TSTP Solution File: KLE091+1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : KLE091+1 : TPTP v8.1.0. Released v4.0.0.
% 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 02:26:36 EDT 2022
% Result : Theorem 2.78s 2.95s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of clauses : 59 ( 57 unt; 0 nHn; 9 RR)
% Number of literals : 61 ( 55 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
addition(X,zero) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
cnf(2,axiom,
addition(X,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
cnf(3,plain,
addition(X,addition(X,Y)) = addition(X,Y),
inference('EMBED',[status(thm)],[2]) ).
cnf(4,axiom,
multiplication(X,multiplication(Y,Z)) = multiplication(multiplication(X,Y),Z),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
cnf(5,axiom,
multiplication(X,one) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
cnf(6,axiom,
multiplication(one,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
cnf(7,axiom,
multiplication(X,addition(Y,Z)) = addition(multiplication(X,Y),multiplication(X,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
cnf(8,axiom,
multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
cnf(9,axiom,
multiplication(X,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
cnf(11,axiom,
( ~ leq(X,Y)
| addition(X,Y) = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
cnf(12,axiom,
( leq(X,Y)
| addition(X,Y) != Y ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
cnf(13,axiom,
multiplication(antidomain(X),X) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
cnf(14,axiom,
addition(antidomain(multiplication(X,Y)),antidomain(multiplication(X,antidomain(antidomain(Y))))) = antidomain(multiplication(X,antidomain(antidomain(Y)))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
cnf(16,axiom,
addition(antidomain(antidomain(X)),antidomain(X)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
cnf(17,plain,
addition(antidomain(antidomain(X)),addition(antidomain(X),Y)) = addition(one,Y),
inference('EMBED',[status(thm)],[16]) ).
cnf(18,axiom,
domain(X) = antidomain(antidomain(X)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
cnf(19,axiom,
multiplication(X,coantidomain(X)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
cnf(20,axiom,
addition(coantidomain(multiplication(X,Y)),coantidomain(multiplication(coantidomain(coantidomain(X)),Y))) = coantidomain(multiplication(coantidomain(coantidomain(X)),Y)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
cnf(22,axiom,
addition(coantidomain(coantidomain(X)),coantidomain(X)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
cnf(23,plain,
addition(coantidomain(coantidomain(X)),addition(coantidomain(X),Y)) = addition(one,Y),
inference('EMBED',[status(thm)],[22]) ).
cnf(24,axiom,
codomain(X) = coantidomain(coantidomain(X)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
cnf(25,negated_conjecture,
domain(codomain('SKOLEMAAAV1')) != codomain('SKOLEMAAAV1'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(26,plain,
antidomain(antidomain(coantidomain(coantidomain('SKOLEMAAAV1')))) != coantidomain(coantidomain('SKOLEMAAAV1')),
inference('REWRITE',[status(thm)],[25,18,24,theory(equality)]) ).
cnf(27,plain,
zero = antidomain(one),
inference('PARAMODULATE',[status(thm)],[5,13,theory(equality)]) ).
cnf(28,plain,
zero = coantidomain(one),
inference('PARAMODULATE',[status(thm)],[6,19,theory(equality)]) ).
cnf(37,plain,
addition(one,antidomain(X)) = one,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,17,theory(equality)]),16,theory(equality)]) ).
cnf(47,plain,
addition(one,coantidomain(X)) = one,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,23,theory(equality)]),22,theory(equality)]) ).
cnf(57,plain,
zero = multiplication(multiplication(X,antidomain(Y)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,13,theory(equality)]),9,theory(equality)]) ).
cnf(64,plain,
X = addition(multiplication(X,antidomain(antidomain(Y))),multiplication(X,antidomain(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,16,theory(equality)]),5,theory(equality)]) ).
cnf(66,plain,
X = addition(multiplication(X,coantidomain(coantidomain(Y))),multiplication(X,coantidomain(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,22,theory(equality)]),5,theory(equality)]) ).
cnf(74,plain,
X = addition(multiplication(antidomain(antidomain(Y)),X),multiplication(antidomain(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,16,theory(equality)]),6,theory(equality)]) ).
cnf(76,plain,
X = addition(multiplication(coantidomain(coantidomain(Y)),X),multiplication(coantidomain(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,22,theory(equality)]),6,theory(equality)]) ).
cnf(93,plain,
addition(antidomain(zero),antidomain(multiplication(X,antidomain(antidomain(coantidomain(X)))))) = antidomain(multiplication(X,antidomain(antidomain(coantidomain(X))))),
inference('PARAMODULATE',[status(thm)],[14,19,theory(equality)]) ).
cnf(129,plain,
addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(X)),coantidomain(X)))) = coantidomain(multiplication(coantidomain(coantidomain(X)),coantidomain(X))),
inference('PARAMODULATE',[status(thm)],[20,19,theory(equality)]) ).
cnf(158,plain,
antidomain(zero) = one,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,27,theory(equality)]),1,theory(equality)]) ).
cnf(160,plain,
one = antidomain(multiplication(X,antidomain(antidomain(coantidomain(X))))),
inference('REWRITE',[status(thm)],[93,37,158,theory(equality)]) ).
cnf(161,plain,
coantidomain(zero) = one,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,28,theory(equality)]),1,theory(equality)]) ).
cnf(162,plain,
one = coantidomain(multiplication(coantidomain(coantidomain(X)),coantidomain(X))),
inference('REWRITE',[status(thm)],[129,47,161,theory(equality)]) ).
cnf(177,plain,
X = addition(X,multiplication(antidomain(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,37,theory(equality)]),6,theory(equality)]) ).
cnf(187,plain,
X = addition(X,multiplication(coantidomain(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,47,theory(equality)]),6,theory(equality)]) ).
cnf(276,plain,
leq(multiplication(coantidomain(X),Y),Y),
inference('HYPERRESOLVE',[status(thm)],[12,187]) ).
cnf(535,plain,
multiplication(coantidomain(coantidomain(X)),coantidomain(X)) = zero,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[19,162,theory(equality)]),5,4,theory(equality)]) ).
cnf(610,plain,
multiplication(X,antidomain(antidomain(coantidomain(X)))) = zero,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13,160,theory(equality)]),6,theory(equality)]) ).
cnf(1073,plain,
X = multiplication(X,antidomain(coantidomain(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[64,610,theory(equality)]),1,theory(equality)]) ).
cnf(1111,plain,
leq(coantidomain(X),antidomain(coantidomain(coantidomain(X)))),
inference('PARAMODULATE',[status(thm)],[276,1073,theory(equality)]) ).
cnf(1186,plain,
coantidomain(X) = multiplication(coantidomain(X),coantidomain(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[66,19,theory(equality)]),1,theory(equality)]) ).
cnf(1191,plain,
antidomain(coantidomain(X)) = multiplication(antidomain(coantidomain(X)),coantidomain(coantidomain(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[66,13,theory(equality)]),1,theory(equality)]) ).
cnf(1196,plain,
coantidomain(coantidomain(coantidomain(X))) = multiplication(coantidomain(coantidomain(coantidomain(X))),coantidomain(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[66,535,theory(equality)]),1,theory(equality)]) ).
cnf(1217,plain,
multiplication(X,antidomain(coantidomain(coantidomain(Y)))) = multiplication(multiplication(X,antidomain(coantidomain(coantidomain(Y)))),coantidomain(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[66,57,theory(equality)]),1,theory(equality)]) ).
cnf(1270,plain,
coantidomain(coantidomain(X)) = addition(coantidomain(coantidomain(X)),antidomain(coantidomain(X))),
inference('PARAMODULATE',[status(thm)],[177,1191,theory(equality)]) ).
cnf(1322,plain,
X = multiplication(antidomain(antidomain(X)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[74,13,theory(equality)]),1,theory(equality)]) ).
cnf(1370,plain,
multiplication(X,Y) = multiplication(multiplication(X,antidomain(antidomain(Y))),Y),
inference('PARAMODULATE',[status(thm)],[4,1322,theory(equality)]) ).
cnf(1454,plain,
coantidomain(X) = coantidomain(coantidomain(coantidomain(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[76,535,theory(equality)]),1,1196,theory(equality)]) ).
cnf(1476,plain,
antidomain(antidomain(coantidomain(X))) = multiplication(coantidomain(X),antidomain(antidomain(coantidomain(X)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[76,610,theory(equality)]),1,1454,theory(equality)]) ).
cnf(1507,plain,
leq(coantidomain(coantidomain(X)),antidomain(coantidomain(X))),
inference('PARAMODULATE',[status(thm)],[1111,1454,theory(equality)]) ).
cnf(1512,plain,
coantidomain(coantidomain(X)) = antidomain(coantidomain(X)),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[11,1507]),1270,theory(equality)]) ).
cnf(1625,plain,
multiplication(X,antidomain(antidomain(coantidomain(Y)))) = multiplication(X,coantidomain(Y)),
inference('REWRITE',[status(thm)],[1217,1370,1512,theory(equality)]) ).
cnf(1626,plain,
antidomain(antidomain(coantidomain(X))) = coantidomain(X),
inference('REWRITE',[status(thm)],[1476,1186,1625,theory(equality)]) ).
cnf(1703,plain,
$false,
inference('REWRITE',[status(thm)],[26,1626,1512,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE091+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 14:15:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T14:15:21
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-06-16T14:15:21
% 0.19/0.48
% 0.19/0.48 ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.19/0.48 ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.19/0.48 ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.19/0.48 ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.19/0.48 ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.19/0.48 ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.19/0.48 ; Recognized possible left inverse assertion (= (|multiplication| (|antidomain| ?X) ?X) |zero|).
% 0.19/0.48 ; Recognized possible right inverse assertion (= (|multiplication| ?X (|coantidomain| ?X)) |zero|).
% 0.19/0.48 ; Declaring addition to be commutative.
% 2.78/2.95 ; Declaring addition to be associative-commutative.
% 2.78/2.95
% 2.78/2.95 #||
% 2.78/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.78/2.95 % SZS output start Refutation
% See solution above
% 2.78/2.96 ||#
% 2.78/2.96
% 2.78/2.96 ; Summary of computation:
% 2.78/2.96 ; 10431 formulas have been input or derived (from 170 formulas).
% 2.78/2.96 ; 1703 (16%) were retained. Of these,
% 2.78/2.96 ; 504 (30%) were simplified or subsumed later,
% 2.78/2.96 ; 1199 (70%) are still being kept.
% 2.78/2.96 ;
% 2.78/2.96 ; Run time in seconds excluding printing time:
% 2.78/2.96 ; 0.005 0% Read assertion file (1 call)
% 2.78/2.96 ; 0.002 0% Assert (21 calls)
% 2.78/2.96 ; 0.187 8% Process new row (10,027 calls)
% 2.78/2.96 ; 0.018 1% Resolution (338 calls)
% 2.78/2.96 ; 0.148 6% Paramodulation (169 calls)
% 2.78/2.96 ; 0.000 0% Embedding (216 calls)
% 2.78/2.96 ; 0.017 1% Condensing (511 calls)
% 2.78/2.96 ; 0.016 1% Forward subsumption (511 calls)
% 2.78/2.96 ; 0.011 0% Backward subsumption (169 calls)
% 2.78/2.96 ; 0.010 0% Clause clause subsumption (1,585 calls)
% 2.78/2.96 ; 1.913 77% Forward simplification (9,785 calls)
% 2.78/2.96 ; 0.077 3% Backward simplification (1,489 calls)
% 2.78/2.96 ; 0.018 1% Ordering (7,183 calls)
% 2.78/2.96 ; 0.008 0% Ordering ac (1,102 calls)
% 2.78/2.96 ; 0.001 0% Sortal reasoning (32 calls)
% 2.78/2.96 ; 0.000 0% Purity testing (1 call)
% 2.78/2.96 ; 0.057 2% Other
% 2.78/2.96 ; 2.488 Total
% 2.78/2.96 ; 2.499 Real time
% 2.78/2.96 ;
% 2.78/2.96 ; Term-hash-array has 3,847 terms in all.
% 2.78/2.96 ; Feature-vector-row-index has 143 entries (143 at peak, 169 added, 26 deleted).
% 2.78/2.96 ; Feature-vector-row-index has 932 nodes (932 at peak, 1,153 added, 221 deleted).
% 2.78/2.96 ; Retrieved 2,208 possibly forward subsuming rows in 511 calls.
% 2.78/2.96 ; Retrieved 90 possibly backward subsumed rows in 169 calls.
% 2.78/2.96 ; Path-index has 2,706 entries (3,046 at peak, 3,918 added, 1,212 deleted).
% 2.78/2.96 ; Path-index has 1,931 nodes (2,012 at peak, 2,510 added, 579 deleted).
% 2.78/2.96 ; Trie-index has 2,706 entries (3,046 at peak, 3,918 added, 1,212 deleted).
% 2.78/2.96 ; Trie-index has 1,980 nodes (2,919 at peak, 3,893 added, 1,913 deleted).
% 2.78/2.96 ; Retrieved 2,690,121 generalization terms in 68,428 calls.
% 2.78/2.96 ; Retrieved 6,249 instance terms in 1,337 calls.
% 2.78/2.96 ; Retrieved 25,887 unifiable terms in 1,180 calls.
% 2.78/2.96 ;
% 2.78/2.96 ; The agenda of input rows to give has 5 entries:
% 2.78/2.96 ; 1 with value 9 2 with value 12 2 with value 24
% 2.78/2.96 ; The agenda of rows to give has 1064 entries:
% 2.78/2.96 ; 1 with value (4 14) 74 with value (4 26) 3 with value (4 37)
% 2.78/2.96 ; 2 with value (4 16) 34 with value (4 27) 4 with value (4 38)
% 2.78/2.96 ; 1 with value (4 17) 52 with value (4 28) 13 with value (4 39)
% 2.78/2.96 ; 57 with value (4 18) 52 with value (4 29) 4 with value (4 40)
% 2.78/2.96 ; 76 with value (4 19) 47 with value (4 30) 4 with value (4 42)
% 2.78/2.96 ; 68 with value (4 20) 33 with value (4 31) 8 with value (4 43)
% 2.78/2.96 ; 82 with value (4 21) 63 with value (4 32) 2 with value (4 44)
% 2.78/2.96 ; 54 with value (4 22) 14 with value (4 33) 2 with value (4 45)
% 2.78/2.96 ; 86 with value (4 23) 24 with value (4 34) 2 with value (4 47)
% 2.78/2.96 ; 55 with value (4 24) 19 with value (4 35) 2 with value (4 48)
% 2.78/2.96 ; 94 with value (4 25) 32 with value (4 36)
% 2.78/2.96 Evaluation took:
% 2.78/2.96 2.499 seconds of real time
% 2.78/2.96 2.433843 seconds of user run time
% 2.78/2.96 0.065689 seconds of system run time
% 2.78/2.96 [Run times include 0.101 seconds GC run time.]
% 2.78/2.96 0 calls to %EVAL
% 2.78/2.96 0 page faults and
% 2.78/2.96 215,009,656 bytes consed.
% 2.78/2.96 :PROOF-FOUND
% 2.78/2.96 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T14:15:24
% 2.78/2.96 :PROOF-FOUND
% 2.78/2.96 *
%------------------------------------------------------------------------------