%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN003-1 : 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 06:45:50 PM UTC 2025
% Result : Unsatisfiable 5.72s 2.35s
% Output : CNFRefutation 5.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 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 : 76 ( 76 !; 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_95,axiom,
! [X,Y] : quotient(X,Y,divide(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_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_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_53,axiom,
! [X,Y] :
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_108,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_95]) ).
tff(c_25,plain,
! [Z_32,X_33,Y_34] :
( less_equal(Z_32,X_33)
| ~ quotient(X_33,Y_34,Z_32) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_29,plain,
! [X_20,Y_21] : less_equal(divide(X_20,Y_21),X_20),
inference(resolution,[status(thm)],[c_16,c_25]) ).
tff(c_10,plain,
! [X_16] : less_equal(zero,X_16),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_45,plain,
! [Y_39,X_40] :
( ( Y_39 = X_40 )
| ~ less_equal(Y_39,X_40)
| ~ less_equal(X_40,Y_39) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_55,plain,
! [X_41] :
( ( zero = X_41 )
| ~ less_equal(X_41,zero) ),
inference(resolution,[status(thm)],[c_10,c_45]) ).
tff(c_67,plain,
! [Y_42] : ( divide(zero,Y_42) = zero ),
inference(resolution,[status(thm)],[c_29,c_55]) ).
tff(c_75,plain,
! [Y_42] : quotient(zero,Y_42,zero),
inference(superposition,[status(thm),theory(equality)],[c_67,c_16]) ).
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_170,plain,
! [Y_64,V4_60,V2_58,V3_59,Z_61,V1_63,V5_65,X_62] :
( less_equal(V4_60,V5_65)
| ~ quotient(V1_63,Z_61,V5_65)
| ~ quotient(V3_59,V2_58,V4_60)
| ~ quotient(X_62,Z_61,V3_59)
| ~ quotient(Y_64,Z_61,V2_58)
| ~ quotient(X_62,Y_64,V1_63) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_1063,plain,
! [V4_133,Y_134,V3_128,V2_129,X_130,Y_132,X_131] :
( less_equal(V4_133,zero)
| ~ quotient(V3_128,V2_129,V4_133)
| ~ quotient(X_131,Y_134,V3_128)
| ~ quotient(Y_132,Y_134,V2_129)
| ~ quotient(X_131,Y_132,X_130)
| ~ less_equal(X_130,Y_134) ),
inference(resolution,[status(thm)],[c_2,c_170]) ).
tff(c_2667,plain,
! [Y_186,X_191,Y_189,X_187,Y_188,X_190] :
( less_equal(divide(X_187,Y_186),zero)
| ~ quotient(X_191,Y_189,X_187)
| ~ quotient(Y_188,Y_189,Y_186)
| ~ quotient(X_191,Y_188,X_190)
| ~ less_equal(X_190,Y_189) ),
inference(resolution,[status(thm)],[c_16,c_1063]) ).
tff(c_4459,plain,
! [X_233,X_232,Y_235,Y_231,Y_234] :
( less_equal(divide(divide(X_232,Y_231),Y_234),zero)
| ~ quotient(Y_235,Y_231,Y_234)
| ~ quotient(X_232,Y_235,X_233)
| ~ less_equal(X_233,Y_231) ),
inference(resolution,[status(thm)],[c_16,c_2667]) ).
tff(c_6564,plain,
! [X_275,Y_276,X_277] :
( less_equal(divide(divide(X_275,Y_276),zero),zero)
| ~ quotient(X_275,zero,X_277)
| ~ less_equal(X_277,Y_276) ),
inference(resolution,[status(thm)],[c_75,c_4459]) ).
tff(c_6724,plain,
! [X_282,Y_283] :
( less_equal(divide(divide(X_282,Y_283),zero),zero)
| ~ less_equal(divide(X_282,zero),Y_283) ),
inference(resolution,[status(thm)],[c_16,c_6564]) ).
tff(c_53,plain,
! [X_16] :
( ( zero = X_16 )
| ~ less_equal(X_16,zero) ),
inference(resolution,[status(thm)],[c_10,c_45]) ).
tff(c_6822,plain,
! [X_284,Y_285] :
( ( divide(divide(X_284,Y_285),zero) = zero )
| ~ less_equal(divide(X_284,zero),Y_285) ),
inference(resolution,[status(thm)],[c_6724,c_53]) ).
tff(c_6996,plain,
! [X_289] : ( divide(divide(X_289,X_289),zero) = zero ),
inference(resolution,[status(thm)],[c_29,c_6822]) ).
tff(c_7290,plain,
! [X_290] : quotient(divide(X_290,X_290),zero,zero),
inference(superposition,[status(thm),theory(equality)],[c_6996,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_7409,plain,
! [X_291] : less_equal(divide(X_291,X_291),zero),
inference(resolution,[status(thm)],[c_7290,c_4]) ).
tff(c_7468,plain,
! [X_292] : ( divide(X_292,X_292) = zero ),
inference(resolution,[status(thm)],[c_7409,c_53]) ).
tff(c_7631,plain,
! [X_292] : quotient(X_292,X_292,zero),
inference(superposition,[status(thm),theory(equality)],[c_7468,c_16]) ).
tff(c_20,plain,
~ quotient(x,x,zero),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_7888,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7631,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : HEN003-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.08 % 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
% 0.07/0.27 % Computer : n010.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon Apr 7 22:50:17 EDT 2025
% 0.07/0.27 % CPUTime :
% 5.72/2.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.72/2.35
% 5.72/2.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------