%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM022-1 : 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/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 : n015.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 07:55:02 PM UTC 2025
% Result : Unsatisfiable 3.55s 2.34s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 50 ( 25 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less > equalish > divides > predecessor_of_1st_minus_2nd > add > #nlpp > successor > d > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(b,type,
b: $i ).
tff(less,type,
less: ( $i * $i ) > $o ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(predecessor_of_1st_minus_2nd,type,
predecessor_of_1st_minus_2nd: ( $i * $i ) > $i ).
tff(d,type,
d: $i ).
tff(divides,type,
divides: ( $i * $i ) > $o ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(successor,type,
successor: $i > $i ).
tff(f_112,axiom,
less(a,b),
file(unknown,unknown) ).
tff(f_113,axiom,
divides(b,d),
file(unknown,unknown) ).
tff(f_91,axiom,
! [A,B] :
( ~ divides(A,B)
| less(A,B)
| equalish(A,B) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [A,B,C] :
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ),
file(unknown,unknown) ).
tff(f_115,axiom,
~ less(a,d),
file(unknown,unknown) ).
tff(f_62,axiom,
! [A,B] :
( ~ less(A,B)
| equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ),
file(unknown,unknown) ).
tff(f_111,axiom,
! [A,B,C] :
( ~ equalish(A,B)
| ~ equalish(C,A)
| equalish(C,B) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [A,B,C] :
( ~ equalish(add(successor(A),B),C)
| less(B,C) ),
file(unknown,unknown) ).
tff(c_16,plain,
less(a,b),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_18,plain,
divides(b,d),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_8,plain,
! [A_9,B_10] :
( equalish(A_9,B_10)
| less(A_9,B_10)
| ~ divides(A_9,B_10) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_37,plain,
! [C_24,B_25,A_26] :
( less(C_24,B_25)
| ~ less(C_24,A_26)
| ~ less(A_26,B_25) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_44,plain,
! [B_27] :
( less(a,B_27)
| ~ less(b,B_27) ),
inference(resolution,[status(thm)],[c_16,c_37]) ).
tff(c_52,plain,
! [B_34] :
( less(a,B_34)
| equalish(b,B_34)
| ~ divides(b,B_34) ),
inference(resolution,[status(thm)],[c_8,c_44]) ).
tff(c_20,plain,
~ less(a,d),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_60,plain,
( equalish(b,d)
| ~ divides(b,d) ),
inference(resolution,[status(thm)],[c_52,c_20]) ).
tff(c_65,plain,
equalish(b,d),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_60]) ).
tff(c_74,plain,
! [B_35,A_36] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B_35,A_36)),A_36),B_35)
| ~ less(A_36,B_35) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_14,plain,
! [C_17,B_16,A_15] :
( equalish(C_17,B_16)
| ~ equalish(C_17,A_15)
| ~ equalish(A_15,B_16) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_157,plain,
! [B_48,A_49,B_50] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B_48,A_49)),A_49),B_50)
| ~ equalish(B_48,B_50)
| ~ less(A_49,B_48) ),
inference(resolution,[status(thm)],[c_74,c_14]) ).
tff(c_4,plain,
! [B_5,C_6,A_4] :
( less(B_5,C_6)
| ~ equalish(add(successor(A_4),B_5),C_6) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_169,plain,
! [A_51,B_52,B_53] :
( less(A_51,B_52)
| ~ equalish(B_53,B_52)
| ~ less(A_51,B_53) ),
inference(resolution,[status(thm)],[c_157,c_4]) ).
tff(c_185,plain,
! [A_54] :
( less(A_54,d)
| ~ less(A_54,b) ),
inference(resolution,[status(thm)],[c_65,c_169]) ).
tff(c_201,plain,
~ less(a,b),
inference(resolution,[status(thm)],[c_185,c_20]) ).
tff(c_214,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM022-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.09 % 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
% 0.09/0.29 % Computer : n015.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Apr 8 09:58:20 EDT 2025
% 0.09/0.29 % CPUTime :
% 3.55/2.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.55/2.35
% 3.55/2.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------