TSTP Solution File: SEU147+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU147+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n011.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 : Tue Aug 22 10:57:45 EDT 2023
% Result : Theorem 4.63s 2.26s
% Output : CNFRefutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 48 ( 11 unt; 14 typ; 0 def)
% Number of atoms : 82 ( 51 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 72 ( 24 ~; 43 |; 0 &)
% ( 4 <=>; 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 : 19 ( 11 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 38 (; 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > #nlpp > singleton > powerset > empty_set > #skF_3 > #skF_5 > #skF_6 > #skF_8 > #skF_2 > #skF_7 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $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_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_54,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_45,axiom,
! [A,B] :
( ( B = powerset(A) )
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
tff(f_56,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
tff(f_38,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_67,axiom,
! [A] :
( subset(A,empty_set)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
tff(c_40,plain,
! [A_13] : subset(A_13,A_13),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_18,plain,
! [C_12,A_8] :
( in(C_12,powerset(A_8))
| ~ subset(C_12,A_8) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_42,plain,
singleton(empty_set) != powerset(empty_set),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_118,plain,
! [A_43,B_44] :
( ( '#skF_1'(A_43,B_44) = A_43 )
| in('#skF_2'(A_43,B_44),B_44)
| ( singleton(A_43) = B_44 ) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_16,plain,
! [C_12,A_8] :
( subset(C_12,A_8)
| ~ in(C_12,powerset(A_8)) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_456,plain,
! [A_99,A_100] :
( subset('#skF_2'(A_99,powerset(A_100)),A_100)
| ( '#skF_1'(A_99,powerset(A_100)) = A_99 )
| ( singleton(A_99) = powerset(A_100) ) ),
inference(resolution,[status(thm)],[c_118,c_16]) ).
tff(c_52,plain,
! [A_18] :
( ( empty_set = A_18 )
| ~ subset(A_18,empty_set) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_463,plain,
! [A_101] :
( ( '#skF_2'(A_101,powerset(empty_set)) = empty_set )
| ( '#skF_1'(A_101,powerset(empty_set)) = A_101 )
| ( singleton(A_101) = powerset(empty_set) ) ),
inference(resolution,[status(thm)],[c_456,c_52]) ).
tff(c_10,plain,
! [A_3,B_4] :
( ( '#skF_1'(A_3,B_4) = A_3 )
| ( '#skF_2'(A_3,B_4) != A_3 )
| ( singleton(A_3) = B_4 ) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_480,plain,
! [A_101] :
( ( '#skF_1'(A_101,powerset(empty_set)) = A_101 )
| ( empty_set != A_101 )
| ( singleton(A_101) = powerset(empty_set) )
| ( '#skF_1'(A_101,powerset(empty_set)) = A_101 )
| ( singleton(A_101) = powerset(empty_set) ) ),
inference(superposition,[status(thm),theory(equality)],[c_463,c_10]) ).
tff(c_901,plain,
! [A_158] :
( ( empty_set != A_158 )
| ( singleton(A_158) = powerset(empty_set) )
| ( '#skF_1'(A_158,powerset(empty_set)) = A_158 ) ),
inference(factorization,[status(thm),theory(equality)],[c_480]) ).
tff(c_254,plain,
! [A_70,B_71] :
( ~ in('#skF_1'(A_70,B_71),B_71)
| in('#skF_2'(A_70,B_71),B_71)
| ( singleton(A_70) = B_71 ) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_633,plain,
! [A_125,A_126] :
( subset('#skF_2'(A_125,powerset(A_126)),A_126)
| ~ in('#skF_1'(A_125,powerset(A_126)),powerset(A_126))
| ( singleton(A_125) = powerset(A_126) ) ),
inference(resolution,[status(thm)],[c_254,c_16]) ).
tff(c_675,plain,
! [A_134,A_135] :
( subset('#skF_2'(A_134,powerset(A_135)),A_135)
| ( singleton(A_134) = powerset(A_135) )
| ~ subset('#skF_1'(A_134,powerset(A_135)),A_135) ),
inference(resolution,[status(thm)],[c_18,c_633]) ).
tff(c_683,plain,
! [A_134] :
( ( '#skF_2'(A_134,powerset(empty_set)) = empty_set )
| ( singleton(A_134) = powerset(empty_set) )
| ~ subset('#skF_1'(A_134,powerset(empty_set)),empty_set) ),
inference(resolution,[status(thm)],[c_675,c_52]) ).
tff(c_907,plain,
! [A_158] :
( ( '#skF_2'(A_158,powerset(empty_set)) = empty_set )
| ( singleton(A_158) = powerset(empty_set) )
| ~ subset(A_158,empty_set)
| ( empty_set != A_158 )
| ( singleton(A_158) = powerset(empty_set) ) ),
inference(superposition,[status(thm),theory(equality)],[c_901,c_683]) ).
tff(c_14,plain,
! [A_3,B_4] :
( ( '#skF_1'(A_3,B_4) = A_3 )
| in('#skF_2'(A_3,B_4),B_4)
| ( singleton(A_3) = B_4 ) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_478,plain,
! [A_101] :
( ( '#skF_1'(A_101,powerset(empty_set)) = A_101 )
| in(empty_set,powerset(empty_set))
| ( singleton(A_101) = powerset(empty_set) )
| ( '#skF_1'(A_101,powerset(empty_set)) = A_101 )
| ( singleton(A_101) = powerset(empty_set) ) ),
inference(superposition,[status(thm),theory(equality)],[c_463,c_14]) ).
tff(c_890,plain,
in(empty_set,powerset(empty_set)),
inference(splitLeft,[status(thm)],[c_478]) ).
tff(c_8,plain,
! [A_3,B_4] :
( ~ in('#skF_1'(A_3,B_4),B_4)
| ( '#skF_2'(A_3,B_4) != A_3 )
| ( singleton(A_3) = B_4 ) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_974,plain,
! [A_161] :
( ~ in(A_161,powerset(empty_set))
| ( '#skF_2'(A_161,powerset(empty_set)) != A_161 )
| ( singleton(A_161) = powerset(empty_set) )
| ( empty_set != A_161 )
| ( singleton(A_161) = powerset(empty_set) ) ),
inference(superposition,[status(thm),theory(equality)],[c_901,c_8]) ).
tff(c_977,plain,
( ( '#skF_2'(empty_set,powerset(empty_set)) != empty_set )
| ( singleton(empty_set) = powerset(empty_set) ) ),
inference(resolution,[status(thm)],[c_890,c_974]) ).
tff(c_1044,plain,
'#skF_2'(empty_set,powerset(empty_set)) != empty_set,
inference(negUnitSimplification,[status(thm)],[c_42,c_42,c_977]) ).
tff(c_1066,plain,
( ~ subset(empty_set,empty_set)
| ( singleton(empty_set) = powerset(empty_set) ) ),
inference(superposition,[status(thm),theory(equality)],[c_907,c_1044]) ).
tff(c_1072,plain,
singleton(empty_set) = powerset(empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_1066]) ).
tff(c_1074,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_42,c_1072]) ).
tff(c_1076,plain,
~ in(empty_set,powerset(empty_set)),
inference(splitRight,[status(thm)],[c_478]) ).
tff(c_1080,plain,
~ subset(empty_set,empty_set),
inference(resolution,[status(thm)],[c_18,c_1076]) ).
tff(c_1084,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_1080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU147+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % 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
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 12:00:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 4.63/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.63/2.26
% 4.63/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.63/2.29
% 4.63/2.29 Inference rules
% 4.63/2.29 ----------------------
% 4.63/2.29 #Ref : 0
% 4.63/2.29 #Sup : 201
% 4.63/2.29 #Fact : 2
% 4.63/2.29 #Define : 0
% 4.63/2.29 #Split : 1
% 4.63/2.29 #Chain : 0
% 4.63/2.29 #Close : 0
% 4.63/2.29
% 4.63/2.29 Ordering : KBO
% 4.63/2.29
% 4.63/2.29 Simplification rules
% 4.63/2.29 ----------------------
% 4.63/2.29 #Subsume : 35
% 4.63/2.29 #Demod : 22
% 4.63/2.29 #Tautology : 70
% 4.63/2.29 #SimpNegUnit : 2
% 4.63/2.29 #BackRed : 0
% 4.63/2.29
% 4.63/2.29 #Partial instantiations: 0
% 4.63/2.29 #Strategies tried : 1
% 4.63/2.29
% 4.63/2.29 Timing (in seconds)
% 4.63/2.29 ----------------------
% 4.92/2.30 Preprocessing : 0.49
% 4.92/2.30 Parsing : 0.25
% 4.92/2.30 CNF conversion : 0.04
% 4.92/2.30 Main loop : 0.59
% 4.92/2.30 Inferencing : 0.25
% 4.92/2.30 Reduction : 0.14
% 4.92/2.30 Demodulation : 0.08
% 4.92/2.30 BG Simplification : 0.03
% 4.92/2.30 Subsumption : 0.13
% 4.92/2.30 Abstraction : 0.03
% 4.92/2.30 MUC search : 0.00
% 4.92/2.30 Cooper : 0.00
% 4.92/2.30 Total : 1.13
% 4.92/2.30 Index Insertion : 0.00
% 4.92/2.30 Index Deletion : 0.00
% 4.92/2.30 Index Matching : 0.00
% 4.92/2.30 BG Taut test : 0.00
%------------------------------------------------------------------------------