TSTP Solution File: SET908+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET908+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 2.81s 1.86s
% Output : CNFRefutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 18
% Syntax : Number of formulae : 25 ( 6 unt; 14 typ; 0 def)
% Number of atoms : 19 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 3 |; 0 &)
% ( 5 <=>; 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 : 17 ( 9 >; 8 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 18 (; 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > set_union2 > #nlpp > singleton > empty_set > #skF_4 > #skF_7 > #skF_6 > #skF_5 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $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(empty,type,
empty: $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 ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_40,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_46,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_79,negated_conjecture,
~ ! [A,B] : ( set_union2(singleton(A),B) != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
tff(f_55,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(c_8,plain,
! [C_9] : in(C_9,singleton(C_9)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_18,plain,
! [B_13] : ~ in(B_13,empty_set),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_52,plain,
set_union2(singleton('#skF_8'),'#skF_9') = empty_set,
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_230,plain,
! [D_46,A_47,B_48] :
( ~ in(D_46,A_47)
| in(D_46,set_union2(A_47,B_48)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_248,plain,
! [D_46] :
( ~ in(D_46,singleton('#skF_8'))
| in(D_46,empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_230]) ).
tff(c_308,plain,
! [D_50] : ~ in(D_50,singleton('#skF_8')),
inference(negUnitSimplification,[status(thm)],[c_18,c_248]) ).
tff(c_313,plain,
$false,
inference(resolution,[status(thm)],[c_8,c_308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET908+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 : n026.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 16:59:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 2.81/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.81/1.86
% 2.81/1.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.81/1.89
% 2.81/1.89 Inference rules
% 2.81/1.89 ----------------------
% 2.81/1.89 #Ref : 0
% 2.81/1.89 #Sup : 65
% 2.81/1.89 #Fact : 0
% 2.81/1.89 #Define : 0
% 2.81/1.89 #Split : 0
% 2.81/1.89 #Chain : 0
% 2.81/1.89 #Close : 0
% 2.81/1.89
% 2.81/1.89 Ordering : KBO
% 2.81/1.89
% 2.81/1.89 Simplification rules
% 2.81/1.89 ----------------------
% 2.81/1.89 #Subsume : 10
% 2.81/1.89 #Demod : 22
% 2.81/1.89 #Tautology : 35
% 2.81/1.89 #SimpNegUnit : 6
% 2.81/1.89 #BackRed : 7
% 2.81/1.89
% 2.81/1.89 #Partial instantiations: 0
% 2.81/1.89 #Strategies tried : 1
% 2.81/1.89
% 2.81/1.89 Timing (in seconds)
% 2.81/1.89 ----------------------
% 2.81/1.89 Preprocessing : 0.49
% 2.81/1.89 Parsing : 0.25
% 2.81/1.89 CNF conversion : 0.04
% 2.81/1.89 Main loop : 0.32
% 2.81/1.89 Inferencing : 0.11
% 2.81/1.89 Reduction : 0.10
% 2.81/1.89 Demodulation : 0.08
% 2.81/1.89 BG Simplification : 0.02
% 2.81/1.89 Subsumption : 0.07
% 2.81/1.89 Abstraction : 0.01
% 2.81/1.89 MUC search : 0.00
% 2.81/1.89 Cooper : 0.00
% 2.81/1.90 Total : 0.86
% 2.81/1.90 Index Insertion : 0.00
% 2.81/1.90 Index Deletion : 0.00
% 2.81/1.90 Index Matching : 0.00
% 2.81/1.90 BG Taut test : 0.00
%------------------------------------------------------------------------------