TSTP Solution File: SET950+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET950+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 : n028.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 5.65s 2.55s
% Output : CNFRefutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 23
% Syntax : Number of formulae : 36 ( 5 unt; 20 typ; 0 def)
% Number of atoms : 39 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 43 ( 20 ~; 13 |; 6 &)
% ( 3 <=>; 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 : 34 ( 14 >; 20 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-4 aty)
% Number of variables : 35 (; 33 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_1 > #skF_11 > #skF_4 > #skF_10 > #skF_13 > #skF_2 > #skF_6 > #skF_9 > #skF_8 > #skF_5 > #skF_3 > #skF_7 > #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(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(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $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_8',type,
'#skF_8': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_46,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_79,negated_conjecture,
~ ! [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/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
tff(f_53,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(c_12,plain,
! [A_5,B_6,D_32] :
( in('#skF_5'(A_5,B_6,cartesian_product2(A_5,B_6),D_32),A_5)
| ~ in(D_32,cartesian_product2(A_5,B_6)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_10,plain,
! [A_5,B_6,D_32] :
( in('#skF_6'(A_5,B_6,cartesian_product2(A_5,B_6),D_32),B_6)
| ~ in(D_32,cartesian_product2(A_5,B_6)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_749,plain,
! [A_123,B_124,D_125] :
( ( ordered_pair('#skF_5'(A_123,B_124,cartesian_product2(A_123,B_124),D_125),'#skF_6'(A_123,B_124,cartesian_product2(A_123,B_124),D_125)) = D_125 )
| ~ in(D_125,cartesian_product2(A_123,B_124)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_46,plain,
! [E_52,F_53] :
( ( ordered_pair(E_52,F_53) != '#skF_13' )
| ~ in(F_53,'#skF_12')
| ~ in(E_52,'#skF_11') ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_890,plain,
! [D_146,A_147,B_148] :
( ( D_146 != '#skF_13' )
| ~ in('#skF_6'(A_147,B_148,cartesian_product2(A_147,B_148),D_146),'#skF_12')
| ~ in('#skF_5'(A_147,B_148,cartesian_product2(A_147,B_148),D_146),'#skF_11')
| ~ in(D_146,cartesian_product2(A_147,B_148)) ),
inference(superposition,[status(thm),theory(equality)],[c_749,c_46]) ).
tff(c_2621,plain,
! [D_232,A_233] :
( ( D_232 != '#skF_13' )
| ~ in('#skF_5'(A_233,'#skF_12',cartesian_product2(A_233,'#skF_12'),D_232),'#skF_11')
| ~ in(D_232,cartesian_product2(A_233,'#skF_12')) ),
inference(resolution,[status(thm)],[c_10,c_890]) ).
tff(c_2627,plain,
~ in('#skF_13',cartesian_product2('#skF_11','#skF_12')),
inference(resolution,[status(thm)],[c_12,c_2621]) ).
tff(c_50,plain,
subset('#skF_10',cartesian_product2('#skF_11','#skF_12')),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_48,plain,
in('#skF_13','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_136,plain,
! [C_71,B_72,A_73] :
( in(C_71,B_72)
| ~ in(C_71,A_73)
| ~ subset(A_73,B_72) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_150,plain,
! [B_78] :
( in('#skF_13',B_78)
| ~ subset('#skF_10',B_78) ),
inference(resolution,[status(thm)],[c_48,c_136]) ).
tff(c_158,plain,
in('#skF_13',cartesian_product2('#skF_11','#skF_12')),
inference(resolution,[status(thm)],[c_50,c_150]) ).
tff(c_2629,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2627,c_158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET950+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % 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
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 16:35:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.65/2.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.65/2.56
% 5.65/2.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.06/2.59
% 6.06/2.59 Inference rules
% 6.06/2.59 ----------------------
% 6.06/2.59 #Ref : 0
% 6.06/2.59 #Sup : 664
% 6.06/2.59 #Fact : 0
% 6.06/2.59 #Define : 0
% 6.06/2.59 #Split : 0
% 6.06/2.59 #Chain : 0
% 6.06/2.59 #Close : 0
% 6.06/2.59
% 6.06/2.59 Ordering : KBO
% 6.06/2.59
% 6.06/2.59 Simplification rules
% 6.06/2.59 ----------------------
% 6.06/2.59 #Subsume : 82
% 6.06/2.59 #Demod : 579
% 6.06/2.59 #Tautology : 169
% 6.06/2.59 #SimpNegUnit : 1
% 6.06/2.59 #BackRed : 1
% 6.06/2.59
% 6.06/2.59 #Partial instantiations: 0
% 6.06/2.59 #Strategies tried : 1
% 6.06/2.59
% 6.06/2.59 Timing (in seconds)
% 6.06/2.59 ----------------------
% 6.06/2.59 Preprocessing : 0.53
% 6.06/2.59 Parsing : 0.27
% 6.06/2.59 CNF conversion : 0.04
% 6.06/2.59 Main loop : 0.93
% 6.06/2.59 Inferencing : 0.29
% 6.06/2.59 Reduction : 0.38
% 6.06/2.59 Demodulation : 0.31
% 6.06/2.59 BG Simplification : 0.06
% 6.06/2.59 Subsumption : 0.16
% 6.06/2.59 Abstraction : 0.05
% 6.06/2.59 MUC search : 0.00
% 6.06/2.59 Cooper : 0.00
% 6.06/2.59 Total : 1.51
% 6.06/2.59 Index Insertion : 0.00
% 6.06/2.59 Index Deletion : 0.00
% 6.06/2.59 Index Matching : 0.00
% 6.06/2.59 BG Taut test : 0.00
%------------------------------------------------------------------------------