TSTP Solution File: SET951+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET951+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 : n027.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 10:57:24 EDT 2023
% Result : Theorem 86.96s 62.72s
% Output : CNFRefutation 87.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 26
% Syntax : Number of formulae : 70 ( 16 unt; 22 typ; 0 def)
% Number of atoms : 106 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 55 ~; 46 |; 7 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 15 >; 23 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-4 aty)
% Number of variables : 96 (; 94 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_intersection2 > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_1 > #skF_11 > #skF_15 > #skF_4 > #skF_10 > #skF_14 > #skF_13 > #skF_2 > #skF_6 > #skF_9 > #skF_7 > #skF_5 > #skF_3 > #skF_8 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_82,negated_conjecture,
~ ! [A,B,C,D,E] :
~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
& ! [F,G] :
~ ( ( A = ordered_pair(F,G) )
& in(F,set_intersection2(B,D))
& in(G,set_intersection2(C,E)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
tff(f_58,axiom,
! [A,B,C] :
( ( C = set_intersection2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
tff(f_49,axiom,
! [A,B,C] :
( ( C = cartesian_product2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& ( D = ordered_pair(E,F) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
tff(f_88,axiom,
! [A,B,C,D] :
( ( ordered_pair(A,B) = ordered_pair(C,D) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
tff(c_62,plain,
in('#skF_11',set_intersection2(cartesian_product2('#skF_12','#skF_13'),cartesian_product2('#skF_14','#skF_15'))),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_36,plain,
! [D_46,A_41,B_42] :
( in(D_46,A_41)
| ~ in(D_46,set_intersection2(A_41,B_42)) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_164,plain,
in('#skF_11',cartesian_product2('#skF_12','#skF_13')),
inference(resolution,[status(thm)],[c_62,c_36]) ).
tff(c_14,plain,
! [A_7,B_8,D_34] :
( in('#skF_5'(A_7,B_8,cartesian_product2(A_7,B_8),D_34),A_7)
| ~ in(D_34,cartesian_product2(A_7,B_8)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_169,plain,
! [D_77,B_78,A_79] :
( in(D_77,B_78)
| ~ in(D_77,set_intersection2(A_79,B_78)) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_182,plain,
in('#skF_11',cartesian_product2('#skF_14','#skF_15')),
inference(resolution,[status(thm)],[c_62,c_169]) ).
tff(c_10,plain,
! [A_7,B_8,D_34] :
( ( ordered_pair('#skF_5'(A_7,B_8,cartesian_product2(A_7,B_8),D_34),'#skF_6'(A_7,B_8,cartesian_product2(A_7,B_8),D_34)) = D_34 )
| ~ in(D_34,cartesian_product2(A_7,B_8)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_2672,plain,
! [A_222,B_223,D_224] :
( ( ordered_pair('#skF_5'(A_222,B_223,cartesian_product2(A_222,B_223),D_224),'#skF_6'(A_222,B_223,cartesian_product2(A_222,B_223),D_224)) = D_224 )
| ~ in(D_224,cartesian_product2(A_222,B_223)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_66,plain,
! [C_59,A_57,D_60,B_58] :
( ( C_59 = A_57 )
| ( ordered_pair(C_59,D_60) != ordered_pair(A_57,B_58) ) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_2942,plain,
! [B_261,C_264,A_265,D_262,D_263] :
( ( C_264 = '#skF_5'(A_265,B_261,cartesian_product2(A_265,B_261),D_262) )
| ( ordered_pair(C_264,D_263) != D_262 )
| ~ in(D_262,cartesian_product2(A_265,B_261)) ),
inference(superposition,[status(thm),theory(equality)],[c_2672,c_66]) ).
tff(c_196859,plain,
! [B_2276,A_2273,A_2275,B_2274,D_2272] :
( ( '#skF_5'(A_2275,B_2274,cartesian_product2(A_2275,B_2274),D_2272) = '#skF_5'(A_2273,B_2276,cartesian_product2(A_2273,B_2276),D_2272) )
| ~ in(D_2272,cartesian_product2(A_2273,B_2276))
| ~ in(D_2272,cartesian_product2(A_2275,B_2274)) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_2942]) ).
tff(c_197577,plain,
! [A_2277,B_2278] :
( ( '#skF_5'(A_2277,B_2278,cartesian_product2(A_2277,B_2278),'#skF_11') = '#skF_5'('#skF_14','#skF_15',cartesian_product2('#skF_14','#skF_15'),'#skF_11') )
| ~ in('#skF_11',cartesian_product2(A_2277,B_2278)) ),
inference(resolution,[status(thm)],[c_182,c_196859]) ).
tff(c_197584,plain,
'#skF_5'('#skF_14','#skF_15',cartesian_product2('#skF_14','#skF_15'),'#skF_11') = '#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),
inference(resolution,[status(thm)],[c_164,c_197577]) ).
tff(c_197598,plain,
( in('#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_14')
| ~ in('#skF_11',cartesian_product2('#skF_14','#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_197584,c_14]) ).
tff(c_197608,plain,
in('#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_197598]) ).
tff(c_12,plain,
! [A_7,B_8,D_34] :
( in('#skF_6'(A_7,B_8,cartesian_product2(A_7,B_8),D_34),B_8)
| ~ in(D_34,cartesian_product2(A_7,B_8)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_8,plain,
! [E_39,F_40,A_7,B_8] :
( in(ordered_pair(E_39,F_40),cartesian_product2(A_7,B_8))
| ~ in(F_40,B_8)
| ~ in(E_39,A_7) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_10652,plain,
! [B_736,A_735,D_737,B_734,A_738] :
( in(D_737,cartesian_product2(A_735,B_734))
| ~ in('#skF_6'(A_738,B_736,cartesian_product2(A_738,B_736),D_737),B_734)
| ~ in('#skF_5'(A_738,B_736,cartesian_product2(A_738,B_736),D_737),A_735)
| ~ in(D_737,cartesian_product2(A_738,B_736)) ),
inference(superposition,[status(thm),theory(equality)],[c_2672,c_8]) ).
tff(c_10666,plain,
! [D_34,A_735,B_8,A_7] :
( in(D_34,cartesian_product2(A_735,B_8))
| ~ in('#skF_5'(A_7,B_8,cartesian_product2(A_7,B_8),D_34),A_735)
| ~ in(D_34,cartesian_product2(A_7,B_8)) ),
inference(resolution,[status(thm)],[c_12,c_10652]) ).
tff(c_197612,plain,
( in('#skF_11',cartesian_product2('#skF_14','#skF_13'))
| ~ in('#skF_11',cartesian_product2('#skF_12','#skF_13')) ),
inference(resolution,[status(thm)],[c_197608,c_10666]) ).
tff(c_197617,plain,
in('#skF_11',cartesian_product2('#skF_14','#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_164,c_197612]) ).
tff(c_64,plain,
! [D_60,B_58,C_59,A_57] :
( ( D_60 = B_58 )
| ( ordered_pair(C_59,D_60) != ordered_pair(A_57,B_58) ) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_2926,plain,
! [D_257,A_260,B_256,C_259,D_258] :
( ( D_258 = '#skF_6'(A_260,B_256,cartesian_product2(A_260,B_256),D_257) )
| ( ordered_pair(C_259,D_258) != D_257 )
| ~ in(D_257,cartesian_product2(A_260,B_256)) ),
inference(superposition,[status(thm),theory(equality)],[c_2672,c_64]) ).
tff(c_197629,plain,
! [B_2281,D_2280,B_2282,A_2279,A_2283] :
( ( '#skF_6'(A_2283,B_2282,cartesian_product2(A_2283,B_2282),D_2280) = '#skF_6'(A_2279,B_2281,cartesian_product2(A_2279,B_2281),D_2280) )
| ~ in(D_2280,cartesian_product2(A_2279,B_2281))
| ~ in(D_2280,cartesian_product2(A_2283,B_2282)) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_2926]) ).
tff(c_198381,plain,
! [A_2285,B_2286] :
( ( '#skF_6'(A_2285,B_2286,cartesian_product2(A_2285,B_2286),'#skF_11') = '#skF_6'('#skF_14','#skF_15',cartesian_product2('#skF_14','#skF_15'),'#skF_11') )
| ~ in('#skF_11',cartesian_product2(A_2285,B_2286)) ),
inference(resolution,[status(thm)],[c_182,c_197629]) ).
tff(c_198394,plain,
'#skF_6'('#skF_14','#skF_15',cartesian_product2('#skF_14','#skF_15'),'#skF_11') = '#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),
inference(resolution,[status(thm)],[c_164,c_198381]) ).
tff(c_198391,plain,
'#skF_6'('#skF_14','#skF_15',cartesian_product2('#skF_14','#skF_15'),'#skF_11') = '#skF_6'('#skF_14','#skF_13',cartesian_product2('#skF_14','#skF_13'),'#skF_11'),
inference(resolution,[status(thm)],[c_197617,c_198381]) ).
tff(c_198451,plain,
'#skF_6'('#skF_14','#skF_13',cartesian_product2('#skF_14','#skF_13'),'#skF_11') = '#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_198394,c_198391]) ).
tff(c_198463,plain,
( in('#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_13')
| ~ in('#skF_11',cartesian_product2('#skF_14','#skF_13')) ),
inference(superposition,[status(thm),theory(equality)],[c_198451,c_12]) ).
tff(c_198473,plain,
in('#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_197617,c_198463]) ).
tff(c_198407,plain,
( in('#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_15')
| ~ in('#skF_11',cartesian_product2('#skF_14','#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_198394,c_12]) ).
tff(c_198417,plain,
in('#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_198407]) ).
tff(c_197592,plain,
( ( ordered_pair('#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_6'('#skF_14','#skF_15',cartesian_product2('#skF_14','#skF_15'),'#skF_11')) = '#skF_11' )
| ~ in('#skF_11',cartesian_product2('#skF_14','#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_197584,c_10]) ).
tff(c_197604,plain,
ordered_pair('#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_6'('#skF_14','#skF_15',cartesian_product2('#skF_14','#skF_15'),'#skF_11')) = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_182,c_197592]) ).
tff(c_198557,plain,
ordered_pair('#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11')) = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_198394,c_197604]) ).
tff(c_32,plain,
! [D_46,A_41,B_42] :
( in(D_46,set_intersection2(A_41,B_42))
| ~ in(D_46,B_42)
| ~ in(D_46,A_41) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_311,plain,
! [D_92,A_93,B_94] :
( in(D_92,set_intersection2(A_93,B_94))
| ~ in(D_92,B_94)
| ~ in(D_92,A_93) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_60,plain,
! [G_56,F_55] :
( ~ in(G_56,set_intersection2('#skF_13','#skF_15'))
| ~ in(F_55,set_intersection2('#skF_12','#skF_14'))
| ( ordered_pair(F_55,G_56) != '#skF_11' ) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_389,plain,
! [F_97,D_98] :
( ~ in(F_97,set_intersection2('#skF_12','#skF_14'))
| ( ordered_pair(F_97,D_98) != '#skF_11' )
| ~ in(D_98,'#skF_15')
| ~ in(D_98,'#skF_13') ),
inference(resolution,[status(thm)],[c_311,c_60]) ).
tff(c_393,plain,
! [D_46,D_98] :
( ( ordered_pair(D_46,D_98) != '#skF_11' )
| ~ in(D_98,'#skF_15')
| ~ in(D_98,'#skF_13')
| ~ in(D_46,'#skF_14')
| ~ in(D_46,'#skF_12') ),
inference(resolution,[status(thm)],[c_32,c_389]) ).
tff(c_198700,plain,
( ~ in('#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_15')
| ~ in('#skF_6'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_13')
| ~ in('#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_14')
| ~ in('#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_198557,c_393]) ).
tff(c_198762,plain,
~ in('#skF_5'('#skF_12','#skF_13',cartesian_product2('#skF_12','#skF_13'),'#skF_11'),'#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_197608,c_198473,c_198417,c_198700]) ).
tff(c_198769,plain,
~ in('#skF_11',cartesian_product2('#skF_12','#skF_13')),
inference(resolution,[status(thm)],[c_14,c_198762]) ).
tff(c_198773,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_164,c_198769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET951+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 : n027.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 16:38:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 86.96/62.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.04/62.73
% 87.04/62.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 87.04/62.76
% 87.04/62.76 Inference rules
% 87.04/62.76 ----------------------
% 87.04/62.76 #Ref : 37
% 87.04/62.76 #Sup : 56093
% 87.04/62.76 #Fact : 0
% 87.04/62.76 #Define : 0
% 87.04/62.76 #Split : 0
% 87.04/62.76 #Chain : 0
% 87.04/62.76 #Close : 0
% 87.04/62.76
% 87.04/62.76 Ordering : KBO
% 87.04/62.76
% 87.04/62.76 Simplification rules
% 87.04/62.76 ----------------------
% 87.04/62.76 #Subsume : 9193
% 87.04/62.76 #Demod : 28967
% 87.04/62.76 #Tautology : 5341
% 87.04/62.76 #SimpNegUnit : 0
% 87.04/62.76 #BackRed : 2
% 87.04/62.76
% 87.04/62.76 #Partial instantiations: 0
% 87.04/62.76 #Strategies tried : 1
% 87.04/62.76
% 87.04/62.76 Timing (in seconds)
% 87.04/62.76 ----------------------
% 87.04/62.76 Preprocessing : 0.52
% 87.04/62.76 Parsing : 0.26
% 87.04/62.76 CNF conversion : 0.04
% 87.04/62.76 Main loop : 61.09
% 87.04/62.76 Inferencing : 7.55
% 87.04/62.76 Reduction : 36.91
% 87.04/62.76 Demodulation : 34.99
% 87.04/62.76 BG Simplification : 1.23
% 87.04/62.76 Subsumption : 11.70
% 87.04/62.76 Abstraction : 1.91
% 87.04/62.76 MUC search : 0.00
% 87.04/62.76 Cooper : 0.00
% 87.04/62.76 Total : 61.67
% 87.04/62.76 Index Insertion : 0.00
% 87.04/62.76 Index Deletion : 0.00
% 87.04/62.76 Index Matching : 0.00
% 87.04/62.76 BG Taut test : 0.00
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