%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP452-1 : TPTP v9.0.0. Released v2.6.0.
% 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 : n014.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 06:26:16 PM UTC 2025
% Result : Unsatisfiable 5.37s 2.35s
% Output : CNFRefutation 5.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > divide > #nlpp > inverse > b2 > a2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(divide,type,
divide: ( $i * $i ) > $i ).
tff(b2,type,
b2: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(a2,type,
a2: $i ).
tff(f_27,axiom,
! [A,B] : ( inverse(A) = divide(divide(B,B),A) ),
file(unknown,unknown) ).
tff(f_23,axiom,
! [A,B,C] : ( divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B ),
file(unknown,unknown) ).
tff(f_25,axiom,
! [A,B,C] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
file(unknown,unknown) ).
tff(f_29,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file(unknown,unknown) ).
tff(c_6,plain,
! [B_8,A_7] : ( divide(divide(B_8,B_8),A_7) = inverse(A_7) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( divide(divide(divide(A_1,A_1),divide(A_1,divide(B_2,divide(divide(divide(A_1,A_1),A_1),C_3)))),C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_10,plain,
! [A_1,B_2,C_3] : ( divide(inverse(divide(A_1,divide(B_2,divide(inverse(A_1),C_3)))),C_3) = B_2 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_2]) ).
tff(c_4,plain,
! [A_4,C_6,B_5] : ( divide(A_4,divide(divide(C_6,C_6),B_5)) = multiply(A_4,B_5) ),
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_9,plain,
! [A_4,B_5] : ( divide(A_4,inverse(B_5)) = multiply(A_4,B_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4]) ).
tff(c_107,plain,
! [A_17,B_18,C_19] : ( divide(inverse(divide(A_17,divide(B_18,divide(inverse(A_17),C_19)))),C_19) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_2]) ).
tff(c_154,plain,
! [A_17,C_19,B_8] : ( divide(inverse(divide(A_17,inverse(divide(inverse(A_17),C_19)))),C_19) = divide(B_8,B_8) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_107]) ).
tff(c_165,plain,
! [A_17,C_19,B_8] : ( divide(inverse(multiply(A_17,divide(inverse(A_17),C_19))),C_19) = divide(B_8,B_8) ),
inference(demodulation,[status(thm),theory(equality)],[c_9,c_154]) ).
tff(c_361,plain,
! [A_30,C_31,B_32] : ( divide(inverse(multiply(A_30,divide(inverse(A_30),C_31))),C_31) = divide(B_32,B_32) ),
inference(demodulation,[status(thm),theory(equality)],[c_9,c_154]) ).
tff(c_496,plain,
! [B_34,B_33] : ( divide(B_34,B_34) = divide(B_33,B_33) ),
inference(superposition,[status(thm),theory(equality)],[c_165,c_361]) ).
tff(c_590,plain,
! [B_8,B_34] : ( inverse(divide(B_8,B_8)) = divide(B_34,B_34) ),
inference(superposition,[status(thm),theory(equality)],[c_496,c_6]) ).
tff(c_3009,plain,
! [A_67,B_68,A_69,C_70] : ( inverse(divide(A_67,divide(B_68,divide(inverse(A_67),divide(inverse(A_69),C_70))))) = divide(inverse(divide(A_69,B_68)),C_70) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_107]) ).
tff(c_3183,plain,
! [A_67,B_8,A_69,C_70] : ( inverse(divide(A_67,inverse(divide(B_8,B_8)))) = divide(inverse(divide(A_69,divide(inverse(A_67),divide(inverse(A_69),C_70)))),C_70) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_3009]) ).
tff(c_3645,plain,
! [A_73,B_74] : ( inverse(multiply(A_73,divide(B_74,B_74))) = inverse(A_73) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_9,c_3183]) ).
tff(c_11,plain,
! [B_9,A_10] : ( divide(divide(B_9,B_9),A_10) = inverse(A_10) ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_22,plain,
! [B_8,A_10] : ( divide(inverse(divide(B_8,B_8)),A_10) = inverse(A_10) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_11]) ).
tff(c_158,plain,
! [B_18,B_8,C_19] : ( divide(inverse(inverse(divide(B_18,divide(inverse(divide(B_8,B_8)),C_19)))),C_19) = B_18 ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_107]) ).
tff(c_166,plain,
! [B_18,C_19] : ( divide(inverse(inverse(multiply(B_18,C_19))),C_19) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_9,c_22,c_158]) ).
tff(c_3715,plain,
! [A_73,B_74] : ( divide(inverse(inverse(A_73)),divide(B_74,B_74)) = A_73 ),
inference(superposition,[status(thm),theory(equality)],[c_3645,c_166]) ).
tff(c_4140,plain,
! [A_77,B_78] : ( divide(inverse(inverse(A_77)),divide(B_78,B_78)) = A_77 ),
inference(superposition,[status(thm),theory(equality)],[c_3645,c_166]) ).
tff(c_434,plain,
! [B_8,B_32] : ( divide(B_8,B_8) = divide(B_32,B_32) ),
inference(superposition,[status(thm),theory(equality)],[c_165,c_361]) ).
tff(c_3197,plain,
! [A_67,B_8,A_69,C_70] : ( inverse(divide(A_67,divide(B_8,B_8))) = divide(inverse(divide(A_69,divide(inverse(A_67),divide(inverse(A_69),C_70)))),C_70) ),
inference(superposition,[status(thm),theory(equality)],[c_434,c_3009]) ).
tff(c_3342,plain,
! [A_67,B_8] : ( inverse(divide(A_67,divide(B_8,B_8))) = inverse(A_67) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_3197]) ).
tff(c_4321,plain,
! [A_79] : ( inverse(inverse(inverse(A_79))) = inverse(A_79) ),
inference(superposition,[status(thm),theory(equality)],[c_4140,c_3342]) ).
tff(c_4333,plain,
! [A_79,B_74] : ( divide(inverse(inverse(A_79)),divide(B_74,B_74)) = inverse(inverse(A_79)) ),
inference(superposition,[status(thm),theory(equality)],[c_4321,c_3715]) ).
tff(c_4460,plain,
! [A_79] : ( inverse(inverse(A_79)) = A_79 ),
inference(demodulation,[status(thm),theory(equality)],[c_3715,c_4333]) ).
tff(c_28,plain,
! [A_11,B_12] : ( divide(A_11,inverse(B_12)) = multiply(A_11,B_12) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4]) ).
tff(c_167,plain,
! [B_20,A_21] : ( divide(multiply(inverse(B_20),B_20),A_21) = inverse(A_21) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_6]) ).
tff(c_190,plain,
! [B_20,B_5] : ( multiply(multiply(inverse(B_20),B_20),B_5) = inverse(inverse(B_5)) ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_9]) ).
tff(c_8,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_348,plain,
inverse(inverse(a2)) != a2,
inference(demodulation,[status(thm),theory(equality)],[c_190,c_8]) ).
tff(c_4486,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4460,c_348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP452-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.13 % 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
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 21:50:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.37/2.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.37/2.35
% 5.37/2.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------