%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET027+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 : 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 08:37:35 PM UTC 2025
% Result : Theorem 2.75s 1.65s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 30 ( 12 ~; 14 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > #nlpp > #skF_2 > #skF_3 > #skF_4 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_46,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,C)
& subset(C,D) )
=> subset(B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
tff(f_35,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(c_10,plain,
~ subset('#skF_2','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_14,plain,
subset('#skF_2','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_12,plain,
subset('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_6,plain,
! [B_1,C_2] :
( member('#skF_1'(B_1,C_2),B_1)
| subset(B_1,C_2) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_24,plain,
! [D_12,C_13,B_14] :
( member(D_12,C_13)
| ~ member(D_12,B_14)
| ~ subset(B_14,C_13) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_28,plain,
! [B_15,C_16,C_17] :
( member('#skF_1'(B_15,C_16),C_17)
| ~ subset(B_15,C_17)
| subset(B_15,C_16) ),
inference(resolution,[status(thm)],[c_6,c_24]) ).
tff(c_2,plain,
! [D_5,C_2,B_1] :
( member(D_5,C_2)
| ~ member(D_5,B_1)
| ~ subset(B_1,C_2) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_37,plain,
! [B_18,C_19,C_20,C_21] :
( member('#skF_1'(B_18,C_19),C_20)
| ~ subset(C_21,C_20)
| ~ subset(B_18,C_21)
| subset(B_18,C_19) ),
inference(resolution,[status(thm)],[c_28,c_2]) ).
tff(c_47,plain,
! [B_22,C_23] :
( member('#skF_1'(B_22,C_23),'#skF_4')
| ~ subset(B_22,'#skF_3')
| subset(B_22,C_23) ),
inference(resolution,[status(thm)],[c_12,c_37]) ).
tff(c_4,plain,
! [B_1,C_2] :
( ~ member('#skF_1'(B_1,C_2),C_2)
| subset(B_1,C_2) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_56,plain,
! [B_24] :
( ~ subset(B_24,'#skF_3')
| subset(B_24,'#skF_4') ),
inference(resolution,[status(thm)],[c_47,c_4]) ).
tff(c_63,plain,
subset('#skF_2','#skF_4'),
inference(resolution,[status(thm)],[c_14,c_56]) ).
tff(c_69,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET027+3 : TPTP v9.0.0. Released v2.2.0.
% 0.14/0.13 % 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
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 8 19:46:41 EDT 2025
% 0.14/0.35 % CPUTime :
% 2.75/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.75/1.65
% 2.75/1.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------