%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV008-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 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 : 300s
% DateTime : Wed Apr 9 09:29:19 PM UTC 2025
% Result : Unsatisfiable 3.90s 2.50s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 11 ( 11 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_than > #nlpp > successor > predecessor > a > one > n > l
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(l,type,
l: $i ).
tff(predecessor,type,
predecessor: $i > $i ).
tff(less_than,type,
less_than: ( $i * $i ) > $o ).
tff(a,type,
a: $i > $i ).
tff(one,type,
one: $i ).
tff(n,type,
n: $i ).
tff(successor,type,
successor: $i > $i ).
tff(f_82,axiom,
! [X] : ~ less_than(X,X),
file(unknown,unknown) ).
tff(f_110,axiom,
less_than(a(l),a(predecessor(l))),
file(unknown,unknown) ).
tff(f_109,axiom,
less_than(one,l),
file(unknown,unknown) ).
tff(f_79,axiom,
! [X,Y] :
( less_than(X,Y)
| less_than(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_108,axiom,
~ less_than(n,l),
file(unknown,unknown) ).
tff(f_129,axiom,
! [X] :
( ~ less_than(one,X)
| ~ less_than(X,n)
| ~ less_than(a(X),a(predecessor(X))) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [X] :
( less_than(X,n)
| less_than(n,X)
| ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n))) ),
file(unknown,unknown) ).
tff(c_18,plain,
! [X_14] : ~ less_than(X_14,X_14),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_30,plain,
less_than(a(l),a(predecessor(l))),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_28,plain,
less_than(one,l),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_135,plain,
! [Y_38,X_39] :
( ( Y_38 = X_39 )
| less_than(Y_38,X_39)
| less_than(X_39,Y_38) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_26,plain,
~ less_than(n,l),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_167,plain,
( ( n = l )
| less_than(l,n) ),
inference(resolution,[status(thm)],[c_135,c_26]) ).
tff(c_172,plain,
less_than(l,n),
inference(splitLeft,[status(thm)],[c_167]) ).
tff(c_244,plain,
! [X_46] :
( ~ less_than(a(X_46),a(predecessor(X_46)))
| ~ less_than(X_46,n)
| ~ less_than(one,X_46) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_249,plain,
( ~ less_than(l,n)
| ~ less_than(one,l) ),
inference(resolution,[status(thm)],[c_30,c_244]) ).
tff(c_256,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_172,c_249]) ).
tff(c_257,plain,
n = l,
inference(splitRight,[status(thm)],[c_167]) ).
tff(c_32,plain,
! [X_23] :
( ~ less_than(a(X_23),a(predecessor(n)))
| ~ less_than(one,n)
| less_than(n,X_23)
| less_than(X_23,n) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_349,plain,
! [X_56] :
( ~ less_than(a(X_56),a(predecessor(l)))
| less_than(l,X_56)
| less_than(X_56,l) ),
inference(demodulation,[status(thm),theory(equality)],[c_257,c_257,c_28,c_257,c_257,c_32]) ).
tff(c_358,plain,
less_than(l,l),
inference(resolution,[status(thm)],[c_30,c_349]) ).
tff(c_364,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_18,c_358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV008-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.33 % Computer : n011.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 : 300
% 0.12/0.33 % DateTime : Wed Apr 9 02:35:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.90/2.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.90/2.51
% 3.90/2.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------