%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP534-1 : 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 : n026.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 06:26:27 PM UTC 2025
% Result : Unsatisfiable 2.42s 1.50s
% Output : CNFRefutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > divide > #nlpp > inverse > identity > 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(identity,type,
identity: $i ).
tff(f_29,axiom,
! [A] : ( identity = divide(A,A) ),
file(unknown,unknown) ).
tff(f_27,axiom,
! [A,B] : ( inverse(A) = divide(divide(B,B),A) ),
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_23,axiom,
! [A,B,C] : ( divide(divide(A,divide(divide(A,B),C)),B) = C ),
file(unknown,unknown) ).
tff(f_31,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file(unknown,unknown) ).
tff(c_8,plain,
! [A_9] : ( divide(A_9,A_9) = identity ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
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_11,plain,
! [A_7] : ( divide(identity,A_7) = inverse(A_7) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
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_42,plain,
! [A_12,B_13] : ( divide(A_12,inverse(B_13)) = multiply(A_12,B_13) ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_8,c_4]) ).
tff(c_53,plain,
! [B_13] : ( multiply(inverse(B_13),B_13) = identity ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_8]) ).
tff(c_12,plain,
! [A_4,B_5] : ( divide(A_4,inverse(B_5)) = multiply(A_4,B_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_11,c_8,c_4]) ).
tff(c_85,plain,
! [A_15,B_16,C_17] : ( divide(divide(A_15,divide(divide(A_15,B_16),C_17)),B_16) = C_17 ),
inference(cnfTransformation,[status(thm)],[f_23]) ).
tff(c_128,plain,
! [A_9,C_17] : ( divide(divide(A_9,divide(identity,C_17)),A_9) = C_17 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_85]) ).
tff(c_167,plain,
! [A_19,C_20] : ( divide(multiply(A_19,C_20),A_19) = C_20 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_11,c_128]) ).
tff(c_194,plain,
! [B_21] : ( divide(identity,inverse(B_21)) = B_21 ),
inference(superposition,[status(thm),theory(equality)],[c_53,c_167]) ).
tff(c_203,plain,
! [B_21] : ( multiply(identity,B_21) = B_21 ),
inference(superposition,[status(thm),theory(equality)],[c_194,c_12]) ).
tff(c_10,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_70,plain,
multiply(identity,a2) != a2,
inference(demodulation,[status(thm),theory(equality)],[c_53,c_10]) ).
tff(c_299,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_203,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP534-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.07 % 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
% 0.05/0.25 % Computer : n026.cluster.edu
% 0.05/0.25 % Model : x86_64 x86_64
% 0.05/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.25 % Memory : 8042.1875MB
% 0.05/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.05/0.25 % CPULimit : 300
% 0.05/0.25 % WCLimit : 300
% 0.05/0.25 % DateTime : Mon Apr 7 21:55:08 EDT 2025
% 0.05/0.25 % CPUTime :
% 2.42/1.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.42/1.50
% 2.42/1.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------