%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET002+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/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 08:37:24 PM UTC 2025
% Result : Theorem 3.21s 2.15s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > #nlpp > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_59,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(f_31,axiom,
! [B,C] :
( subset(B,C)
=> ( union(B,C) = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).
tff(f_71,negated_conjecture,
~ ! [B] : ( union(B,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
tff(c_24,plain,
! [B_15] : subset(B_15,B_15),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_75,plain,
! [B_24,C_25] :
( ( union(B_24,C_25) = C_25 )
| ~ subset(B_24,C_25) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_79,plain,
! [B_15] : ( union(B_15,B_15) = B_15 ),
inference(resolution,[status(thm)],[c_24,c_75]) ).
tff(c_38,plain,
union('#skF_4','#skF_4') != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_82,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_79,c_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET002+3 : TPTP v9.0.0. Released v2.2.0.
% 0.10/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/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 : Tue Apr 8 19:39:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.21/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.21/2.16
% 3.21/2.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------