%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN006-2 : 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 06:45:53 PM UTC 2025
% Result : Unsatisfiable 26.39s 13.85s
% Output : CNFRefutation 26.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 43 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ quotient > less_equal > divide > #nlpp > zero > z > y > xQz > xQy > x > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(less_equal,type,
less_equal: ( $i * $i ) > $o ).
tff(divide,type,
divide: ( $i * $i ) > $i ).
tff(x,type,
x: $i ).
tff(xQy,type,
xQy: $i ).
tff(xQz,type,
xQz: $i ).
tff(y,type,
y: $i ).
tff(quotient,type,
quotient: ( $i * $i * $i ) > $o ).
tff(identity,type,
identity: $i ).
tff(z,type,
z: $i ).
tff(zero,type,
zero: $i ).
tff(f_128,axiom,
~ less_equal(xQz,y),
file(unknown,unknown) ).
tff(f_125,axiom,
less_equal(xQy,z),
file(unknown,unknown) ).
tff(f_124,axiom,
quotient(x,y,xQy),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file(unknown,unknown) ).
tff(f_126,axiom,
quotient(x,z,xQz),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [V3,V5,Z,V1,X,Y,V2,V4] :
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_89,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X,Y,Z] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ),
file(unknown,unknown) ).
tff(c_36,plain,
~ less_equal(xQz,y),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_32,plain,
less_equal(xQy,z),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_30,plain,
quotient(x,y,xQy),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_16,plain,
! [X_20,Y_21] : quotient(X_20,Y_21,divide(X_20,Y_21)),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_34,plain,
quotient(x,z,xQz),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_2,plain,
! [X_1,Y_2] :
( quotient(X_1,Y_2,zero)
| ~ less_equal(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_232,plain,
! [Y_69,V4_65,V3_64,V1_68,V5_70,Z_66,V2_63,X_67] :
( less_equal(V4_65,V5_70)
| ~ quotient(V1_68,Z_66,V5_70)
| ~ quotient(V3_64,V2_63,V4_65)
| ~ quotient(X_67,Z_66,V3_64)
| ~ quotient(Y_69,Z_66,V2_63)
| ~ quotient(X_67,Y_69,V1_68) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_6765,plain,
! [Y_282,X_281,V2_278,Y_280,V4_279,V3_277,X_276] :
( less_equal(V4_279,zero)
| ~ quotient(V3_277,V2_278,V4_279)
| ~ quotient(X_281,Y_282,V3_277)
| ~ quotient(Y_280,Y_282,V2_278)
| ~ quotient(X_281,Y_280,X_276)
| ~ less_equal(X_276,Y_282) ),
inference(resolution,[status(thm)],[c_2,c_232]) ).
tff(c_45959,plain,
! [X_866,X_867,X_868,Y_870,Y_869,Y_865] :
( less_equal(divide(X_866,Y_865),zero)
| ~ quotient(X_868,Y_869,X_866)
| ~ quotient(Y_870,Y_869,Y_865)
| ~ quotient(X_868,Y_870,X_867)
| ~ less_equal(X_867,Y_869) ),
inference(resolution,[status(thm)],[c_16,c_6765]) ).
tff(c_65037,plain,
! [Y_1153,Y_1154,X_1155] :
( less_equal(divide(xQz,Y_1153),zero)
| ~ quotient(Y_1154,z,Y_1153)
| ~ quotient(x,Y_1154,X_1155)
| ~ less_equal(X_1155,z) ),
inference(resolution,[status(thm)],[c_34,c_45959]) ).
tff(c_107946,plain,
! [X_1523,X_1524] :
( less_equal(divide(xQz,divide(X_1523,z)),zero)
| ~ quotient(x,X_1523,X_1524)
| ~ less_equal(X_1524,z) ),
inference(resolution,[status(thm)],[c_16,c_65037]) ).
tff(c_107990,plain,
( less_equal(divide(xQz,divide(y,z)),zero)
| ~ less_equal(xQy,z) ),
inference(resolution,[status(thm)],[c_30,c_107946]) ).
tff(c_108028,plain,
less_equal(divide(xQz,divide(y,z)),zero),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_107990]) ).
tff(c_10,plain,
! [X_16] : less_equal(zero,X_16),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_110,plain,
! [Y_51,X_52] :
( ( Y_51 = X_52 )
| ~ less_equal(Y_51,X_52)
| ~ less_equal(X_52,Y_51) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_132,plain,
! [X_16] :
( ( zero = X_16 )
| ~ less_equal(X_16,zero) ),
inference(resolution,[status(thm)],[c_10,c_110]) ).
tff(c_109823,plain,
divide(xQz,divide(y,z)) = zero,
inference(resolution,[status(thm)],[c_108028,c_132]) ).
tff(c_110773,plain,
quotient(xQz,divide(y,z),zero),
inference(superposition,[status(thm),theory(equality)],[c_109823,c_16]) ).
tff(c_4,plain,
! [X_3,Y_4] :
( less_equal(X_3,Y_4)
| ~ quotient(X_3,Y_4,zero) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_111226,plain,
less_equal(xQz,divide(y,z)),
inference(resolution,[status(thm)],[c_110773,c_4]) ).
tff(c_45,plain,
! [Z_43,X_44,Y_45] :
( less_equal(Z_43,X_44)
| ~ quotient(X_44,Y_45,Z_43) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_72,plain,
! [X_20,Y_21] : less_equal(divide(X_20,Y_21),X_20),
inference(resolution,[status(thm)],[c_16,c_45]) ).
tff(c_135,plain,
! [X_53,Z_54,Y_55] :
( less_equal(X_53,Z_54)
| ~ less_equal(Y_55,Z_54)
| ~ less_equal(X_53,Y_55) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_150,plain,
! [X_53,X_20,Y_21] :
( less_equal(X_53,X_20)
| ~ less_equal(X_53,divide(X_20,Y_21)) ),
inference(resolution,[status(thm)],[c_72,c_135]) ).
tff(c_111279,plain,
less_equal(xQz,y),
inference(resolution,[status(thm)],[c_111226,c_150]) ).
tff(c_111316,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_36,c_111279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : HEN006-2 : TPTP v9.0.0. Released v1.0.0.
% 0.09/0.10 % 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
% 0.09/0.29 % Computer : n010.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
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 7 22:51:17 EDT 2025
% 0.09/0.30 % CPUTime :
% 26.39/13.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.39/13.86
% 26.39/13.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------