%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : SWC473_1 : TPTP v8.3.0. Released v8.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n014.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 : 300s
% DateTime : Tue May 14 09:01:53 EDT 2024
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 'CODE-FOR-$$SUM')
% Comments :
%------------------------------------------------------------------------------
tff(13,axiom,
! [X: $int] :
( ~ $lesseq('mod:(Int*Int)>Int'(X,2),0)
| ( small(X) = $sum(1,$sum($product(X,X),X)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_1) ).
tff(14,plain,
! [X: $int] :
( ~ $lesseq('mod:(Int*Int)>Int'(X,2),0)
| ( small(X) = $sum(1,$sum($product(X,X),X)) ) ),
inference('REWRITE',[status(thm)],[13,'CODE-FOR-$$SUM']) ).
tff(15,axiom,
! [X: $int] :
( $lesseq('mod:(Int*Int)>Int'(X,2),0)
| ( small(X) = $sum(1,$sum($product(0,X),X)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_1) ).
tff(16,plain,
! [X: $int] :
( $lesseq('mod:(Int*Int)>Int'(X,2),0)
| ( small(X) = $sum(1,X) ) ),
inference('REWRITE',[status(thm)],[15,'CODE-FOR-$$SUM','CODE-FOR-$$PRODUCT']) ).
tff(17,axiom,
f0 = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_2) ).
tff(18,axiom,
! [X: $int] : ( g0(X) = 'mod:(Int*Int)>Int'(X,2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_3) ).
tff(19,axiom,
! [X: $int] : ( h0(X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_4) ).
tff(20,axiom,
! [X: $int,Y: $int] :
( ~ $lesseq(X,0)
| ( u0(X,Y) = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_5) ).
tff(21,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,0)
| ( u0(X,Y) = f0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_5) ).
tff(22,plain,
! [X: $int,Y: $int] :
( $lesseq(X,0)
| ( u0(X,Y) = 0 ) ),
inference('REWRITE',[status(thm)],[21,17,theory(equality)]) ).
tff(23,axiom,
! [X: $int] : ( v0(X) = u0(g0(X),h0(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_6) ).
tff(24,plain,
! [X: $int] : ( v0(X) = u0(g0(X),X) ),
inference('REWRITE',[status(thm)],[23,19,theory(equality)]) ).
tff(25,axiom,
! [X: $int] : ( fast(X) = $sum(1,$sum($product(v0(X),X),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_7) ).
tff(26,plain,
! [X: $int] : ( fast(X) = $sum(1,$sum($product(v0(X),X),X)) ),
inference('REWRITE',[status(thm)],[25,'CODE-FOR-$$SUM']) ).
tff(28,negated_conjecture,
small('SKOLEMAAAO1.$int') != fast('SKOLEMAAAO1.$int'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
tff(29,plain,
! [X: $int] :
( ~ $lesseq(g0(X),0)
| ( small(X) = $sum(1,$sum($product(X,X),X)) ) ),
inference('REWRITE',[status(thm)],[14,18,theory(equality)]) ).
tff(30,plain,
! [X: $int] :
( $lesseq(g0(X),0)
| ( small(X) = $sum(1,X) ) ),
inference('REWRITE',[status(thm)],[16,18,theory(equality)]) ).
tff(35,plain,
! [X: $int,Y: $int,Z: $int] :
( ( u0(X,Y) = 0 )
| ( u0(X,Z) = Z ) ),
inference('HYPERRESOLVE',[status(thm)],[20,22]) ).
tff(37,plain,
! [X: $int,Y: $int] :
( ( small(X) = $sum(1,X) )
| ( u0(g0(X),Y) = Y ) ),
inference('HYPERRESOLVE',[status(thm)],[20,30]) ).
tff(39,plain,
! [X: $int] :
( ( small(X) = $sum(1,X) )
| ( small(X) = $sum(1,$sum($product(X,X),X)) ) ),
inference('HYPERRESOLVE',[status(thm)],[29,30]) ).
tff(40,plain,
! [X: $int,Y: $int] :
( ( u0(g0(X),Y) = 0 )
| ( small(X) = $sum(1,$sum($product(X,X),X)) ) ),
inference('HYPERRESOLVE',[status(thm)],[29,22]) ).
tff(42,plain,
! [X: $int,Y: $int] :
( ( u0(g0(X),Y) = Y )
| ( v0(X) = 0 ) ),
inference('PARAMODULATE',[status(thm)],[24,35,theory(equality)]) ).
tff(46,plain,
! [X: $int] :
( ( v0(X) = 0 )
| ( v0(X) = X ) ),
inference('PARAMODULATE',[status(thm)],[24,42,theory(equality)]) ).
tff(48,plain,
! [X: $int] :
( ( v0(X) = X )
| ( fast(X) = $sum(1,X) ) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[26,46,theory(equality)]),'CODE-FOR-$$SUM','CODE-FOR-$$PRODUCT']) ).
tff(51,plain,
! [X: $int] :
( ( small(X) = $sum(1,X) )
| ( v0(X) = X ) ),
inference('PARAMODULATE',[status(thm)],[24,37,theory(equality)]) ).
tff(52,plain,
! [X: $int] :
( ( small(X) = $sum(1,X) )
| ( fast(X) = $sum(1,$sum($product(X,X),X)) ) ),
inference('PARAMODULATE',[status(thm)],[26,51,theory(equality)]) ).
tff(54,plain,
! [X: $int] :
( ( fast(X) = $sum(1,X) )
| ( fast(X) = $sum(1,$sum($product(X,X),X)) ) ),
inference('PARAMODULATE',[status(thm)],[26,48,theory(equality)]) ).
tff(55,plain,
( ( small('SKOLEMAAAO1.$int') = $sum(1,'SKOLEMAAAO1.$int') )
| ( $sum(1,$sum($product('SKOLEMAAAO1.$int','SKOLEMAAAO1.$int'),'SKOLEMAAAO1.$int')) != fast('SKOLEMAAAO1.$int') ) ),
inference('PARAMODULATE',[status(thm)],[28,39,theory(equality)]) ).
tff(56,plain,
! [X: $int] :
( ( small(X) = $sum(1,$sum($product(X,X),X)) )
| ( v0(X) = 0 ) ),
inference('PARAMODULATE',[status(thm)],[24,40,theory(equality)]) ).
tff(57,plain,
! [X: $int] :
( ( small(X) = $sum(1,$sum($product(X,X),X)) )
| ( fast(X) = $sum(1,X) ) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[26,56,theory(equality)]),'CODE-FOR-$$SUM','CODE-FOR-$$PRODUCT']) ).
tff(59,plain,
( ( $sum(1,$sum($product('SKOLEMAAAO1.$int','SKOLEMAAAO1.$int'),'SKOLEMAAAO1.$int')) = fast('SKOLEMAAAO1.$int') )
| ( $sum(1,'SKOLEMAAAO1.$int') != fast('SKOLEMAAAO1.$int') ) ),
inference('PARAMODULATE',[status(thm)],[28,52,theory(equality)]) ).
tff(61,plain,
( ( $sum(1,'SKOLEMAAAO1.$int') = fast('SKOLEMAAAO1.$int') )
| ( $sum(1,$sum($product('SKOLEMAAAO1.$int','SKOLEMAAAO1.$int'),'SKOLEMAAAO1.$int')) != fast('SKOLEMAAAO1.$int') ) ),
inference('PARAMODULATE',[status(thm)],[28,57,theory(equality)]) ).
tff(65,plain,
$sum(1,'SKOLEMAAAO1.$int') = fast('SKOLEMAAAO1.$int'),
inference('HYPERRESOLVE',[status(thm)],[61,54]) ).
tff(66,plain,
small('SKOLEMAAAO1.$int') != $sum(1,'SKOLEMAAAO1.$int'),
inference('REWRITE',[status(thm)],[28,65,theory(equality)]) ).
tff(67,plain,
$sum(1,$sum($product('SKOLEMAAAO1.$int','SKOLEMAAAO1.$int'),'SKOLEMAAAO1.$int')) != $sum(1,'SKOLEMAAAO1.$int'),
inference('REWRITE',[status(thm)],[55,66,65,theory(equality)]) ).
cnf(69,plain,
$false,
inference('REWRITE',[status(thm)],[59,67,65,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC473_1 : TPTP v8.3.0. Released v8.3.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n014.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 : 300
% 0.13/0.34 % DateTime : Mon May 13 14:57:38 EDT 2024
% 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 2024-05-13T14:57:38
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2024-05-13T14:57:38
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 #||
% 0.19/0.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 ||#
% 0.19/0.50
% 0.19/0.50 ; Summary of computation:
% 0.19/0.50 ; 187 formulas have been input or derived (from 53 formulas).
% 0.19/0.50 ; 69 (37%) were retained. Of these,
% 0.19/0.50 ; 13 (19%) were simplified or subsumed later,
% 0.19/0.50 ; 56 (81%) are still being kept.
% 0.19/0.50 ;
% 0.19/0.50 ; Run time in seconds excluding printing time:
% 0.19/0.50 ; 0.002 6% Read assertion file (1 call)
% 0.19/0.50 ; 0.001 3% Assert (8 calls)
% 0.19/0.50 ; 0.002 6% Process new row (168 calls)
% 0.19/0.50 ; 0.002 6% Resolution (104 calls)
% 0.19/0.50 ; 0.004 11% Paramodulation (52 calls)
% 0.19/0.50 ; 0.000 0% Factoring (27 calls)
% 0.19/0.50 ; 0.003 8% Condensing (69 calls)
% 0.19/0.50 ; 0.002 6% Forward subsumption (69 calls)
% 0.19/0.50 ; 0.000 0% Backward subsumption (44 calls)
% 0.19/0.50 ; 0.001 3% Clause clause subsumption (35 calls)
% 0.19/0.50 ; 0.004 11% Forward simplification (168 calls)
% 0.19/0.50 ; 0.000 0% Backward simplification (64 calls)
% 0.19/0.50 ; 0.000 0% Ordering (493 calls)
% 0.19/0.50 ; 0.000 0% Ordering ac (48 calls)
% 0.19/0.50 ; 0.002 6% Sortal reasoning (563 calls)
% 0.19/0.50 ; 0.000 0% Purity testing (1 call)
% 0.19/0.50 ; 0.013 36% Other
% 0.19/0.50 ; 0.036 Total
% 0.19/0.50 ; 0.041 Real time
% 0.19/0.50 ;
% 0.19/0.50 ; Term-hash-array has 72 terms in all.
% 0.19/0.50 ; Feature-vector-row-index has 37 entries (41 at peak, 44 added, 7 deleted).
% 0.19/0.50 ; Feature-vector-row-index has 172 nodes (235 at peak, 267 added, 95 deleted).
% 0.19/0.50 ; Retrieved 46 possibly forward subsuming rows in 69 calls.
% 0.19/0.50 ; Retrieved 2 possibly backward subsumed rows in 44 calls.
% 0.19/0.50 ; Path-index has 73 entries (75 at peak, 92 added, 19 deleted).
% 0.19/0.50 ; Path-index has 130 nodes (130 at peak, 152 added, 22 deleted).
% 0.19/0.50 ; Trie-index has 73 entries (75 at peak, 92 added, 19 deleted).
% 0.19/0.50 ; Trie-index has 118 nodes (120 at peak, 143 added, 25 deleted).
% 0.19/0.50 ; Retrieved 160 generalization terms in 487 calls.
% 0.19/0.50 ; Retrieved 19 instance terms in 19 calls.
% 0.19/0.50 ; Retrieved 248 unifiable terms in 199 calls.
% 0.19/0.50 ;
% 0.19/0.50 ; The agenda of backward simplifiable rows to process has 2 entries:
% 0.19/0.50 ; 2 with value 0
% 0.19/0.50 ; The agenda of rows to process has 8 entries:
% 0.19/0.50 ; 1 with value 22 1 with value 27 1 with value 40
% 0.19/0.50 ; 1 with value 26 1 with value 38 3 with value 46
% 0.19/0.50 ; The agenda of input rows to give has 1 entry:
% 0.19/0.50 ; 1 with value 8
% 0.19/0.50 ; The agenda of rows to give has 6 entries:
% 0.19/0.50 ; 1 with value (4 14) 1 with value (4 28) 1 with value (4 37)
% 0.19/0.50 ; 2 with value (4 16) 1 with value (4 32)
% 0.19/0.50 Evaluation took:
% 0.19/0.50 0.041 seconds of real time
% 0.19/0.50 0.031477 seconds of user run time
% 0.19/0.50 0.009829 seconds of system run time
% 0.19/0.50 0 calls to %EVAL
% 0.19/0.50 0 page faults and
% 0.19/0.50 5,663,000 bytes consed.
% 0.19/0.50 :PROOF-FOUND
% 0.19/0.50 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2024-05-13T14:57:38
% 0.19/0.50 :PROOF-FOUND
% 0.19/0.50 *
%------------------------------------------------------------------------------