TSTP Solution File: SET882+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET882+1 : TPTP v8.1.2. 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 : n010.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 10:57:16 EDT 2023
% Result : Theorem 3.14s 1.80s
% Output : CNFRefutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 27 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 28 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 7 |; 1 &)
% ( 3 <=>; 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 : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 21 (; 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_difference > #nlpp > singleton > #skF_5 > #skF_6 > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_60,negated_conjecture,
~ ! [A,B] :
( ( A != B )
=> ( set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
tff(f_40,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_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_49,axiom,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
tff(c_32,plain,
'#skF_5' != '#skF_6',
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_8,plain,
! [C_9] : in(C_9,singleton(C_9)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
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_155,plain,
! [B_45,C_46,A_47] :
( ~ in(B_45,C_46)
| ( set_difference(unordered_pair(A_47,B_45),C_46) = singleton(A_47) )
| in(A_47,C_46) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_198,plain,
! [A_50,C_51,B_52] :
( ~ in(A_50,C_51)
| ( set_difference(unordered_pair(A_50,B_52),C_51) = singleton(B_52) )
| in(B_52,C_51) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_155]) ).
tff(c_30,plain,
set_difference(unordered_pair('#skF_5','#skF_6'),singleton('#skF_6')) != singleton('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_33,plain,
set_difference(unordered_pair('#skF_6','#skF_5'),singleton('#skF_6')) != singleton('#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_30]) ).
tff(c_223,plain,
( ~ in('#skF_6',singleton('#skF_6'))
| in('#skF_5',singleton('#skF_6')) ),
inference(superposition,[status(thm),theory(equality)],[c_198,c_33]) ).
tff(c_245,plain,
in('#skF_5',singleton('#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_223]) ).
tff(c_6,plain,
! [C_9,A_5] :
( ( C_9 = A_5 )
| ~ in(C_9,singleton(A_5)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_250,plain,
'#skF_5' = '#skF_6',
inference(resolution,[status(thm)],[c_245,c_6]) ).
tff(c_256,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_32,c_250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % 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 : n010.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 : Thu Aug 3 16:52:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.14/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.24/1.80
% 3.24/1.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.24/1.83
% 3.24/1.83 Inference rules
% 3.24/1.83 ----------------------
% 3.24/1.83 #Ref : 0
% 3.24/1.83 #Sup : 54
% 3.24/1.83 #Fact : 0
% 3.24/1.83 #Define : 0
% 3.24/1.83 #Split : 0
% 3.24/1.83 #Chain : 0
% 3.24/1.83 #Close : 0
% 3.24/1.83
% 3.24/1.83 Ordering : KBO
% 3.24/1.83
% 3.24/1.83 Simplification rules
% 3.24/1.83 ----------------------
% 3.24/1.83 #Subsume : 8
% 3.24/1.83 #Demod : 3
% 3.24/1.83 #Tautology : 30
% 3.24/1.83 #SimpNegUnit : 1
% 3.24/1.83 #BackRed : 0
% 3.24/1.83
% 3.24/1.83 #Partial instantiations: 0
% 3.24/1.83 #Strategies tried : 1
% 3.24/1.83
% 3.24/1.83 Timing (in seconds)
% 3.24/1.83 ----------------------
% 3.24/1.83 Preprocessing : 0.49
% 3.24/1.83 Parsing : 0.25
% 3.24/1.83 CNF conversion : 0.04
% 3.24/1.83 Main loop : 0.30
% 3.24/1.83 Inferencing : 0.11
% 3.24/1.83 Reduction : 0.08
% 3.24/1.83 Demodulation : 0.06
% 3.24/1.84 BG Simplification : 0.02
% 3.24/1.84 Subsumption : 0.07
% 3.29/1.84 Abstraction : 0.01
% 3.29/1.84 MUC search : 0.00
% 3.29/1.84 Cooper : 0.00
% 3.29/1.84 Total : 0.84
% 3.29/1.84 Index Insertion : 0.00
% 3.29/1.84 Index Deletion : 0.00
% 3.29/1.84 Index Matching : 0.00
% 3.29/1.84 BG Taut test : 0.00
%------------------------------------------------------------------------------