%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM024-1 : 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 : n013.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 07:55:03 PM UTC 2025
% Result : Unsatisfiable 4.08s 2.03s
% Output : CNFRefutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less > equalish > predecessor_of_1st_minus_2nd > multiply > add > #nlpp > successor > n0 > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $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(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(successor,type,
successor: $i > $i ).
tff(f_133,axiom,
! [A] : ~ equalish(successor(A),n0),
file(unknown,unknown) ).
tff(f_105,axiom,
! [A,B] :
( ~ less(A,B)
| equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ),
file(unknown,unknown) ).
tff(f_129,axiom,
! [A,B] : equalish(add(A,B),add(B,A)),
file(unknown,unknown) ).
tff(f_49,axiom,
! [A] : equalish(add(A,n0),A),
file(unknown,unknown) ).
tff(f_122,axiom,
! [X,Y,Z] :
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) ),
file(unknown,unknown) ).
tff(f_114,axiom,
! [X,Y] :
( ~ equalish(X,Y)
| equalish(Y,X) ),
file(unknown,unknown) ).
tff(f_127,axiom,
! [A,B,C] :
( ~ equalish(add(A,B),add(C,B))
| equalish(A,C) ),
file(unknown,unknown) ).
tff(f_130,axiom,
less(a,a),
file(unknown,unknown) ).
tff(c_32,plain,
! [A_30] : ~ equalish(successor(A_30),n0),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_18,plain,
! [B_18,A_17] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(B_18,A_17)),A_17),B_18)
| ~ less(A_17,B_18) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_28,plain,
! [A_28,B_29] : equalish(add(A_28,B_29),add(B_29,A_28)),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_2,plain,
! [A_1] : equalish(add(A_1,n0),A_1),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_166,plain,
! [X_68,Z_69,Y_70] :
( equalish(X_68,Z_69)
| ~ equalish(Y_70,Z_69)
| ~ equalish(X_68,Y_70) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_251,plain,
! [X_78,A_79] :
( equalish(X_78,A_79)
| ~ equalish(X_78,add(A_79,n0)) ),
inference(resolution,[status(thm)],[c_2,c_166]) ).
tff(c_290,plain,
! [B_82] : equalish(add(n0,B_82),B_82),
inference(resolution,[status(thm)],[c_28,c_251]) ).
tff(c_22,plain,
! [Y_21,X_20] :
( equalish(Y_21,X_20)
| ~ equalish(X_20,Y_21) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_307,plain,
! [B_83] : equalish(B_83,add(n0,B_83)),
inference(resolution,[status(thm)],[c_290,c_22]) ).
tff(c_24,plain,
! [X_22,Z_24,Y_23] :
( equalish(X_22,Z_24)
| ~ equalish(Y_23,Z_24)
| ~ equalish(X_22,Y_23) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_1057,plain,
! [X_124,B_125] :
( equalish(X_124,add(n0,B_125))
| ~ equalish(X_124,B_125) ),
inference(resolution,[status(thm)],[c_307,c_24]) ).
tff(c_26,plain,
! [A_25,C_27,B_26] :
( equalish(A_25,C_27)
| ~ equalish(add(A_25,B_26),add(C_27,B_26)) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_1238,plain,
! [A_133,B_134] :
( equalish(A_133,n0)
| ~ equalish(add(A_133,B_134),B_134) ),
inference(resolution,[status(thm)],[c_1057,c_26]) ).
tff(c_1266,plain,
! [B_18] :
( equalish(successor(predecessor_of_1st_minus_2nd(B_18,B_18)),n0)
| ~ less(B_18,B_18) ),
inference(resolution,[status(thm)],[c_18,c_1238]) ).
tff(c_1292,plain,
! [B_18] : ~ less(B_18,B_18),
inference(negUnitSimplification,[status(thm)],[c_32,c_1266]) ).
tff(c_30,plain,
less(a,a),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_1302,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1292,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM024-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.12/0.13 % 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
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 09:58:02 EDT 2025
% 0.14/0.34 % CPUTime :
% 4.08/2.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/2.03
% 4.08/2.03 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------