%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : COL078-2 : TPTP v8.1.0. Released v1.2.0.
% 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 00:41:48 EDT 2022
% Result : Unsatisfiable 0.76s 1.00s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 17 unt; 0 nHn; 7 RR)
% Number of literals : 23 ( 22 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(k(X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstraction) ).
cnf(extensionality2,axiom,
( X = Y
| apply(X,n(X,Y)) != apply(Y,n(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
cnf(identity_definition,axiom,
apply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_definition) ).
cnf(prove_TRC1b,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC1b) ).
cnf(6,plain,
apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction)) != k(k(identity)),
inference('REWRITE',[status(thm)],[prove_TRC1b,abstraction,theory(equality)]) ).
cnf(7,plain,
( identity = X
| n(identity,X) != apply(X,n(identity,X)) ),
inference('PARAMODULATE',[status(thm)],[extensionality2,identity_definition,theory(equality)]) ).
cnf(9,plain,
( k(X) = Y
| X != apply(Y,n(k(X),Y)) ),
inference('PARAMODULATE',[status(thm)],[extensionality2,k_definition,theory(equality)]) ).
cnf(11,plain,
apply(apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction)),n(apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction)),k(k(identity)))) != k(identity),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[extensionality2,6]),k_definition,theory(equality)]) ).
cnf(15,plain,
apply(apply(apply(abstraction,k(X)),Y),Z) = apply(X,apply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[abstraction,k_definition,theory(equality)]) ).
cnf(17,plain,
apply(apply(apply(apply(abstraction,abstraction),X),Y),Z) = apply(Y,apply(apply(X,Y),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[abstraction,abstraction,theory(equality)]),k_definition,theory(equality)]) ).
cnf(59,plain,
apply(apply(apply(abstraction,k(k(X))),Y),Z) = X,
inference('PARAMODULATE',[status(thm)],[k_definition,15,theory(equality)]) ).
cnf(83,plain,
k(X) = apply(apply(abstraction,k(k(X))),Y),
inference('HYPERRESOLVE',[status(thm)],[9,59]) ).
cnf(84,plain,
k(k(X)) = apply(abstraction,k(k(X))),
inference('HYPERRESOLVE',[status(thm)],[9,83]) ).
cnf(86,plain,
apply(apply(apply(abstraction,abstraction),X),k(Y)) = k(Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[abstraction,84,theory(equality)]),k_definition,theory(equality)]) ).
cnf(121,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X)),Y),Z) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[abstraction,86,theory(equality)]),k_definition,theory(equality)]) ).
cnf(522,plain,
identity = apply(apply(abstraction,apply(apply(abstraction,abstraction),X)),Y),
inference('HYPERRESOLVE',[status(thm)],[7,121]) ).
cnf(523,plain,
k(identity) = apply(abstraction,apply(apply(abstraction,abstraction),X)),
inference('HYPERRESOLVE',[status(thm)],[9,522]) ).
cnf(524,plain,
apply(apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction)),X) = k(identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,523,theory(equality)]),abstraction,theory(equality)]) ).
cnf(525,plain,
$false,
inference('REWRITE',[status(thm)],[11,524,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL078-2 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13 % Command : run-snark %s %d
% 0.14/0.34 % Computer : n026.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 : Tue May 31 07:17:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.46 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47 *
% 0.21/0.47 *
% 0.21/0.48 #<PACKAGE "SNARK-USER">
% 0.21/0.48 *
% 0.21/0.48 SNARK-TPTP-OPTIONS
% 0.21/0.48 *
% 0.21/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.48 (USE-FACTORING :POS)
% 0.21/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.48 *
% 0.21/0.48 "."
% 0.21/0.48 *
% 0.21/0.48 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T07:17:11
% 0.21/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-05-31T07:17:11
% 0.21/0.49
% 0.76/1.00 ; Recognized left identity assertion (= (|apply| |identity| ?X) ?X).
% 0.76/1.00
% 0.76/1.00 #||
% 0.76/1.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.76/1.00 % SZS output start Refutation
% See solution above
% 0.76/1.00 ||#
% 0.76/1.00
% 0.76/1.00 ; Summary of computation:
% 0.76/1.00 ; 1723 formulas have been input or derived (from 50 formulas).
% 0.76/1.00 ; 525 (30%) were retained. Of these,
% 0.76/1.00 ; 54 (10%) were simplified or subsumed later,
% 0.76/1.00 ; 471 (90%) are still being kept.
% 0.76/1.00 ;
% 0.76/1.00 ; Run time in seconds excluding printing time:
% 0.76/1.00 ; 0.001 0% Read assertion file (1 call)
% 0.76/1.00 ; 0.001 0% Assert (5 calls)
% 0.76/1.00 ; 0.065 13% Process new row (1,534 calls)
% 0.76/1.00 ; 0.006 1% Resolution (98 calls)
% 0.76/1.00 ; 0.034 7% Paramodulation (49 calls)
% 0.76/1.00 ; 0.004 1% Condensing (113 calls)
% 0.76/1.00 ; 0.010 2% Forward subsumption (113 calls)
% 0.76/1.00 ; 0.003 1% Backward subsumption (68 calls)
% 0.76/1.00 ; 0.001 0% Clause clause subsumption (277 calls)
% 0.76/1.00 ; 0.110 22% Forward simplification (1,170 calls)
% 0.76/1.00 ; 0.024 5% Backward simplification (524 calls)
% 0.76/1.00 ; 0.217 43% Ordering (23,644 calls)
% 0.76/1.00 ; 0.000 0% Sortal reasoning (32 calls)
% 0.76/1.00 ; 0.000 0% Purity testing (1 call)
% 0.76/1.00 ; 0.028 6% Other
% 0.76/1.00 ; 0.504 Total
% 0.76/1.00 ; 0.519 Real time
% 0.76/1.00 ;
% 0.76/1.00 ; Term-hash-array has 2,232 terms in all.
% 0.76/1.00 ; Feature-vector-row-index has 56 entries (56 at peak, 68 added, 12 deleted).
% 0.76/1.00 ; Feature-vector-row-index has 425 nodes (425 at peak, 532 added, 107 deleted).
% 0.76/1.00 ; Retrieved 256 possibly forward subsuming rows in 113 calls.
% 0.76/1.00 ; Retrieved 49 possibly backward subsumed rows in 68 calls.
% 0.76/1.00 ; Path-index has 2,081 entries (2,088 at peak, 2,244 added, 163 deleted).
% 0.76/1.00 ; Path-index has 2,174 nodes (2,198 at peak, 2,271 added, 97 deleted).
% 0.76/1.00 ; Trie-index has 2,081 entries (2,088 at peak, 2,244 added, 163 deleted).
% 0.76/1.00 ; Trie-index has 10,975 nodes (11,058 at peak, 11,682 added, 707 deleted).
% 0.76/1.00 ; Retrieved 25,655 generalization terms in 12,617 calls.
% 0.76/1.00 ; Retrieved 5,097 instance terms in 1,196 calls.
% 0.76/1.00 ; Retrieved 9,295 unifiable terms in 517 calls.
% 0.76/1.00 ;
% 0.76/1.00 ; The agenda of rows to process has 21 entries:
% 0.76/1.00 ; 1 with value 27 3 with value 32 2 with value 35
% 0.76/1.00 ; 1 with value 29 2 with value 33 2 with value 38
% 0.76/1.00 ; 2 with value 30 2 with value 34 1 with value 39
% 0.76/1.00 ; 5 with value 31
% 0.76/1.00 ; The agenda of rows to give has 436 entries:
% 0.76/1.00 ; 1 with value (4 25) 38 with value (4 36) 6 with value (4 47)
% 0.76/1.00 ; 7 with value (4 26) 25 with value (4 37) 5 with value (4 48)
% 0.76/1.00 ; 8 with value (4 27) 28 with value (4 38) 4 with value (4 49)
% 0.76/1.00 ; 12 with value (4 28) 13 with value (4 39) 2 with value (4 50)
% 0.76/1.00 ; 16 with value (4 29) 22 with value (4 40) 3 with value (4 51)
% 0.76/1.00 ; 15 with value (4 30) 21 with value (4 41) 2 with value (4 56)
% 0.76/1.00 ; 27 with value (4 31) 13 with value (4 42) 1 with value (4 57)
% 0.76/1.00 ; 29 with value (4 32) 5 with value (4 43) 2 with value (4 62)
% 0.76/1.00 ; 33 with value (4 33) 9 with value (4 44) 1 with value (4 63)
% 0.76/1.00 ; 38 with value (4 34) 11 with value (4 45) 2 with value (4 64)
% 0.76/1.00 ; 36 with value (4 35) 1 with value (4 46)
% 0.76/1.00 Evaluation took:
% 0.76/1.00 0.52 seconds of real time
% 0.76/1.00 0.457824 seconds of user run time
% 0.76/1.00 0.048929 seconds of system run time
% 0.76/1.00 [Run times include 0.019 seconds GC run time.]
% 0.76/1.00 0 calls to %EVAL
% 0.76/1.00 0 page faults and
% 0.76/1.00 30,022,192 bytes consed.
% 0.76/1.00 :PROOF-FOUND
% 0.76/1.00 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T07:17:11
% 0.76/1.00 :PROOF-FOUND
% 0.76/1.00 *
%------------------------------------------------------------------------------