TSTP Solution File: SET617+3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET617+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 : n024.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 10:56:43 EDT 2023
% Result : Theorem 3.50s 1.96s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 19
% Syntax : Number of formulae : 35 ( 19 unt; 13 typ; 0 def)
% Number of atoms : 25 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 2 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 21 (; 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > union > symmetric_difference > difference > #nlpp > empty_set > #skF_4 > #skF_3 > #skF_5 > #skF_6 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(symmetric_difference,type,
symmetric_difference: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_33,axiom,
! [B] : ( union(B,empty_set) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).
tff(f_39,axiom,
! [B] : ( difference(empty_set,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
tff(f_36,axiom,
! [B] : ( difference(B,empty_set) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
tff(f_30,axiom,
! [B,C] : ( symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
tff(f_56,axiom,
! [B,C] : ( symmetric_difference(B,C) = symmetric_difference(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
tff(f_88,negated_conjecture,
~ ! [B] :
( ( symmetric_difference(B,empty_set) = B )
& ( symmetric_difference(empty_set,B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th92) ).
tff(c_4,plain,
! [B_3] : ( union(B_3,empty_set) = B_3 ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_8,plain,
! [B_5] : ( difference(empty_set,B_5) = empty_set ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_6,plain,
! [B_4] : ( difference(B_4,empty_set) = B_4 ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_558,plain,
! [B_89,C_90] : ( union(difference(B_89,C_90),difference(C_90,B_89)) = symmetric_difference(B_89,C_90) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_579,plain,
! [B_4] : ( union(B_4,difference(empty_set,B_4)) = symmetric_difference(B_4,empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_558]) ).
tff(c_591,plain,
! [B_4] : ( symmetric_difference(B_4,empty_set) = B_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_8,c_579]) ).
tff(c_345,plain,
! [B_64,C_65] : ( union(difference(B_64,C_65),difference(C_65,B_64)) = symmetric_difference(B_64,C_65) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_366,plain,
! [B_4] : ( union(B_4,difference(empty_set,B_4)) = symmetric_difference(B_4,empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_345]) ).
tff(c_378,plain,
! [B_4] : ( symmetric_difference(B_4,empty_set) = B_4 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_8,c_366]) ).
tff(c_20,plain,
! [C_12,B_11] : ( symmetric_difference(C_12,B_11) = symmetric_difference(B_11,C_12) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_46,plain,
( ( symmetric_difference('#skF_6',empty_set) != '#skF_6' )
| ( symmetric_difference(empty_set,'#skF_5') != '#skF_5' ) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_47,plain,
( ( symmetric_difference('#skF_6',empty_set) != '#skF_6' )
| ( symmetric_difference('#skF_5',empty_set) != '#skF_5' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_46]) ).
tff(c_145,plain,
symmetric_difference('#skF_5',empty_set) != '#skF_5',
inference(splitLeft,[status(thm)],[c_47]) ).
tff(c_384,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_378,c_145]) ).
tff(c_385,plain,
symmetric_difference('#skF_6',empty_set) != '#skF_6',
inference(splitRight,[status(thm)],[c_47]) ).
tff(c_598,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_591,c_385]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % 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
% 0.13/0.35 % Computer : n024.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 16:27:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.50/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.50/1.96
% 3.50/1.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.76/1.99
% 3.76/1.99 Inference rules
% 3.76/1.99 ----------------------
% 3.76/1.99 #Ref : 0
% 3.76/1.99 #Sup : 120
% 3.76/1.99 #Fact : 0
% 3.76/1.99 #Define : 0
% 3.76/1.99 #Split : 1
% 3.76/1.99 #Chain : 0
% 3.76/1.99 #Close : 0
% 3.76/1.99
% 3.76/1.99 Ordering : KBO
% 3.76/1.99
% 3.76/1.99 Simplification rules
% 3.76/1.99 ----------------------
% 3.76/1.99 #Subsume : 4
% 3.76/1.99 #Demod : 43
% 3.76/1.99 #Tautology : 84
% 3.76/1.99 #SimpNegUnit : 0
% 3.76/1.99 #BackRed : 2
% 3.76/1.99
% 3.76/1.99 #Partial instantiations: 0
% 3.76/1.99 #Strategies tried : 1
% 3.76/1.99
% 3.76/1.99 Timing (in seconds)
% 3.76/1.99 ----------------------
% 3.76/1.99 Preprocessing : 0.49
% 3.76/1.99 Parsing : 0.26
% 3.76/1.99 CNF conversion : 0.03
% 3.76/1.99 Main loop : 0.37
% 3.76/1.99 Inferencing : 0.14
% 3.76/1.99 Reduction : 0.11
% 3.76/1.99 Demodulation : 0.09
% 3.76/1.99 BG Simplification : 0.02
% 3.76/1.99 Subsumption : 0.07
% 3.76/1.99 Abstraction : 0.02
% 3.76/1.99 MUC search : 0.00
% 3.76/1.99 Cooper : 0.00
% 3.76/1.99 Total : 0.91
% 3.76/1.99 Index Insertion : 0.00
% 3.76/1.99 Index Deletion : 0.00
% 3.76/1.99 Index Matching : 0.00
% 3.76/1.99 BG Taut test : 0.00
%------------------------------------------------------------------------------