TSTP Solution File: SEU103+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU103+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 : n019.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 10:57:36 EDT 2023
% Result : Theorem 15.70s 5.79s
% Output : CNFRefutation 15.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 44
% Syntax : Number of formulae : 82 ( 19 unt; 36 typ; 0 def)
% Number of atoms : 126 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 52 ~; 60 |; 14 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 28 >; 10 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 57 (; 57 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation > preboolean > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > diff_closed > cup_closed > cap_closed > prebool_union2 > prebool_difference > symmetric_difference > set_union2 > set_difference > #nlpp > powerset > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_11 > #skF_1 > #skF_5 > #skF_10 > #skF_13 > #skF_2 > #skF_3 > #skF_8 > #skF_6 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(prebool_difference,type,
prebool_difference: ( $i * $i * $i ) > $i ).
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(cup_closed,type,
cup_closed: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(prebool_union2,type,
prebool_union2: ( $i * $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(finite,type,
finite: $i > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff(symmetric_difference,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(preboolean,type,
preboolean: $i > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(diff_closed,type,
diff_closed: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(cap_closed,type,
cap_closed: $i > $o ).
tff(natural,type,
natural: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_69,axiom,
! [A,B] : ( symmetric_difference(A,B) = symmetric_difference(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
tff(f_255,negated_conjecture,
~ ! [A,B,C] :
( ( ~ empty(C)
& preboolean(C) )
=> ( ( element(A,C)
& element(B,C) )
=> element(symmetric_difference(A,B),C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finsub_1) ).
tff(f_241,axiom,
! [A,B,C] :
( ( ~ empty(A)
& preboolean(A)
& element(B,A)
& element(C,A) )
=> ( prebool_difference(A,B,C) = set_difference(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
tff(f_93,axiom,
! [A,B,C] :
( ( ~ empty(A)
& preboolean(A)
& element(B,A)
& element(C,A) )
=> element(prebool_difference(A,B,C),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
tff(f_67,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_71,axiom,
! [A,B] : ( symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
tff(f_230,axiom,
! [A,B,C] :
( ( ~ empty(A)
& preboolean(A)
& element(B,A)
& element(C,A) )
=> ( prebool_union2(A,B,C) = set_union2(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
tff(f_82,axiom,
! [A,B,C] :
( ( ~ empty(A)
& preboolean(A)
& element(B,A)
& element(C,A) )
=> element(prebool_union2(A,B,C),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
tff(c_18,plain,
! [B_15,A_14] : ( symmetric_difference(B_15,A_14) = symmetric_difference(A_14,B_15) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_110,plain,
~ element(symmetric_difference('#skF_11','#skF_12'),'#skF_13'),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_145,plain,
~ element(symmetric_difference('#skF_12','#skF_11'),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_110]) ).
tff(c_118,plain,
~ empty('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_116,plain,
preboolean('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_114,plain,
element('#skF_11','#skF_13'),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_112,plain,
element('#skF_12','#skF_13'),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_1287,plain,
! [A_211,B_212,C_213] :
( ( prebool_difference(A_211,B_212,C_213) = set_difference(B_212,C_213) )
| ~ element(C_213,A_211)
| ~ element(B_212,A_211)
| ~ preboolean(A_211)
| empty(A_211) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_1305,plain,
! [B_212] :
( ( prebool_difference('#skF_13',B_212,'#skF_12') = set_difference(B_212,'#skF_12') )
| ~ element(B_212,'#skF_13')
| ~ preboolean('#skF_13')
| empty('#skF_13') ),
inference(resolution,[status(thm)],[c_112,c_1287]) ).
tff(c_1328,plain,
! [B_212] :
( ( prebool_difference('#skF_13',B_212,'#skF_12') = set_difference(B_212,'#skF_12') )
| ~ element(B_212,'#skF_13')
| empty('#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_1305]) ).
tff(c_1343,plain,
! [B_217] :
( ( prebool_difference('#skF_13',B_217,'#skF_12') = set_difference(B_217,'#skF_12') )
| ~ element(B_217,'#skF_13') ),
inference(negUnitSimplification,[status(thm)],[c_118,c_1328]) ).
tff(c_1372,plain,
prebool_difference('#skF_13','#skF_11','#skF_12') = set_difference('#skF_11','#skF_12'),
inference(resolution,[status(thm)],[c_114,c_1343]) ).
tff(c_24,plain,
! [A_21,B_22,C_23] :
( element(prebool_difference(A_21,B_22,C_23),A_21)
| ~ element(C_23,A_21)
| ~ element(B_22,A_21)
| ~ preboolean(A_21)
| empty(A_21) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_1426,plain,
( element(set_difference('#skF_11','#skF_12'),'#skF_13')
| ~ element('#skF_12','#skF_13')
| ~ element('#skF_11','#skF_13')
| ~ preboolean('#skF_13')
| empty('#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_1372,c_24]) ).
tff(c_1434,plain,
( element(set_difference('#skF_11','#skF_12'),'#skF_13')
| empty('#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_114,c_112,c_1426]) ).
tff(c_1435,plain,
element(set_difference('#skF_11','#skF_12'),'#skF_13'),
inference(negUnitSimplification,[status(thm)],[c_118,c_1434]) ).
tff(c_16,plain,
! [B_13,A_12] : ( set_union2(B_13,A_12) = set_union2(A_12,B_13) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_772,plain,
! [A_174,B_175] : ( set_union2(set_difference(A_174,B_175),set_difference(B_175,A_174)) = symmetric_difference(A_174,B_175) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_803,plain,
! [B_175,A_174] : ( set_union2(set_difference(B_175,A_174),set_difference(A_174,B_175)) = symmetric_difference(A_174,B_175) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_772]) ).
tff(c_1307,plain,
! [B_212] :
( ( prebool_difference('#skF_13',B_212,'#skF_11') = set_difference(B_212,'#skF_11') )
| ~ element(B_212,'#skF_13')
| ~ preboolean('#skF_13')
| empty('#skF_13') ),
inference(resolution,[status(thm)],[c_114,c_1287]) ).
tff(c_1332,plain,
! [B_212] :
( ( prebool_difference('#skF_13',B_212,'#skF_11') = set_difference(B_212,'#skF_11') )
| ~ element(B_212,'#skF_13')
| empty('#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_1307]) ).
tff(c_1578,plain,
! [B_224] :
( ( prebool_difference('#skF_13',B_224,'#skF_11') = set_difference(B_224,'#skF_11') )
| ~ element(B_224,'#skF_13') ),
inference(negUnitSimplification,[status(thm)],[c_118,c_1332]) ).
tff(c_1618,plain,
prebool_difference('#skF_13','#skF_12','#skF_11') = set_difference('#skF_12','#skF_11'),
inference(resolution,[status(thm)],[c_112,c_1578]) ).
tff(c_1629,plain,
( element(set_difference('#skF_12','#skF_11'),'#skF_13')
| ~ element('#skF_11','#skF_13')
| ~ element('#skF_12','#skF_13')
| ~ preboolean('#skF_13')
| empty('#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_1618,c_24]) ).
tff(c_1637,plain,
( element(set_difference('#skF_12','#skF_11'),'#skF_13')
| empty('#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_112,c_114,c_1629]) ).
tff(c_1638,plain,
element(set_difference('#skF_12','#skF_11'),'#skF_13'),
inference(negUnitSimplification,[status(thm)],[c_118,c_1637]) ).
tff(c_1466,plain,
! [A_220,B_221,C_222] :
( ( prebool_union2(A_220,B_221,C_222) = set_union2(B_221,C_222) )
| ~ element(C_222,A_220)
| ~ element(B_221,A_220)
| ~ preboolean(A_220)
| empty(A_220) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_10268,plain,
! [A_406,B_407,B_408,C_409] :
( ( prebool_union2(A_406,B_407,prebool_difference(A_406,B_408,C_409)) = set_union2(B_407,prebool_difference(A_406,B_408,C_409)) )
| ~ element(B_407,A_406)
| ~ element(C_409,A_406)
| ~ element(B_408,A_406)
| ~ preboolean(A_406)
| empty(A_406) ),
inference(resolution,[status(thm)],[c_24,c_1466]) ).
tff(c_10401,plain,
! [B_407] :
( ( prebool_union2('#skF_13',B_407,set_difference('#skF_12','#skF_11')) = set_union2(B_407,prebool_difference('#skF_13','#skF_12','#skF_11')) )
| ~ element(B_407,'#skF_13')
| ~ element('#skF_11','#skF_13')
| ~ element('#skF_12','#skF_13')
| ~ preboolean('#skF_13')
| empty('#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_1618,c_10268]) ).
tff(c_10516,plain,
! [B_407] :
( ( prebool_union2('#skF_13',B_407,set_difference('#skF_12','#skF_11')) = set_union2(B_407,set_difference('#skF_12','#skF_11')) )
| ~ element(B_407,'#skF_13')
| empty('#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_112,c_114,c_1618,c_10401]) ).
tff(c_17076,plain,
! [B_464] :
( ( prebool_union2('#skF_13',B_464,set_difference('#skF_12','#skF_11')) = set_union2(B_464,set_difference('#skF_12','#skF_11')) )
| ~ element(B_464,'#skF_13') ),
inference(negUnitSimplification,[status(thm)],[c_118,c_10516]) ).
tff(c_22,plain,
! [A_18,B_19,C_20] :
( element(prebool_union2(A_18,B_19,C_20),A_18)
| ~ element(C_20,A_18)
| ~ element(B_19,A_18)
| ~ preboolean(A_18)
| empty(A_18) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_17129,plain,
! [B_464] :
( element(set_union2(B_464,set_difference('#skF_12','#skF_11')),'#skF_13')
| ~ element(set_difference('#skF_12','#skF_11'),'#skF_13')
| ~ element(B_464,'#skF_13')
| ~ preboolean('#skF_13')
| empty('#skF_13')
| ~ element(B_464,'#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_17076,c_22]) ).
tff(c_17193,plain,
! [B_464] :
( element(set_union2(B_464,set_difference('#skF_12','#skF_11')),'#skF_13')
| empty('#skF_13')
| ~ element(B_464,'#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_116,c_1638,c_17129]) ).
tff(c_17271,plain,
! [B_465] :
( element(set_union2(B_465,set_difference('#skF_12','#skF_11')),'#skF_13')
| ~ element(B_465,'#skF_13') ),
inference(negUnitSimplification,[status(thm)],[c_118,c_17193]) ).
tff(c_17305,plain,
( element(symmetric_difference('#skF_12','#skF_11'),'#skF_13')
| ~ element(set_difference('#skF_11','#skF_12'),'#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_803,c_17271]) ).
tff(c_17355,plain,
element(symmetric_difference('#skF_12','#skF_11'),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_1435,c_17305]) ).
tff(c_17357,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_145,c_17355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU103+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
% 0.18/0.35 % Computer : n019.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 3 11:43:02 EDT 2023
% 0.18/0.35 % CPUTime :
% 15.70/5.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.70/5.79
% 15.70/5.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.70/5.82
% 15.70/5.82 Inference rules
% 15.70/5.82 ----------------------
% 15.70/5.82 #Ref : 0
% 15.70/5.82 #Sup : 3480
% 15.70/5.82 #Fact : 0
% 15.70/5.82 #Define : 0
% 15.70/5.82 #Split : 47
% 15.70/5.82 #Chain : 0
% 15.70/5.82 #Close : 0
% 15.70/5.82
% 15.70/5.82 Ordering : KBO
% 15.70/5.82
% 15.70/5.82 Simplification rules
% 15.70/5.82 ----------------------
% 15.70/5.82 #Subsume : 320
% 15.70/5.82 #Demod : 3871
% 15.70/5.82 #Tautology : 742
% 15.70/5.82 #SimpNegUnit : 1502
% 15.70/5.82 #BackRed : 13
% 15.70/5.82
% 15.70/5.82 #Partial instantiations: 0
% 15.70/5.82 #Strategies tried : 1
% 15.70/5.82
% 15.70/5.82 Timing (in seconds)
% 15.70/5.82 ----------------------
% 15.70/5.83 Preprocessing : 0.66
% 15.70/5.83 Parsing : 0.33
% 15.70/5.83 CNF conversion : 0.05
% 15.70/5.83 Main loop : 4.02
% 15.70/5.83 Inferencing : 0.97
% 15.70/5.83 Reduction : 1.97
% 15.70/5.83 Demodulation : 1.62
% 15.70/5.83 BG Simplification : 0.09
% 15.70/5.83 Subsumption : 0.80
% 15.70/5.83 Abstraction : 0.14
% 15.70/5.83 MUC search : 0.00
% 15.70/5.83 Cooper : 0.00
% 15.70/5.83 Total : 4.73
% 15.70/5.83 Index Insertion : 0.00
% 15.70/5.83 Index Deletion : 0.00
% 15.70/5.83 Index Matching : 0.00
% 15.70/5.83 BG Taut test : 0.00
%------------------------------------------------------------------------------