%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN003-2 : 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 : n007.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 06:45:51 PM UTC 2025
% Result : Unsatisfiable 7.03s 2.74s
% Output : CNFRefutation 7.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 39 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ quotient > less_equal > divide > #nlpp > zero > 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(quotient,type,
quotient: ( $i * $i * $i ) > $o ).
tff(identity,type,
identity: $i ).
tff(zero,type,
zero: $i ).
tff(f_96,axiom,
! [X,Y] : quotient(X,Y,divide(X,Y)),
file(unknown,unknown) ).
tff(f_60,axiom,
! [X,Y,Z] :
( ~ quotient(X,Y,Z)
| less_equal(Z,X) ),
file(unknown,unknown) ).
tff(f_112,axiom,
! [X] : quotient(zero,X,zero),
file(unknown,unknown) ).
tff(f_49,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ),
file(unknown,unknown) ).
tff(f_78,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_81,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_90,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_114,axiom,
~ quotient(x,x,zero),
file(unknown,unknown) ).
tff(c_16,plain,
! [X_20,Y_21] : quotient(X_20,Y_21,divide(X_20,Y_21)),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_30,plain,
! [Z_34,X_35,Y_36] :
( less_equal(Z_34,X_35)
| ~ quotient(X_35,Y_36,Z_34) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_40,plain,
! [X_20,Y_21] : less_equal(divide(X_20,Y_21),X_20),
inference(resolution,[status(thm)],[c_16,c_30]) ).
tff(c_22,plain,
! [X_27] : quotient(zero,X_27,zero),
inference(cnfTransformation,[status(thm)],[f_112]) ).
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_49]) ).
tff(c_202,plain,
! [V1_62,X_61,V4_59,Z_60,V3_58,Y_63,V5_64,V2_57] :
( less_equal(V4_59,V5_64)
| ~ quotient(V1_62,Z_60,V5_64)
| ~ quotient(V3_58,V2_57,V4_59)
| ~ quotient(X_61,Z_60,V3_58)
| ~ quotient(Y_63,Z_60,V2_57)
| ~ quotient(X_61,Y_63,V1_62) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_1807,plain,
! [Y_164,X_166,V2_163,V4_162,X_161,Y_165,V3_160] :
( less_equal(V4_162,zero)
| ~ quotient(V3_160,V2_163,V4_162)
| ~ quotient(X_166,Y_165,V3_160)
| ~ quotient(Y_164,Y_165,V2_163)
| ~ quotient(X_166,Y_164,X_161)
| ~ less_equal(X_161,Y_165) ),
inference(resolution,[status(thm)],[c_2,c_202]) ).
tff(c_4387,plain,
! [X_240,X_239,Y_237,Y_242,X_238,Y_241] :
( less_equal(divide(X_238,Y_237),zero)
| ~ quotient(X_239,Y_241,X_238)
| ~ quotient(Y_242,Y_241,Y_237)
| ~ quotient(X_239,Y_242,X_240)
| ~ less_equal(X_240,Y_241) ),
inference(resolution,[status(thm)],[c_16,c_1807]) ).
tff(c_7175,plain,
! [Y_290,Y_293,X_294,X_291,Y_292] :
( less_equal(divide(divide(X_291,Y_290),Y_293),zero)
| ~ quotient(Y_292,Y_290,Y_293)
| ~ quotient(X_291,Y_292,X_294)
| ~ less_equal(X_294,Y_290) ),
inference(resolution,[status(thm)],[c_16,c_4387]) ).
tff(c_9951,plain,
! [X_343,X_344,X_345] :
( less_equal(divide(divide(X_343,X_344),zero),zero)
| ~ quotient(X_343,zero,X_345)
| ~ less_equal(X_345,X_344) ),
inference(resolution,[status(thm)],[c_22,c_7175]) ).
tff(c_10165,plain,
! [X_350,X_351] :
( less_equal(divide(divide(X_350,X_351),zero),zero)
| ~ less_equal(divide(X_350,zero),X_351) ),
inference(resolution,[status(thm)],[c_16,c_9951]) ).
tff(c_10,plain,
! [X_16] : less_equal(zero,X_16),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_71,plain,
! [Y_43,X_44] :
( ( Y_43 = X_44 )
| ~ less_equal(Y_43,X_44)
| ~ less_equal(X_44,Y_43) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_79,plain,
! [X_16] :
( ( zero = X_16 )
| ~ less_equal(X_16,zero) ),
inference(resolution,[status(thm)],[c_10,c_71]) ).
tff(c_10287,plain,
! [X_352,X_353] :
( ( divide(divide(X_352,X_353),zero) = zero )
| ~ less_equal(divide(X_352,zero),X_353) ),
inference(resolution,[status(thm)],[c_10165,c_79]) ).
tff(c_10515,plain,
! [X_357] : ( divide(divide(X_357,X_357),zero) = zero ),
inference(resolution,[status(thm)],[c_40,c_10287]) ).
tff(c_10947,plain,
! [X_358] : quotient(divide(X_358,X_358),zero,zero),
inference(superposition,[status(thm),theory(equality)],[c_10515,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_54]) ).
tff(c_11092,plain,
! [X_359] : less_equal(divide(X_359,X_359),zero),
inference(resolution,[status(thm)],[c_10947,c_4]) ).
tff(c_11161,plain,
! [X_360] : ( divide(X_360,X_360) = zero ),
inference(resolution,[status(thm)],[c_11092,c_79]) ).
tff(c_11434,plain,
! [X_360] : quotient(X_360,X_360,zero),
inference(superposition,[status(thm),theory(equality)],[c_11161,c_16]) ).
tff(c_24,plain,
~ quotient(x,x,zero),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_11591,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11434,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : HEN003-2 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.13 % 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 : n007.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 : Mon Apr 7 22:50:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.03/2.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.03/2.74
% 7.03/2.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------