TSTP Solution File: SET957+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : 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 10:57:25 EDT 2023
% Result : Theorem 16.78s 6.37s
% Output : CNFRefutation 16.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 57 ( 13 unt; 19 typ; 0 def)
% Number of atoms : 101 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 46 ~; 53 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 11 >; 13 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 79 (; 79 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_11 > #skF_7 > #skF_10 > #skF_12 > #skF_5 > #skF_6 > #skF_2 > #skF_1 > #skF_9 > #skF_4 > #skF_8 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_12',type,
'#skF_12': ( $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 ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_71,negated_conjecture,
~ ! [A,B,C,D,E,F] :
( ( subset(A,cartesian_product2(B,C))
& subset(D,cartesian_product2(E,F))
& ! [G,H] :
( in(ordered_pair(G,H),A)
<=> in(ordered_pair(G,H),D) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
tff(f_78,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
tff(f_59,axiom,
! [A,B,C,D] :
~ ( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
~ ( in(E,B)
& in(F,C)
& ( D = ordered_pair(E,F) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
tff(c_22,plain,
'#skF_5' != '#skF_8',
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_38,plain,
! [A_21,B_22] :
( in('#skF_11'(A_21,B_22),B_22)
| in('#skF_12'(A_21,B_22),A_21)
| ( B_22 = A_21 ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_16,plain,
! [A_11,B_12,C_13,D_14] :
( ( ordered_pair('#skF_3'(A_11,B_12,C_13,D_14),'#skF_4'(A_11,B_12,C_13,D_14)) = D_14 )
| ~ in(D_14,A_11)
| ~ subset(A_11,cartesian_product2(B_12,C_13)) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_453,plain,
! [A_81,B_82,C_83,D_84] :
( ( ordered_pair('#skF_3'(A_81,B_82,C_83,D_84),'#skF_4'(A_81,B_82,C_83,D_84)) = D_84 )
| ~ in(D_84,A_81)
| ~ subset(A_81,cartesian_product2(B_82,C_83)) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_24,plain,
! [G_19,H_20] :
( in(ordered_pair(G_19,H_20),'#skF_8')
| ~ in(ordered_pair(G_19,H_20),'#skF_5') ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_912,plain,
! [A_114,B_115,C_116,D_117] :
( in(ordered_pair('#skF_3'(A_114,B_115,C_116,D_117),'#skF_4'(A_114,B_115,C_116,D_117)),'#skF_8')
| ~ in(D_117,'#skF_5')
| ~ in(D_117,A_114)
| ~ subset(A_114,cartesian_product2(B_115,C_116)) ),
inference(superposition,[status(thm),theory(equality)],[c_453,c_24]) ).
tff(c_4060,plain,
! [D_239,A_240,B_241,C_242] :
( in(D_239,'#skF_8')
| ~ in(D_239,'#skF_5')
| ~ in(D_239,A_240)
| ~ subset(A_240,cartesian_product2(B_241,C_242))
| ~ in(D_239,A_240)
| ~ subset(A_240,cartesian_product2(B_241,C_242)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_912]) ).
tff(c_16980,plain,
! [A_353,A_354,B_355,C_356] :
( in('#skF_11'(A_353,'#skF_5'),'#skF_8')
| ~ in('#skF_11'(A_353,'#skF_5'),A_354)
| ~ subset(A_354,cartesian_product2(B_355,C_356))
| in('#skF_12'(A_353,'#skF_5'),A_353)
| ( A_353 = '#skF_5' ) ),
inference(resolution,[status(thm)],[c_38,c_4060]) ).
tff(c_17002,plain,
! [A_21,B_355,C_356] :
( in('#skF_11'(A_21,'#skF_5'),'#skF_8')
| ~ subset('#skF_5',cartesian_product2(B_355,C_356))
| in('#skF_12'(A_21,'#skF_5'),A_21)
| ( A_21 = '#skF_5' ) ),
inference(resolution,[status(thm)],[c_38,c_16980]) ).
tff(c_17003,plain,
! [B_355,C_356] : ~ subset('#skF_5',cartesian_product2(B_355,C_356)),
inference(splitLeft,[status(thm)],[c_17002]) ).
tff(c_30,plain,
subset('#skF_5',cartesian_product2('#skF_6','#skF_7')),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_17005,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17003,c_30]) ).
tff(c_17007,plain,
! [A_357] :
( in('#skF_11'(A_357,'#skF_5'),'#skF_8')
| in('#skF_12'(A_357,'#skF_5'),A_357)
| ( A_357 = '#skF_5' ) ),
inference(splitRight,[status(thm)],[c_17002]) ).
tff(c_36,plain,
! [A_21,B_22] :
( ~ in('#skF_11'(A_21,B_22),A_21)
| in('#skF_12'(A_21,B_22),A_21)
| ( B_22 = A_21 ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_17015,plain,
( in('#skF_12'('#skF_8','#skF_5'),'#skF_8')
| ( '#skF_5' = '#skF_8' ) ),
inference(resolution,[status(thm)],[c_17007,c_36]) ).
tff(c_17038,plain,
in('#skF_12'('#skF_8','#skF_5'),'#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_22,c_22,c_17015]) ).
tff(c_26,plain,
! [G_19,H_20] :
( in(ordered_pair(G_19,H_20),'#skF_5')
| ~ in(ordered_pair(G_19,H_20),'#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_1358,plain,
! [D_128,A_129,B_130,C_131] :
( in(D_128,'#skF_5')
| ~ in(ordered_pair('#skF_3'(A_129,B_130,C_131,D_128),'#skF_4'(A_129,B_130,C_131,D_128)),'#skF_8')
| ~ in(D_128,A_129)
| ~ subset(A_129,cartesian_product2(B_130,C_131)) ),
inference(superposition,[status(thm),theory(equality)],[c_453,c_26]) ).
tff(c_1364,plain,
! [D_14,A_11,B_12,C_13] :
( in(D_14,'#skF_5')
| ~ in(D_14,'#skF_8')
| ~ in(D_14,A_11)
| ~ subset(A_11,cartesian_product2(B_12,C_13))
| ~ in(D_14,A_11)
| ~ subset(A_11,cartesian_product2(B_12,C_13)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_1358]) ).
tff(c_17050,plain,
! [B_12,C_13] :
( in('#skF_12'('#skF_8','#skF_5'),'#skF_5')
| ~ in('#skF_12'('#skF_8','#skF_5'),'#skF_8')
| ~ subset('#skF_8',cartesian_product2(B_12,C_13)) ),
inference(resolution,[status(thm)],[c_17038,c_1364]) ).
tff(c_17061,plain,
! [B_12,C_13] :
( in('#skF_12'('#skF_8','#skF_5'),'#skF_5')
| ~ subset('#skF_8',cartesian_product2(B_12,C_13)) ),
inference(demodulation,[status(thm),theory(equality)],[c_17038,c_17050]) ).
tff(c_17065,plain,
! [B_12,C_13] : ~ subset('#skF_8',cartesian_product2(B_12,C_13)),
inference(splitLeft,[status(thm)],[c_17061]) ).
tff(c_28,plain,
subset('#skF_8',cartesian_product2('#skF_9','#skF_10')),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_17067,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17065,c_28]) ).
tff(c_17068,plain,
in('#skF_12'('#skF_8','#skF_5'),'#skF_5'),
inference(splitRight,[status(thm)],[c_17061]) ).
tff(c_34,plain,
! [A_21,B_22] :
( in('#skF_11'(A_21,B_22),B_22)
| ~ in('#skF_12'(A_21,B_22),B_22)
| ( B_22 = A_21 ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_19761,plain,
! [A_389,A_390,B_391,C_392] :
( in('#skF_11'(A_389,'#skF_5'),'#skF_8')
| ~ in('#skF_11'(A_389,'#skF_5'),A_390)
| ~ subset(A_390,cartesian_product2(B_391,C_392))
| ~ in('#skF_12'(A_389,'#skF_5'),'#skF_5')
| ( A_389 = '#skF_5' ) ),
inference(resolution,[status(thm)],[c_34,c_4060]) ).
tff(c_19789,plain,
! [A_21,B_391,C_392] :
( in('#skF_11'(A_21,'#skF_5'),'#skF_8')
| ~ subset('#skF_5',cartesian_product2(B_391,C_392))
| ~ in('#skF_12'(A_21,'#skF_5'),'#skF_5')
| ( A_21 = '#skF_5' ) ),
inference(resolution,[status(thm)],[c_34,c_19761]) ).
tff(c_19791,plain,
! [B_391,C_392] : ~ subset('#skF_5',cartesian_product2(B_391,C_392)),
inference(splitLeft,[status(thm)],[c_19789]) ).
tff(c_19793,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19791,c_30]) ).
tff(c_19795,plain,
! [A_393] :
( in('#skF_11'(A_393,'#skF_5'),'#skF_8')
| ~ in('#skF_12'(A_393,'#skF_5'),'#skF_5')
| ( A_393 = '#skF_5' ) ),
inference(splitRight,[status(thm)],[c_19789]) ).
tff(c_32,plain,
! [A_21,B_22] :
( ~ in('#skF_11'(A_21,B_22),A_21)
| ~ in('#skF_12'(A_21,B_22),B_22)
| ( B_22 = A_21 ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_19806,plain,
( ~ in('#skF_12'('#skF_8','#skF_5'),'#skF_5')
| ( '#skF_5' = '#skF_8' ) ),
inference(resolution,[status(thm)],[c_19795,c_32]) ).
tff(c_19817,plain,
'#skF_5' = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_17068,c_19806]) ).
tff(c_19819,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_19817]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n027.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 16:49:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 16.78/6.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.78/6.38
% 16.78/6.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.97/6.41
% 16.97/6.41 Inference rules
% 16.97/6.41 ----------------------
% 16.97/6.41 #Ref : 0
% 16.97/6.41 #Sup : 5440
% 16.97/6.41 #Fact : 0
% 16.97/6.41 #Define : 0
% 16.97/6.41 #Split : 11
% 16.97/6.41 #Chain : 0
% 16.97/6.41 #Close : 0
% 16.97/6.41
% 16.97/6.41 Ordering : KBO
% 16.97/6.41
% 16.97/6.41 Simplification rules
% 16.97/6.41 ----------------------
% 16.97/6.41 #Subsume : 767
% 16.97/6.41 #Demod : 11678
% 16.97/6.41 #Tautology : 1096
% 16.97/6.41 #SimpNegUnit : 21
% 16.97/6.41 #BackRed : 3
% 16.97/6.41
% 16.97/6.41 #Partial instantiations: 0
% 16.97/6.41 #Strategies tried : 1
% 16.97/6.41
% 16.97/6.41 Timing (in seconds)
% 16.97/6.41 ----------------------
% 16.97/6.41 Preprocessing : 0.49
% 16.97/6.41 Parsing : 0.25
% 16.97/6.41 CNF conversion : 0.03
% 16.97/6.41 Main loop : 4.83
% 16.97/6.41 Inferencing : 0.91
% 16.97/6.41 Reduction : 2.97
% 16.97/6.41 Demodulation : 2.66
% 16.97/6.41 BG Simplification : 0.14
% 16.97/6.41 Subsumption : 0.62
% 16.97/6.41 Abstraction : 0.32
% 16.97/6.41 MUC search : 0.00
% 16.97/6.41 Cooper : 0.00
% 16.97/6.41 Total : 5.37
% 16.97/6.41 Index Insertion : 0.00
% 16.97/6.41 Index Deletion : 0.00
% 16.97/6.41 Index Matching : 0.00
% 16.97/6.41 BG Taut test : 0.00
%------------------------------------------------------------------------------