%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP445-1 : 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/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 : n017.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 06:26:15 PM UTC 2025
% Result : Unsatisfiable 4.74s 2.68s
% Output : CNFRefutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 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 : 45 ( 45 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > divide > #nlpp > inverse > b1 > a1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a1,type,
a1: $i ).
tff(divide,type,
divide: ( $i * $i ) > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b1,type,
b1: $i ).
tff(f_28,axiom,
! [A,B] : ( inverse(A) = divide(divide(B,B),A) ),
file(unknown,unknown) ).
tff(f_26,axiom,
! [A,B,C] : ( multiply(A,B) = divide(A,divide(divide(C,C),B)) ),
file(unknown,unknown) ).
tff(f_24,axiom,
! [A,B,C] : ( divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C))) = B ),
file(unknown,unknown) ).
tff(f_30,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
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_28]) ).
tff(c_11,plain,
! [B_9,A_10] : ( divide(divide(B_9,B_9),A_10) = inverse(A_10) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
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_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_26]) ).
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_2,plain,
! [A_1,B_2,C_3] : ( divide(A_1,divide(divide(divide(divide(A_1,A_1),B_2),C_3),divide(divide(divide(A_1,A_1),A_1),C_3))) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_107,plain,
! [A_17,B_18,C_19] : ( divide(A_17,divide(divide(inverse(B_18),C_19),divide(inverse(A_17),C_19))) = B_18 ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_2]) ).
tff(c_126,plain,
! [B_18,C_19,B_8] : ( inverse(divide(divide(inverse(B_18),C_19),divide(inverse(divide(B_8,B_8)),C_19))) = B_18 ),
inference(superposition,[status(thm),theory(equality)],[c_107,c_6]) ).
tff(c_197,plain,
! [B_22,C_23] : ( inverse(multiply(divide(inverse(B_22),C_23),C_23)) = B_22 ),
inference(demodulation,[status(thm),theory(equality)],[c_9,c_22,c_126]) ).
tff(c_509,plain,
! [A_34,B_35] : ( inverse(multiply(inverse(A_34),A_34)) = divide(B_35,B_35) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_197]) ).
tff(c_228,plain,
! [A_10,B_8] : ( inverse(multiply(inverse(A_10),A_10)) = divide(B_8,B_8) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_197]) ).
tff(c_636,plain,
! [B_37,B_36] : ( divide(B_37,B_37) = divide(B_36,B_36) ),
inference(superposition,[status(thm),theory(equality)],[c_509,c_228]) ).
tff(c_716,plain,
! [B_5,B_37] : ( multiply(inverse(B_5),B_5) = divide(B_37,B_37) ),
inference(superposition,[status(thm),theory(equality)],[c_636,c_9]) ).
tff(c_1109,plain,
! [B_42,B_43] : ( multiply(inverse(B_42),B_42) = divide(B_43,B_43) ),
inference(superposition,[status(thm),theory(equality)],[c_636,c_9]) ).
tff(c_8,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_2081,plain,
! [B_57] : ( multiply(inverse(a1),a1) != divide(B_57,B_57) ),
inference(superposition,[status(thm),theory(equality)],[c_1109,c_8]) ).
tff(c_2091,plain,
! [B_57,B_37] : ( divide(B_57,B_57) != divide(B_37,B_37) ),
inference(superposition,[status(thm),theory(equality)],[c_716,c_2081]) ).
tff(c_516,plain,
! [B_8,B_35] : ( divide(B_8,B_8) = divide(B_35,B_35) ),
inference(superposition,[status(thm),theory(equality)],[c_509,c_228]) ).
tff(c_2122,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2091,c_516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRP445-1 : TPTP v9.0.0. Released v2.6.0.
% 0.05/0.10 % 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
% 0.09/0.29 % Computer : n017.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 7 21:50:10 EDT 2025
% 0.09/0.29 % CPUTime :
% 4.74/2.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.74/2.68
% 4.74/2.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------