%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV002-1 : 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 : n010.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 09:29:18 PM UTC 2025
% Result : Unsatisfiable 4.88s 2.29s
% Output : CNFRefutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 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 : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_than > #nlpp > successor > predecessor > a > q > one > n > k > j > i
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(i,type,
i: $i ).
tff(j,type,
j: $i ).
tff(predecessor,type,
predecessor: $i > $i ).
tff(k,type,
k: $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(q,type,
q: $i ).
tff(successor,type,
successor: $i > $i ).
tff(f_113,axiom,
less_than(a(j),a(k)),
file(unknown,unknown) ).
tff(f_82,axiom,
! [X] : ~ less_than(X,X),
file(unknown,unknown) ).
tff(f_144,axiom,
~ less_than(j,q),
file(unknown,unknown) ).
tff(f_79,axiom,
! [X,Y] :
( less_than(X,Y)
| less_than(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_142,axiom,
~ less_than(q,i),
file(unknown,unknown) ).
tff(f_88,axiom,
! [X,Y] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ),
file(unknown,unknown) ).
tff(f_121,axiom,
! [X] :
( less_than(X,i)
| ~ less_than(X,j)
| ~ less_than(a(X),a(k)) ),
file(unknown,unknown) ).
tff(f_145,axiom,
less_than(a(q),a(j)),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X,Z,Y] :
( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) ),
file(unknown,unknown) ).
tff(c_34,plain,
less_than(a(j),a(k)),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_18,plain,
! [X_14] : ~ less_than(X_14,X_14),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_44,plain,
~ less_than(j,q),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_16,plain,
! [Y_13,X_12] :
( ( Y_13 = X_12 )
| less_than(Y_13,X_12)
| less_than(X_12,Y_13) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_42,plain,
~ less_than(q,i),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_106,plain,
! [Y_35,X_36] :
( ~ less_than(Y_35,X_36)
| ~ less_than(X_36,Y_35) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_119,plain,
~ less_than(a(k),a(j)),
inference(resolution,[status(thm)],[c_34,c_106]) ).
tff(c_268,plain,
! [X_44] :
( ~ less_than(a(X_44),a(k))
| ~ less_than(X_44,j)
| less_than(X_44,i) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_1555,plain,
! [X_88] :
( ~ less_than(X_88,j)
| less_than(X_88,i)
| ( a(k) = a(X_88) )
| less_than(a(k),a(X_88)) ),
inference(resolution,[status(thm)],[c_16,c_268]) ).
tff(c_46,plain,
less_than(a(q),a(j)),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_232,plain,
! [Y_41,Z_42,X_43] :
( ~ less_than(Y_41,Z_42)
| ~ less_than(X_43,Y_41)
| less_than(X_43,Z_42) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_255,plain,
! [X_43] :
( ~ less_than(X_43,a(q))
| less_than(X_43,a(j)) ),
inference(resolution,[status(thm)],[c_46,c_232]) ).
tff(c_1561,plain,
( less_than(a(k),a(j))
| ~ less_than(q,j)
| less_than(q,i)
| ( a(q) = a(k) ) ),
inference(resolution,[status(thm)],[c_1555,c_255]) ).
tff(c_1580,plain,
( ~ less_than(q,j)
| ( a(q) = a(k) ) ),
inference(negUnitSimplification,[status(thm)],[c_42,c_119,c_1561]) ).
tff(c_1595,plain,
~ less_than(q,j),
inference(splitLeft,[status(thm)],[c_1580]) ).
tff(c_1601,plain,
( ( q = j )
| less_than(j,q) ),
inference(resolution,[status(thm)],[c_16,c_1595]) ).
tff(c_1608,plain,
q = j,
inference(negUnitSimplification,[status(thm)],[c_44,c_1601]) ).
tff(c_1627,plain,
less_than(a(j),a(j)),
inference(demodulation,[status(thm),theory(equality)],[c_1608,c_46]) ).
tff(c_1634,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_1627]) ).
tff(c_1635,plain,
a(q) = a(k),
inference(splitRight,[status(thm)],[c_1580]) ).
tff(c_120,plain,
~ less_than(a(j),a(q)),
inference(resolution,[status(thm)],[c_46,c_106]) ).
tff(c_1655,plain,
~ less_than(a(j),a(k)),
inference(demodulation,[status(thm),theory(equality)],[c_1635,c_120]) ).
tff(c_1659,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34,c_1655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % 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
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Apr 9 02:36:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.88/2.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.88/2.29
% 4.88/2.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------