%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET890+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/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 08:39:32 PM UTC 2025
% Result : Theorem 14.10s 5.09s
% Output : CNFRefutation 14.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 21 ~; 31 |; 1 &)
% ( 4 <=>; 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 32 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > #nlpp > union > singleton > #skF_6 > #skF_3 > #skF_10 > #skF_9 > #skF_7 > #skF_8 > #skF_2 > #skF_1 > #skF_5 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(union,type,
union: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_75,negated_conjecture,
~ ! [A] : ( union(singleton(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
tff(f_44,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_61,axiom,
! [A,B] :
( ( B = union(A) )
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
tff(c_54,plain,
union(singleton('#skF_10')) != '#skF_10',
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_12,plain,
! [C_9] : in(C_9,singleton(C_9)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_42,plain,
! [A_15,B_16] :
( in('#skF_5'(A_15,B_16),A_15)
| in('#skF_6'(A_15,B_16),B_16)
| ( union(A_15) = B_16 ) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_1011,plain,
! [A_131,B_132,D_133] :
( in('#skF_5'(A_131,B_132),A_131)
| ~ in(D_133,A_131)
| ~ in('#skF_6'(A_131,B_132),D_133)
| ( union(A_131) = B_132 ) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_1292,plain,
! [B_153,A_154] :
( ~ in(B_153,A_154)
| in('#skF_5'(A_154,B_153),A_154)
| ( union(A_154) = B_153 ) ),
inference(resolution,[status(thm)],[c_42,c_1011]) ).
tff(c_10,plain,
! [C_9,A_5] :
( ( C_9 = A_5 )
| ~ in(C_9,singleton(A_5)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_20133,plain,
! [A_580,B_581] :
( ( '#skF_5'(singleton(A_580),B_581) = A_580 )
| ~ in(B_581,singleton(A_580))
| ( union(singleton(A_580)) = B_581 ) ),
inference(resolution,[status(thm)],[c_1292,c_10]) ).
tff(c_20228,plain,
! [C_582] :
( ( '#skF_5'(singleton(C_582),C_582) = C_582 )
| ( union(singleton(C_582)) = C_582 ) ),
inference(resolution,[status(thm)],[c_12,c_20133]) ).
tff(c_21134,plain,
'#skF_5'(singleton('#skF_10'),'#skF_10') = '#skF_10',
inference(superposition,[status(thm),theory(equality)],[c_20228,c_54]) ).
tff(c_44,plain,
! [A_15,B_16] :
( in('#skF_4'(A_15,B_16),'#skF_5'(A_15,B_16))
| in('#skF_6'(A_15,B_16),B_16)
| ( union(A_15) = B_16 ) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_21168,plain,
( in('#skF_4'(singleton('#skF_10'),'#skF_10'),'#skF_10')
| in('#skF_6'(singleton('#skF_10'),'#skF_10'),'#skF_10')
| ( union(singleton('#skF_10')) = '#skF_10' ) ),
inference(superposition,[status(thm),theory(equality)],[c_21134,c_44]) ).
tff(c_21192,plain,
( in('#skF_4'(singleton('#skF_10'),'#skF_10'),'#skF_10')
| in('#skF_6'(singleton('#skF_10'),'#skF_10'),'#skF_10') ),
inference(negUnitSimplification,[status(thm)],[c_54,c_21168]) ).
tff(c_23083,plain,
in('#skF_6'(singleton('#skF_10'),'#skF_10'),'#skF_10'),
inference(splitLeft,[status(thm)],[c_21192]) ).
tff(c_38,plain,
! [A_15,B_16,D_29] :
( in('#skF_4'(A_15,B_16),'#skF_5'(A_15,B_16))
| ~ in(D_29,A_15)
| ~ in('#skF_6'(A_15,B_16),D_29)
| ( union(A_15) = B_16 ) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_23089,plain,
( in('#skF_4'(singleton('#skF_10'),'#skF_10'),'#skF_5'(singleton('#skF_10'),'#skF_10'))
| ~ in('#skF_10',singleton('#skF_10'))
| ( union(singleton('#skF_10')) = '#skF_10' ) ),
inference(resolution,[status(thm)],[c_23083,c_38]) ).
tff(c_23102,plain,
( in('#skF_4'(singleton('#skF_10'),'#skF_10'),'#skF_10')
| ( union(singleton('#skF_10')) = '#skF_10' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_21134,c_23089]) ).
tff(c_23103,plain,
in('#skF_4'(singleton('#skF_10'),'#skF_10'),'#skF_10'),
inference(negUnitSimplification,[status(thm)],[c_54,c_23102]) ).
tff(c_34,plain,
! [A_15,B_16,D_29] :
( ~ in('#skF_4'(A_15,B_16),B_16)
| ~ in(D_29,A_15)
| ~ in('#skF_6'(A_15,B_16),D_29)
| ( union(A_15) = B_16 ) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_23121,plain,
! [D_29] :
( ~ in(D_29,singleton('#skF_10'))
| ~ in('#skF_6'(singleton('#skF_10'),'#skF_10'),D_29)
| ( union(singleton('#skF_10')) = '#skF_10' ) ),
inference(resolution,[status(thm)],[c_23103,c_34]) ).
tff(c_23621,plain,
! [D_598] :
( ~ in(D_598,singleton('#skF_10'))
| ~ in('#skF_6'(singleton('#skF_10'),'#skF_10'),D_598) ),
inference(negUnitSimplification,[status(thm)],[c_54,c_23121]) ).
tff(c_23627,plain,
~ in('#skF_10',singleton('#skF_10')),
inference(resolution,[status(thm)],[c_23083,c_23621]) ).
tff(c_23780,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_23627]) ).
tff(c_23781,plain,
in('#skF_4'(singleton('#skF_10'),'#skF_10'),'#skF_10'),
inference(splitRight,[status(thm)],[c_21192]) ).
tff(c_40,plain,
! [A_15,B_16] :
( ~ in('#skF_4'(A_15,B_16),B_16)
| in('#skF_6'(A_15,B_16),B_16)
| ( union(A_15) = B_16 ) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_23782,plain,
~ in('#skF_6'(singleton('#skF_10'),'#skF_10'),'#skF_10'),
inference(splitRight,[status(thm)],[c_21192]) ).
tff(c_23825,plain,
( ~ in('#skF_4'(singleton('#skF_10'),'#skF_10'),'#skF_10')
| ( union(singleton('#skF_10')) = '#skF_10' ) ),
inference(resolution,[status(thm)],[c_40,c_23782]) ).
tff(c_23834,plain,
union(singleton('#skF_10')) = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_23781,c_23825]) ).
tff(c_23836,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_23834]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET890+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 21:49:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 14.10/5.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.41/5.10
% 14.41/5.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------