%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET633+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 : n022.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 08:38:57 PM UTC 2025
% Result : Theorem 4.60s 2.15s
% Output : CNFRefutation 4.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 5 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > symmetric_difference > difference > #nlpp > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(union,type,
union: ( $i * $i ) > $i ).
tff(symmetric_difference,type,
symmetric_difference: ( $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('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_79,negated_conjecture,
~ ! [B,C,D] :
( ( subset(difference(B,C),D)
& subset(difference(C,B),D) )
=> subset(symmetric_difference(B,C),D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th115) ).
tff(f_31,axiom,
! [B,C] : ( symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
tff(f_38,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(D,C) )
=> subset(union(B,D),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_subset) ).
tff(c_40,plain,
subset(difference('#skF_4','#skF_5'),'#skF_6'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_38,plain,
subset(difference('#skF_5','#skF_4'),'#skF_6'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_2,plain,
! [B_1,C_2] : ( union(difference(B_1,C_2),difference(C_2,B_1)) = symmetric_difference(B_1,C_2) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_186,plain,
! [B_46,D_47,C_48] :
( subset(union(B_46,D_47),C_48)
| ~ subset(D_47,C_48)
| ~ subset(B_46,C_48) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_1000,plain,
! [B_148,C_149,C_150] :
( subset(symmetric_difference(B_148,C_149),C_150)
| ~ subset(difference(C_149,B_148),C_150)
| ~ subset(difference(B_148,C_149),C_150) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_186]) ).
tff(c_36,plain,
~ subset(symmetric_difference('#skF_4','#skF_5'),'#skF_6'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_1018,plain,
( ~ subset(difference('#skF_5','#skF_4'),'#skF_6')
| ~ subset(difference('#skF_4','#skF_5'),'#skF_6') ),
inference(resolution,[status(thm)],[c_1000,c_36]) ).
tff(c_1033,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_38,c_1018]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET633+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.13 % 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 : n022.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 : Tue Apr 8 21:21:06 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.60/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.60/2.16
% 4.60/2.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------