TSTP Solution File: SEU104+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU104+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n021.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 7.13s 2.76s
% Output : CNFRefutation 7.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 43
% Syntax : Number of formulae : 93 ( 23 unt; 34 typ; 0 def)
% Number of atoms : 125 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 63 ~; 53 |; 4 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 28 >; 6 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 66 (; 66 !; 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 > symmetric_difference > set_union2 > set_difference > #nlpp > powerset > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_1 > #skF_5 > #skF_10 > #skF_13 > #skF_2 > #skF_3 > #skF_8 > #skF_11 > #skF_12 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
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_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
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('#skF_11',type,
'#skF_11': $i > $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_12',type,
'#skF_12': $i > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_204,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(symmetric_difference(B,C),A)
& in(set_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finsub_1) ).
tff(f_177,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_188,axiom,
! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(B,A)
& in(C,A) )
=> ( in(set_union2(B,C),A)
& in(set_difference(B,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
tff(f_222,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_230,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
tff(f_258,axiom,
! [A,B] : ( set_union2(A,B) = symmetric_difference(A,set_difference(B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_xboole_1) ).
tff(f_56,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_210,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
tff(f_97,axiom,
! [A,B] : ( set_union2(A,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
tff(c_108,plain,
~ preboolean('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_96,plain,
! [A_40] : subset(A_40,A_40),
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_106,plain,
! [A_42] :
( in('#skF_11'(A_42),A_42)
| preboolean(A_42) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_126,plain,
! [A_61,B_62] :
( element(A_61,powerset(B_62))
| ~ subset(A_61,B_62) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_1026,plain,
! [A_188,C_189,B_190] :
( element(A_188,C_189)
| ~ element(B_190,powerset(C_189))
| ~ in(A_188,B_190) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_1480,plain,
! [A_221,B_222,A_223] :
( element(A_221,B_222)
| ~ in(A_221,A_223)
| ~ subset(A_223,B_222) ),
inference(resolution,[status(thm)],[c_126,c_1026]) ).
tff(c_1498,plain,
! [A_42,B_222] :
( element('#skF_11'(A_42),B_222)
| ~ subset(A_42,B_222)
| preboolean(A_42) ),
inference(resolution,[status(thm)],[c_106,c_1480]) ).
tff(c_104,plain,
! [A_42] :
( in('#skF_12'(A_42),A_42)
| preboolean(A_42) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_1499,plain,
! [A_42,B_222] :
( element('#skF_12'(A_42),B_222)
| ~ subset(A_42,B_222)
| preboolean(A_42) ),
inference(resolution,[status(thm)],[c_104,c_1480]) ).
tff(c_870,plain,
! [A_174,B_175] : ( symmetric_difference(A_174,set_difference(B_175,A_174)) = set_union2(A_174,B_175) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_114,plain,
! [B_52,C_54] :
( in(symmetric_difference(B_52,C_54),'#skF_13')
| ~ element(C_54,'#skF_13')
| ~ element(B_52,'#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_886,plain,
! [A_174,B_175] :
( in(set_union2(A_174,B_175),'#skF_13')
| ~ element(set_difference(B_175,A_174),'#skF_13')
| ~ element(A_174,'#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_870,c_114]) ).
tff(c_14,plain,
! [B_10,A_9] : ( set_union2(B_10,A_9) = set_union2(A_9,B_10) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_102,plain,
! [A_42] :
( ~ in(set_difference('#skF_11'(A_42),'#skF_12'(A_42)),A_42)
| ~ in(set_union2('#skF_11'(A_42),'#skF_12'(A_42)),A_42)
| preboolean(A_42) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_1699,plain,
! [A_241] :
( ~ in(set_difference('#skF_11'(A_241),'#skF_12'(A_241)),A_241)
| ~ in(set_union2('#skF_12'(A_241),'#skF_11'(A_241)),A_241)
| preboolean(A_241) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_102]) ).
tff(c_1703,plain,
( ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
| preboolean('#skF_13')
| ~ element(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
| ~ element('#skF_12'('#skF_13'),'#skF_13') ),
inference(resolution,[status(thm)],[c_886,c_1699]) ).
tff(c_1714,plain,
( ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
| ~ element(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
| ~ element('#skF_12'('#skF_13'),'#skF_13') ),
inference(negUnitSimplification,[status(thm)],[c_108,c_1703]) ).
tff(c_2563,plain,
~ element('#skF_12'('#skF_13'),'#skF_13'),
inference(splitLeft,[status(thm)],[c_1714]) ).
tff(c_2566,plain,
( ~ subset('#skF_13','#skF_13')
| preboolean('#skF_13') ),
inference(resolution,[status(thm)],[c_1499,c_2563]) ).
tff(c_2572,plain,
preboolean('#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_2566]) ).
tff(c_2574,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_108,c_2572]) ).
tff(c_2576,plain,
element('#skF_12'('#skF_13'),'#skF_13'),
inference(splitRight,[status(thm)],[c_1714]) ).
tff(c_112,plain,
! [B_52,C_54] :
( in(set_difference(B_52,C_54),'#skF_13')
| ~ element(C_54,'#skF_13')
| ~ element(B_52,'#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_1501,plain,
! [B_52,C_54,B_222] :
( element(set_difference(B_52,C_54),B_222)
| ~ subset('#skF_13',B_222)
| ~ element(C_54,'#skF_13')
| ~ element(B_52,'#skF_13') ),
inference(resolution,[status(thm)],[c_112,c_1480]) ).
tff(c_142,plain,
! [A_76,B_77] : ( symmetric_difference(A_76,set_difference(B_77,A_76)) = set_union2(A_76,B_77) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_596,plain,
! [A_131,B_132] :
( element(A_131,B_132)
| ~ in(A_131,B_132) ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_983,plain,
! [B_182,C_183] :
( element(symmetric_difference(B_182,C_183),'#skF_13')
| ~ element(C_183,'#skF_13')
| ~ element(B_182,'#skF_13') ),
inference(resolution,[status(thm)],[c_114,c_596]) ).
tff(c_4280,plain,
! [A_374,B_375] :
( element(set_union2(A_374,B_375),'#skF_13')
| ~ element(set_difference(B_375,A_374),'#skF_13')
| ~ element(A_374,'#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_142,c_983]) ).
tff(c_36,plain,
! [A_28] : ( set_union2(A_28,A_28) = A_28 ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_1399,plain,
! [A_215,B_216] :
( in(set_union2(A_215,B_216),'#skF_13')
| ~ element(set_difference(B_216,A_215),'#skF_13')
| ~ element(A_215,'#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_870,c_114]) ).
tff(c_2656,plain,
! [A_310] :
( in(A_310,'#skF_13')
| ~ element(set_difference(A_310,A_310),'#skF_13')
| ~ element(A_310,'#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_1399]) ).
tff(c_2660,plain,
! [C_54] :
( in(C_54,'#skF_13')
| ~ subset('#skF_13','#skF_13')
| ~ element(C_54,'#skF_13') ),
inference(resolution,[status(thm)],[c_1501,c_2656]) ).
tff(c_2677,plain,
! [C_311] :
( in(C_311,'#skF_13')
| ~ element(C_311,'#skF_13') ),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_2660]) ).
tff(c_143,plain,
! [A_42] :
( ~ in(set_difference('#skF_11'(A_42),'#skF_12'(A_42)),A_42)
| ~ in(set_union2('#skF_12'(A_42),'#skF_11'(A_42)),A_42)
| preboolean(A_42) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_102]) ).
tff(c_2681,plain,
( ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
| preboolean('#skF_13')
| ~ element(set_union2('#skF_12'('#skF_13'),'#skF_11'('#skF_13')),'#skF_13') ),
inference(resolution,[status(thm)],[c_2677,c_143]) ).
tff(c_2699,plain,
( ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
| ~ element(set_union2('#skF_12'('#skF_13'),'#skF_11'('#skF_13')),'#skF_13') ),
inference(negUnitSimplification,[status(thm)],[c_108,c_2681]) ).
tff(c_2773,plain,
~ element(set_union2('#skF_12'('#skF_13'),'#skF_11'('#skF_13')),'#skF_13'),
inference(splitLeft,[status(thm)],[c_2699]) ).
tff(c_4286,plain,
( ~ element(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
| ~ element('#skF_12'('#skF_13'),'#skF_13') ),
inference(resolution,[status(thm)],[c_4280,c_2773]) ).
tff(c_4316,plain,
~ element(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_2576,c_4286]) ).
tff(c_4327,plain,
( ~ subset('#skF_13','#skF_13')
| ~ element('#skF_12'('#skF_13'),'#skF_13')
| ~ element('#skF_11'('#skF_13'),'#skF_13') ),
inference(resolution,[status(thm)],[c_1501,c_4316]) ).
tff(c_4334,plain,
~ element('#skF_11'('#skF_13'),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_2576,c_96,c_4327]) ).
tff(c_4340,plain,
( ~ subset('#skF_13','#skF_13')
| preboolean('#skF_13') ),
inference(resolution,[status(thm)],[c_1498,c_4334]) ).
tff(c_4346,plain,
preboolean('#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_4340]) ).
tff(c_4348,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_108,c_4346]) ).
tff(c_4349,plain,
~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13'),
inference(splitRight,[status(thm)],[c_2699]) ).
tff(c_4362,plain,
( ~ element('#skF_12'('#skF_13'),'#skF_13')
| ~ element('#skF_11'('#skF_13'),'#skF_13') ),
inference(resolution,[status(thm)],[c_112,c_4349]) ).
tff(c_4370,plain,
~ element('#skF_11'('#skF_13'),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_2576,c_4362]) ).
tff(c_4373,plain,
( ~ subset('#skF_13','#skF_13')
| preboolean('#skF_13') ),
inference(resolution,[status(thm)],[c_1498,c_4370]) ).
tff(c_4379,plain,
preboolean('#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_4373]) ).
tff(c_4381,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_108,c_4379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU104+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 11:41:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 7.13/2.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.13/2.77
% 7.13/2.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.13/2.80
% 7.13/2.80 Inference rules
% 7.13/2.80 ----------------------
% 7.13/2.80 #Ref : 0
% 7.13/2.80 #Sup : 973
% 7.13/2.80 #Fact : 0
% 7.13/2.80 #Define : 0
% 7.13/2.80 #Split : 19
% 7.13/2.80 #Chain : 0
% 7.13/2.80 #Close : 0
% 7.13/2.80
% 7.13/2.80 Ordering : KBO
% 7.13/2.80
% 7.13/2.80 Simplification rules
% 7.13/2.80 ----------------------
% 7.13/2.80 #Subsume : 273
% 7.13/2.80 #Demod : 388
% 7.13/2.80 #Tautology : 250
% 7.13/2.80 #SimpNegUnit : 64
% 7.13/2.80 #BackRed : 13
% 7.13/2.80
% 7.13/2.80 #Partial instantiations: 0
% 7.13/2.80 #Strategies tried : 1
% 7.13/2.80
% 7.13/2.80 Timing (in seconds)
% 7.13/2.80 ----------------------
% 7.41/2.80 Preprocessing : 0.56
% 7.41/2.80 Parsing : 0.30
% 7.41/2.81 CNF conversion : 0.05
% 7.41/2.81 Main loop : 1.18
% 7.41/2.81 Inferencing : 0.42
% 7.41/2.81 Reduction : 0.37
% 7.41/2.81 Demodulation : 0.26
% 7.41/2.81 BG Simplification : 0.04
% 7.41/2.81 Subsumption : 0.26
% 7.41/2.81 Abstraction : 0.03
% 7.41/2.81 MUC search : 0.00
% 7.41/2.81 Cooper : 0.00
% 7.41/2.81 Total : 1.80
% 7.41/2.81 Index Insertion : 0.00
% 7.41/2.81 Index Deletion : 0.00
% 7.41/2.81 Index Matching : 0.00
% 7.41/2.81 BG Taut test : 0.00
%------------------------------------------------------------------------------