%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN005-2 : 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 : n022.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 06:45:52 PM UTC 2025
% Result : Unsatisfiable 11.58s 4.37s
% Output : CNFRefutation 11.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 10 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ quotient > less_equal > divide > #nlpp > zero > z > y > 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(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_119,axiom,
~ less_equal(x,z),
file(unknown,unknown) ).
tff(f_117,axiom,
less_equal(y,z),
file(unknown,unknown) ).
tff(f_116,axiom,
less_equal(x,y),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file(unknown,unknown) ).
tff(f_95,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file(unknown,unknown) ).
tff(f_104,axiom,
! [X,Y,Z,W] :
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W)
| ( Z = W ) ),
file(unknown,unknown) ).
tff(f_115,axiom,
! [X] : quotient(X,zero,X),
file(unknown,unknown) ).
tff(f_111,axiom,
! [X] : quotient(zero,X,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(c_32,plain,
~ less_equal(x,z),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_30,plain,
less_equal(y,z),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_28,plain,
less_equal(x,y),
inference(cnfTransformation,[status(thm)],[f_116]) ).
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_16,plain,
! [X_20,Y_21] : quotient(X_20,Y_21,divide(X_20,Y_21)),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_166,plain,
! [Z_53,W_54,X_55,Y_56] :
( ( Z_53 = W_54 )
| ~ quotient(X_55,Y_56,W_54)
| ~ quotient(X_55,Y_56,Z_53) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_431,plain,
! [X_76,Y_77,Z_78] :
( ( divide(X_76,Y_77) = Z_78 )
| ~ quotient(X_76,Y_77,Z_78) ),
inference(resolution,[status(thm)],[c_16,c_166]) ).
tff(c_461,plain,
! [X_79,Y_80] :
( ( divide(X_79,Y_80) = zero )
| ~ less_equal(X_79,Y_80) ),
inference(resolution,[status(thm)],[c_2,c_431]) ).
tff(c_485,plain,
divide(x,y) = zero,
inference(resolution,[status(thm)],[c_28,c_461]) ).
tff(c_495,plain,
quotient(x,y,zero),
inference(superposition,[status(thm),theory(equality)],[c_485,c_16]) ).
tff(c_26,plain,
! [X_29] : quotient(X_29,zero,X_29),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_22,plain,
! [X_27] : quotient(zero,X_27,zero),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_215,plain,
! [Z_62,V3_60,V2_59,Y_65,V1_64,V5_66,V4_61,X_63] :
( less_equal(V4_61,V5_66)
| ~ quotient(V1_64,Z_62,V5_66)
| ~ quotient(V3_60,V2_59,V4_61)
| ~ quotient(X_63,Z_62,V3_60)
| ~ quotient(Y_65,Z_62,V2_59)
| ~ quotient(X_63,Y_65,V1_64) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_965,plain,
! [X_115,V3_110,X_114,Y_113,V4_111,V2_112] :
( less_equal(V4_111,zero)
| ~ quotient(V3_110,V2_112,V4_111)
| ~ quotient(X_115,X_114,V3_110)
| ~ quotient(Y_113,X_114,V2_112)
| ~ quotient(X_115,Y_113,zero) ),
inference(resolution,[status(thm)],[c_22,c_215]) ).
tff(c_1000,plain,
! [X_116,X_117,X_118,Y_119] :
( less_equal(X_116,zero)
| ~ quotient(X_117,X_118,X_116)
| ~ quotient(Y_119,X_118,zero)
| ~ quotient(X_117,Y_119,zero) ),
inference(resolution,[status(thm)],[c_26,c_965]) ).
tff(c_11769,plain,
! [X_437,Y_438,Y_439] :
( less_equal(divide(X_437,Y_438),zero)
| ~ quotient(Y_439,Y_438,zero)
| ~ quotient(X_437,Y_439,zero) ),
inference(resolution,[status(thm)],[c_16,c_1000]) ).
tff(c_11974,plain,
! [X_442,Y_443,X_444] :
( less_equal(divide(X_442,Y_443),zero)
| ~ quotient(X_442,X_444,zero)
| ~ less_equal(X_444,Y_443) ),
inference(resolution,[status(thm)],[c_2,c_11769]) ).
tff(c_12426,plain,
! [Y_452] :
( less_equal(divide(x,Y_452),zero)
| ~ less_equal(y,Y_452) ),
inference(resolution,[status(thm)],[c_495,c_11974]) ).
tff(c_10,plain,
! [X_16] : less_equal(zero,X_16),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_98,plain,
! [Y_48,X_49] :
( ( Y_48 = X_49 )
| ~ less_equal(Y_48,X_49)
| ~ less_equal(X_49,Y_48) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_116,plain,
! [X_16] :
( ( zero = X_16 )
| ~ less_equal(X_16,zero) ),
inference(resolution,[status(thm)],[c_10,c_98]) ).
tff(c_12708,plain,
! [Y_455] :
( ( divide(x,Y_455) = zero )
| ~ less_equal(y,Y_455) ),
inference(resolution,[status(thm)],[c_12426,c_116]) ).
tff(c_12734,plain,
divide(x,z) = zero,
inference(resolution,[status(thm)],[c_30,c_12708]) ).
tff(c_12906,plain,
quotient(x,z,zero),
inference(superposition,[status(thm),theory(equality)],[c_12734,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_13024,plain,
less_equal(x,z),
inference(resolution,[status(thm)],[c_12906,c_4]) ).
tff(c_13078,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_13024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : HEN005-2 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.10 % 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 : n022.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 : Mon Apr 7 22:50:35 EDT 2025
% 0.09/0.29 % CPUTime :
% 11.58/4.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.80/4.38
% 11.80/4.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------