% 3.44/3.64 *
%------------------------------------------------------------------------------