TSTP Solution File: NUM401+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM401+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 : n032.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 10:51:35 EDT 2023
% Result : Theorem 16.53s 6.19s
% Output : CNFRefutation 16.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 62
% Syntax : Number of formulae : 151 ( 52 unt; 39 typ; 0 def)
% Number of atoms : 229 ( 26 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 211 ( 94 ~; 78 |; 17 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 23 >; 11 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 16 con; 0-3 aty)
% Number of variables : 114 (; 112 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > ordinal_subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > set_union2 > #nlpp > succ > singleton > powerset > empty_set > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_4 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_13 > #skF_5 > #skF_21 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_6 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(ordinal_subset,type,
ordinal_subset: ( $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(succ,type,
succ: $i > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_306,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,succ(B))
<=> ordinal_subset(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).
tff(f_262,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ordinal_subset(A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
tff(f_209,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A)
& epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
tff(f_89,axiom,
! [A] : ( succ(A) = set_union2(A,singleton(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
tff(f_73,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_327,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_189,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_271,axiom,
! [A] : ( set_union2(A,empty_set) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
tff(f_162,axiom,
! [A] :
( ordinal(A)
=> ( ~ empty(succ(A))
& epsilon_transitive(succ(A))
& epsilon_connected(succ(A))
& ordinal(succ(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
tff(f_41,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
tff(f_266,axiom,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
tff(f_275,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
tff(f_256,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
tff(f_290,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(A,B)
& ( A != B )
& ~ in(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
tff(f_112,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(f_310,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_323,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
tff(f_316,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_296,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
tff(f_31,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
tff(f_123,axiom,
! [A] : ~ empty(succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
tff(f_103,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
tff(f_96,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(c_214,plain,
ordinal('#skF_21'),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_198,plain,
! [A_45,B_46] :
( ordinal_subset(A_45,A_45)
| ~ ordinal(B_46)
| ~ ordinal(A_45) ),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_21761,plain,
! [B_46] : ~ ordinal(B_46),
inference(splitLeft,[status(thm)],[c_198]) ).
tff(c_144,plain,
ordinal('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_21678,plain,
! [A_932] : ( set_union2(A_932,singleton(A_932)) = succ(A_932) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_21515,plain,
! [B_921,A_922] : ( set_union2(B_921,A_922) = set_union2(A_922,B_921) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_150,plain,
empty('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_21349,plain,
! [A_901] :
( ( empty_set = A_901 )
| ~ empty(A_901) ),
inference(cnfTransformation,[status(thm)],[f_327]) ).
tff(c_21367,plain,
empty_set = '#skF_12',
inference(resolution,[status(thm)],[c_150,c_21349]) ).
tff(c_136,plain,
empty('#skF_10'),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_21365,plain,
empty_set = '#skF_10',
inference(resolution,[status(thm)],[c_136,c_21349]) ).
tff(c_21395,plain,
'#skF_10' = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_21367,c_21365]) ).
tff(c_206,plain,
! [A_51] : ( set_union2(A_51,empty_set) = A_51 ),
inference(cnfTransformation,[status(thm)],[f_271]) ).
tff(c_21372,plain,
! [A_51] : ( set_union2(A_51,'#skF_10') = A_51 ),
inference(demodulation,[status(thm),theory(equality)],[c_21365,c_206]) ).
tff(c_21473,plain,
! [A_51] : ( set_union2(A_51,'#skF_12') = A_51 ),
inference(demodulation,[status(thm),theory(equality)],[c_21395,c_21372]) ).
tff(c_21543,plain,
! [A_922] : ( set_union2('#skF_12',A_922) = A_922 ),
inference(superposition,[status(thm),theory(equality)],[c_21515,c_21473]) ).
tff(c_21685,plain,
succ('#skF_12') = singleton('#skF_12'),
inference(superposition,[status(thm),theory(equality)],[c_21678,c_21543]) ).
tff(c_106,plain,
! [A_38] :
( ordinal(succ(A_38))
| ~ ordinal(A_38) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_21711,plain,
( ordinal(singleton('#skF_12'))
| ~ ordinal('#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_21685,c_106]) ).
tff(c_21730,plain,
ordinal(singleton('#skF_12')),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_21711]) ).
tff(c_21771,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21761,c_21730]) ).
tff(c_21772,plain,
! [A_45] :
( ordinal_subset(A_45,A_45)
| ~ ordinal(A_45) ),
inference(splitRight,[status(thm)],[c_198]) ).
tff(c_21282,plain,
! [A_892] :
( epsilon_transitive(A_892)
| ~ ordinal(A_892) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_21313,plain,
epsilon_transitive('#skF_21'),
inference(resolution,[status(thm)],[c_214,c_21282]) ).
tff(c_224,plain,
( in('#skF_20',succ('#skF_21'))
| ordinal_subset('#skF_20','#skF_21') ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_247,plain,
ordinal_subset('#skF_20','#skF_21'),
inference(splitLeft,[status(thm)],[c_224]) ).
tff(c_202,plain,
! [A_49] : in(A_49,succ(A_49)),
inference(cnfTransformation,[status(thm)],[f_266]) ).
tff(c_713,plain,
! [A_115,B_116] :
( element(A_115,B_116)
| ~ in(A_115,B_116) ),
inference(cnfTransformation,[status(thm)],[f_275]) ).
tff(c_724,plain,
! [A_49] : element(A_49,succ(A_49)),
inference(resolution,[status(thm)],[c_202,c_713]) ).
tff(c_216,plain,
ordinal('#skF_20'),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_196,plain,
! [A_43,B_44] :
( subset(A_43,B_44)
| ~ ordinal_subset(A_43,B_44)
| ~ ordinal(B_44)
| ~ ordinal(A_43) ),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_1760,plain,
! [B_210,A_211] :
( in(B_210,A_211)
| ( B_210 = A_211 )
| in(A_211,B_210)
| ~ ordinal(B_210)
| ~ ordinal(A_211) ),
inference(cnfTransformation,[status(thm)],[f_290]) ).
tff(c_36,plain,
! [A_15] : ( set_union2(A_15,singleton(A_15)) = succ(A_15) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_872,plain,
! [D_140,A_141,B_142] :
( ~ in(D_140,A_141)
| in(D_140,set_union2(A_141,B_142)) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_1306,plain,
! [D_176,A_177] :
( ~ in(D_176,A_177)
| in(D_176,succ(A_177)) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_872]) ).
tff(c_218,plain,
( ~ ordinal_subset('#skF_20','#skF_21')
| ~ in('#skF_20',succ('#skF_21')) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_248,plain,
~ in('#skF_20',succ('#skF_21')),
inference(splitLeft,[status(thm)],[c_218]) ).
tff(c_1364,plain,
~ in('#skF_20','#skF_21'),
inference(resolution,[status(thm)],[c_1306,c_248]) ).
tff(c_1803,plain,
( ( '#skF_20' = '#skF_21' )
| in('#skF_21','#skF_20')
| ~ ordinal('#skF_20')
| ~ ordinal('#skF_21') ),
inference(resolution,[status(thm)],[c_1760,c_1364]) ).
tff(c_1967,plain,
( ( '#skF_20' = '#skF_21' )
| in('#skF_21','#skF_20') ),
inference(demodulation,[status(thm),theory(equality)],[c_214,c_216,c_1803]) ).
tff(c_2017,plain,
in('#skF_21','#skF_20'),
inference(splitLeft,[status(thm)],[c_1967]) ).
tff(c_228,plain,
! [A_60,B_61] :
( element(A_60,powerset(B_61))
| ~ subset(A_60,B_61) ),
inference(cnfTransformation,[status(thm)],[f_310]) ).
tff(c_1180,plain,
! [C_158,B_159,A_160] :
( ~ empty(C_158)
| ~ element(B_159,powerset(C_158))
| ~ in(A_160,B_159) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_3403,plain,
! [B_270,A_271,A_272] :
( ~ empty(B_270)
| ~ in(A_271,A_272)
| ~ subset(A_272,B_270) ),
inference(resolution,[status(thm)],[c_228,c_1180]) ).
tff(c_3464,plain,
! [B_273] :
( ~ empty(B_273)
| ~ subset('#skF_20',B_273) ),
inference(resolution,[status(thm)],[c_2017,c_3403]) ).
tff(c_3468,plain,
! [B_44] :
( ~ empty(B_44)
| ~ ordinal_subset('#skF_20',B_44)
| ~ ordinal(B_44)
| ~ ordinal('#skF_20') ),
inference(resolution,[status(thm)],[c_196,c_3464]) ).
tff(c_3516,plain,
! [B_278] :
( ~ empty(B_278)
| ~ ordinal_subset('#skF_20',B_278)
| ~ ordinal(B_278) ),
inference(demodulation,[status(thm),theory(equality)],[c_216,c_3468]) ).
tff(c_3531,plain,
( ~ empty('#skF_21')
| ~ ordinal('#skF_21') ),
inference(resolution,[status(thm)],[c_247,c_3516]) ).
tff(c_3543,plain,
~ empty('#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_214,c_3531]) ).
tff(c_1445,plain,
! [A_184,C_185,B_186] :
( element(A_184,C_185)
| ~ element(B_186,powerset(C_185))
| ~ in(A_184,B_186) ),
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_4187,plain,
! [A_306,B_307,A_308] :
( element(A_306,B_307)
| ~ in(A_306,A_308)
| ~ subset(A_308,B_307) ),
inference(resolution,[status(thm)],[c_228,c_1445]) ).
tff(c_4251,plain,
! [B_309] :
( element('#skF_21',B_309)
| ~ subset('#skF_20',B_309) ),
inference(resolution,[status(thm)],[c_2017,c_4187]) ).
tff(c_4255,plain,
! [B_44] :
( element('#skF_21',B_44)
| ~ ordinal_subset('#skF_20',B_44)
| ~ ordinal(B_44)
| ~ ordinal('#skF_20') ),
inference(resolution,[status(thm)],[c_196,c_4251]) ).
tff(c_4423,plain,
! [B_317] :
( element('#skF_21',B_317)
| ~ ordinal_subset('#skF_20',B_317)
| ~ ordinal(B_317) ),
inference(demodulation,[status(thm),theory(equality)],[c_216,c_4255]) ).
tff(c_4442,plain,
( element('#skF_21','#skF_21')
| ~ ordinal('#skF_21') ),
inference(resolution,[status(thm)],[c_247,c_4423]) ).
tff(c_4457,plain,
element('#skF_21','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_214,c_4442]) ).
tff(c_212,plain,
! [A_57,B_58] :
( in(A_57,B_58)
| empty(B_58)
| ~ element(A_57,B_58) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_1094,plain,
! [A_155,B_156] :
( in(A_155,B_156)
| empty(B_156)
| ~ element(A_155,B_156) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_2,plain,
! [B_2,A_1] :
( ~ in(B_2,A_1)
| ~ in(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_3113,plain,
! [B_257,A_258] :
( ~ in(B_257,A_258)
| empty(B_257)
| ~ element(A_258,B_257) ),
inference(resolution,[status(thm)],[c_1094,c_2]) ).
tff(c_20946,plain,
! [A_884,B_885] :
( empty(A_884)
| ~ element(B_885,A_884)
| empty(B_885)
| ~ element(A_884,B_885) ),
inference(resolution,[status(thm)],[c_212,c_3113]) ).
tff(c_21054,plain,
( empty('#skF_21')
| ~ element('#skF_21','#skF_21') ),
inference(resolution,[status(thm)],[c_4457,c_20946]) ).
tff(c_21216,plain,
empty('#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_4457,c_21054]) ).
tff(c_21218,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3543,c_21216]) ).
tff(c_21219,plain,
'#skF_20' = '#skF_21',
inference(splitRight,[status(thm)],[c_1967]) ).
tff(c_82,plain,
! [A_33] : ~ empty(succ(A_33)),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_1154,plain,
( empty(succ('#skF_21'))
| ~ element('#skF_20',succ('#skF_21')) ),
inference(resolution,[status(thm)],[c_1094,c_248]) ).
tff(c_1178,plain,
~ element('#skF_20',succ('#skF_21')),
inference(negUnitSimplification,[status(thm)],[c_82,c_1154]) ).
tff(c_21223,plain,
~ element('#skF_21',succ('#skF_21')),
inference(demodulation,[status(thm),theory(equality)],[c_21219,c_1178]) ).
tff(c_21231,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_724,c_21223]) ).
tff(c_21232,plain,
~ ordinal_subset('#skF_20','#skF_21'),
inference(splitRight,[status(thm)],[c_218]) ).
tff(c_21235,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_247,c_21232]) ).
tff(c_21236,plain,
in('#skF_20',succ('#skF_21')),
inference(splitRight,[status(thm)],[c_224]) ).
tff(c_22358,plain,
! [D_998,B_999,A_1000] :
( in(D_998,B_999)
| in(D_998,A_1000)
| ~ in(D_998,set_union2(A_1000,B_999)) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_26509,plain,
! [D_1171,A_1172] :
( in(D_1171,singleton(A_1172))
| in(D_1171,A_1172)
| ~ in(D_1171,succ(A_1172)) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_22358]) ).
tff(c_26607,plain,
( in('#skF_20',singleton('#skF_21'))
| in('#skF_20','#skF_21') ),
inference(resolution,[status(thm)],[c_21236,c_26509]) ).
tff(c_26608,plain,
in('#skF_20','#skF_21'),
inference(splitLeft,[status(thm)],[c_26607]) ).
tff(c_50,plain,
! [B_24,A_21] :
( subset(B_24,A_21)
| ~ in(B_24,A_21)
| ~ epsilon_transitive(A_21) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_22206,plain,
! [A_979,B_980] :
( ordinal_subset(A_979,B_980)
| ~ subset(A_979,B_980)
| ~ ordinal(B_980)
| ~ ordinal(A_979) ),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_28387,plain,
! [B_1215,A_1216] :
( ordinal_subset(B_1215,A_1216)
| ~ ordinal(A_1216)
| ~ ordinal(B_1215)
| ~ in(B_1215,A_1216)
| ~ epsilon_transitive(A_1216) ),
inference(resolution,[status(thm)],[c_50,c_22206]) ).
tff(c_21237,plain,
~ ordinal_subset('#skF_20','#skF_21'),
inference(splitRight,[status(thm)],[c_224]) ).
tff(c_28402,plain,
( ~ ordinal('#skF_21')
| ~ ordinal('#skF_20')
| ~ in('#skF_20','#skF_21')
| ~ epsilon_transitive('#skF_21') ),
inference(resolution,[status(thm)],[c_28387,c_21237]) ).
tff(c_28415,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_21313,c_26608,c_216,c_214,c_28402]) ).
tff(c_28416,plain,
in('#skF_20',singleton('#skF_21')),
inference(splitRight,[status(thm)],[c_26607]) ).
tff(c_38,plain,
! [C_20,A_16] :
( ( C_20 = A_16 )
| ~ in(C_20,singleton(A_16)) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_28466,plain,
'#skF_20' = '#skF_21',
inference(resolution,[status(thm)],[c_28416,c_38]) ).
tff(c_28483,plain,
~ ordinal_subset('#skF_21','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_28466,c_21237]) ).
tff(c_28499,plain,
~ ordinal('#skF_21'),
inference(resolution,[status(thm)],[c_21772,c_28483]) ).
tff(c_28503,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_214,c_28499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % 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
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Aug 3 15:12:21 EDT 2023
% 0.11/0.31 % CPUTime :
% 16.53/6.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.53/6.20
% 16.53/6.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.69/6.24
% 16.69/6.24 Inference rules
% 16.69/6.24 ----------------------
% 16.69/6.24 #Ref : 0
% 16.69/6.24 #Sup : 6185
% 16.69/6.24 #Fact : 26
% 16.69/6.24 #Define : 0
% 16.69/6.24 #Split : 44
% 16.69/6.24 #Chain : 0
% 16.69/6.24 #Close : 0
% 16.69/6.24
% 16.69/6.24 Ordering : KBO
% 16.69/6.24
% 16.69/6.24 Simplification rules
% 16.69/6.24 ----------------------
% 16.69/6.24 #Subsume : 2350
% 16.69/6.24 #Demod : 1185
% 16.69/6.24 #Tautology : 595
% 16.69/6.24 #SimpNegUnit : 361
% 16.69/6.24 #BackRed : 84
% 16.69/6.24
% 16.69/6.24 #Partial instantiations: 0
% 16.69/6.24 #Strategies tried : 1
% 16.69/6.24
% 16.69/6.24 Timing (in seconds)
% 16.69/6.24 ----------------------
% 16.69/6.24 Preprocessing : 0.63
% 16.69/6.24 Parsing : 0.31
% 16.69/6.24 CNF conversion : 0.06
% 16.69/6.24 Main loop : 4.58
% 16.69/6.24 Inferencing : 1.08
% 16.69/6.24 Reduction : 1.78
% 16.69/6.24 Demodulation : 1.15
% 16.69/6.24 BG Simplification : 0.09
% 16.69/6.24 Subsumption : 1.27
% 16.69/6.24 Abstraction : 0.10
% 16.69/6.24 MUC search : 0.00
% 16.69/6.24 Cooper : 0.00
% 16.69/6.24 Total : 5.28
% 16.69/6.24 Index Insertion : 0.00
% 16.69/6.24 Index Deletion : 0.00
% 16.69/6.24 Index Matching : 0.00
% 16.69/6.24 BG Taut test : 0.00
%------------------------------------------------------------------------------