TSTP Solution File: SET929+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET929+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 : n032.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 10:57:22 EDT 2023
% Result : Theorem 3.39s 1.99s
% Output : CNFRefutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 67 ( 26 unt; 14 typ; 0 def)
% Number of atoms : 92 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 84 ( 45 ~; 34 |; 2 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 (; 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > set_difference > #nlpp > empty_set > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $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 ).
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_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_58,negated_conjecture,
~ ! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = empty_set )
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
tff(f_45,axiom,
! [A,B] :
( ( set_difference(A,B) = empty_set )
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
tff(f_51,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
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(c_26,plain,
( in('#skF_4','#skF_5')
| ~ in('#skF_7','#skF_8')
| ~ in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_89,plain,
~ in('#skF_6','#skF_8'),
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_32,plain,
( in('#skF_4','#skF_5')
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_162,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set,
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_14,plain,
! [A_7,B_8] :
( subset(A_7,B_8)
| ( set_difference(A_7,B_8) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_136,plain,
! [A_31,C_32,B_33] :
( in(A_31,C_32)
| ~ subset(unordered_pair(A_31,B_33),C_32) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_168,plain,
! [A_36,B_37,B_38] :
( in(A_36,B_37)
| ( set_difference(unordered_pair(A_36,B_38),B_37) != empty_set ) ),
inference(resolution,[status(thm)],[c_14,c_136]) ).
tff(c_171,plain,
in('#skF_6','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_162,c_168]) ).
tff(c_185,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_89,c_171]) ).
tff(c_186,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_187,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') != empty_set,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_34,plain,
( in('#skF_3','#skF_5')
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_191,plain,
in('#skF_3','#skF_5'),
inference(negUnitSimplification,[status(thm)],[c_187,c_34]) ).
tff(c_195,plain,
! [A_39,B_40,C_41] :
( subset(unordered_pair(A_39,B_40),C_41)
| ~ in(B_40,C_41)
| ~ in(A_39,C_41) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_16,plain,
! [A_7,B_8] :
( ( set_difference(A_7,B_8) = empty_set )
| ~ subset(A_7,B_8) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_241,plain,
! [A_48,B_49,C_50] :
( ( set_difference(unordered_pair(A_48,B_49),C_50) = empty_set )
| ~ in(B_49,C_50)
| ~ in(A_48,C_50) ),
inference(resolution,[status(thm)],[c_195,c_16]) ).
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_30,plain,
( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != empty_set )
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_36,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set )
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_30]) ).
tff(c_240,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set,
inference(negUnitSimplification,[status(thm)],[c_187,c_36]) ).
tff(c_247,plain,
( ~ in('#skF_3','#skF_5')
| ~ in('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_241,c_240]) ).
tff(c_278,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_186,c_191,c_247]) ).
tff(c_279,plain,
( ~ in('#skF_7','#skF_8')
| in('#skF_4','#skF_5') ),
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_284,plain,
~ in('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_279]) ).
tff(c_302,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set,
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_285,plain,
! [B_51,C_52,A_53] :
( in(B_51,C_52)
| ~ subset(unordered_pair(A_53,B_51),C_52) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_383,plain,
! [B_68,B_69,A_70] :
( in(B_68,B_69)
| ( set_difference(unordered_pair(A_70,B_68),B_69) != empty_set ) ),
inference(resolution,[status(thm)],[c_14,c_285]) ).
tff(c_386,plain,
in('#skF_7','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_302,c_383]) ).
tff(c_400,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_284,c_386]) ).
tff(c_401,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_402,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') != empty_set,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_463,plain,
in('#skF_3','#skF_5'),
inference(negUnitSimplification,[status(thm)],[c_402,c_34]) ).
tff(c_493,plain,
! [A_88,B_89,C_90] :
( subset(unordered_pair(A_88,B_89),C_90)
| ~ in(B_89,C_90)
| ~ in(A_88,C_90) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_515,plain,
! [A_91,B_92,C_93] :
( ( set_difference(unordered_pair(A_91,B_92),C_93) = empty_set )
| ~ in(B_92,C_93)
| ~ in(A_91,C_93) ),
inference(resolution,[status(thm)],[c_493,c_16]) ).
tff(c_512,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set,
inference(negUnitSimplification,[status(thm)],[c_402,c_36]) ).
tff(c_521,plain,
( ~ in('#skF_3','#skF_5')
| ~ in('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_515,c_512]) ).
tff(c_552,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_401,c_463,c_521]) ).
tff(c_553,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_279]) ).
tff(c_280,plain,
in('#skF_6','#skF_8'),
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_554,plain,
in('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_279]) ).
tff(c_28,plain,
( in('#skF_3','#skF_5')
| ~ in('#skF_7','#skF_8')
| ~ in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_640,plain,
in('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_280,c_554,c_28]) ).
tff(c_681,plain,
! [A_114,B_115,C_116] :
( subset(unordered_pair(A_114,B_115),C_116)
| ~ in(B_115,C_116)
| ~ in(A_114,C_116) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_702,plain,
! [A_117,B_118,C_119] :
( ( set_difference(unordered_pair(A_117,B_118),C_119) = empty_set )
| ~ in(B_118,C_119)
| ~ in(A_117,C_119) ),
inference(resolution,[status(thm)],[c_681,c_16]) ).
tff(c_24,plain,
( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != empty_set )
| ~ in('#skF_7','#skF_8')
| ~ in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_35,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set )
| ~ in('#skF_7','#skF_8')
| ~ in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_24]) ).
tff(c_701,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_280,c_554,c_35]) ).
tff(c_708,plain,
( ~ in('#skF_3','#skF_5')
| ~ in('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_702,c_701]) ).
tff(c_742,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_553,c_640,c_708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % 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
% 0.14/0.33 % Computer : n032.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 3 16:15:21 EDT 2023
% 0.14/0.33 % CPUTime :
% 3.39/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.99
% 3.39/1.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.65/2.03
% 3.65/2.03 Inference rules
% 3.65/2.03 ----------------------
% 3.65/2.03 #Ref : 0
% 3.65/2.03 #Sup : 172
% 3.65/2.03 #Fact : 0
% 3.65/2.03 #Define : 0
% 3.65/2.03 #Split : 5
% 3.65/2.03 #Chain : 0
% 3.65/2.03 #Close : 0
% 3.65/2.03
% 3.65/2.03 Ordering : KBO
% 3.65/2.03
% 3.65/2.03 Simplification rules
% 3.65/2.03 ----------------------
% 3.65/2.03 #Subsume : 59
% 3.65/2.03 #Demod : 45
% 3.65/2.03 #Tautology : 56
% 3.65/2.03 #SimpNegUnit : 6
% 3.65/2.03 #BackRed : 0
% 3.65/2.03
% 3.65/2.03 #Partial instantiations: 0
% 3.65/2.03 #Strategies tried : 1
% 3.65/2.03
% 3.65/2.03 Timing (in seconds)
% 3.65/2.03 ----------------------
% 3.65/2.03 Preprocessing : 0.47
% 3.65/2.03 Parsing : 0.25
% 3.65/2.03 CNF conversion : 0.03
% 3.65/2.03 Main loop : 0.48
% 3.65/2.03 Inferencing : 0.18
% 3.65/2.03 Reduction : 0.15
% 3.65/2.03 Demodulation : 0.11
% 3.65/2.03 BG Simplification : 0.02
% 3.65/2.03 Subsumption : 0.10
% 3.65/2.03 Abstraction : 0.02
% 3.65/2.03 MUC search : 0.00
% 3.65/2.03 Cooper : 0.00
% 3.65/2.03 Total : 1.00
% 3.65/2.03 Index Insertion : 0.00
% 3.65/2.03 Index Deletion : 0.00
% 3.65/2.03 Index Matching : 0.00
% 3.65/2.03 BG Taut test : 0.00
%------------------------------------------------------------------------------