TSTP Solution File: SEU126+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU126+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 : n021.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 10:57:40 EDT 2023
% Result : Theorem 20.13s 8.85s
% Output : CNFRefutation 20.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 64 ( 19 unt; 12 typ; 0 def)
% Number of atoms : 110 ( 44 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 91 ( 33 ~; 52 |; 0 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 7 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 106 (; 105 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > set_union2 > #nlpp > empty_set > #skF_1 > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_2 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $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_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(f_83,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> ( set_union2(A,B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
tff(f_71,axiom,
! [A,B] : ( set_union2(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
tff(f_33,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_48,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(f_55,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_73,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_89,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_85,axiom,
! [A] : ( set_union2(A,empty_set) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
tff(c_54,plain,
set_union2('#skF_6','#skF_7') != '#skF_7',
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_46,plain,
! [A_22] : ( set_union2(A_22,A_22) = A_22 ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_4,plain,
! [B_4,A_3] : ( set_union2(B_4,A_3) = set_union2(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_56,plain,
subset('#skF_6','#skF_7'),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_866,plain,
! [A_138,B_139,C_140] :
( in('#skF_1'(A_138,B_139,C_140),B_139)
| in('#skF_1'(A_138,B_139,C_140),A_138)
| in('#skF_2'(A_138,B_139,C_140),C_140)
| ( set_union2(A_138,B_139) = C_140 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_26,plain,
! [A_7,B_8,C_9] :
( ~ in('#skF_1'(A_7,B_8,C_9),C_9)
| in('#skF_2'(A_7,B_8,C_9),C_9)
| ( set_union2(A_7,B_8) = C_9 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_955,plain,
! [A_138,B_139] :
( in('#skF_1'(A_138,B_139,A_138),B_139)
| in('#skF_2'(A_138,B_139,A_138),A_138)
| ( set_union2(A_138,B_139) = A_138 ) ),
inference(resolution,[status(thm)],[c_866,c_26]) ).
tff(c_742,plain,
! [A_130,B_131,C_132] :
( in('#skF_1'(A_130,B_131,C_132),B_131)
| in('#skF_1'(A_130,B_131,C_132),A_130)
| ~ in('#skF_2'(A_130,B_131,C_132),A_130)
| ( set_union2(A_130,B_131) = C_132 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_22,plain,
! [A_7,B_8,C_9] :
( ~ in('#skF_1'(A_7,B_8,C_9),C_9)
| ~ in('#skF_2'(A_7,B_8,C_9),A_7)
| ( set_union2(A_7,B_8) = C_9 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_4015,plain,
! [A_370,B_371] :
( in('#skF_1'(A_370,B_371,A_370),B_371)
| ~ in('#skF_2'(A_370,B_371,A_370),A_370)
| ( set_union2(A_370,B_371) = A_370 ) ),
inference(resolution,[status(thm)],[c_742,c_22]) ).
tff(c_4068,plain,
! [A_372,B_373] :
( in('#skF_1'(A_372,B_373,A_372),B_373)
| ( set_union2(A_372,B_373) = A_372 ) ),
inference(resolution,[status(thm)],[c_955,c_4015]) ).
tff(c_30,plain,
! [C_17,B_14,A_13] :
( in(C_17,B_14)
| ~ in(C_17,A_13)
| ~ subset(A_13,B_14) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_4116,plain,
! [A_372,B_373,B_14] :
( in('#skF_1'(A_372,B_373,A_372),B_14)
| ~ subset(B_373,B_14)
| ( set_union2(A_372,B_373) = A_372 ) ),
inference(resolution,[status(thm)],[c_4068,c_30]) ).
tff(c_140,plain,
! [B_45,A_46] : ( set_union2(B_45,A_46) = set_union2(A_46,B_45) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_48,plain,
empty('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_68,plain,
! [A_33] :
( ( empty_set = A_33 )
| ~ empty(A_33) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_77,plain,
empty_set = '#skF_4',
inference(resolution,[status(thm)],[c_48,c_68]) ).
tff(c_58,plain,
! [A_26] : ( set_union2(A_26,empty_set) = A_26 ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_94,plain,
! [A_26] : ( set_union2(A_26,'#skF_4') = A_26 ),
inference(demodulation,[status(thm),theory(equality)],[c_77,c_58]) ).
tff(c_168,plain,
! [A_46] : ( set_union2('#skF_4',A_46) = A_46 ),
inference(superposition,[status(thm),theory(equality)],[c_140,c_94]) ).
tff(c_14,plain,
! [D_12,B_8,A_7] :
( ~ in(D_12,B_8)
| in(D_12,set_union2(A_7,B_8)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_515,plain,
! [A_91,B_92,C_93] :
( ~ in('#skF_1'(A_91,B_92,C_93),C_93)
| in('#skF_2'(A_91,B_92,C_93),C_93)
| ( set_union2(A_91,B_92) = C_93 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_15627,plain,
! [A_662,B_663,A_664,B_665] :
( in('#skF_2'(A_662,B_663,set_union2(A_664,B_665)),set_union2(A_664,B_665))
| ( set_union2(A_664,B_665) = set_union2(A_662,B_663) )
| ~ in('#skF_1'(A_662,B_663,set_union2(A_664,B_665)),B_665) ),
inference(resolution,[status(thm)],[c_14,c_515]) ).
tff(c_612,plain,
! [A_113,B_114,C_115] :
( ~ in('#skF_1'(A_113,B_114,C_115),C_115)
| ~ in('#skF_2'(A_113,B_114,C_115),A_113)
| ( set_union2(A_113,B_114) = C_115 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_620,plain,
! [A_113,B_114,A_7,B_8] :
( ~ in('#skF_2'(A_113,B_114,set_union2(A_7,B_8)),A_113)
| ( set_union2(A_7,B_8) = set_union2(A_113,B_114) )
| ~ in('#skF_1'(A_113,B_114,set_union2(A_7,B_8)),B_8) ),
inference(resolution,[status(thm)],[c_14,c_612]) ).
tff(c_53730,plain,
! [A_1160,B_1161,B_1162] :
( ( set_union2(set_union2(A_1160,B_1161),B_1162) = set_union2(A_1160,B_1161) )
| ~ in('#skF_1'(set_union2(A_1160,B_1161),B_1162,set_union2(A_1160,B_1161)),B_1161) ),
inference(resolution,[status(thm)],[c_15627,c_620]) ).
tff(c_53963,plain,
! [A_46,B_1162] :
( ( set_union2(set_union2('#skF_4',A_46),B_1162) = set_union2('#skF_4',A_46) )
| ~ in('#skF_1'(A_46,B_1162,set_union2('#skF_4',A_46)),A_46) ),
inference(superposition,[status(thm),theory(equality)],[c_168,c_53730]) ).
tff(c_54038,plain,
! [A_1163,B_1164] :
( ( set_union2(A_1163,B_1164) = A_1163 )
| ~ in('#skF_1'(A_1163,B_1164,A_1163),A_1163) ),
inference(demodulation,[status(thm),theory(equality)],[c_168,c_168,c_168,c_53963]) ).
tff(c_54311,plain,
! [B_1165,B_1166] :
( ~ subset(B_1165,B_1166)
| ( set_union2(B_1166,B_1165) = B_1166 ) ),
inference(resolution,[status(thm)],[c_4116,c_54038]) ).
tff(c_54525,plain,
set_union2('#skF_7','#skF_6') = '#skF_7',
inference(resolution,[status(thm)],[c_56,c_54311]) ).
tff(c_945,plain,
! [A_138,B_139] :
( in('#skF_1'(A_138,B_139,B_139),A_138)
| in('#skF_2'(A_138,B_139,B_139),B_139)
| ( set_union2(A_138,B_139) = B_139 ) ),
inference(resolution,[status(thm)],[c_866,c_26]) ).
tff(c_1095,plain,
! [A_149,B_150,C_151] :
( in('#skF_1'(A_149,B_150,C_151),B_150)
| in('#skF_1'(A_149,B_150,C_151),A_149)
| ~ in('#skF_2'(A_149,B_150,C_151),B_150)
| ( set_union2(A_149,B_150) = C_151 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_18,plain,
! [A_7,B_8,C_9] :
( ~ in('#skF_1'(A_7,B_8,C_9),C_9)
| ~ in('#skF_2'(A_7,B_8,C_9),B_8)
| ( set_union2(A_7,B_8) = C_9 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_2886,plain,
! [A_285,B_286] :
( in('#skF_1'(A_285,B_286,B_286),A_285)
| ~ in('#skF_2'(A_285,B_286,B_286),B_286)
| ( set_union2(A_285,B_286) = B_286 ) ),
inference(resolution,[status(thm)],[c_1095,c_18]) ).
tff(c_2918,plain,
! [A_138,B_139] :
( in('#skF_1'(A_138,B_139,B_139),A_138)
| ( set_union2(A_138,B_139) = B_139 ) ),
inference(resolution,[status(thm)],[c_945,c_2886]) ).
tff(c_16,plain,
! [D_12,A_7,B_8] :
( ~ in(D_12,A_7)
| in(D_12,set_union2(A_7,B_8)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_15916,plain,
! [A_670,B_671,A_672,B_673] :
( in('#skF_2'(A_670,B_671,set_union2(A_672,B_673)),set_union2(A_672,B_673))
| ( set_union2(A_672,B_673) = set_union2(A_670,B_671) )
| ~ in('#skF_1'(A_670,B_671,set_union2(A_672,B_673)),A_672) ),
inference(resolution,[status(thm)],[c_16,c_515]) ).
tff(c_603,plain,
! [A_110,B_111,C_112] :
( ~ in('#skF_1'(A_110,B_111,C_112),C_112)
| ~ in('#skF_2'(A_110,B_111,C_112),B_111)
| ( set_union2(A_110,B_111) = C_112 ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_610,plain,
! [A_110,B_111,A_7,B_8] :
( ~ in('#skF_2'(A_110,B_111,set_union2(A_7,B_8)),B_111)
| ( set_union2(A_7,B_8) = set_union2(A_110,B_111) )
| ~ in('#skF_1'(A_110,B_111,set_union2(A_7,B_8)),A_7) ),
inference(resolution,[status(thm)],[c_16,c_603]) ).
tff(c_48118,plain,
! [A_1118,A_1119,B_1120] :
( ( set_union2(A_1118,set_union2(A_1119,B_1120)) = set_union2(A_1119,B_1120) )
| ~ in('#skF_1'(A_1118,set_union2(A_1119,B_1120),set_union2(A_1119,B_1120)),A_1119) ),
inference(resolution,[status(thm)],[c_15916,c_610]) ).
tff(c_48397,plain,
! [A_138,B_1120] : ( set_union2(A_138,set_union2(A_138,B_1120)) = set_union2(A_138,B_1120) ),
inference(resolution,[status(thm)],[c_2918,c_48118]) ).
tff(c_54563,plain,
set_union2('#skF_7','#skF_7') = set_union2('#skF_7','#skF_6'),
inference(superposition,[status(thm),theory(equality)],[c_54525,c_48397]) ).
tff(c_55328,plain,
set_union2('#skF_6','#skF_7') = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_46,c_4,c_54563]) ).
tff(c_55330,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_55328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n021.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 11:57:36 EDT 2023
% 0.13/0.35 % CPUTime :
% 20.13/8.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.13/8.85
% 20.13/8.85 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.13/8.88
% 20.13/8.88 Inference rules
% 20.13/8.88 ----------------------
% 20.13/8.88 #Ref : 0
% 20.13/8.88 #Sup : 15061
% 20.13/8.88 #Fact : 48
% 20.13/8.88 #Define : 0
% 20.13/8.88 #Split : 9
% 20.13/8.88 #Chain : 0
% 20.13/8.88 #Close : 0
% 20.13/8.88
% 20.13/8.88 Ordering : KBO
% 20.13/8.88
% 20.13/8.88 Simplification rules
% 20.13/8.88 ----------------------
% 20.13/8.88 #Subsume : 8019
% 20.13/8.88 #Demod : 6020
% 20.13/8.88 #Tautology : 1728
% 20.13/8.88 #SimpNegUnit : 115
% 20.13/8.88 #BackRed : 5
% 20.13/8.88
% 20.13/8.88 #Partial instantiations: 0
% 20.13/8.88 #Strategies tried : 1
% 20.13/8.88
% 20.13/8.88 Timing (in seconds)
% 20.13/8.88 ----------------------
% 20.13/8.89 Preprocessing : 0.51
% 20.13/8.89 Parsing : 0.26
% 20.13/8.89 CNF conversion : 0.04
% 20.13/8.89 Main loop : 7.30
% 20.13/8.89 Inferencing : 1.32
% 20.13/8.89 Reduction : 2.23
% 20.13/8.89 Demodulation : 1.83
% 20.13/8.89 BG Simplification : 0.10
% 20.13/8.89 Subsumption : 3.12
% 20.13/8.89 Abstraction : 0.16
% 20.13/8.89 MUC search : 0.00
% 20.13/8.89 Cooper : 0.00
% 20.13/8.89 Total : 7.86
% 20.13/8.89 Index Insertion : 0.00
% 20.13/8.89 Index Deletion : 0.00
% 20.13/8.89 Index Matching : 0.00
% 20.13/8.89 BG Taut test : 0.00
%------------------------------------------------------------------------------