%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM021-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 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 : n019.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 27.14s 16.52s
% Output : CNFRefutation 27.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 29 ~; 30 |; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less > equalish > divides > predecessor_of_1st_minus_2nd > multiply > add > #nlpp > successor > n0 > c > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(less,type,
less: ( $i * $i ) > $o ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(n0,type,
n0: $i ).
tff(predecessor_of_1st_minus_2nd,type,
predecessor_of_1st_minus_2nd: ( $i * $i ) > $i ).
tff(divides,type,
divides: ( $i * $i ) > $o ).
tff(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(successor,type,
successor: $i > $i ).
tff(c,type,
c: $i ).
tff(f_165,axiom,
~ less(b,a),
file(unknown,unknown) ).
tff(f_163,axiom,
less(b,c),
file(unknown,unknown) ).
tff(f_166,axiom,
divides(c,a),
file(unknown,unknown) ).
tff(f_135,axiom,
! [A,B] :
( ~ divides(A,B)
| less(A,B)
| equalish(A,B) ),
file(unknown,unknown) ).
tff(f_96,axiom,
! [A,B,C] :
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ),
file(unknown,unknown) ).
tff(f_154,axiom,
! [X,Y] :
( ~ equalish(X,Y)
| equalish(Y,X) ),
file(unknown,unknown) ).
tff(f_106,axiom,
! [A,B] :
( ~ less(A,B)
| equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ),
file(unknown,unknown) ).
tff(f_162,axiom,
! [X,Y,Z] :
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) ),
file(unknown,unknown) ).
tff(f_101,axiom,
! [A,B,C] :
( ~ equalish(add(successor(A),B),C)
| less(B,C) ),
file(unknown,unknown) ).
tff(c_34,plain,
~ less(b,a),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_32,plain,
less(b,c),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_36,plain,
divides(c,a),
inference(cnfTransformation,[status(thm)],[f_166]) ).
tff(c_208,plain,
! [A_80,B_81] :
( equalish(A_80,B_81)
| less(A_80,B_81)
| ~ divides(A_80,B_81) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_128,plain,
! [C_59,B_60,A_61] :
( less(C_59,B_60)
| ~ less(C_59,A_61)
| ~ less(A_61,B_60) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_131,plain,
! [B_60] :
( less(b,B_60)
| ~ less(c,B_60) ),
inference(resolution,[status(thm)],[c_32,c_128]) ).
tff(c_694,plain,
! [B_150] :
( less(b,B_150)
| equalish(c,B_150)
| ~ divides(c,B_150) ),
inference(resolution,[status(thm)],[c_208,c_131]) ).
tff(c_702,plain,
( equalish(c,a)
| ~ divides(c,a) ),
inference(resolution,[status(thm)],[c_694,c_34]) ).
tff(c_707,plain,
equalish(c,a),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_702]) ).
tff(c_28,plain,
! [Y_27,X_26] :
( equalish(Y_27,X_26)
| ~ equalish(X_26,Y_27) ),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_718,plain,
equalish(a,c),
inference(resolution,[status(thm)],[c_707,c_28]) ).
tff(c_376,plain,
! [B_100,A_101] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B_100,A_101)),A_101),B_100)
| ~ less(A_101,B_100) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_1006,plain,
! [B_160,A_161] :
( equalish(B_160,add(successor(predecessor_of_1st_minus_2nd(B_160,A_161)),A_161))
| ~ less(A_161,B_160) ),
inference(resolution,[status(thm)],[c_376,c_28]) ).
tff(c_30,plain,
! [X_28,Z_30,Y_29] :
( equalish(X_28,Z_30)
| ~ equalish(Y_29,Z_30)
| ~ equalish(X_28,Y_29) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_6788,plain,
! [X_361,B_362,A_363] :
( equalish(X_361,add(successor(predecessor_of_1st_minus_2nd(B_362,A_363)),A_363))
| ~ equalish(X_361,B_362)
| ~ less(A_363,B_362) ),
inference(resolution,[status(thm)],[c_1006,c_30]) ).
tff(c_64888,plain,
! [B_1311,A_1312,X_1313] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B_1311,A_1312)),A_1312),X_1313)
| ~ equalish(X_1313,B_1311)
| ~ less(A_1312,B_1311) ),
inference(resolution,[status(thm)],[c_6788,c_28]) ).
tff(c_16,plain,
! [B_15,C_16,A_14] :
( less(B_15,C_16)
| ~ equalish(add(successor(A_14),B_15),C_16) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_65352,plain,
! [A_1314,X_1315,B_1316] :
( less(A_1314,X_1315)
| ~ equalish(X_1315,B_1316)
| ~ less(A_1314,B_1316) ),
inference(resolution,[status(thm)],[c_64888,c_16]) ).
tff(c_66184,plain,
! [A_1317] :
( less(A_1317,a)
| ~ less(A_1317,c) ),
inference(resolution,[status(thm)],[c_718,c_65352]) ).
tff(c_66205,plain,
less(b,a),
inference(resolution,[status(thm)],[c_32,c_66184]) ).
tff(c_66217,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_34,c_66205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM021-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n019.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 : Tue Apr 8 09:58:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 27.14/16.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.14/16.52
% 27.14/16.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------