TSTP Solution File: LCL146-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Sun Jul 17 14:20:33 EDT 2022
% Result : Unsatisfiable 0.43s 0.61s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of clauses : 45 ( 43 unt; 0 nHn; 9 RR)
% Number of literals : 47 ( 35 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(big_V_definition,axiom,
big_V(X,Y) = implies(implies(X,Y),Y),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).
cnf(big_hat_definition,axiom,
big_hat(X,Y) = not(big_V(not(X),not(Y))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',big_hat_definition) ).
cnf(partial_order_definition1,axiom,
( ~ ordered(X,Y)
| implies(X,Y) = truth ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',partial_order_definition1) ).
cnf(partial_order_definition2,axiom,
( implies(X,Y) != truth
| ordered(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',partial_order_definition2) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
cnf(10,plain,
not(not(big_V(not(x),not(y)))) != big_V(not(x),not(y)),
inference('REWRITE',[status(thm)],[prove_wajsberg_theorem,big_hat_definition,theory(equality)]) ).
cnf(11,plain,
big_V(X,Y) = big_V(Y,X),
inference('REWRITE',[status(thm)],[wajsberg_3,big_V_definition,theory(equality)]) ).
cnf(16,plain,
big_V(implies(X,Y),Y) = implies(big_V(X,Y),Y),
inference('PARAMODULATE',[status(thm)],[big_V_definition,big_V_definition,theory(equality)]) ).
cnf(18,plain,
implies(implies(not(X),not(truth)),X) = truth,
inference('PARAMODULATE',[status(thm)],[wajsberg_4,wajsberg_1,theory(equality)]) ).
cnf(22,plain,
ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),
inference('HYPERRESOLVE',[status(thm)],[partial_order_definition2,wajsberg_2]) ).
cnf(24,plain,
implies(X,big_V(X,Y)) = truth,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_2,wajsberg_1,theory(equality)]),big_V_definition,wajsberg_1,theory(equality)]) ).
cnf(25,plain,
implies(implies(X,truth),implies(Y,implies(X,Y))) = truth,
inference('PARAMODULATE',[status(thm)],[wajsberg_2,wajsberg_1,theory(equality)]) ).
cnf(38,plain,
not(not(big_V(not(y),not(x)))) != big_V(not(y),not(x)),
inference('PARAMODULATE',[status(thm)],[10,11,theory(equality)]) ).
cnf(45,plain,
ordered(X,big_V(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[partial_order_definition2,24]) ).
cnf(46,plain,
big_V(truth,X) = truth,
inference('PARAMODULATE',[status(thm)],[wajsberg_1,24,theory(equality)]) ).
cnf(52,plain,
big_V(X,big_V(X,Y)) = big_V(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,24,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(58,plain,
ordered(X,big_V(Y,X)),
inference('PARAMODULATE',[status(thm)],[45,11,theory(equality)]) ).
cnf(60,plain,
ordered(X,truth),
inference('PARAMODULATE',[status(thm)],[58,46,theory(equality)]) ).
cnf(61,plain,
implies(X,truth) = truth,
inference('HYPERRESOLVE',[status(thm)],[partial_order_definition1,60]) ).
cnf(62,plain,
implies(X,implies(Y,X)) = truth,
inference('REWRITE',[status(thm)],[25,wajsberg_1,61,theory(equality)]) ).
cnf(64,plain,
big_V(X,implies(Y,X)) = implies(Y,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,62,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(72,plain,
big_V(not(not(truth)),not(truth)) = truth,
inference('PARAMODULATE',[status(thm)],[big_V_definition,18,theory(equality)]) ).
cnf(73,plain,
big_V(implies(not(X),not(truth)),X) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,18,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(76,plain,
big_V(X,Y) = big_V(big_V(X,Y),X),
inference('PARAMODULATE',[status(thm)],[11,52,theory(equality)]) ).
cnf(77,plain,
implies(X,Y) = big_V(implies(X,Y),Y),
inference('PARAMODULATE',[status(thm)],[11,64,theory(equality)]) ).
cnf(78,plain,
implies(X,Y) = implies(big_V(X,Y),Y),
inference('REWRITE',[status(thm)],[16,77,theory(equality)]) ).
cnf(79,plain,
implies(X,Y) = implies(big_V(Y,X),Y),
inference('PARAMODULATE',[status(thm)],[78,11,theory(equality)]) ).
cnf(91,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[79,72,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(97,plain,
ordered(implies(X,Y),implies(X,big_V(Y,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,24,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(106,plain,
ordered(implies(X,implies(not(Y),not(truth))),implies(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,18,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(114,plain,
ordered(truth,implies(X,big_V(implies(Y,X),Z))),
inference('PARAMODULATE',[status(thm)],[97,62,theory(equality)]) ).
cnf(162,plain,
ordered(truth,implies(not(truth),X)),
inference('PARAMODULATE',[status(thm)],[114,73,theory(equality)]) ).
cnf(164,plain,
implies(not(truth),X) = truth,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[partial_order_definition1,162]),wajsberg_1,theory(equality)]) ).
cnf(166,plain,
truth = not(not(truth)),
inference('REWRITE',[status(thm)],[91,164,theory(equality)]) ).
cnf(309,plain,
ordered(truth,implies(not(not(X)),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[106,wajsberg_4,theory(equality)]),wajsberg_1,166,theory(equality)]) ).
cnf(319,plain,
implies(not(not(X)),X) = truth,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[partial_order_definition1,309]),wajsberg_1,theory(equality)]) ).
cnf(327,plain,
big_V(not(not(X)),X) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,319,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(328,plain,
implies(X,not(not(X))) = truth,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_4,319,theory(equality)]),wajsberg_1,theory(equality)]) ).
cnf(339,plain,
X = big_V(X,not(not(X))),
inference('PARAMODULATE',[status(thm)],[76,327,theory(equality)]) ).
cnf(350,plain,
X = not(not(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,328,theory(equality)]),wajsberg_1,339,theory(equality)]) ).
cnf(351,plain,
$false,
inference('REWRITE',[status(thm)],[38,350,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 18:46:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.47 (USE-FACTORING :POS)
% 0.18/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.47 *
% 0.18/0.47 "."
% 0.18/0.47 *
% 0.18/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-03T18:46:36
% 0.18/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-07-03T18:46:36
% 0.18/0.48
% 0.43/0.61 ; Recognized left identity assertion (= (|implies| |truth| ?X) ?X).
% 0.43/0.61
% 0.43/0.61 #||
% 0.43/0.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.43/0.61 % SZS output start Refutation
% See solution above
% 0.43/0.61 ||#
% 0.43/0.61
% 0.43/0.61 ; Summary of computation:
% 0.43/0.61 ; 2261 formulas have been input or derived (from 92 formulas).
% 0.43/0.61 ; 351 (16%) were retained. Of these,
% 0.43/0.61 ; 117 (33%) were simplified or subsumed later,
% 0.43/0.61 ; 234 (67%) are still being kept.
% 0.43/0.61 ;
% 0.43/0.61 ; Run time in seconds excluding printing time:
% 0.43/0.61 ; 0.003 2% Read assertion file (1 call)
% 0.43/0.61 ; 0.000 0% Assert (9 calls)
% 0.43/0.61 ; 0.033 23% Process new row (1,945 calls)
% 0.43/0.61 ; 0.007 5% Resolution (182 calls)
% 0.43/0.61 ; 0.032 22% Paramodulation (91 calls)
% 0.43/0.61 ; 0.000 0% Condensing (44 calls)
% 0.43/0.61 ; 0.000 0% Forward subsumption (44 calls)
% 0.43/0.61 ; 0.000 0% Backward subsumption (12 calls)
% 0.43/0.61 ; 0.000 0% Clause clause subsumption (48 calls)
% 0.43/0.61 ; 0.026 18% Forward simplification (1,936 calls)
% 0.43/0.61 ; 0.007 5% Backward simplification (350 calls)
% 0.43/0.61 ; 0.005 3% Ordering (2,116 calls)
% 0.43/0.61 ; 0.000 0% Sortal reasoning (32 calls)
% 0.43/0.61 ; 0.000 0% Purity testing (1 call)
% 0.43/0.61 ; 0.031 22% Other
% 0.43/0.61 ; 0.144 Total
% 0.43/0.61 ; 0.148 Real time
% 0.43/0.61 ;
% 0.43/0.61 ; Term-hash-array has 740 terms in all.
% 0.43/0.61 ; Feature-vector-row-index has 9 entries (10 at peak, 12 added, 3 deleted).
% 0.43/0.61 ; Feature-vector-row-index has 32 nodes (39 at peak, 53 added, 21 deleted).
% 0.43/0.61 ; Retrieved 58 possibly forward subsuming rows in 44 calls.
% 0.43/0.61 ; Retrieved 2 possibly backward subsumed rows in 12 calls.
% 0.43/0.61 ; Path-index has 540 entries (602 at peak, 761 added, 221 deleted).
% 0.43/0.61 ; Path-index has 1,333 nodes (1,397 at peak, 1,615 added, 282 deleted).
% 0.43/0.61 ; Trie-index has 540 entries (602 at peak, 761 added, 221 deleted).
% 0.43/0.61 ; Trie-index has 1,857 nodes (2,043 at peak, 2,762 added, 905 deleted).
% 0.43/0.61 ; Retrieved 8,407 generalization terms in 6,409 calls.
% 0.43/0.61 ; Retrieved 751 instance terms in 338 calls.
% 0.43/0.61 ; Retrieved 3,434 unifiable terms in 669 calls.
% 0.43/0.61 ;
% 0.43/0.61 ; The agenda of backward simplifiable rows to process has 24 entries:
% 0.43/0.61 ; 24 with value 0
% 0.43/0.61 ; The agenda of rows to process has 20 entries:
% 0.43/0.61 ; 7 with value 22 1 with value 24 4 with value 25
% 0.43/0.61 ; 8 with value 23
% 0.43/0.61 ; The agenda of rows to give has 164 entries:
% 0.43/0.61 ; 1 with value (4 14) 46 with value (4 20) 3 with value (4 24)
% 0.43/0.61 ; 17 with value (4 17) 30 with value (4 21) 3 with value (4 25)
% 0.43/0.61 ; 17 with value (4 18) 10 with value (4 22) 2 with value (4 27)
% 0.43/0.61 ; 14 with value (4 19) 21 with value (4 23)
% 0.43/0.61 Evaluation took:
% 0.43/0.61 0.149 seconds of real time
% 0.43/0.61 0.123984 seconds of user run time
% 0.43/0.61 0.024493 seconds of system run time
% 0.43/0.61 0 calls to %EVAL
% 0.43/0.61 0 page faults and
% 0.43/0.61 10,876,216 bytes consed.
% 0.43/0.61 :PROOF-FOUND
% 0.43/0.61 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-03T18:46:36
% 0.43/0.61 :PROOF-FOUND
% 0.43/0.61 *
%------------------------------------------------------------------------------