%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET585+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 : n026.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 08:38:46 PM UTC 2025
% Result : Theorem 3.69s 2.15s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 3 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > intersection > #nlpp > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(intersection,type,
intersection: ( $i * $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('#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_39,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
tff(f_36,axiom,
! [B,C] : subset(B,union(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
tff(f_33,axiom,
! [B,C,D] :
( ( subset(B,C)
& subset(C,D) )
=> subset(B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subset) ).
tff(f_82,negated_conjecture,
~ ! [B,C,D] : subset(intersection(B,C),union(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_subset_of_union) ).
tff(c_6,plain,
! [B_6,C_7] : subset(intersection(B_6,C_7),B_6),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_4,plain,
! [B_4,C_5] : subset(B_4,union(B_4,C_5)),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_212,plain,
! [B_61,D_62,C_63] :
( subset(B_61,D_62)
| ~ subset(C_63,D_62)
| ~ subset(B_61,C_63) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_228,plain,
! [B_64,B_65,C_66] :
( subset(B_64,union(B_65,C_66))
| ~ subset(B_64,B_65) ),
inference(resolution,[status(thm)],[c_4,c_212]) ).
tff(c_44,plain,
~ subset(intersection('#skF_4','#skF_5'),union('#skF_4','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_233,plain,
~ subset(intersection('#skF_4','#skF_5'),'#skF_4'),
inference(resolution,[status(thm)],[c_228,c_44]) ).
tff(c_244,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET585+3 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.13 % 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
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 8 21:16:08 EDT 2025
% 0.15/0.35 % CPUTime :
% 3.69/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.69/2.16
% 3.69/2.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------