TSTP Solution File: SET928+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET928+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/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 : n008.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 3.62s 1.94s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 86 ( 38 unt; 13 typ; 0 def)
% Number of atoms : 116 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 92 ( 49 ~; 36 |; 4 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 63 (; 63 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > disjoint > empty > unordered_pair > set_difference > #nlpp > #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('#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(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_66,negated_conjecture,
~ ! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) )
<=> ( ~ in(A,C)
& ~ in(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
tff(f_57,axiom,
! [A,B,C] :
~ ( ~ in(A,B)
& ~ in(C,B)
& ~ disjoint(unordered_pair(A,C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
tff(f_70,axiom,
! [A,B] :
( disjoint(A,B)
<=> ( set_difference(A,B) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
tff(f_33,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_42,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
tff(f_47,axiom,
! [A,B,C] :
~ ( disjoint(unordered_pair(A,B),C)
& in(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
tff(c_18,plain,
( ~ in('#skF_4','#skF_5')
| in('#skF_7','#skF_8')
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_102,plain,
~ in('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_20,plain,
( ~ in('#skF_3','#skF_5')
| in('#skF_7','#skF_8')
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_121,plain,
~ in('#skF_3','#skF_5'),
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_136,plain,
! [A_41,C_42,B_43] :
( disjoint(unordered_pair(A_41,C_42),B_43)
| in(C_42,B_43)
| in(A_41,B_43) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_28,plain,
! [A_13,B_14] :
( ( set_difference(A_13,B_14) = A_13 )
| ~ disjoint(A_13,B_14) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_255,plain,
! [A_62,C_63,B_64] :
( ( set_difference(unordered_pair(A_62,C_63),B_64) = unordered_pair(A_62,C_63) )
| in(C_63,B_64)
| in(A_62,B_64) ),
inference(resolution,[status(thm)],[c_136,c_28]) ).
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_16,plain,
( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != unordered_pair('#skF_3','#skF_4') )
| in('#skF_7','#skF_8')
| in('#skF_6','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_31,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != unordered_pair('#skF_4','#skF_3') )
| in('#skF_7','#skF_8')
| in('#skF_6','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_16]) ).
tff(c_189,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != unordered_pair('#skF_4','#skF_3'),
inference(splitLeft,[status(thm)],[c_31]) ).
tff(c_274,plain,
( in('#skF_3','#skF_5')
| in('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_255,c_189]) ).
tff(c_307,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_102,c_121,c_274]) ).
tff(c_308,plain,
( in('#skF_6','#skF_8')
| in('#skF_7','#skF_8') ),
inference(splitRight,[status(thm)],[c_31]) ).
tff(c_310,plain,
in('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_308]) ).
tff(c_309,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') = unordered_pair('#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_31]) ).
tff(c_22,plain,
( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != unordered_pair('#skF_3','#skF_4') )
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7') ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_32,plain,
( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != unordered_pair('#skF_4','#skF_3') )
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_22]) ).
tff(c_326,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_309,c_32]) ).
tff(c_68,plain,
! [A_21,B_22] :
( disjoint(A_21,B_22)
| ( set_difference(A_21,B_22) != A_21 ) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_10,plain,
! [B_6,A_5] :
( disjoint(B_6,A_5)
| ~ disjoint(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_77,plain,
! [B_25,A_26] :
( disjoint(B_25,A_26)
| ( set_difference(A_26,B_25) != A_26 ) ),
inference(resolution,[status(thm)],[c_68,c_10]) ).
tff(c_83,plain,
! [B_25,A_26] :
( ( set_difference(B_25,A_26) = B_25 )
| ( set_difference(A_26,B_25) != A_26 ) ),
inference(resolution,[status(thm)],[c_77,c_28]) ).
tff(c_336,plain,
set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
inference(superposition,[status(thm),theory(equality)],[c_326,c_83]) ).
tff(c_71,plain,
! [B_22,A_21] :
( disjoint(B_22,A_21)
| ( set_difference(A_21,B_22) != A_21 ) ),
inference(resolution,[status(thm)],[c_68,c_10]) ).
tff(c_85,plain,
! [A_27,C_28,B_29] :
( ~ in(A_27,C_28)
| ~ disjoint(unordered_pair(A_27,B_29),C_28) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_103,plain,
! [B_30,C_31,A_32] :
( ~ in(B_30,C_31)
| ~ disjoint(unordered_pair(A_32,B_30),C_31) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_85]) ).
tff(c_118,plain,
! [B_30,A_21,A_32] :
( ~ in(B_30,A_21)
| ( set_difference(A_21,unordered_pair(A_32,B_30)) != A_21 ) ),
inference(resolution,[status(thm)],[c_71,c_103]) ).
tff(c_357,plain,
~ in('#skF_7','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_336,c_118]) ).
tff(c_368,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_310,c_357]) ).
tff(c_369,plain,
in('#skF_6','#skF_8'),
inference(splitRight,[status(thm)],[c_308]) ).
tff(c_414,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_309,c_32]) ).
tff(c_30,plain,
! [A_13,B_14] :
( disjoint(A_13,B_14)
| ( set_difference(A_13,B_14) != A_13 ) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_101,plain,
! [A_27,B_14,B_29] :
( ~ in(A_27,B_14)
| ( set_difference(unordered_pair(A_27,B_29),B_14) != unordered_pair(A_27,B_29) ) ),
inference(resolution,[status(thm)],[c_30,c_85]) ).
tff(c_421,plain,
~ in('#skF_6','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_414,c_101]) ).
tff(c_431,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_369,c_421]) ).
tff(c_432,plain,
( in('#skF_6','#skF_8')
| in('#skF_7','#skF_8') ),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_437,plain,
in('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_432]) ).
tff(c_433,plain,
in('#skF_3','#skF_5'),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_26,plain,
( ~ in('#skF_3','#skF_5')
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7') ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_456,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_433,c_26]) ).
tff(c_462,plain,
set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
inference(superposition,[status(thm),theory(equality)],[c_456,c_83]) ).
tff(c_467,plain,
~ in('#skF_7','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_462,c_118]) ).
tff(c_478,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_437,c_467]) ).
tff(c_479,plain,
in('#skF_6','#skF_8'),
inference(splitRight,[status(thm)],[c_432]) ).
tff(c_492,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_433,c_26]) ).
tff(c_498,plain,
set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
inference(superposition,[status(thm),theory(equality)],[c_492,c_83]) ).
tff(c_512,plain,
! [A_77,A_78,B_79] :
( ~ in(A_77,A_78)
| ( set_difference(A_78,unordered_pair(A_77,B_79)) != A_78 ) ),
inference(resolution,[status(thm)],[c_71,c_85]) ).
tff(c_515,plain,
~ in('#skF_6','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_498,c_512]) ).
tff(c_525,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_479,c_515]) ).
tff(c_526,plain,
( in('#skF_6','#skF_8')
| in('#skF_7','#skF_8') ),
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_532,plain,
in('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_526]) ).
tff(c_527,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_24,plain,
( ~ in('#skF_4','#skF_5')
| ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7') ) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_591,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_527,c_24]) ).
tff(c_597,plain,
set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
inference(superposition,[status(thm),theory(equality)],[c_591,c_83]) ).
tff(c_554,plain,
! [B_83,C_84,A_85] :
( ~ in(B_83,C_84)
| ~ disjoint(unordered_pair(A_85,B_83),C_84) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_85]) ).
tff(c_573,plain,
! [B_83,A_21,A_85] :
( ~ in(B_83,A_21)
| ( set_difference(A_21,unordered_pair(A_85,B_83)) != A_21 ) ),
inference(resolution,[status(thm)],[c_71,c_554]) ).
tff(c_603,plain,
~ in('#skF_7','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_597,c_573]) ).
tff(c_614,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_532,c_603]) ).
tff(c_615,plain,
in('#skF_6','#skF_8'),
inference(splitRight,[status(thm)],[c_526]) ).
tff(c_621,plain,
set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_527,c_24]) ).
tff(c_643,plain,
! [B_97,A_98] :
( ( set_difference(B_97,A_98) = B_97 )
| ( set_difference(A_98,B_97) != A_98 ) ),
inference(resolution,[status(thm)],[c_77,c_28]) ).
tff(c_646,plain,
set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
inference(superposition,[status(thm),theory(equality)],[c_621,c_643]) ).
tff(c_667,plain,
! [A_102,A_103,B_104] :
( ~ in(A_102,A_103)
| ( set_difference(A_103,unordered_pair(A_102,B_104)) != A_103 ) ),
inference(resolution,[status(thm)],[c_71,c_85]) ).
tff(c_670,plain,
~ in('#skF_6','#skF_8'),
inference(superposition,[status(thm),theory(equality)],[c_646,c_667]) ).
tff(c_680,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_615,c_670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET928+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 16:44:34 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.62/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.62/1.94
% 3.62/1.94 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/1.98
% 3.81/1.98 Inference rules
% 3.81/1.98 ----------------------
% 3.81/1.98 #Ref : 0
% 3.81/1.98 #Sup : 174
% 3.81/1.98 #Fact : 0
% 3.81/1.98 #Define : 0
% 3.81/1.98 #Split : 7
% 3.81/1.98 #Chain : 0
% 3.81/1.98 #Close : 0
% 3.81/1.98
% 3.81/1.98 Ordering : KBO
% 3.81/1.98
% 3.81/1.98 Simplification rules
% 3.81/1.98 ----------------------
% 3.81/1.98 #Subsume : 54
% 3.81/1.98 #Demod : 24
% 3.81/1.98 #Tautology : 53
% 3.81/1.98 #SimpNegUnit : 1
% 3.81/1.98 #BackRed : 0
% 3.81/1.98
% 3.81/1.98 #Partial instantiations: 0
% 3.81/1.98 #Strategies tried : 1
% 3.81/1.98
% 3.81/1.98 Timing (in seconds)
% 3.81/1.98 ----------------------
% 3.81/1.98 Preprocessing : 0.44
% 3.81/1.98 Parsing : 0.24
% 3.81/1.98 CNF conversion : 0.03
% 3.81/1.98 Main loop : 0.47
% 3.81/1.98 Inferencing : 0.18
% 3.81/1.98 Reduction : 0.13
% 3.81/1.98 Demodulation : 0.10
% 3.81/1.98 BG Simplification : 0.02
% 3.81/1.98 Subsumption : 0.10
% 3.81/1.99 Abstraction : 0.02
% 3.81/1.99 MUC search : 0.00
% 3.81/1.99 Cooper : 0.00
% 3.81/1.99 Total : 0.97
% 3.81/1.99 Index Insertion : 0.00
% 3.81/1.99 Index Deletion : 0.00
% 3.81/1.99 Index Matching : 0.00
% 3.81/1.99 BG Taut test : 0.00
%------------------------------------------------------------------------------