%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET902+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 : 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 08:39:33 PM UTC 2025
% Result : Theorem 3.00s 1.76s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 53 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 19 |; 6 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > set_union2 > #nlpp > singleton > empty_set > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(f_80,negated_conjecture,
~ ! [A,B,C] :
~ ( ( singleton(A) = set_union2(B,C) )
& ~ ( ( B = singleton(A) )
& ( C = singleton(A) ) )
& ~ ( ( B = empty_set )
& ( C = singleton(A) ) )
& ~ ( ( B = singleton(A) )
& ( C = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
tff(f_82,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
tff(f_54,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( ( A = empty_set )
| ( A = singleton(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
tff(f_30,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_48,axiom,
! [A] : ( singleton(A) != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
tff(f_45,axiom,
! [A,B] : ( set_union2(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
tff(c_28,plain,
( ( singleton('#skF_3') != '#skF_5' )
| ( empty_set != '#skF_4' ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_52,plain,
empty_set != '#skF_4',
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_26,plain,
( ( empty_set != '#skF_5' )
| ( singleton('#skF_3') != '#skF_4' ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_53,plain,
singleton('#skF_3') != '#skF_4',
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_32,plain,
set_union2('#skF_4','#skF_5') = singleton('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_54,plain,
! [A_20,B_21] : subset(A_20,set_union2(A_20,B_21)),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_57,plain,
subset('#skF_4',singleton('#skF_3')),
inference(superposition,[status(thm),theory(equality)],[c_32,c_54]) ).
tff(c_145,plain,
! [B_30,A_31] :
( ( singleton(B_30) = A_31 )
| ( empty_set = A_31 )
| ~ subset(A_31,singleton(B_30)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_151,plain,
( ( singleton('#skF_3') = '#skF_4' )
| ( empty_set = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_57,c_145]) ).
tff(c_163,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52,c_53,c_151]) ).
tff(c_164,plain,
empty_set != '#skF_5',
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_165,plain,
singleton('#skF_3') = '#skF_4',
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_30,plain,
( ( singleton('#skF_3') != '#skF_5' )
| ( singleton('#skF_3') != '#skF_4' ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_176,plain,
'#skF_5' != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_165,c_165,c_30]) ).
tff(c_166,plain,
set_union2('#skF_4','#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_165,c_32]) ).
tff(c_197,plain,
! [B_36,A_37] : ( set_union2(B_36,A_37) = set_union2(A_37,B_36) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_34,plain,
! [A_14,B_15] : subset(A_14,set_union2(A_14,B_15)),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_242,plain,
! [A_38,B_39] : subset(A_38,set_union2(B_39,A_38)),
inference(superposition,[status(thm),theory(equality)],[c_197,c_34]) ).
tff(c_251,plain,
subset('#skF_5','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_166,c_242]) ).
tff(c_272,plain,
! [B_42,A_43] :
( ( singleton(B_42) = A_43 )
| ( empty_set = A_43 )
| ~ subset(A_43,singleton(B_42)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_275,plain,
! [A_43] :
( ( singleton('#skF_3') = A_43 )
| ( empty_set = A_43 )
| ~ subset(A_43,'#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_165,c_272]) ).
tff(c_293,plain,
! [A_44] :
( ( A_44 = '#skF_4' )
| ( empty_set = A_44 )
| ~ subset(A_44,'#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_165,c_275]) ).
tff(c_296,plain,
( ( '#skF_5' = '#skF_4' )
| ( empty_set = '#skF_5' ) ),
inference(resolution,[status(thm)],[c_251,c_293]) ).
tff(c_307,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_164,c_176,c_296]) ).
tff(c_309,plain,
empty_set = '#skF_4',
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_12,plain,
! [A_9] : ( singleton(A_9) != empty_set ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_311,plain,
! [A_9] : ( singleton(A_9) != '#skF_4' ),
inference(demodulation,[status(thm),theory(equality)],[c_309,c_12]) ).
tff(c_10,plain,
! [A_7] : ( set_union2(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_308,plain,
singleton('#skF_3') != '#skF_5',
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_337,plain,
! [B_51,A_52] : ( set_union2(B_51,A_52) = set_union2(A_52,B_51) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_396,plain,
! [A_55,B_56] : subset(A_55,set_union2(B_56,A_55)),
inference(superposition,[status(thm),theory(equality)],[c_337,c_34]) ).
tff(c_405,plain,
subset('#skF_5',singleton('#skF_3')),
inference(superposition,[status(thm),theory(equality)],[c_32,c_396]) ).
tff(c_14,plain,
! [B_11,A_10] :
( ( singleton(B_11) = A_10 )
| ( empty_set = A_10 )
| ~ subset(A_10,singleton(B_11)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_414,plain,
! [B_57,A_58] :
( ( singleton(B_57) = A_58 )
| ( A_58 = '#skF_4' )
| ~ subset(A_58,singleton(B_57)) ),
inference(demodulation,[status(thm),theory(equality)],[c_309,c_14]) ).
tff(c_417,plain,
( ( singleton('#skF_3') = '#skF_5' )
| ( '#skF_5' = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_405,c_414]) ).
tff(c_427,plain,
'#skF_5' = '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_308,c_417]) ).
tff(c_438,plain,
set_union2('#skF_4','#skF_4') = singleton('#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_32]) ).
tff(c_440,plain,
singleton('#skF_3') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_10,c_438]) ).
tff(c_442,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_311,c_440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET902+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.11 % 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
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 8 21:49:26 EDT 2025
% 0.11/0.32 % CPUTime :
% 3.00/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.00/1.77
% 3.00/1.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------