%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET618+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 : 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 08:38:54 PM UTC 2025
% Result : Theorem 3.26s 2.03s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 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; 2 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > union > symmetric_difference > difference > #nlpp > empty_set > #skF_4 > #skF_3 > #skF_5 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_4',type,
'#skF_4': $i > $i ).
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(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $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_35,axiom,
! [B] : ( difference(B,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
tff(f_29,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_32,axiom,
! [B] : ( union(B,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotency_of_union) ).
tff(f_82,negated_conjecture,
~ ! [B] : ( symmetric_difference(B,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th93) ).
tff(c_6,plain,
! [B_4] : ( difference(B_4,B_4) = empty_set ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_219,plain,
! [B_54,C_55] : ( union(difference(B_54,C_55),difference(C_55,B_54)) = symmetric_difference(B_54,C_55) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_4,plain,
! [B_3] : ( union(B_3,B_3) = B_3 ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_232,plain,
! [C_55] : ( symmetric_difference(C_55,C_55) = difference(C_55,C_55) ),
inference(superposition,[status(thm),theory(equality)],[c_219,c_4]) ).
tff(c_253,plain,
! [C_55] : ( symmetric_difference(C_55,C_55) = empty_set ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_232]) ).
tff(c_44,plain,
symmetric_difference('#skF_5','#skF_5') != empty_set,
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_260,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_253,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET618+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.11 % 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
% 0.10/0.30 % Computer : n009.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Apr 8 21:19:26 EDT 2025
% 0.10/0.30 % CPUTime :
% 3.26/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.26/2.04
% 3.26/2.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------