%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET909+1 : TPTP v9.0.0. Released v3.2.0.
% 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 : n005.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 08:39:33 PM UTC 2025
% Result : Theorem 3.39s 1.83s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 7 ~; 4 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 25 ( 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_union2 > #nlpp > empty_set > #skF_1 > #skF_4 > #skF_7 > #skF_10 > #skF_6 > #skF_5 > #skF_2 > #skF_9 > #skF_8 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(f_50,axiom,
! [A,B,C] :
( ( C = unordered_pair(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
tff(f_41,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_83,negated_conjecture,
~ ! [A,B,C] : ( set_union2(unordered_pair(A,B),C) != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
tff(f_35,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_59,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(c_14,plain,
! [D_16,A_11] : in(D_16,unordered_pair(A_11,D_16)),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_8,plain,
! [B_10] : ~ in(B_10,empty_set),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_60,plain,
set_union2(unordered_pair('#skF_8','#skF_9'),'#skF_10') = empty_set,
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_166,plain,
! [B_46,A_47] : ( set_union2(B_46,A_47) = set_union2(A_47,B_46) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_205,plain,
set_union2('#skF_10',unordered_pair('#skF_8','#skF_9')) = empty_set,
inference(superposition,[status(thm),theory(equality)],[c_60,c_166]) ).
tff(c_250,plain,
! [D_51,B_52,A_53] :
( ~ in(D_51,B_52)
| in(D_51,set_union2(A_53,B_52)) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_263,plain,
! [D_51] :
( ~ in(D_51,unordered_pair('#skF_8','#skF_9'))
| in(D_51,empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_205,c_250]) ).
tff(c_298,plain,
! [D_55] : ~ in(D_55,unordered_pair('#skF_8','#skF_9')),
inference(negUnitSimplification,[status(thm)],[c_8,c_263]) ).
tff(c_306,plain,
$false,
inference(resolution,[status(thm)],[c_14,c_298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET909+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % 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
% 0.12/0.34 % Computer : n005.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 21:49:57 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.39/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.39/1.83
% 3.39/1.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------