TSTP Solution File: LCL159-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n011.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 : Sun Jul 17 14:20:38 EDT 2022
% Result : Unsatisfiable 0.55s 0.75s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 8 RR)
% Number of literals : 34 ( 33 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(or_definition,axiom,
or(X,Y) = implies(not(X),Y),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_definition) ).
cnf(and_definition,axiom,
and(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',and_definition) ).
cnf(8,plain,
and(X,Y) = not(implies(not(not(X)),not(Y))),
inference('REWRITE',[status(thm)],[and_definition,or_definition,theory(equality)]) ).
cnf(xor_definition,axiom,
xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
cnf(10,plain,
xor(X,Y) = implies(not(and(X,not(Y))),and(not(X),Y)),
inference('REWRITE',[status(thm)],[xor_definition,or_definition,theory(equality)]) ).
cnf(false_definition,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',false_definition) ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(16,plain,
implies(not(and(x,not(implies(not(and(truth,not(y))),and(falsehood,y))))),and(not(x),implies(not(and(truth,not(y))),and(falsehood,y)))) != implies(not(and(implies(not(and(x,falsehood)),and(not(x),truth)),not(y))),and(not(implies(not(and(x,falsehood)),and(not(x),truth))),y)),
inference('REWRITE',[status(thm)],[prove_alternative_wajsberg_axiom,false_definition,10,theory(equality)]) ).
cnf(17,plain,
implies(not(X),Y) = implies(not(Y),X),
inference('PARAMODULATE',[status(thm)],[or_definition,or_definition,theory(equality)]) ).
cnf(18,plain,
implies(not(and(x,not(implies(not(and(falsehood,y)),and(truth,not(y)))))),and(not(x),implies(not(and(falsehood,y)),and(truth,not(y))))) != implies(not(and(not(implies(not(and(x,falsehood)),and(not(x),truth))),y)),and(implies(not(and(x,falsehood)),and(not(x),truth)),not(y))),
inference('REWRITE',[status(thm)],[16,17,theory(equality)]) ).
cnf(100,plain,
implies(X,X) = implies(implies(X,truth),truth),
inference('PARAMODULATE',[status(thm)],[wajsberg_3,wajsberg_1,theory(equality)]) ).
cnf(102,plain,
implies(implies(not(X),falsehood),X) = truth,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_4,wajsberg_1,theory(equality)]),false_definition,theory(equality)]) ).
cnf(106,plain,
and(truth,X) = not(implies(not(falsehood),not(X))),
inference('PARAMODULATE',[status(thm)],[8,false_definition,theory(equality)]) ).
cnf(108,plain,
and(X,implies(not(not(Y)),not(Z))) = not(implies(not(not(X)),and(Y,Z))),
inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]) ).
cnf(112,plain,
implies(X,implies(implies(X,Y),Y)) = truth,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_2,wajsberg_1,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(126,plain,
implies(falsehood,X) = implies(not(X),truth),
inference('PARAMODULATE',[status(thm)],[17,false_definition,theory(equality)]) ).
cnf(135,plain,
implies(not(X),not(X)) = implies(implies(falsehood,X),truth),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[100,17,theory(equality)]),false_definition,theory(equality)]) ).
cnf(141,plain,
implies(implies(not(falsehood),X),X) = truth,
inference('PARAMODULATE',[status(thm)],[102,17,theory(equality)]) ).
cnf(161,plain,
truth = implies(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_1,112,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(162,plain,
truth = implies(implies(falsehood,X),truth),
inference('REWRITE',[status(thm)],[135,161,theory(equality)]) ).
cnf(168,plain,
implies(falsehood,X) = truth,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[112,126,theory(equality)]),126,162,theory(equality)]) ).
cnf(201,plain,
not(falsehood) = truth,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[141,161,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(202,plain,
and(truth,X) = not(not(X)),
inference('REWRITE',[status(thm)],[106,wajsberg_1,201,theory(equality)]) ).
cnf(203,plain,
and(truth,and(X,Y)) = and(not(not(X)),Y),
inference('EMBED',[status(thm)],[202]) ).
cnf(204,plain,
implies(not(not(not(and(not(not(y)),x)))),and(not(x),implies(not(not(not(not(y)))),and(falsehood,y)))) != implies(not(not(not(and(y,not(not(x)))))),and(implies(not(not(not(not(x)))),and(x,falsehood)),not(y))),
inference('REWRITE',[status(thm)],[18,168,false_definition,201,108,17,202,theory(equality)]) ).
cnf(205,plain,
X = implies(not(X),falsehood),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,201,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(206,plain,
and(falsehood,X) = falsehood,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,201,theory(equality)]),168,false_definition,theory(equality)]) ).
cnf(208,plain,
implies(not(not(not(and(not(not(y)),x)))),and(not(x),not(not(not(y))))) != implies(not(not(not(and(y,not(not(x)))))),and(not(not(not(x))),not(y))),
inference('REWRITE',[status(thm)],[204,205,206,theory(equality)]) ).
cnf(212,plain,
and(not(not(X)),Y) = not(not(and(X,Y))),
inference('PARAMODULATE',[status(thm)],[202,203,theory(equality)]) ).
cnf(214,plain,
$false,
inference('REWRITE',[status(thm)],[208,212,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 10:12:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.46 #<PACKAGE "SNARK-USER">
% 0.20/0.46 *
% 0.20/0.46 SNARK-TPTP-OPTIONS
% 0.20/0.46 *
% 0.20/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.46 (USE-FACTORING :POS)
% 0.20/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.46 *
% 0.20/0.46 "."
% 0.20/0.46 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-02T10:12:50
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-07-02T10:12:50
% 0.20/0.48
% 0.20/0.48 ; Recognized left identity assertion (= (|implies| |truth| ?X) ?X).
% 0.20/0.48 ; Recognized associativity assertion (= (|or| (|or| ?X ?Y) ?Z) (|or| ?X (|or| ?Y ?Z))).
% 0.20/0.48 ; Recognized commutativity assertion (= (|or| ?X ?Y) (|or| ?Y ?X)).
% 0.20/0.48 ; Recognized associativity assertion (= (|and| (|and| ?X ?Y) ?Z) (|and| ?X (|and| ?Y ?Z))).
% 0.20/0.48 ; Recognized commutativity assertion (= (|and| ?X ?Y) (|and| ?Y ?X)).
% 0.20/0.48 ; Recognized commutativity assertion (= (|xor| ?X ?Y) (|xor| ?Y ?X)).
% 0.20/0.48 ; Recognized associativity assertion (= (|and_star| (|and_star| ?X ?Y) ?Z) (|and_star| ?X (|and_star| ?Y ?Z))).
% 0.20/0.48 ; Recognized commutativity assertion (= (|and_star| ?X ?Y) (|and_star| ?Y ?X)).
% 0.20/0.48 ; Declaring or to be commutative.
% 0.20/0.48 ; Declaring or to be associative-commutative.
% 0.20/0.48 ; Declaring and to be commutative.
% 0.20/0.48 ; Declaring and to be associative-commutative.
% 0.20/0.48 ; Declaring xor to be commutative.
% 0.20/0.48 ; Declaring and_star to be commutative.
% 0.55/0.75 ; Declaring and_star to be associative-commutative.
% 0.55/0.75
% 0.55/0.75 #||
% 0.55/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.75 % SZS output start Refutation
% See solution above
% 0.55/0.75 ||#
% 0.55/0.75
% 0.55/0.75 ; Summary of computation:
% 0.55/0.75 ; 703 formulas have been input or derived (from 34 formulas).
% 0.55/0.75 ; 214 (30%) were retained. Of these,
% 0.55/0.75 ; 71 (33%) were simplified or subsumed later,
% 0.55/0.75 ; 143 (67%) are still being kept.
% 0.55/0.75 ;
% 0.55/0.75 ; Run time in seconds excluding printing time:
% 0.55/0.75 ; 0.004 1% Read assertion file (1 call)
% 0.55/0.75 ; 0.001 0% Assert (17 calls)
% 0.55/0.75 ; 0.037 13% Process new row (642 calls)
% 0.55/0.75 ; 0.000 0% Resolution (66 calls)
% 0.55/0.75 ; 0.010 4% Paramodulation (33 calls)
% 0.55/0.75 ; 0.000 0% Embedding (15 calls)
% 0.55/0.75 ; 0.069 24% Forward simplification (615 calls)
% 0.55/0.75 ; 0.010 4% Backward simplification (199 calls)
% 0.55/0.75 ; 0.121 43% Ordering (14,294 calls)
% 0.55/0.75 ; 0.004 1% Ordering ac (328 calls)
% 0.55/0.75 ; 0.002 1% Sortal reasoning (32 calls)
% 0.55/0.75 ; 0.000 0% Purity testing (1 call)
% 0.55/0.75 ; 0.024 9% Other
% 0.55/0.75 ; 0.282 Total
% 0.55/0.75 ; 0.285 Real time
% 0.55/0.75 ;
% 0.55/0.75 ; Term-hash-array has 839 terms in all.
% 0.55/0.75 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.55/0.75 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.55/0.75 ; Path-index has 607 entries (691 at peak, 890 added, 283 deleted).
% 0.55/0.75 ; Path-index has 718 nodes (819 at peak, 1,098 added, 380 deleted).
% 0.55/0.75 ; Trie-index has 607 entries (691 at peak, 890 added, 283 deleted).
% 0.55/0.75 ; Trie-index has 1,460 nodes (1,842 at peak, 2,109 added, 649 deleted).
% 0.55/0.75 ; Retrieved 10,502 generalization terms in 5,993 calls.
% 0.55/0.75 ; Retrieved 1,824 instance terms in 341 calls.
% 0.55/0.75 ; Retrieved 2,417 unifiable terms in 243 calls.
% 0.55/0.75 ;
% 0.55/0.75 ; The agenda of rows to process has 21 entries:
% 0.55/0.75 ; 1 with value 17 5 with value 22 3 with value 25
% 0.55/0.75 ; 3 with value 18 2 with value 23 2 with value 27
% 0.55/0.75 ; 1 with value 19 1 with value 24 2 with value 29
% 0.55/0.75 ; 1 with value 20
% 0.55/0.75 ; The agenda of rows to give has 120 entries:
% 0.55/0.75 ; 2 with value (4 11) 11 with value (4 21) 11 with value (4 36)
% 0.55/0.75 ; 1 with value (4 13) 4 with value (4 22) 6 with value (4 37)
% 0.55/0.75 ; 2 with value (4 14) 7 with value (4 23) 6 with value (4 42)
% 0.55/0.75 ; 1 with value (4 15) 2 with value (4 24) 7 with value (4 43)
% 0.55/0.75 ; 2 with value (4 16) 1 with value (4 27) 3 with value (4 44)
% 0.55/0.75 ; 5 with value (4 17) 10 with value (4 28) 2 with value (4 49)
% 0.55/0.75 ; 2 with value (4 18) 15 with value (4 29) 3 with value (4 50)
% 0.55/0.75 ; 5 with value (4 20) 11 with value (4 35) 1 with value (4 56)
% 0.55/0.75 Evaluation took:
% 0.55/0.75 0.286 seconds of real time
% 0.55/0.75 0.25348 seconds of user run time
% 0.55/0.75 0.032109 seconds of system run time
% 0.55/0.75 [Run times include 0.006 seconds GC run time.]
% 0.55/0.75 0 calls to %EVAL
% 0.55/0.75 0 page faults and
% 0.55/0.75 17,863,184 bytes consed.
% 0.55/0.75 :PROOF-FOUND
% 0.55/0.75 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-02T10:12:50
% 0.55/0.75 :PROOF-FOUND
% 0.55/0.75 *
%------------------------------------------------------------------------------