TSTP Solution File: SET914+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET914+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 : n026.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 10:57:19 EDT 2023
% Result : Theorem 3.81s 1.99s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 32 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 31 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 12 ~; 7 |; 2 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 10 >; 12 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 25 (; 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > disjoint > empty > unordered_pair > set_intersection2 > #nlpp > empty_set > #skF_1 > #skF_4 > #skF_7 > #skF_10 > #skF_6 > #skF_5 > #skF_2 > #skF_9 > #skF_8 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(f_81,negated_conjecture,
~ ! [A,B,C] :
~ ( disjoint(unordered_pair(A,B),C)
& in(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
tff(f_50,axiom,
! [A,B,C] :
( ( C = unordered_pair(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
tff(f_41,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_63,axiom,
! [A,B] :
( disjoint(A,B)
<=> ( set_intersection2(A,B) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
tff(f_59,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(c_62,plain,
in('#skF_8','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_16,plain,
! [D_16,B_12] : in(D_16,unordered_pair(D_16,B_12)),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_8,plain,
! [B_10] : ~ in(B_10,empty_set),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_64,plain,
disjoint(unordered_pair('#skF_8','#skF_9'),'#skF_10'),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_187,plain,
! [A_44,B_45] :
( ( set_intersection2(A_44,B_45) = empty_set )
| ~ disjoint(A_44,B_45) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_195,plain,
set_intersection2(unordered_pair('#skF_8','#skF_9'),'#skF_10') = empty_set,
inference(resolution,[status(thm)],[c_64,c_187]) ).
tff(c_400,plain,
! [D_71,A_72,B_73] :
( in(D_71,set_intersection2(A_72,B_73))
| ~ in(D_71,B_73)
| ~ in(D_71,A_72) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_422,plain,
! [D_71] :
( in(D_71,empty_set)
| ~ in(D_71,'#skF_10')
| ~ in(D_71,unordered_pair('#skF_8','#skF_9')) ),
inference(superposition,[status(thm),theory(equality)],[c_195,c_400]) ).
tff(c_561,plain,
! [D_79] :
( ~ in(D_79,'#skF_10')
| ~ in(D_79,unordered_pair('#skF_8','#skF_9')) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_422]) ).
tff(c_573,plain,
~ in('#skF_8','#skF_10'),
inference(resolution,[status(thm)],[c_16,c_561]) ).
tff(c_583,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_62,c_573]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET914+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 3 16:54:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 3.81/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.81/1.99
% 3.81/1.99 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/2.01
% 3.81/2.01 Inference rules
% 3.81/2.01 ----------------------
% 3.81/2.01 #Ref : 0
% 3.81/2.01 #Sup : 128
% 3.81/2.01 #Fact : 0
% 3.81/2.01 #Define : 0
% 3.81/2.01 #Split : 0
% 3.81/2.01 #Chain : 0
% 3.81/2.01 #Close : 0
% 3.81/2.01
% 3.81/2.01 Ordering : KBO
% 3.81/2.01
% 3.81/2.01 Simplification rules
% 3.81/2.01 ----------------------
% 3.81/2.01 #Subsume : 25
% 3.81/2.01 #Demod : 28
% 3.81/2.01 #Tautology : 70
% 3.81/2.01 #SimpNegUnit : 7
% 3.81/2.01 #BackRed : 0
% 3.81/2.01
% 3.81/2.01 #Partial instantiations: 0
% 3.81/2.01 #Strategies tried : 1
% 3.81/2.01
% 3.81/2.01 Timing (in seconds)
% 3.81/2.01 ----------------------
% 3.81/2.02 Preprocessing : 0.52
% 3.81/2.02 Parsing : 0.26
% 3.81/2.02 CNF conversion : 0.04
% 3.81/2.02 Main loop : 0.42
% 3.81/2.02 Inferencing : 0.14
% 3.81/2.02 Reduction : 0.15
% 3.81/2.02 Demodulation : 0.11
% 3.81/2.02 BG Simplification : 0.03
% 3.81/2.02 Subsumption : 0.09
% 3.81/2.02 Abstraction : 0.02
% 3.81/2.02 MUC search : 0.00
% 3.81/2.02 Cooper : 0.00
% 3.81/2.02 Total : 0.99
% 3.81/2.02 Index Insertion : 0.00
% 3.81/2.02 Index Deletion : 0.00
% 3.81/2.02 Index Matching : 0.00
% 3.81/2.02 BG Taut test : 0.00
%------------------------------------------------------------------------------