%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HEN006-3 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n023.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 4.86s 2.23s
% Output : CNFRefutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 34 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 80 ( 80 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_equal > divide > #nlpp > zero > identity > d > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(less_equal,type,
less_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(divide,type,
divide: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(d,type,
d: $i ).
tff(identity,type,
identity: $i ).
tff(zero,type,
zero: $i ).
tff(f_53,axiom,
! [X,Y] :
( ( divide(X,Y) != zero )
| less_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_80,axiom,
~ less_equal(divide(a,d),b),
file(unknown,unknown) ).
tff(f_56,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file(unknown,unknown) ).
tff(f_48,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ( divide(X,Y) = zero ) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] : less_equal(zero,X),
file(unknown,unknown) ).
tff(f_59,axiom,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y] :
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_78,axiom,
less_equal(divide(a,b),d),
file(unknown,unknown) ).
tff(c_77,plain,
! [X_22,Y_23] :
( less_equal(X_22,Y_23)
| ( divide(X_22,Y_23) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_18,plain,
~ less_equal(divide(a,d),b),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_85,plain,
divide(divide(a,d),b) != zero,
inference(resolution,[status(thm)],[c_77,c_18]) ).
tff(c_6,plain,
! [X_5,Y_6] : less_equal(divide(X_5,Y_6),X_5),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_22,plain,
! [X_18,Y_19] :
( ( divide(X_18,Y_19) = zero )
| ~ less_equal(X_18,Y_19) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_35,plain,
! [X_5,Y_6] : ( divide(divide(X_5,Y_6),X_5) = zero ),
inference(resolution,[status(thm)],[c_6,c_22]) ).
tff(c_10,plain,
! [X_10] : less_equal(zero,X_10),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_37,plain,
! [X_10] : ( divide(zero,X_10) = zero ),
inference(resolution,[status(thm)],[c_10,c_22]) ).
tff(c_171,plain,
! [X_30,Z_31,Y_32] : less_equal(divide(divide(X_30,Z_31),divide(Y_32,Z_31)),divide(divide(X_30,Y_32),Z_31)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_586,plain,
! [X_46,Y_47] : less_equal(divide(divide(X_46,X_46),divide(Y_47,X_46)),zero),
inference(superposition,[status(thm),theory(equality)],[c_35,c_171]) ).
tff(c_664,plain,
! [X_48] : less_equal(divide(divide(X_48,X_48),zero),zero),
inference(superposition,[status(thm),theory(equality)],[c_35,c_586]) ).
tff(c_4,plain,
! [X_3,Y_4] :
( less_equal(X_3,Y_4)
| ( divide(X_3,Y_4) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_125,plain,
! [Y_26,X_27] :
( ( Y_26 = X_27 )
| ~ less_equal(Y_26,X_27)
| ~ less_equal(X_27,Y_26) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_136,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ less_equal(Y_4,X_3)
| ( divide(X_3,Y_4) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_125]) ).
tff(c_667,plain,
! [X_48] :
( ( divide(divide(X_48,X_48),zero) = zero )
| ( divide(zero,divide(divide(X_48,X_48),zero)) != zero ) ),
inference(resolution,[status(thm)],[c_664,c_136]) ).
tff(c_702,plain,
! [X_49] : ( divide(divide(X_49,X_49),zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_37,c_667]) ).
tff(c_141,plain,
! [X_28] :
( ( zero = X_28 )
| ~ less_equal(X_28,zero) ),
inference(resolution,[status(thm)],[c_10,c_125]) ).
tff(c_154,plain,
! [X_3] :
( ( zero = X_3 )
| ( divide(X_3,zero) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_141]) ).
tff(c_771,plain,
! [X_49] : ( divide(X_49,X_49) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_702,c_154]) ).
tff(c_2216,plain,
! [X_70,X_71] : less_equal(divide(divide(X_70,X_71),zero),divide(divide(X_70,zero),X_71)),
inference(superposition,[status(thm),theory(equality)],[c_37,c_171]) ).
tff(c_2864,plain,
! [X_75] : less_equal(divide(divide(X_75,divide(X_75,zero)),zero),zero),
inference(superposition,[status(thm),theory(equality)],[c_771,c_2216]) ).
tff(c_2867,plain,
! [X_75] :
( ( divide(divide(X_75,divide(X_75,zero)),zero) = zero )
| ( divide(zero,divide(divide(X_75,divide(X_75,zero)),zero)) != zero ) ),
inference(resolution,[status(thm)],[c_2864,c_136]) ).
tff(c_2922,plain,
! [X_76] : ( divide(divide(X_76,divide(X_76,zero)),zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_37,c_2867]) ).
tff(c_294,plain,
! [Y_37,X_38] :
( ( Y_37 = X_38 )
| ~ less_equal(Y_37,X_38)
| ( divide(X_38,Y_37) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_125]) ).
tff(c_314,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ( divide(Y_4,X_3) != zero )
| ( divide(X_3,Y_4) != zero ) ),
inference(resolution,[status(thm)],[c_4,c_294]) ).
tff(c_2947,plain,
! [X_76] :
( ( divide(X_76,divide(X_76,zero)) = zero )
| ( divide(zero,divide(X_76,divide(X_76,zero))) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_2922,c_314]) ).
tff(c_3091,plain,
! [X_77] : ( divide(X_77,divide(X_77,zero)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_37,c_2947]) ).
tff(c_3111,plain,
! [X_77] :
( ( divide(X_77,zero) = X_77 )
| ( divide(divide(X_77,zero),X_77) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_3091,c_314]) ).
tff(c_3241,plain,
! [X_77] : ( divide(X_77,zero) = X_77 ),
inference(demodulation,[status(thm),theory(equality)],[c_35,c_3111]) ).
tff(c_785,plain,
! [X_50] : ( divide(X_50,X_50) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_702,c_154]) ).
tff(c_8,plain,
! [X_7,Z_8,Y_9] : less_equal(divide(divide(X_7,Z_8),divide(Y_9,Z_8)),divide(divide(X_7,Y_9),Z_8)),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_831,plain,
! [X_7,X_50] : less_equal(divide(divide(X_7,X_50),zero),divide(divide(X_7,X_50),X_50)),
inference(superposition,[status(thm),theory(equality)],[c_785,c_8]) ).
tff(c_3496,plain,
! [X_80,X_81] : less_equal(divide(X_80,X_81),divide(divide(X_80,X_81),X_81)),
inference(demodulation,[status(thm),theory(equality)],[c_3241,c_831]) ).
tff(c_3499,plain,
! [X_80,X_81] :
( ( divide(divide(X_80,X_81),X_81) = divide(X_80,X_81) )
| ( divide(divide(divide(X_80,X_81),X_81),divide(X_80,X_81)) != zero ) ),
inference(resolution,[status(thm)],[c_3496,c_136]) ).
tff(c_3647,plain,
! [X_82,X_83] : ( divide(divide(X_82,X_83),X_83) = divide(X_82,X_83) ),
inference(demodulation,[status(thm),theory(equality)],[c_35,c_3499]) ).
tff(c_16,plain,
less_equal(divide(a,b),d),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_36,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[c_16,c_22]) ).
tff(c_12,plain,
! [Y_12,X_11] :
( ( Y_12 = X_11 )
| ~ less_equal(Y_12,X_11)
| ~ less_equal(X_11,Y_12) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_891,plain,
! [X_51,Z_52,Y_53] :
( ( divide(divide(X_51,Z_52),divide(Y_53,Z_52)) = divide(divide(X_51,Y_53),Z_52) )
| ~ less_equal(divide(divide(X_51,Y_53),Z_52),divide(divide(X_51,Z_52),divide(Y_53,Z_52))) ),
inference(resolution,[status(thm)],[c_171,c_12]) ).
tff(c_957,plain,
! [Z_52] :
( ( divide(divide(divide(a,b),Z_52),divide(d,Z_52)) = divide(divide(divide(a,b),d),Z_52) )
| ~ less_equal(divide(zero,Z_52),divide(divide(divide(a,b),Z_52),divide(d,Z_52))) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_891]) ).
tff(c_1022,plain,
! [Z_52] : ( divide(divide(divide(a,b),Z_52),divide(d,Z_52)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_37,c_37,c_36,c_957]) ).
tff(c_3693,plain,
divide(divide(a,b),divide(d,b)) = zero,
inference(superposition,[status(thm),theory(equality)],[c_3647,c_1022]) ).
tff(c_227,plain,
! [X_30,Z_31,Y_32] :
( ( divide(divide(X_30,Z_31),divide(Y_32,Z_31)) = divide(divide(X_30,Y_32),Z_31) )
| ~ less_equal(divide(divide(X_30,Y_32),Z_31),divide(divide(X_30,Z_31),divide(Y_32,Z_31))) ),
inference(resolution,[status(thm)],[c_171,c_12]) ).
tff(c_3909,plain,
( ( divide(divide(a,b),divide(d,b)) = divide(divide(a,d),b) )
| ~ less_equal(divide(divide(a,d),b),zero) ),
inference(superposition,[status(thm),theory(equality)],[c_3693,c_227]) ).
tff(c_3969,plain,
( ( divide(divide(a,d),b) = zero )
| ~ less_equal(divide(divide(a,d),b),zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_3693,c_3909]) ).
tff(c_3970,plain,
~ less_equal(divide(divide(a,d),b),zero),
inference(negUnitSimplification,[status(thm)],[c_85,c_3969]) ).
tff(c_960,plain,
( ( divide(divide(a,d),divide(b,d)) = divide(divide(a,b),d) )
| ~ less_equal(zero,divide(divide(a,d),divide(b,d))) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_891]) ).
tff(c_1024,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_36,c_960]) ).
tff(c_182,plain,
! [X_30,X_5,Y_6] : less_equal(divide(divide(X_30,X_5),zero),divide(divide(X_30,divide(X_5,Y_6)),X_5)),
inference(superposition,[status(thm),theory(equality)],[c_35,c_171]) ).
tff(c_3990,plain,
! [X_84,X_85,Y_86] : less_equal(divide(X_84,X_85),divide(divide(X_84,divide(X_85,Y_86)),X_85)),
inference(demodulation,[status(thm),theory(equality)],[c_3241,c_182]) ).
tff(c_4078,plain,
less_equal(divide(divide(a,d),b),divide(zero,b)),
inference(superposition,[status(thm),theory(equality)],[c_1024,c_3990]) ).
tff(c_4175,plain,
less_equal(divide(divide(a,d),b),zero),
inference(demodulation,[status(thm),theory(equality)],[c_37,c_4078]) ).
tff(c_4177,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3970,c_4175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN006-3 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 22:50:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.86/2.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.86/2.24
% 4.86/2.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------