%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET162+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 08:38:09 PM UTC 2025
% Result : Theorem 8.73s 3.57s
% Output : CNFRefutation 8.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 11 ~; 13 |; 1 &)
% ( 3 <=>; 1 =>; 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > union > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_5 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $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(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_47,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_55,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_33,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
tff(f_37,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_44,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(f_77,negated_conjecture,
~ ! [B] : ( union(B,empty_set) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_empty_set) ).
tff(c_16,plain,
! [C_8,B_7] : ( union(C_8,B_7) = union(B_7,C_8) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_22,plain,
! [B_9,C_10] :
( member('#skF_1'(B_9,C_10),B_9)
| subset(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_92,plain,
! [D_33,C_34,B_35] :
( ~ member(D_33,C_34)
| member(D_33,union(B_35,C_34)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_20,plain,
! [B_9,C_10] :
( ~ member('#skF_1'(B_9,C_10),C_10)
| subset(B_9,C_10) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_628,plain,
! [B_105,B_106,C_107] :
( subset(B_105,union(B_106,C_107))
| ~ member('#skF_1'(B_105,union(B_106,C_107)),C_107) ),
inference(resolution,[status(thm)],[c_92,c_20]) ).
tff(c_655,plain,
! [B_108,B_109] : subset(B_108,union(B_109,B_108)),
inference(resolution,[status(thm)],[c_22,c_628]) ).
tff(c_677,plain,
! [C_8,B_7] : subset(C_8,union(C_8,B_7)),
inference(superposition,[status(thm),theory(equality)],[c_16,c_655]) ).
tff(c_233,plain,
! [D_63,C_64,B_65] :
( member(D_63,C_64)
| member(D_63,B_65)
| ~ member(D_63,union(B_65,C_64)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_2041,plain,
! [B_198,C_199,C_200] :
( member('#skF_1'(union(B_198,C_199),C_200),C_199)
| member('#skF_1'(union(B_198,C_199),C_200),B_198)
| subset(union(B_198,C_199),C_200) ),
inference(resolution,[status(thm)],[c_22,c_233]) ).
tff(c_8,plain,
! [B_4] : ~ member(B_4,empty_set),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_5640,plain,
! [B_265,C_266] :
( member('#skF_1'(union(B_265,empty_set),C_266),B_265)
| subset(union(B_265,empty_set),C_266) ),
inference(resolution,[status(thm)],[c_2041,c_8]) ).
tff(c_5707,plain,
! [B_267] : subset(union(B_267,empty_set),B_267),
inference(resolution,[status(thm)],[c_5640,c_20]) ).
tff(c_10,plain,
! [C_6,B_5] :
( ( C_6 = B_5 )
| ~ subset(C_6,B_5)
| ~ subset(B_5,C_6) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_5771,plain,
! [B_267] :
( ( union(B_267,empty_set) = B_267 )
| ~ subset(B_267,union(B_267,empty_set)) ),
inference(resolution,[status(thm)],[c_5707,c_10]) ).
tff(c_5816,plain,
! [B_267] : ( union(B_267,empty_set) = B_267 ),
inference(demodulation,[status(thm),theory(equality)],[c_677,c_5771]) ).
tff(c_42,plain,
union('#skF_5',empty_set) != '#skF_5',
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_5837,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5816,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET162+3 : TPTP v9.0.0. Released v2.2.0.
% 0.02/0.10 % 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
% 0.09/0.29 % Computer : n009.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Apr 8 20:12:56 EDT 2025
% 0.09/0.29 % CPUTime :
% 8.73/3.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.73/3.58
% 8.73/3.58 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------