%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET887+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 : n028.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 08:39:31 PM UTC 2025
% Result : Theorem 9.16s 3.22s
% Output : CNFRefutation 9.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 47 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 48 ( 19 ~; 19 |; 5 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 37 ( 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > #nlpp > singleton > empty_set > #skF_1 > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_9 > #skF_8 > #skF_4 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $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_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(f_90,negated_conjecture,
~ ! [A,B,C,D] :
~ ( subset(unordered_pair(A,B),unordered_pair(C,D))
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_zfmisc_1) ).
tff(f_39,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_64,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
tff(f_48,axiom,
! [A,B,C] :
( ( C = unordered_pair(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
tff(f_33,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_94,axiom,
! [A,B,C] :
( ( singleton(A) = unordered_pair(B,C) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
tff(c_48,plain,
'#skF_6' != '#skF_9',
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_50,plain,
'#skF_6' != '#skF_8',
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_6,plain,
! [B_8] : ~ in(B_8,empty_set),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_52,plain,
subset(unordered_pair('#skF_6','#skF_7'),unordered_pair('#skF_8','#skF_9')),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_645,plain,
! [B_93,C_94,A_95] :
( ( unordered_pair(B_93,C_94) = A_95 )
| ( singleton(C_94) = A_95 )
| ( singleton(B_93) = A_95 )
| ( empty_set = A_95 )
| ~ subset(A_95,unordered_pair(B_93,C_94)) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_674,plain,
( ( unordered_pair('#skF_6','#skF_7') = unordered_pair('#skF_8','#skF_9') )
| ( unordered_pair('#skF_6','#skF_7') = singleton('#skF_9') )
| ( unordered_pair('#skF_6','#skF_7') = singleton('#skF_8') )
| ( unordered_pair('#skF_6','#skF_7') = empty_set ) ),
inference(resolution,[status(thm)],[c_52,c_645]) ).
tff(c_7772,plain,
unordered_pair('#skF_6','#skF_7') = empty_set,
inference(splitLeft,[status(thm)],[c_674]) ).
tff(c_14,plain,
! [D_14,B_10] : in(D_14,unordered_pair(D_14,B_10)),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_7864,plain,
in('#skF_6',empty_set),
inference(superposition,[status(thm),theory(equality)],[c_7772,c_14]) ).
tff(c_7986,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6,c_7864]) ).
tff(c_7987,plain,
( ( unordered_pair('#skF_6','#skF_7') = singleton('#skF_8') )
| ( unordered_pair('#skF_6','#skF_7') = singleton('#skF_9') )
| ( unordered_pair('#skF_6','#skF_7') = unordered_pair('#skF_8','#skF_9') ) ),
inference(splitRight,[status(thm)],[c_674]) ).
tff(c_7999,plain,
unordered_pair('#skF_6','#skF_7') = unordered_pair('#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_7987]) ).
tff(c_8092,plain,
in('#skF_6',unordered_pair('#skF_8','#skF_9')),
inference(superposition,[status(thm),theory(equality)],[c_7999,c_14]) ).
tff(c_4,plain,
! [B_4,A_3] : ( unordered_pair(B_4,A_3) = unordered_pair(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_180,plain,
! [D_55,B_56,A_57] :
( ( D_55 = B_56 )
| ( D_55 = A_57 )
| ~ in(D_55,unordered_pair(A_57,B_56)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_187,plain,
! [D_55,B_4,A_3] :
( ( D_55 = B_4 )
| ( D_55 = A_3 )
| ~ in(D_55,unordered_pair(B_4,A_3)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_180]) ).
tff(c_8586,plain,
( ( '#skF_6' = '#skF_8' )
| ( '#skF_6' = '#skF_9' ) ),
inference(resolution,[status(thm)],[c_8092,c_187]) ).
tff(c_8703,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_50,c_8586]) ).
tff(c_8704,plain,
( ( unordered_pair('#skF_6','#skF_7') = singleton('#skF_9') )
| ( unordered_pair('#skF_6','#skF_7') = singleton('#skF_8') ) ),
inference(splitRight,[status(thm)],[c_7987]) ).
tff(c_8716,plain,
unordered_pair('#skF_6','#skF_7') = singleton('#skF_8'),
inference(splitLeft,[status(thm)],[c_8704]) ).
tff(c_54,plain,
! [B_25,A_24,C_26] :
( ( B_25 = A_24 )
| ( unordered_pair(B_25,C_26) != singleton(A_24) ) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_8793,plain,
! [A_24] :
( ( A_24 = '#skF_6' )
| ( singleton(A_24) != singleton('#skF_8') ) ),
inference(superposition,[status(thm),theory(equality)],[c_8716,c_54]) ).
tff(c_9647,plain,
'#skF_6' = '#skF_8',
inference(reflexivity,[status(thm),theory(equality)],[c_8793]) ).
tff(c_9649,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_9647]) ).
tff(c_9650,plain,
unordered_pair('#skF_6','#skF_7') = singleton('#skF_9'),
inference(splitRight,[status(thm)],[c_8704]) ).
tff(c_9728,plain,
! [A_24] :
( ( A_24 = '#skF_6' )
| ( singleton(A_24) != singleton('#skF_9') ) ),
inference(superposition,[status(thm),theory(equality)],[c_9650,c_54]) ).
tff(c_9913,plain,
'#skF_6' = '#skF_9',
inference(reflexivity,[status(thm),theory(equality)],[c_9728]) ).
tff(c_9915,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48,c_9913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET887+1 : TPTP v9.0.0. Released v3.2.0.
% 0.13/0.13 % 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 : n028.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 21:49:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 9.16/3.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.16/3.23
% 9.16/3.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------