TSTP Solution File: SET604+3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET604+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n005.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 10:56:41 EDT 2023
% Result : Theorem 2.72s 1.65s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 16 ( 6 unt; 8 typ; 0 def)
% Number of atoms : 10 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 (; 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > difference > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_29,axiom,
! [B] : subset(empty_set,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_subset) ).
tff(f_34,axiom,
! [B,C] :
( ( difference(B,C) = empty_set )
<=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
tff(f_75,negated_conjecture,
~ ! [B] : ( difference(empty_set,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_no_difference_with_empty_set) ).
tff(c_2,plain,
! [B_1] : subset(empty_set,B_1),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_52,plain,
! [B_28,C_29] :
( ( difference(B_28,C_29) = empty_set )
| ~ subset(B_28,C_29) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_63,plain,
! [B_1] : ( difference(empty_set,B_1) = empty_set ),
inference(resolution,[status(thm)],[c_2,c_52]) ).
tff(c_34,plain,
difference(empty_set,'#skF_3') != empty_set,
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_83,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_63,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET604+3 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.14/0.35 % Computer : n005.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 16:33:27 EDT 2023
% 0.14/0.36 % CPUTime :
% 2.72/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.72/1.65
% 2.72/1.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.72/1.67
% 2.72/1.67 Inference rules
% 2.72/1.67 ----------------------
% 2.72/1.67 #Ref : 0
% 2.72/1.67 #Sup : 9
% 2.72/1.67 #Fact : 0
% 2.72/1.67 #Define : 0
% 2.72/1.67 #Split : 0
% 2.72/1.67 #Chain : 0
% 2.72/1.67 #Close : 0
% 2.72/1.67
% 2.72/1.67 Ordering : KBO
% 2.72/1.67
% 2.72/1.67 Simplification rules
% 2.72/1.67 ----------------------
% 2.72/1.67 #Subsume : 1
% 2.72/1.67 #Demod : 3
% 2.72/1.67 #Tautology : 6
% 2.72/1.67 #SimpNegUnit : 0
% 2.72/1.67 #BackRed : 1
% 2.72/1.67
% 2.72/1.67 #Partial instantiations: 0
% 2.72/1.67 #Strategies tried : 1
% 2.72/1.67
% 2.72/1.67 Timing (in seconds)
% 2.72/1.67 ----------------------
% 2.72/1.68 Preprocessing : 0.45
% 2.72/1.68 Parsing : 0.24
% 2.72/1.68 CNF conversion : 0.03
% 2.72/1.68 Main loop : 0.17
% 2.72/1.68 Inferencing : 0.07
% 2.72/1.68 Reduction : 0.04
% 2.72/1.68 Demodulation : 0.03
% 2.72/1.68 BG Simplification : 0.01
% 2.72/1.68 Subsumption : 0.04
% 2.72/1.68 Abstraction : 0.01
% 2.72/1.68 MUC search : 0.00
% 2.72/1.68 Cooper : 0.00
% 2.72/1.68 Total : 0.66
% 2.72/1.68 Index Insertion : 0.00
% 2.72/1.68 Index Deletion : 0.00
% 2.72/1.68 Index Matching : 0.00
% 2.72/1.68 BG Taut test : 0.00
%------------------------------------------------------------------------------