%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET012-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 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 : n009.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 08:37:27 PM UTC 2025
% Result : Unsatisfiable 4.92s 2.21s
% Output : CNFRefutation 5.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 67 ( 28 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > little_set > f1 > #nlpp > complement > universal_set > empty_set > cs > bs > as
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(bs,type,
bs: $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(little_set,type,
little_set: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(universal_set,type,
universal_set: $i ).
tff(as,type,
as: $i ).
tff(f1,type,
f1: ( $i * $i ) > $i ).
tff(cs,type,
cs: $i ).
tff(f_75,axiom,
as != cs,
file(unknown,unknown) ).
tff(f_33,axiom,
! [X,Y] :
( little_set(f1(X,Y))
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_73,axiom,
complement(bs) = cs,
file(unknown,unknown) ).
tff(f_72,axiom,
complement(as) = bs,
file(unknown,unknown) ).
tff(f_61,axiom,
! [Z,X] :
( member(Z,complement(X))
| ~ little_set(Z)
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_39,axiom,
! [X,Y] :
( member(f1(X,Y),X)
| member(f1(X,Y),Y)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [X,Y] :
( ~ member(f1(X,Y),X)
| ~ member(f1(X,Y),Y)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(c_22,plain,
cs != as,
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_4,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| little_set(f1(X_3,Y_4)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_20,plain,
complement(bs) = cs,
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_18,plain,
complement(as) = bs,
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_47,plain,
! [Z_24,X_25] :
( member(Z_24,X_25)
| ~ little_set(Z_24)
| member(Z_24,complement(X_25)) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_56,plain,
! [Z_24] :
( member(Z_24,as)
| ~ little_set(Z_24)
| member(Z_24,bs) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_47]) ).
tff(c_136,plain,
! [Y_32,X_33] :
( ( Y_32 = X_33 )
| member(f1(X_33,Y_32),Y_32)
| member(f1(X_33,Y_32),X_33) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_10,plain,
! [Z_9,X_10] :
( ~ member(Z_9,X_10)
| ~ member(Z_9,complement(X_10)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_390,plain,
! [X_40,X_41] :
( ~ member(f1(X_40,complement(X_41)),X_41)
| ( complement(X_41) = X_40 )
| member(f1(X_40,complement(X_41)),X_40) ),
inference(resolution,[status(thm)],[c_136,c_10]) ).
tff(c_396,plain,
! [X_40] :
( ( complement(bs) = X_40 )
| member(f1(X_40,complement(bs)),X_40)
| member(f1(X_40,complement(bs)),as)
| ~ little_set(f1(X_40,complement(bs))) ),
inference(resolution,[status(thm)],[c_56,c_390]) ).
tff(c_412,plain,
! [X_40] :
( ( cs = X_40 )
| member(f1(X_40,cs),X_40)
| member(f1(X_40,cs),as)
| ~ little_set(f1(X_40,cs)) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_20,c_20,c_20,c_396]) ).
tff(c_2652,plain,
( ( cs = as )
| ~ little_set(f1(as,cs))
| member(f1(as,cs),as) ),
inference(factorization,[status(thm),theory(equality)],[c_412]) ).
tff(c_2655,plain,
( ~ little_set(f1(as,cs))
| member(f1(as,cs),as) ),
inference(negUnitSimplification,[status(thm)],[c_22,c_2652]) ).
tff(c_2707,plain,
~ little_set(f1(as,cs)),
inference(splitLeft,[status(thm)],[c_2655]) ).
tff(c_2710,plain,
cs = as,
inference(resolution,[status(thm)],[c_4,c_2707]) ).
tff(c_2714,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_2710]) ).
tff(c_2715,plain,
member(f1(as,cs),as),
inference(splitRight,[status(thm)],[c_2655]) ).
tff(c_2716,plain,
little_set(f1(as,cs)),
inference(splitRight,[status(thm)],[c_2655]) ).
tff(c_59,plain,
! [Z_24] :
( member(Z_24,bs)
| ~ little_set(Z_24)
| member(Z_24,cs) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_47]) ).
tff(c_81,plain,
! [Y_29,X_30] :
( ( Y_29 = X_30 )
| ~ member(f1(X_30,Y_29),Y_29)
| ~ member(f1(X_30,Y_29),X_30) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_95,plain,
! [X_30] :
( ( cs = X_30 )
| ~ member(f1(X_30,cs),X_30)
| member(f1(X_30,cs),bs)
| ~ little_set(f1(X_30,cs)) ),
inference(resolution,[status(thm)],[c_59,c_81]) ).
tff(c_2724,plain,
( ( cs = as )
| member(f1(as,cs),bs)
| ~ little_set(f1(as,cs)) ),
inference(resolution,[status(thm)],[c_2715,c_95]) ).
tff(c_2730,plain,
( ( cs = as )
| member(f1(as,cs),bs) ),
inference(demodulation,[status(thm),theory(equality)],[c_2716,c_2724]) ).
tff(c_2731,plain,
member(f1(as,cs),bs),
inference(negUnitSimplification,[status(thm)],[c_22,c_2730]) ).
tff(c_39,plain,
! [Z_21,X_22] :
( ~ member(Z_21,X_22)
| ~ member(Z_21,complement(X_22)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_42,plain,
! [Z_21] :
( ~ member(Z_21,as)
| ~ member(Z_21,bs) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_39]) ).
tff(c_2804,plain,
~ member(f1(as,cs),as),
inference(resolution,[status(thm)],[c_2731,c_42]) ).
tff(c_2814,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2715,c_2804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SET012-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.02/0.13 % 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
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 19:40:11 EDT 2025
% 0.14/0.34 % CPUTime :
% 4.92/2.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.92/2.21
% 4.92/2.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------