TSTP Solution File: COL074-3 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n032.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 00:41:47 EDT 2022
% Result : Unsatisfiable 0.47s 0.63s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 27 unt; 2 nHn; 12 RR)
% Number of literals : 33 ( 32 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 34 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,negated_conjecture,
apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(pairwise_application,axiom,
apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairwise_application) ).
cnf(abstraction,negated_conjecture,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
cnf(equality,axiom,
apply(eq,pair(X,X)) = projection1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).
cnf(extensionality1,axiom,
( X = Y
| apply(eq,pair(X,Y)) = projection2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
cnf(extensionality2,axiom,
( X = Y
| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
cnf(different_projections,axiom,
projection1 != projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_projections) ).
cnf(k_projection2,axiom,
apply(k,projection2) = k_projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_projection2) ).
cnf(self_referential,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_referential) ).
cnf(14,plain,
s = apply(eq,pair(apply(k,s),k_projection2)),
inference('REWRITE',[status(thm)],[self_referential,k_projection2,theory(equality)]) ).
cnf(17,plain,
apply(k_projection2,X) = projection2,
inference('PARAMODULATE',[status(thm)],[k_definition,k_projection2,theory(equality)]) ).
cnf(20,plain,
( apply(k,s) = k_projection2
| s = projection2 ),
inference('PARAMODULATE',[status(thm)],[14,extensionality1,theory(equality)]) ).
cnf(21,plain,
apply(eq,apply(pair(X,X),Y)) = projection1,
inference('PARAMODULATE',[status(thm)],[equality,pairwise_application,theory(equality)]) ).
cnf(22,plain,
apply(pair(k,X),projection2) = pair(k_projection2,apply(X,projection2)),
inference('PARAMODULATE',[status(thm)],[pairwise_application,k_projection2,theory(equality)]) ).
cnf(28,plain,
apply(pair(apply(k,X),Y),Z) = pair(X,apply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[pairwise_application,k_definition,theory(equality)]) ).
cnf(30,plain,
apply(pair(k,X),projection2) = apply(pair(apply(k,k_projection2),X),projection2),
inference('REWRITE',[status(thm)],[22,28,theory(equality)]) ).
cnf(32,plain,
apply(pair(X,apply(k,Y)),Z) = pair(apply(X,Z),Y),
inference('PARAMODULATE',[status(thm)],[pairwise_application,k_definition,theory(equality)]) ).
cnf(35,plain,
s = apply(eq,apply(apply(pair(apply(k,k),k),k_projection2),s)),
inference('REWRITE',[status(thm)],[14,28,32,theory(equality)]) ).
cnf(54,plain,
apply(apply(apply(abstraction,k),X),Y) = apply(k,Y),
inference('PARAMODULATE',[status(thm)],[k_definition,abstraction,theory(equality)]) ).
cnf(98,plain,
s = projection2,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[k_definition,20,theory(equality)]),17,theory(equality)]) ).
cnf(99,plain,
projection2 = apply(eq,apply(apply(pair(apply(k,k),k),k_projection2),projection2)),
inference('REWRITE',[status(thm)],[35,98,theory(equality)]) ).
cnf(129,plain,
apply(apply(abstraction,k),X) = k,
inference('HYPERRESOLVE',[status(thm)],[extensionality2,54]) ).
cnf(130,plain,
apply(pair(apply(abstraction,k),X),Y) = pair(k,apply(X,Y)),
inference('PARAMODULATE',[status(thm)],[pairwise_application,129,theory(equality)]) ).
cnf(131,plain,
apply(pair(X,apply(abstraction,k)),Y) = pair(apply(X,Y),k),
inference('PARAMODULATE',[status(thm)],[pairwise_application,129,theory(equality)]) ).
cnf(132,plain,
projection2 = apply(eq,apply(apply(apply(apply(pair(apply(abstraction,k),abstraction),k),k),k_projection2),projection2)),
inference('REWRITE',[status(thm)],[99,130,131,theory(equality)]) ).
cnf(285,plain,
apply(pair(apply(k,X),k),projection2) = pair(X,k_projection2),
inference('PARAMODULATE',[status(thm)],[28,k_projection2,theory(equality)]) ).
cnf(365,plain,
apply(pair(k,k),projection2) = pair(k_projection2,k_projection2),
inference('PARAMODULATE',[status(thm)],[285,30,theory(equality)]) ).
cnf(379,plain,
apply(pair(k,apply(k,X)),projection2) = pair(k_projection2,X),
inference('PARAMODULATE',[status(thm)],[32,k_projection2,theory(equality)]) ).
cnf(539,plain,
apply(apply(apply(apply(pair(apply(abstraction,k),abstraction),k),k),X),projection2) = pair(k_projection2,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[379,28,theory(equality)]),130,131,theory(equality)]) ).
cnf(540,plain,
$false,
inference('REWRITE',[status(thm)],[132,different_projections,21,365,539,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.11 % Command : run-snark %s %d
% 0.11/0.31 % Computer : n032.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 : Tue May 31 06:26:28 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.39 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.40 *
% 0.16/0.40 *
% 0.16/0.40 #<PACKAGE "SNARK-USER">
% 0.16/0.40 *
% 0.16/0.40 SNARK-TPTP-OPTIONS
% 0.16/0.40 *
% 0.16/0.40 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.16/0.40 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.16/0.40 (USE-FACTORING :POS)
% 0.16/0.40 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.16/0.40 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.16/0.40 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.16/0.40 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.16/0.40 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.16/0.40 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.16/0.40 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.16/0.40 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.16/0.41 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.16/0.41 (DECLARE-TPTP-SYMBOLS2))
% 0.16/0.41 *
% 0.16/0.41 "."
% 0.16/0.41 *
% 0.16/0.41 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-31T06:26:28
% 0.16/0.41 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-05-31T06:26:28
% 0.47/0.63
% 0.47/0.63
% 0.47/0.63 #||
% 0.47/0.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.63 % SZS output start Refutation
% See solution above
% 0.47/0.63 ||#
% 0.47/0.63
% 0.47/0.63 ; Summary of computation:
% 0.47/0.63 ; 914 formulas have been input or derived (from 67 formulas).
% 0.47/0.63 ; 540 (59%) were retained. Of these,
% 0.47/0.63 ; 202 (37%) were simplified or subsumed later,
% 0.47/0.63 ; 338 (63%) are still being kept.
% 0.47/0.63 ;
% 0.47/0.63 ; Run time in seconds excluding printing time:
% 0.47/0.63 ; 0.002 1% Read assertion file (1 call)
% 0.47/0.63 ; 0.000 0% Assert (13 calls)
% 0.47/0.63 ; 0.067 30% Process new row (877 calls)
% 0.47/0.63 ; 0.006 3% Resolution (132 calls)
% 0.47/0.63 ; 0.010 4% Paramodulation (66 calls)
% 0.47/0.63 ; 0.000 0% Factoring (2 calls)
% 0.47/0.63 ; 0.000 0% Condensing (82 calls)
% 0.47/0.63 ; 0.002 1% Forward subsumption (82 calls)
% 0.47/0.63 ; 0.001 0% Backward subsumption (68 calls)
% 0.47/0.63 ; 0.000 0% Clause clause subsumption (93 calls)
% 0.47/0.63 ; 0.045 20% Forward simplification (858 calls)
% 0.47/0.63 ; 0.025 11% Backward simplification (539 calls)
% 0.47/0.63 ; 0.051 23% Ordering (7,921 calls)
% 0.47/0.63 ; 0.000 0% Sortal reasoning (32 calls)
% 0.47/0.63 ; 0.000 0% Purity testing (1 call)
% 0.47/0.63 ; 0.014 6% Other
% 0.47/0.63 ; 0.223 Total
% 0.47/0.63 ; 0.225 Real time
% 0.47/0.63 ;
% 0.47/0.63 ; Term-hash-array has 2,069 terms in all.
% 0.47/0.63 ; Feature-vector-row-index has 61 entries (61 at peak, 68 added, 7 deleted).
% 0.47/0.63 ; Feature-vector-row-index has 500 nodes (500 at peak, 560 added, 60 deleted).
% 0.47/0.63 ; Retrieved 73 possibly forward subsuming rows in 82 calls.
% 0.47/0.63 ; Retrieved 27 possibly backward subsumed rows in 68 calls.
% 0.47/0.63 ; Path-index has 1,461 entries (1,486 at peak, 2,238 added, 777 deleted).
% 0.47/0.63 ; Path-index has 2,527 nodes (2,552 at peak, 3,065 added, 538 deleted).
% 0.47/0.63 ; Trie-index has 1,461 entries (1,486 at peak, 2,238 added, 777 deleted).
% 0.47/0.63 ; Trie-index has 9,078 nodes (9,432 at peak, 13,705 added, 4,627 deleted).
% 0.47/0.63 ; Retrieved 6,144 generalization terms in 7,584 calls.
% 0.47/0.63 ; Retrieved 2,092 instance terms in 874 calls.
% 0.47/0.63 ; Retrieved 2,755 unifiable terms in 478 calls.
% 0.47/0.63 ;
% 0.47/0.63 ; The agenda of backward simplifiable rows to process has 8 entries:
% 0.47/0.63 ; 8 with value 0
% 0.47/0.63 ; The agenda of rows to process has 9 entries:
% 0.47/0.63 ; 4 with value 23 4 with value 25 1 with value 29
% 0.47/0.63 ; The agenda of rows to give has 283 entries:
% 0.47/0.63 ; 1 with value (4 17) 10 with value (4 35) 12 with value (4 55)
% 0.47/0.63 ; 6 with value (4 18) 1 with value (4 36) 3 with value (4 56)
% 0.47/0.63 ; 13 with value (4 19) 5 with value (4 37) 5 with value (4 57)
% 0.47/0.63 ; 13 with value (4 20) 1 with value (4 38) 1 with value (4 59)
% 0.47/0.63 ; 28 with value (4 21) 2 with value (4 39) 2 with value (4 60)
% 0.47/0.63 ; 13 with value (4 22) 2 with value (4 40) 2 with value (4 62)
% 0.47/0.63 ; 21 with value (4 23) 2 with value (4 41) 1 with value (4 64)
% 0.47/0.63 ; 15 with value (4 24) 10 with value (4 42) 3 with value (4 65)
% 0.47/0.63 ; 12 with value (4 25) 3 with value (4 43) 8 with value (4 66)
% 0.47/0.63 ; 3 with value (4 26) 2 with value (4 45) 1 with value (4 67)
% 0.47/0.63 ; 8 with value (4 27) 4 with value (4 46) 1 with value (4 69)
% 0.47/0.63 ; 1 with value (4 28) 2 with value (4 47) 1 with value (4 70)
% 0.47/0.63 ; 7 with value (4 29) 5 with value (4 49) 2 with value (4 71)
% 0.47/0.63 ; 9 with value (4 30) 2 with value (4 50) 2 with value (4 72)
% 0.47/0.63 ; 2 with value (4 31) 2 with value (4 51) 2 with value (4 78)
% 0.47/0.63 ; 5 with value (4 32) 4 with value (4 52) 2 with value (4 79)
% 0.47/0.63 ; 4 with value (4 33) 2 with value (4 53) 4 with value (4 80)
% 0.47/0.63 ; 3 with value (4 34) 4 with value (4 54) 4 with value (4 86)
% 0.47/0.63 Evaluation took:
% 0.47/0.63 0.226 seconds of real time
% 0.47/0.63 0.201289 seconds of user run time
% 0.47/0.63 0.024373 seconds of system run time
% 0.47/0.63 [Run times include 0.01 seconds GC run time.]
% 0.47/0.63 0 calls to %EVAL
% 0.47/0.63 0 page faults and
% 0.47/0.63 19,025,336 bytes consed.
% 0.47/0.63 :PROOF-FOUND
% 0.47/0.63 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-31T06:26:28
% 0.47/0.63 :PROOF-FOUND
% 0.47/0.63 *
%------------------------------------------------------------------------------