%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP006-1 : 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 06:24:43 PM UTC 2025
% Result : Unsatisfiable 2.57s 1.60s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ product > an_element > #nlpp > inverse > the_element > identity
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(the_element,type,
the_element: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse,type,
inverse: $i > $i ).
tff(identity,type,
identity: $i ).
tff(an_element,type,
an_element: $i > $o ).
tff(f_68,axiom,
an_element(the_element),
file(unknown,unknown) ).
tff(f_32,axiom,
! [X] : product(X,inverse(X),identity),
file(unknown,unknown) ).
tff(f_45,axiom,
! [X,Y,Z] :
( ~ an_element(X)
| ~ an_element(Y)
| ~ product(X,inverse(Y),Z)
| an_element(Z) ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [X] : product(identity,X,X),
file(unknown,unknown) ).
tff(f_70,axiom,
~ an_element(inverse(the_element)),
file(unknown,unknown) ).
tff(c_16,plain,
an_element(the_element),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_6,plain,
! [X_3] : product(X_3,inverse(X_3),identity),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_23,plain,
! [Z_24,X_25,Y_26] :
( an_element(Z_24)
| ~ product(X_25,inverse(Y_26),Z_24)
| ~ an_element(Y_26)
| ~ an_element(X_25) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_36,plain,
! [X_3] :
( an_element(identity)
| ~ an_element(X_3) ),
inference(resolution,[status(thm)],[c_6,c_23]) ).
tff(c_38,plain,
! [X_3] : ~ an_element(X_3),
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_41,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_16]) ).
tff(c_42,plain,
an_element(identity),
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_2,plain,
! [X_1] : product(identity,X_1,X_1),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_37,plain,
! [Y_26] :
( an_element(inverse(Y_26))
| ~ an_element(Y_26)
| ~ an_element(identity) ),
inference(resolution,[status(thm)],[c_2,c_23]) ).
tff(c_58,plain,
! [Y_33] :
( an_element(inverse(Y_33))
| ~ an_element(Y_33) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_37]) ).
tff(c_18,plain,
~ an_element(inverse(the_element)),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_61,plain,
~ an_element(the_element),
inference(resolution,[status(thm)],[c_58,c_18]) ).
tff(c_65,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP006-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % 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 : n010.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 21:10:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.57/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.57/1.60
% 2.57/1.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------