TSTP Solution File: SEU321+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n010.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 10:58:24 EDT 2023
% Result : Theorem 12.00s 3.78s
% Output : CNFRefutation 12.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 65 ( 20 unt; 28 typ; 0 def)
% Number of atoms : 76 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 73 ( 34 ~; 19 |; 10 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 21 >; 4 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 24 (; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > one_sorted_str > natural > empty_carrier > empty > subset_complement > #nlpp > the_carrier > powerset > empty_set > #skF_4 > #skF_1 > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_8
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(empty_carrier,type,
empty_carrier: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(v1_int_1,type,
v1_int_1: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(v1_xreal_0,type,
v1_xreal_0: $i > $o ).
tff(v5_membered,type,
v5_membered: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(v2_membered,type,
v2_membered: $i > $o ).
tff(v1_membered,type,
v1_membered: $i > $o ).
tff(v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(v1_rat_1,type,
v1_rat_1: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(subset_complement,type,
subset_complement: ( $i * $i ) > $i ).
tff(natural,type,
natural: $i > $o ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff(f_294,negated_conjecture,
~ ! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(C,subset_complement(the_carrier(A),B))
<=> ~ in(C,B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).
tff(f_254,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
tff(f_308,axiom,
! [A] :
( ( A != empty_set )
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
tff(f_203,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
tff(f_243,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
tff(f_315,axiom,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,subset_complement(A,C))
& in(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
tff(c_156,plain,
element('#skF_7',powerset(the_carrier('#skF_6'))),
inference(cnfTransformation,[status(thm)],[f_294]) ).
tff(c_160,plain,
~ empty_carrier('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_294]) ).
tff(c_158,plain,
one_sorted_str('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_294]) ).
tff(c_140,plain,
empty(empty_set),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_168,plain,
( in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7'))
| ~ in('#skF_8','#skF_7') ),
inference(cnfTransformation,[status(thm)],[f_294]) ).
tff(c_240,plain,
~ in('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_168]) ).
tff(c_154,plain,
element('#skF_8',the_carrier('#skF_6')),
inference(cnfTransformation,[status(thm)],[f_294]) ).
tff(c_10685,plain,
! [C_1316,A_1317,B_1318] :
( in(C_1316,subset_complement(A_1317,B_1318))
| in(C_1316,B_1318)
| ~ element(C_1316,A_1317)
| ~ element(B_1318,powerset(A_1317))
| ( empty_set = A_1317 ) ),
inference(cnfTransformation,[status(thm)],[f_308]) ).
tff(c_162,plain,
( in('#skF_8','#skF_7')
| ~ in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')) ),
inference(cnfTransformation,[status(thm)],[f_294]) ).
tff(c_253,plain,
~ in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')),
inference(negUnitSimplification,[status(thm)],[c_240,c_162]) ).
tff(c_10698,plain,
( in('#skF_8','#skF_7')
| ~ element('#skF_8',the_carrier('#skF_6'))
| ~ element('#skF_7',powerset(the_carrier('#skF_6')))
| ( the_carrier('#skF_6') = empty_set ) ),
inference(resolution,[status(thm)],[c_10685,c_253]) ).
tff(c_10714,plain,
( in('#skF_8','#skF_7')
| ( the_carrier('#skF_6') = empty_set ) ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_154,c_10698]) ).
tff(c_10715,plain,
the_carrier('#skF_6') = empty_set,
inference(negUnitSimplification,[status(thm)],[c_240,c_10714]) ).
tff(c_9996,plain,
! [C_1243,B_1244,A_1245] :
( ~ empty(C_1243)
| ~ element(B_1244,powerset(C_1243))
| ~ in(A_1245,B_1244) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_10006,plain,
! [A_1245] :
( ~ empty(the_carrier('#skF_6'))
| ~ in(A_1245,'#skF_7') ),
inference(resolution,[status(thm)],[c_156,c_9996]) ).
tff(c_10007,plain,
~ empty(the_carrier('#skF_6')),
inference(splitLeft,[status(thm)],[c_10006]) ).
tff(c_10720,plain,
~ empty(empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_10715,c_10007]) ).
tff(c_10739,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_140,c_10720]) ).
tff(c_10741,plain,
empty(the_carrier('#skF_6')),
inference(splitRight,[status(thm)],[c_10006]) ).
tff(c_128,plain,
! [A_55] :
( ~ empty(the_carrier(A_55))
| ~ one_sorted_str(A_55)
| empty_carrier(A_55) ),
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_10750,plain,
( ~ one_sorted_str('#skF_6')
| empty_carrier('#skF_6') ),
inference(resolution,[status(thm)],[c_10741,c_128]) ).
tff(c_10758,plain,
empty_carrier('#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_158,c_10750]) ).
tff(c_10760,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_160,c_10758]) ).
tff(c_10762,plain,
in('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_168]) ).
tff(c_10761,plain,
in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')),
inference(splitRight,[status(thm)],[c_168]) ).
tff(c_10763,plain,
~ in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')),
inference(splitLeft,[status(thm)],[c_162]) ).
tff(c_10800,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10761,c_10763]) ).
tff(c_10802,plain,
in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')),
inference(splitRight,[status(thm)],[c_162]) ).
tff(c_12522,plain,
! [B_1540,C_1541,A_1542] :
( ~ in(B_1540,C_1541)
| ~ in(B_1540,subset_complement(A_1542,C_1541))
| ~ element(C_1541,powerset(A_1542)) ),
inference(cnfTransformation,[status(thm)],[f_315]) ).
tff(c_12532,plain,
( ~ in('#skF_8','#skF_7')
| ~ element('#skF_7',powerset(the_carrier('#skF_6'))) ),
inference(resolution,[status(thm)],[c_10802,c_12522]) ).
tff(c_12537,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_156,c_10762,c_12532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.15/0.33 % Computer : n010.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Thu Aug 3 11:53:59 EDT 2023
% 0.15/0.34 % CPUTime :
% 12.00/3.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.00/3.79
% 12.00/3.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.14/3.81
% 12.14/3.81 Inference rules
% 12.14/3.81 ----------------------
% 12.14/3.81 #Ref : 0
% 12.14/3.81 #Sup : 2634
% 12.14/3.81 #Fact : 0
% 12.14/3.81 #Define : 0
% 12.14/3.81 #Split : 79
% 12.14/3.82 #Chain : 0
% 12.14/3.82 #Close : 0
% 12.14/3.82
% 12.14/3.82 Ordering : KBO
% 12.14/3.82
% 12.14/3.82 Simplification rules
% 12.14/3.82 ----------------------
% 12.14/3.82 #Subsume : 790
% 12.14/3.82 #Demod : 820
% 12.14/3.82 #Tautology : 418
% 12.14/3.82 #SimpNegUnit : 54
% 12.14/3.82 #BackRed : 274
% 12.14/3.82
% 12.14/3.82 #Partial instantiations: 0
% 12.14/3.82 #Strategies tried : 1
% 12.14/3.82
% 12.14/3.82 Timing (in seconds)
% 12.14/3.82 ----------------------
% 12.14/3.82 Preprocessing : 0.59
% 12.14/3.82 Parsing : 0.32
% 12.14/3.82 CNF conversion : 0.05
% 12.14/3.82 Main loop : 2.19
% 12.14/3.82 Inferencing : 0.80
% 12.14/3.82 Reduction : 0.69
% 12.14/3.82 Demodulation : 0.44
% 12.14/3.82 BG Simplification : 0.06
% 12.14/3.82 Subsumption : 0.45
% 12.14/3.82 Abstraction : 0.05
% 12.14/3.82 MUC search : 0.00
% 12.14/3.82 Cooper : 0.00
% 12.14/3.82 Total : 2.82
% 12.14/3.82 Index Insertion : 0.00
% 12.14/3.82 Index Deletion : 0.00
% 12.14/3.82 Index Matching : 0.00
% 12.14/3.82 BG Taut test : 0.00
%------------------------------------------------------------------------------