%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET605+3 : TPTP v9.0.0. Released v2.2.0.
% 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 : n021.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 08:38:51 PM UTC 2025
% Result : Theorem 3.74s 2.25s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > union > difference > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_5 > #skF_6 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_63,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_29,axiom,
! [B,C] : subset(B,union(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
tff(f_34,axiom,
! [B,C] :
( ( difference(B,C) = empty_set )
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
tff(f_93,negated_conjecture,
~ ! [B,C] : ( difference(B,union(B,C)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th76) ).
tff(c_62,plain,
! [C_37,B_38] : ( union(C_37,B_38) = union(B_38,C_37) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_2,plain,
! [B_1,C_2] : subset(B_1,union(B_1,C_2)),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_77,plain,
! [B_38,C_37] : subset(B_38,union(C_37,B_38)),
inference(superposition,[status(thm),theory(equality)],[c_62,c_2]) ).
tff(c_122,plain,
! [B_44,C_45] :
( ( difference(B_44,C_45) = empty_set )
| ~ subset(B_44,C_45) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_136,plain,
! [B_38,C_37] : ( difference(B_38,union(C_37,B_38)) = empty_set ),
inference(resolution,[status(thm)],[c_77,c_122]) ).
tff(c_28,plain,
! [C_15,B_14] : ( union(C_15,B_14) = union(B_14,C_15) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_54,plain,
difference('#skF_5',union('#skF_5','#skF_6')) != empty_set,
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_55,plain,
difference('#skF_5',union('#skF_6','#skF_5')) != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_54]) ).
tff(c_161,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_136,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SET605+3 : TPTP v9.0.0. Released v2.2.0.
% 0.09/0.12 % 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
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 8 21:18:14 EDT 2025
% 0.15/0.32 % CPUTime :
% 3.74/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.74/2.26
% 3.74/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------