%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT002_1 : TPTP v9.0.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n007.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 : Wed Apr 9 06:07:53 PM UTC 2025
% Result : Theorem 2.89s 1.79s
% Output : CNFRefutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 45 ( 22 ~; 19 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 91 ( 19 atm; 8 fun; 45 num; 19 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 2 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
%$ fib_sorted > mycons > #nlpp > nil
%Foreground sorts:
tff(list,type,
list: $tType ).
%Background operators:
%Foreground operators:
tff(nil,type,
nil: list ).
tff(mycons,type,
mycons: ( $int * list ) > list ).
tff(fib_sorted,type,
fib_sorted: list > $o ).
tff(f_36,axiom,
! [Xa: $int,Ya: $int] :
( $less(Xa,Ya)
=> fib_sorted(mycons(Xa,mycons(Ya,nil))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',double_is_fib_sorted_if_ordered) ).
tff(f_44,axiom,
! [Xa: $int,Ya: $int,Za: $int,R: list] :
( ( $less(Xa,Ya)
& $greatereq(Za,$sum(Xa,Ya))
& fib_sorted(mycons(Ya,mycons(Za,R))) )
=> fib_sorted(mycons(Xa,mycons(Ya,mycons(Za,R)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',recursive_fib_sort) ).
tff(f_46,negated_conjecture,
~ fib_sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',check_list) ).
tff(c_13,plain,
! [X_2a: $int,Y_3a: $int] :
( fib_sorted(mycons(X_2a,mycons(Y_3a,nil)))
| ~ $less(X_2a,Y_3a) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_6,plain,
! [X_4a: $int,Y_5a: $int,Z_6a: $int,R_7: list] :
( fib_sorted(mycons(X_4a,mycons(Y_5a,mycons(Z_6a,R_7))))
| ~ fib_sorted(mycons(Y_5a,mycons(Z_6a,R_7)))
| ~ $less(X_4a,Y_5a)
| ~ $greatereq(Z_6a,$sum(X_4a,Y_5a)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_7,plain,
! [X_4a: $int,Y_5a: $int,Z_6a: $int,R_7: list] :
( fib_sorted(mycons(X_4a,mycons(Y_5a,mycons(Z_6a,R_7))))
| ~ fib_sorted(mycons(Y_5a,mycons(Z_6a,R_7)))
| ~ $less(X_4a,Y_5a)
| $less(Z_6a,$sum(Y_5a,X_4a)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_12,plain,
! [X_4a: $int,Y_5a: $int,Z_6a: $int,R_7: list] :
( fib_sorted(mycons(X_4a,mycons(Y_5a,mycons(Z_6a,R_7))))
| ~ fib_sorted(mycons(Y_5a,mycons(Z_6a,R_7)))
| ~ $less(X_4a,Y_5a)
| $less(Z_6a,$sum(X_4a,Y_5a)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7]) ).
tff(c_17,plain,
! [X_11a: $int,Y_12a: $int,Z_13a: $int,R_14: list] :
( fib_sorted(mycons(X_11a,mycons(Y_12a,mycons(Z_13a,R_14))))
| ~ fib_sorted(mycons(Y_12a,mycons(Z_13a,R_14)))
| ~ $less(X_11a,Y_12a)
| $less(Z_13a,$sum(X_11a,Y_12a)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7]) ).
tff(c_10,plain,
~ fib_sorted(mycons(1,mycons(2,mycons(4,mycons(7,mycons(100,nil)))))),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_21,plain,
( ~ fib_sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil)))))
| ~ $less(1,2)
| $less(4,$sum(1,2)) ),
inference(resolution,[status(thm)],[c_17,c_10]) ).
tff(c_23,plain,
~ fib_sorted(mycons(2,mycons(4,mycons(7,mycons(100,nil))))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_21]) ).
tff(c_27,plain,
( ~ fib_sorted(mycons(4,mycons(7,mycons(100,nil))))
| ~ $less(2,4)
| $less(7,$sum(2,4)) ),
inference(resolution,[status(thm)],[c_12,c_23]) ).
tff(c_29,plain,
~ fib_sorted(mycons(4,mycons(7,mycons(100,nil)))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_27]) ).
tff(c_33,plain,
( ~ fib_sorted(mycons(7,mycons(100,nil)))
| ~ $less(4,7)
| $less(100,$sum(4,7)) ),
inference(resolution,[status(thm)],[c_12,c_29]) ).
tff(c_35,plain,
~ fib_sorted(mycons(7,mycons(100,nil))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_33]) ).
tff(c_39,plain,
~ $less(7,100),
inference(resolution,[status(thm)],[c_13,c_35]) ).
tff(c_42,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : DAT002_1 : TPTP v9.0.0. Released v5.0.0.
% 0.13/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 7 18:14:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 2.89/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.89/1.80
% 2.89/1.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------