TSTP Solution File: SEU235+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU235+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 : n013.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 10:58:07 EDT 2023
% Result : Theorem 22.61s 10.70s
% Output : CNFRefutation 22.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 55
% Syntax : Number of formulae : 296 ( 83 unt; 32 typ; 0 def)
% Number of atoms : 669 ( 81 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 795 ( 390 ~; 357 |; 27 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 17 >; 5 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-2 aty)
% Number of variables : 245 (; 240 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > ordinal_subset > in > element > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_2 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_18 > #skF_5 > #skF_6 > #skF_13 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_17 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_15',type,
'#skF_15': $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(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
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('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(ordinal_subset,type,
ordinal_subset: ( $i * $i ) > $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_150,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A)
& epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
tff(f_273,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_130,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_128,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_252,negated_conjecture,
~ ! [A,B] :
( ordinal(B)
=> ~ ( subset(A,B)
& ( A != empty_set )
& ! [C] :
( ordinal(C)
=> ~ ( in(C,A)
& ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
tff(f_90,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
tff(f_230,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
tff(f_269,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
tff(f_256,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_191,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
tff(f_71,axiom,
! [A] :
( empty(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
tff(f_224,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(A,B)
& ( A != B )
& ~ in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
tff(f_86,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
tff(f_262,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
tff(f_209,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
tff(f_63,axiom,
! [A] :
( ( epsilon_transitive(A)
& epsilon_connected(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
tff(f_199,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_291,axiom,
! [A,B] :
~ ( in(A,B)
& ! [C] :
~ ( in(C,B)
& ! [D] :
~ ( in(D,B)
& in(D,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
tff(f_197,axiom,
! [A,B] :
( ( ordinal(A)
& ordinal(B) )
=> ordinal_subset(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
tff(f_124,axiom,
? [A] :
( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
tff(f_41,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
tff(f_203,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
tff(f_278,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
tff(c_98,plain,
empty('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_220,plain,
! [A_62] :
( ( empty_set = A_62 )
| ~ empty(A_62) ),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_240,plain,
empty_set = '#skF_8',
inference(resolution,[status(thm)],[c_98,c_220]) ).
tff(c_84,plain,
empty('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_237,plain,
empty_set = '#skF_6',
inference(resolution,[status(thm)],[c_84,c_220]) ).
tff(c_263,plain,
'#skF_6' = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_240,c_237]) ).
tff(c_82,plain,
empty('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_236,plain,
empty_set = '#skF_5',
inference(resolution,[status(thm)],[c_82,c_220]) ).
tff(c_258,plain,
'#skF_5' = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_237,c_236]) ).
tff(c_152,plain,
empty_set != '#skF_15',
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_250,plain,
'#skF_15' != '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_236,c_152]) ).
tff(c_296,plain,
'#skF_15' != '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_258,c_250]) ).
tff(c_298,plain,
'#skF_15' != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_263,c_296]) ).
tff(c_40,plain,
! [A_15] : element('#skF_2'(A_15),A_15),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_92,plain,
ordinal('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_150,plain,
! [A_30,B_31] :
( in(A_30,B_31)
| empty(B_31)
| ~ element(A_30,B_31) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_560,plain,
! [C_112,B_113,A_114] :
( ~ empty(C_112)
| ~ element(B_113,powerset(C_112))
| ~ in(A_114,B_113) ),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_52419,plain,
! [C_1209,A_1210] :
( ~ empty(C_1209)
| ~ in(A_1210,'#skF_2'(powerset(C_1209))) ),
inference(resolution,[status(thm)],[c_40,c_560]) ).
tff(c_57149,plain,
! [C_1476,A_1477] :
( ~ empty(C_1476)
| empty('#skF_2'(powerset(C_1476)))
| ~ element(A_1477,'#skF_2'(powerset(C_1476))) ),
inference(resolution,[status(thm)],[c_150,c_52419]) ).
tff(c_57189,plain,
! [C_1478] :
( ~ empty(C_1478)
| empty('#skF_2'(powerset(C_1478))) ),
inference(resolution,[status(thm)],[c_40,c_57149]) ).
tff(c_300,plain,
'#skF_5' = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_263,c_258]) ).
tff(c_172,plain,
! [A_45] :
( ( empty_set = A_45 )
| ~ empty(A_45) ),
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_242,plain,
! [A_45] :
( ( A_45 = '#skF_5' )
| ~ empty(A_45) ),
inference(demodulation,[status(thm),theory(equality)],[c_236,c_172]) ).
tff(c_353,plain,
! [A_45] :
( ( A_45 = '#skF_8' )
| ~ empty(A_45) ),
inference(demodulation,[status(thm),theory(equality)],[c_300,c_242]) ).
tff(c_57197,plain,
! [C_1479] :
( ( '#skF_2'(powerset(C_1479)) = '#skF_8' )
| ~ empty(C_1479) ),
inference(resolution,[status(thm)],[c_57189,c_353]) ).
tff(c_403,plain,
! [A_87,B_88] :
( subset(A_87,B_88)
| ~ element(A_87,powerset(B_88)) ),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_413,plain,
! [B_88] : subset('#skF_2'(powerset(B_88)),B_88),
inference(resolution,[status(thm)],[c_40,c_403]) ).
tff(c_57251,plain,
! [C_1480] :
( subset('#skF_8',C_1480)
| ~ empty(C_1480) ),
inference(superposition,[status(thm),theory(equality)],[c_57197,c_413]) ).
tff(c_136,plain,
! [A_17,B_18] :
( ordinal_subset(A_17,B_18)
| ~ subset(A_17,B_18)
| ~ ordinal(B_18)
| ~ ordinal(A_17) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_57265,plain,
! [C_1480] :
( ordinal_subset('#skF_8',C_1480)
| ~ ordinal(C_1480)
| ~ ordinal('#skF_8')
| ~ empty(C_1480) ),
inference(resolution,[status(thm)],[c_57251,c_136]) ).
tff(c_57276,plain,
! [C_1480] :
( ordinal_subset('#skF_8',C_1480)
| ~ ordinal(C_1480)
| ~ empty(C_1480) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_57265]) ).
tff(c_20,plain,
! [A_8] :
( ordinal(A_8)
| ~ empty(A_8) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_156,plain,
ordinal('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_154,plain,
subset('#skF_15','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_576,plain,
! [A_115,B_116] :
( ordinal_subset(A_115,B_116)
| ~ subset(A_115,B_116)
| ~ ordinal(B_116)
| ~ ordinal(A_115) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_591,plain,
( ordinal_subset('#skF_15','#skF_16')
| ~ ordinal('#skF_16')
| ~ ordinal('#skF_15') ),
inference(resolution,[status(thm)],[c_154,c_576]) ).
tff(c_598,plain,
( ordinal_subset('#skF_15','#skF_16')
| ~ ordinal('#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_591]) ).
tff(c_599,plain,
~ ordinal('#skF_15'),
inference(splitLeft,[status(thm)],[c_598]) ).
tff(c_607,plain,
~ empty('#skF_15'),
inference(resolution,[status(thm)],[c_20,c_599]) ).
tff(c_162,plain,
! [C_35] :
( ordinal('#skF_17'(C_35))
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_148,plain,
! [B_29,A_27] :
( in(B_29,A_27)
| ( B_29 = A_27 )
| in(A_27,B_29)
| ~ ordinal(B_29)
| ~ ordinal(A_27) ),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_57277,plain,
! [C_1481] :
( element('#skF_8',powerset(C_1481))
| ~ empty(C_1481) ),
inference(superposition,[status(thm),theory(equality)],[c_57197,c_40]) ).
tff(c_170,plain,
! [C_44,B_43,A_42] :
( ~ empty(C_44)
| ~ element(B_43,powerset(C_44))
| ~ in(A_42,B_43) ),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_57295,plain,
! [A_42,C_1481] :
( ~ in(A_42,'#skF_8')
| ~ empty(C_1481) ),
inference(resolution,[status(thm)],[c_57277,c_170]) ).
tff(c_57323,plain,
! [C_1481] : ~ empty(C_1481),
inference(splitLeft,[status(thm)],[c_57295]) ).
tff(c_57340,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_57323,c_98]) ).
tff(c_57342,plain,
! [A_1484] : ~ in(A_1484,'#skF_8'),
inference(splitRight,[status(thm)],[c_57295]) ).
tff(c_57358,plain,
! [A_27] :
( in('#skF_8',A_27)
| ( A_27 = '#skF_8' )
| ~ ordinal('#skF_8')
| ~ ordinal(A_27) ),
inference(resolution,[status(thm)],[c_148,c_57342]) ).
tff(c_57396,plain,
! [A_1486] :
( in('#skF_8',A_1486)
| ( A_1486 = '#skF_8' )
| ~ ordinal(A_1486) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_57358]) ).
tff(c_28,plain,
! [B_14,A_11] :
( subset(B_14,A_11)
| ~ in(B_14,A_11)
| ~ epsilon_transitive(A_11) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_57081,plain,
! [B_1469,A_1470] :
( ordinal_subset(B_1469,A_1470)
| ~ ordinal(A_1470)
| ~ ordinal(B_1469)
| ~ in(B_1469,A_1470)
| ~ epsilon_transitive(A_1470) ),
inference(resolution,[status(thm)],[c_28,c_576]) ).
tff(c_158,plain,
! [C_35] :
( ~ ordinal_subset(C_35,'#skF_17'(C_35))
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_57086,plain,
! [B_1469] :
( ~ in(B_1469,'#skF_15')
| ~ ordinal('#skF_17'(B_1469))
| ~ ordinal(B_1469)
| ~ in(B_1469,'#skF_17'(B_1469))
| ~ epsilon_transitive('#skF_17'(B_1469)) ),
inference(resolution,[status(thm)],[c_57081,c_158]) ).
tff(c_57404,plain,
( ~ in('#skF_8','#skF_15')
| ~ ordinal('#skF_8')
| ~ epsilon_transitive('#skF_17'('#skF_8'))
| ( '#skF_17'('#skF_8') = '#skF_8' )
| ~ ordinal('#skF_17'('#skF_8')) ),
inference(resolution,[status(thm)],[c_57396,c_57086]) ).
tff(c_57464,plain,
( ~ in('#skF_8','#skF_15')
| ~ epsilon_transitive('#skF_17'('#skF_8'))
| ( '#skF_17'('#skF_8') = '#skF_8' )
| ~ ordinal('#skF_17'('#skF_8')) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_57404]) ).
tff(c_59412,plain,
~ ordinal('#skF_17'('#skF_8')),
inference(splitLeft,[status(thm)],[c_57464]) ).
tff(c_59421,plain,
( ~ in('#skF_8','#skF_15')
| ~ ordinal('#skF_8') ),
inference(resolution,[status(thm)],[c_162,c_59412]) ).
tff(c_59426,plain,
~ in('#skF_8','#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_59421]) ).
tff(c_59440,plain,
( empty('#skF_15')
| ~ element('#skF_8','#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_59426]) ).
tff(c_59453,plain,
~ element('#skF_8','#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_607,c_59440]) ).
tff(c_166,plain,
! [A_37,B_38] :
( element(A_37,powerset(B_38))
| ~ subset(A_37,B_38) ),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_52462,plain,
! [B_1216,A_1217,A_1218] :
( ~ empty(B_1216)
| ~ in(A_1217,A_1218)
| ~ subset(A_1218,B_1216) ),
inference(resolution,[status(thm)],[c_166,c_560]) ).
tff(c_52700,plain,
! [B_1253,B_1254,A_1255] :
( ~ empty(B_1253)
| ~ subset(B_1254,B_1253)
| empty(B_1254)
| ~ element(A_1255,B_1254) ),
inference(resolution,[status(thm)],[c_150,c_52462]) ).
tff(c_52714,plain,
! [A_1255] :
( ~ empty('#skF_16')
| empty('#skF_15')
| ~ element(A_1255,'#skF_15') ),
inference(resolution,[status(thm)],[c_154,c_52700]) ).
tff(c_52723,plain,
! [A_1255] :
( ~ empty('#skF_16')
| ~ element(A_1255,'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_607,c_52714]) ).
tff(c_52724,plain,
~ empty('#skF_16'),
inference(splitLeft,[status(thm)],[c_52723]) ).
tff(c_52403,plain,
! [A_1206,C_1207,B_1208] :
( element(A_1206,C_1207)
| ~ element(B_1208,powerset(C_1207))
| ~ in(A_1206,B_1208) ),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_52562,plain,
! [A_1230,B_1231,A_1232] :
( element(A_1230,B_1231)
| ~ in(A_1230,A_1232)
| ~ subset(A_1232,B_1231) ),
inference(resolution,[status(thm)],[c_166,c_52403]) ).
tff(c_56805,plain,
! [A_1452,B_1453,B_1454] :
( element(A_1452,B_1453)
| ~ subset(B_1454,B_1453)
| empty(B_1454)
| ~ element(A_1452,B_1454) ),
inference(resolution,[status(thm)],[c_150,c_52562]) ).
tff(c_56823,plain,
! [A_1452] :
( element(A_1452,'#skF_16')
| empty('#skF_15')
| ~ element(A_1452,'#skF_15') ),
inference(resolution,[status(thm)],[c_154,c_56805]) ).
tff(c_56835,plain,
! [A_1455] :
( element(A_1455,'#skF_16')
| ~ element(A_1455,'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_607,c_56823]) ).
tff(c_56877,plain,
element('#skF_2'('#skF_15'),'#skF_16'),
inference(resolution,[status(thm)],[c_40,c_56835]) ).
tff(c_448,plain,
! [A_98,B_99] :
( in(A_98,B_99)
| empty(B_99)
| ~ element(A_98,B_99) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_146,plain,
! [A_25,B_26] :
( ordinal(A_25)
| ~ in(A_25,B_26)
| ~ ordinal(B_26) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_467,plain,
! [A_98,B_99] :
( ordinal(A_98)
| ~ ordinal(B_99)
| empty(B_99)
| ~ element(A_98,B_99) ),
inference(resolution,[status(thm)],[c_448,c_146]) ).
tff(c_56960,plain,
( ordinal('#skF_2'('#skF_15'))
| ~ ordinal('#skF_16')
| empty('#skF_16') ),
inference(resolution,[status(thm)],[c_56877,c_467]) ).
tff(c_56966,plain,
( ordinal('#skF_2'('#skF_15'))
| empty('#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_56960]) ).
tff(c_56967,plain,
ordinal('#skF_2'('#skF_15')),
inference(negUnitSimplification,[status(thm)],[c_52724,c_56966]) ).
tff(c_18,plain,
! [A_7] :
( ordinal(A_7)
| ~ epsilon_connected(A_7)
| ~ epsilon_transitive(A_7) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_606,plain,
( ~ epsilon_connected('#skF_15')
| ~ epsilon_transitive('#skF_15') ),
inference(resolution,[status(thm)],[c_18,c_599]) ).
tff(c_608,plain,
~ epsilon_transitive('#skF_15'),
inference(splitLeft,[status(thm)],[c_606]) ).
tff(c_32,plain,
! [A_11] :
( in('#skF_1'(A_11),A_11)
| epsilon_transitive(A_11) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_142,plain,
! [A_21] : subset(A_21,A_21),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_630,plain,
! [B_120,A_121,A_122] :
( ~ empty(B_120)
| ~ in(A_121,A_122)
| ~ subset(A_122,B_120) ),
inference(resolution,[status(thm)],[c_166,c_560]) ).
tff(c_643,plain,
! [B_123,A_124] :
( ~ empty(B_123)
| ~ subset(A_124,B_123)
| epsilon_transitive(A_124) ),
inference(resolution,[status(thm)],[c_32,c_630]) ).
tff(c_658,plain,
( ~ empty('#skF_16')
| epsilon_transitive('#skF_15') ),
inference(resolution,[status(thm)],[c_154,c_643]) ).
tff(c_665,plain,
~ empty('#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_608,c_658]) ).
tff(c_178,plain,
! [A_48,B_49] :
( in('#skF_18'(A_48,B_49),B_49)
| ~ in(A_48,B_49) ),
inference(cnfTransformation,[status(thm)],[f_291]) ).
tff(c_666,plain,
! [A_125,C_126,B_127] :
( element(A_125,C_126)
| ~ element(B_127,powerset(C_126))
| ~ in(A_125,B_127) ),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_754,plain,
! [A_139,B_140,A_141] :
( element(A_139,B_140)
| ~ in(A_139,A_141)
| ~ subset(A_141,B_140) ),
inference(resolution,[status(thm)],[c_166,c_666]) ).
tff(c_763,plain,
! [A_48,B_49,B_140] :
( element('#skF_18'(A_48,B_49),B_140)
| ~ subset(B_49,B_140)
| ~ in(A_48,B_49) ),
inference(resolution,[status(thm)],[c_178,c_754]) ).
tff(c_4614,plain,
! [A_340,B_341,B_342] :
( element(A_340,B_341)
| ~ subset(B_342,B_341)
| empty(B_342)
| ~ element(A_340,B_342) ),
inference(resolution,[status(thm)],[c_150,c_754]) ).
tff(c_4632,plain,
! [A_340] :
( element(A_340,'#skF_16')
| empty('#skF_15')
| ~ element(A_340,'#skF_15') ),
inference(resolution,[status(thm)],[c_154,c_4614]) ).
tff(c_4644,plain,
! [A_343] :
( element(A_343,'#skF_16')
| ~ element(A_343,'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_607,c_4632]) ).
tff(c_6225,plain,
! [A_411,B_412] :
( element('#skF_18'(A_411,B_412),'#skF_16')
| ~ subset(B_412,'#skF_15')
| ~ in(A_411,B_412) ),
inference(resolution,[status(thm)],[c_763,c_4644]) ).
tff(c_6230,plain,
! [A_411,B_412] :
( ordinal('#skF_18'(A_411,B_412))
| ~ ordinal('#skF_16')
| empty('#skF_16')
| ~ subset(B_412,'#skF_15')
| ~ in(A_411,B_412) ),
inference(resolution,[status(thm)],[c_6225,c_467]) ).
tff(c_6236,plain,
! [A_411,B_412] :
( ordinal('#skF_18'(A_411,B_412))
| empty('#skF_16')
| ~ subset(B_412,'#skF_15')
| ~ in(A_411,B_412) ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_6230]) ).
tff(c_6237,plain,
! [A_411,B_412] :
( ordinal('#skF_18'(A_411,B_412))
| ~ subset(B_412,'#skF_15')
| ~ in(A_411,B_412) ),
inference(negUnitSimplification,[status(thm)],[c_665,c_6236]) ).
tff(c_140,plain,
! [A_19,B_20] :
( ordinal_subset(A_19,A_19)
| ~ ordinal(B_20)
| ~ ordinal(A_19) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_429,plain,
! [B_20] : ~ ordinal(B_20),
inference(splitLeft,[status(thm)],[c_140]) ).
tff(c_74,plain,
ordinal('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_438,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_429,c_74]) ).
tff(c_439,plain,
! [A_19] :
( ordinal_subset(A_19,A_19)
| ~ ordinal(A_19) ),
inference(splitRight,[status(thm)],[c_140]) ).
tff(c_318,plain,
! [A_66] :
( epsilon_transitive(A_66)
| ~ ordinal(A_66) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_340,plain,
! [C_35] :
( epsilon_transitive('#skF_17'(C_35))
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_162,c_318]) ).
tff(c_160,plain,
! [C_35] :
( in('#skF_17'(C_35),'#skF_15')
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_1058,plain,
! [B_177,A_178] :
( in(B_177,A_178)
| ( B_177 = A_178 )
| in(A_178,B_177)
| ~ ordinal(B_177)
| ~ ordinal(A_178) ),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_176,plain,
! [D_54,A_48,B_49] :
( ~ in(D_54,'#skF_18'(A_48,B_49))
| ~ in(D_54,B_49)
| ~ in(A_48,B_49) ),
inference(cnfTransformation,[status(thm)],[f_291]) ).
tff(c_5438,plain,
! [B_383,B_384,A_385] :
( ~ in(B_383,B_384)
| ~ in(A_385,B_384)
| ( B_383 = '#skF_18'(A_385,B_384) )
| in('#skF_18'(A_385,B_384),B_383)
| ~ ordinal(B_383)
| ~ ordinal('#skF_18'(A_385,B_384)) ),
inference(resolution,[status(thm)],[c_1058,c_176]) ).
tff(c_4738,plain,
! [B_345,A_346] :
( ordinal_subset(B_345,A_346)
| ~ ordinal(A_346)
| ~ ordinal(B_345)
| ~ in(B_345,A_346)
| ~ epsilon_transitive(A_346) ),
inference(resolution,[status(thm)],[c_28,c_576]) ).
tff(c_4743,plain,
! [B_345] :
( ~ in(B_345,'#skF_15')
| ~ ordinal('#skF_17'(B_345))
| ~ ordinal(B_345)
| ~ in(B_345,'#skF_17'(B_345))
| ~ epsilon_transitive('#skF_17'(B_345)) ),
inference(resolution,[status(thm)],[c_4738,c_158]) ).
tff(c_41395,plain,
! [A_1111,B_1112] :
( ~ in('#skF_18'(A_1111,B_1112),'#skF_15')
| ~ epsilon_transitive('#skF_17'('#skF_18'(A_1111,B_1112)))
| ~ in('#skF_17'('#skF_18'(A_1111,B_1112)),B_1112)
| ~ in(A_1111,B_1112)
| ( '#skF_17'('#skF_18'(A_1111,B_1112)) = '#skF_18'(A_1111,B_1112) )
| ~ ordinal('#skF_17'('#skF_18'(A_1111,B_1112)))
| ~ ordinal('#skF_18'(A_1111,B_1112)) ),
inference(resolution,[status(thm)],[c_5438,c_4743]) ).
tff(c_42399,plain,
! [A_1121] :
( ~ epsilon_transitive('#skF_17'('#skF_18'(A_1121,'#skF_15')))
| ~ in(A_1121,'#skF_15')
| ( '#skF_17'('#skF_18'(A_1121,'#skF_15')) = '#skF_18'(A_1121,'#skF_15') )
| ~ ordinal('#skF_17'('#skF_18'(A_1121,'#skF_15')))
| ~ in('#skF_18'(A_1121,'#skF_15'),'#skF_15')
| ~ ordinal('#skF_18'(A_1121,'#skF_15')) ),
inference(resolution,[status(thm)],[c_160,c_41395]) ).
tff(c_42751,plain,
! [A_1127] :
( ~ epsilon_transitive('#skF_17'('#skF_18'(A_1127,'#skF_15')))
| ~ in(A_1127,'#skF_15')
| ( '#skF_17'('#skF_18'(A_1127,'#skF_15')) = '#skF_18'(A_1127,'#skF_15') )
| ~ in('#skF_18'(A_1127,'#skF_15'),'#skF_15')
| ~ ordinal('#skF_18'(A_1127,'#skF_15')) ),
inference(resolution,[status(thm)],[c_162,c_42399]) ).
tff(c_43874,plain,
! [A_1135] :
( ~ in(A_1135,'#skF_15')
| ( '#skF_17'('#skF_18'(A_1135,'#skF_15')) = '#skF_18'(A_1135,'#skF_15') )
| ~ in('#skF_18'(A_1135,'#skF_15'),'#skF_15')
| ~ ordinal('#skF_18'(A_1135,'#skF_15')) ),
inference(resolution,[status(thm)],[c_340,c_42751]) ).
tff(c_51080,plain,
! [A_1192] :
( ( '#skF_17'('#skF_18'(A_1192,'#skF_15')) = '#skF_18'(A_1192,'#skF_15') )
| ~ ordinal('#skF_18'(A_1192,'#skF_15'))
| ~ in(A_1192,'#skF_15') ),
inference(resolution,[status(thm)],[c_178,c_43874]) ).
tff(c_51084,plain,
! [A_411] :
( ( '#skF_17'('#skF_18'(A_411,'#skF_15')) = '#skF_18'(A_411,'#skF_15') )
| ~ subset('#skF_15','#skF_15')
| ~ in(A_411,'#skF_15') ),
inference(resolution,[status(thm)],[c_6237,c_51080]) ).
tff(c_51299,plain,
! [A_1196] :
( ( '#skF_17'('#skF_18'(A_1196,'#skF_15')) = '#skF_18'(A_1196,'#skF_15') )
| ~ in(A_1196,'#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_51084]) ).
tff(c_51444,plain,
! [A_1200] :
( ~ ordinal_subset('#skF_18'(A_1200,'#skF_15'),'#skF_18'(A_1200,'#skF_15'))
| ~ in('#skF_18'(A_1200,'#skF_15'),'#skF_15')
| ~ ordinal('#skF_18'(A_1200,'#skF_15'))
| ~ in(A_1200,'#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_51299,c_158]) ).
tff(c_52250,plain,
! [A_1203] :
( ~ in('#skF_18'(A_1203,'#skF_15'),'#skF_15')
| ~ in(A_1203,'#skF_15')
| ~ ordinal('#skF_18'(A_1203,'#skF_15')) ),
inference(resolution,[status(thm)],[c_439,c_51444]) ).
tff(c_52284,plain,
! [A_1204] :
( ~ ordinal('#skF_18'(A_1204,'#skF_15'))
| ~ in(A_1204,'#skF_15') ),
inference(resolution,[status(thm)],[c_178,c_52250]) ).
tff(c_52288,plain,
! [A_411] :
( ~ subset('#skF_15','#skF_15')
| ~ in(A_411,'#skF_15') ),
inference(resolution,[status(thm)],[c_6237,c_52284]) ).
tff(c_52310,plain,
! [A_1205] : ~ in(A_1205,'#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_52288]) ).
tff(c_52374,plain,
epsilon_transitive('#skF_15'),
inference(resolution,[status(thm)],[c_32,c_52310]) ).
tff(c_52396,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_608,c_52374]) ).
tff(c_52398,plain,
epsilon_transitive('#skF_15'),
inference(splitRight,[status(thm)],[c_606]) ).
tff(c_52416,plain,
! [A_1206,B_38,A_37] :
( element(A_1206,B_38)
| ~ in(A_1206,A_37)
| ~ subset(A_37,B_38) ),
inference(resolution,[status(thm)],[c_166,c_52403]) ).
tff(c_57854,plain,
! [B_1506,A_1507] :
( element('#skF_8',B_1506)
| ~ subset(A_1507,B_1506)
| ( A_1507 = '#skF_8' )
| ~ ordinal(A_1507) ),
inference(resolution,[status(thm)],[c_57396,c_52416]) ).
tff(c_59542,plain,
! [A_1581,B_1582] :
( element('#skF_8',A_1581)
| ( B_1582 = '#skF_8' )
| ~ ordinal(B_1582)
| ~ in(B_1582,A_1581)
| ~ epsilon_transitive(A_1581) ),
inference(resolution,[status(thm)],[c_28,c_57854]) ).
tff(c_59572,plain,
! [C_35] :
( element('#skF_8','#skF_15')
| ( '#skF_17'(C_35) = '#skF_8' )
| ~ ordinal('#skF_17'(C_35))
| ~ epsilon_transitive('#skF_15')
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_160,c_59542]) ).
tff(c_59586,plain,
! [C_35] :
( element('#skF_8','#skF_15')
| ( '#skF_17'(C_35) = '#skF_8' )
| ~ ordinal('#skF_17'(C_35))
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_52398,c_59572]) ).
tff(c_59588,plain,
! [C_1583] :
( ( '#skF_17'(C_1583) = '#skF_8' )
| ~ ordinal('#skF_17'(C_1583))
| ~ in(C_1583,'#skF_15')
| ~ ordinal(C_1583) ),
inference(negUnitSimplification,[status(thm)],[c_59453,c_59586]) ).
tff(c_59601,plain,
! [C_1584] :
( ( '#skF_17'(C_1584) = '#skF_8' )
| ~ in(C_1584,'#skF_15')
| ~ ordinal(C_1584) ),
inference(resolution,[status(thm)],[c_162,c_59588]) ).
tff(c_59633,plain,
! [A_30] :
( ( '#skF_17'(A_30) = '#skF_8' )
| ~ ordinal(A_30)
| empty('#skF_15')
| ~ element(A_30,'#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_59601]) ).
tff(c_59657,plain,
! [A_1585] :
( ( '#skF_17'(A_1585) = '#skF_8' )
| ~ ordinal(A_1585)
| ~ element(A_1585,'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_607,c_59633]) ).
tff(c_59712,plain,
( ( '#skF_17'('#skF_2'('#skF_15')) = '#skF_8' )
| ~ ordinal('#skF_2'('#skF_15')) ),
inference(resolution,[status(thm)],[c_40,c_59657]) ).
tff(c_59737,plain,
'#skF_17'('#skF_2'('#skF_15')) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_56967,c_59712]) ).
tff(c_374,plain,
! [A_76,B_77] :
( element(A_76,B_77)
| ~ in(A_76,B_77) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_378,plain,
! [C_35] :
( element('#skF_17'(C_35),'#skF_15')
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_160,c_374]) ).
tff(c_59770,plain,
( element('#skF_8','#skF_15')
| ~ in('#skF_2'('#skF_15'),'#skF_15')
| ~ ordinal('#skF_2'('#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_59737,c_378]) ).
tff(c_59812,plain,
( element('#skF_8','#skF_15')
| ~ in('#skF_2'('#skF_15'),'#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_56967,c_59770]) ).
tff(c_59813,plain,
~ in('#skF_2'('#skF_15'),'#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_59453,c_59812]) ).
tff(c_59842,plain,
( empty('#skF_15')
| ~ element('#skF_2'('#skF_15'),'#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_59813]) ).
tff(c_59857,plain,
empty('#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_59842]) ).
tff(c_59859,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_607,c_59857]) ).
tff(c_59861,plain,
ordinal('#skF_17'('#skF_8')),
inference(splitRight,[status(thm)],[c_57464]) ).
tff(c_8,plain,
! [A_4] :
( epsilon_transitive(A_4)
| ~ ordinal(A_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_59868,plain,
epsilon_transitive('#skF_17'('#skF_8')),
inference(resolution,[status(thm)],[c_59861,c_8]) ).
tff(c_59860,plain,
( ~ epsilon_transitive('#skF_17'('#skF_8'))
| ~ in('#skF_8','#skF_15')
| ( '#skF_17'('#skF_8') = '#skF_8' ) ),
inference(splitRight,[status(thm)],[c_57464]) ).
tff(c_59871,plain,
( ~ in('#skF_8','#skF_15')
| ( '#skF_17'('#skF_8') = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_59868,c_59860]) ).
tff(c_59872,plain,
~ in('#skF_8','#skF_15'),
inference(splitLeft,[status(thm)],[c_59871]) ).
tff(c_59886,plain,
( empty('#skF_15')
| ~ element('#skF_8','#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_59872]) ).
tff(c_59899,plain,
~ element('#skF_8','#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_607,c_59886]) ).
tff(c_59977,plain,
! [A_1591,B_1592] :
( element('#skF_8',A_1591)
| ( B_1592 = '#skF_8' )
| ~ ordinal(B_1592)
| ~ in(B_1592,A_1591)
| ~ epsilon_transitive(A_1591) ),
inference(resolution,[status(thm)],[c_28,c_57854]) ).
tff(c_60007,plain,
! [C_35] :
( element('#skF_8','#skF_15')
| ( '#skF_17'(C_35) = '#skF_8' )
| ~ ordinal('#skF_17'(C_35))
| ~ epsilon_transitive('#skF_15')
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_160,c_59977]) ).
tff(c_60021,plain,
! [C_35] :
( element('#skF_8','#skF_15')
| ( '#skF_17'(C_35) = '#skF_8' )
| ~ ordinal('#skF_17'(C_35))
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_52398,c_60007]) ).
tff(c_60023,plain,
! [C_1593] :
( ( '#skF_17'(C_1593) = '#skF_8' )
| ~ ordinal('#skF_17'(C_1593))
| ~ in(C_1593,'#skF_15')
| ~ ordinal(C_1593) ),
inference(negUnitSimplification,[status(thm)],[c_59899,c_60021]) ).
tff(c_60042,plain,
! [C_1594] :
( ( '#skF_17'(C_1594) = '#skF_8' )
| ~ in(C_1594,'#skF_15')
| ~ ordinal(C_1594) ),
inference(resolution,[status(thm)],[c_162,c_60023]) ).
tff(c_60074,plain,
! [A_30] :
( ( '#skF_17'(A_30) = '#skF_8' )
| ~ ordinal(A_30)
| empty('#skF_15')
| ~ element(A_30,'#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_60042]) ).
tff(c_60098,plain,
! [A_1595] :
( ( '#skF_17'(A_1595) = '#skF_8' )
| ~ ordinal(A_1595)
| ~ element(A_1595,'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_607,c_60074]) ).
tff(c_60153,plain,
( ( '#skF_17'('#skF_2'('#skF_15')) = '#skF_8' )
| ~ ordinal('#skF_2'('#skF_15')) ),
inference(resolution,[status(thm)],[c_40,c_60098]) ).
tff(c_60178,plain,
'#skF_17'('#skF_2'('#skF_15')) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_56967,c_60153]) ).
tff(c_60211,plain,
( element('#skF_8','#skF_15')
| ~ in('#skF_2'('#skF_15'),'#skF_15')
| ~ ordinal('#skF_2'('#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_60178,c_378]) ).
tff(c_60253,plain,
( element('#skF_8','#skF_15')
| ~ in('#skF_2'('#skF_15'),'#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_56967,c_60211]) ).
tff(c_60254,plain,
~ in('#skF_2'('#skF_15'),'#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_59899,c_60253]) ).
tff(c_60283,plain,
( empty('#skF_15')
| ~ element('#skF_2'('#skF_15'),'#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_60254]) ).
tff(c_60298,plain,
empty('#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_60283]) ).
tff(c_60300,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_607,c_60298]) ).
tff(c_60301,plain,
'#skF_17'('#skF_8') = '#skF_8',
inference(splitRight,[status(thm)],[c_59871]) ).
tff(c_57388,plain,
! [C_1485] :
( ordinal_subset('#skF_8',C_1485)
| ~ ordinal(C_1485)
| ~ empty(C_1485) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_57265]) ).
tff(c_57392,plain,
( ~ in('#skF_8','#skF_15')
| ~ ordinal('#skF_8')
| ~ ordinal('#skF_17'('#skF_8'))
| ~ empty('#skF_17'('#skF_8')) ),
inference(resolution,[status(thm)],[c_57388,c_158]) ).
tff(c_57395,plain,
( ~ in('#skF_8','#skF_15')
| ~ ordinal('#skF_17'('#skF_8'))
| ~ empty('#skF_17'('#skF_8')) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_57392]) ).
tff(c_57585,plain,
~ empty('#skF_17'('#skF_8')),
inference(splitLeft,[status(thm)],[c_57395]) ).
tff(c_60332,plain,
~ empty('#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_60301,c_57585]) ).
tff(c_60338,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_60332]) ).
tff(c_60340,plain,
empty('#skF_17'('#skF_8')),
inference(splitRight,[status(thm)],[c_57395]) ).
tff(c_60350,plain,
'#skF_17'('#skF_8') = '#skF_8',
inference(resolution,[status(thm)],[c_60340,c_353]) ).
tff(c_60388,plain,
( ~ ordinal_subset('#skF_8','#skF_8')
| ~ in('#skF_8','#skF_15')
| ~ ordinal('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_60350,c_158]) ).
tff(c_60420,plain,
( ~ ordinal_subset('#skF_8','#skF_8')
| ~ in('#skF_8','#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_60388]) ).
tff(c_60426,plain,
~ in('#skF_8','#skF_15'),
inference(splitLeft,[status(thm)],[c_60420]) ).
tff(c_60440,plain,
( empty('#skF_15')
| ~ element('#skF_8','#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_60426]) ).
tff(c_60453,plain,
~ element('#skF_8','#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_607,c_60440]) ).
tff(c_60830,plain,
! [B_1614,A_1615] :
( element('#skF_8',B_1614)
| ~ subset(A_1615,B_1614)
| ( A_1615 = '#skF_8' )
| ~ ordinal(A_1615) ),
inference(resolution,[status(thm)],[c_57396,c_52416]) ).
tff(c_62341,plain,
! [A_1681,B_1682] :
( element('#skF_8',A_1681)
| ( B_1682 = '#skF_8' )
| ~ ordinal(B_1682)
| ~ in(B_1682,A_1681)
| ~ epsilon_transitive(A_1681) ),
inference(resolution,[status(thm)],[c_28,c_60830]) ).
tff(c_62371,plain,
! [C_35] :
( element('#skF_8','#skF_15')
| ( '#skF_17'(C_35) = '#skF_8' )
| ~ ordinal('#skF_17'(C_35))
| ~ epsilon_transitive('#skF_15')
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(resolution,[status(thm)],[c_160,c_62341]) ).
tff(c_62385,plain,
! [C_35] :
( element('#skF_8','#skF_15')
| ( '#skF_17'(C_35) = '#skF_8' )
| ~ ordinal('#skF_17'(C_35))
| ~ in(C_35,'#skF_15')
| ~ ordinal(C_35) ),
inference(demodulation,[status(thm),theory(equality)],[c_52398,c_62371]) ).
tff(c_62387,plain,
! [C_1683] :
( ( '#skF_17'(C_1683) = '#skF_8' )
| ~ ordinal('#skF_17'(C_1683))
| ~ in(C_1683,'#skF_15')
| ~ ordinal(C_1683) ),
inference(negUnitSimplification,[status(thm)],[c_60453,c_62385]) ).
tff(c_62405,plain,
! [C_1684] :
( ( '#skF_17'(C_1684) = '#skF_8' )
| ~ in(C_1684,'#skF_15')
| ~ ordinal(C_1684) ),
inference(resolution,[status(thm)],[c_162,c_62387]) ).
tff(c_62437,plain,
! [A_30] :
( ( '#skF_17'(A_30) = '#skF_8' )
| ~ ordinal(A_30)
| empty('#skF_15')
| ~ element(A_30,'#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_62405]) ).
tff(c_62461,plain,
! [A_1685] :
( ( '#skF_17'(A_1685) = '#skF_8' )
| ~ ordinal(A_1685)
| ~ element(A_1685,'#skF_15') ),
inference(negUnitSimplification,[status(thm)],[c_607,c_62437]) ).
tff(c_62516,plain,
( ( '#skF_17'('#skF_2'('#skF_15')) = '#skF_8' )
| ~ ordinal('#skF_2'('#skF_15')) ),
inference(resolution,[status(thm)],[c_40,c_62461]) ).
tff(c_62541,plain,
'#skF_17'('#skF_2'('#skF_15')) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_56967,c_62516]) ).
tff(c_62574,plain,
( element('#skF_8','#skF_15')
| ~ in('#skF_2'('#skF_15'),'#skF_15')
| ~ ordinal('#skF_2'('#skF_15')) ),
inference(superposition,[status(thm),theory(equality)],[c_62541,c_378]) ).
tff(c_62616,plain,
( element('#skF_8','#skF_15')
| ~ in('#skF_2'('#skF_15'),'#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_56967,c_62574]) ).
tff(c_62617,plain,
~ in('#skF_2'('#skF_15'),'#skF_15'),
inference(negUnitSimplification,[status(thm)],[c_60453,c_62616]) ).
tff(c_62672,plain,
( empty('#skF_15')
| ~ element('#skF_2'('#skF_15'),'#skF_15') ),
inference(resolution,[status(thm)],[c_150,c_62617]) ).
tff(c_62687,plain,
empty('#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_62672]) ).
tff(c_62689,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_607,c_62687]) ).
tff(c_62690,plain,
~ ordinal_subset('#skF_8','#skF_8'),
inference(splitRight,[status(thm)],[c_60420]) ).
tff(c_62694,plain,
( ~ ordinal('#skF_8')
| ~ empty('#skF_8') ),
inference(resolution,[status(thm)],[c_57276,c_62690]) ).
tff(c_62706,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_92,c_62694]) ).
tff(c_62731,plain,
! [A_1688] : ~ element(A_1688,'#skF_15'),
inference(splitRight,[status(thm)],[c_52723]) ).
tff(c_62759,plain,
$false,
inference(resolution,[status(thm)],[c_40,c_62731]) ).
tff(c_62761,plain,
ordinal('#skF_15'),
inference(splitRight,[status(thm)],[c_598]) ).
tff(c_62780,plain,
! [C_1691,A_1692] :
( ~ empty(C_1691)
| ~ in(A_1692,'#skF_2'(powerset(C_1691))) ),
inference(resolution,[status(thm)],[c_40,c_560]) ).
tff(c_66151,plain,
! [C_1883,A_1884] :
( ~ empty(C_1883)
| empty('#skF_2'(powerset(C_1883)))
| ~ element(A_1884,'#skF_2'(powerset(C_1883))) ),
inference(resolution,[status(thm)],[c_150,c_62780]) ).
tff(c_66212,plain,
! [C_1887] :
( ~ empty(C_1887)
| empty('#skF_2'(powerset(C_1887))) ),
inference(resolution,[status(thm)],[c_40,c_66151]) ).
tff(c_66220,plain,
! [C_1888] :
( ( '#skF_2'(powerset(C_1888)) = '#skF_8' )
| ~ empty(C_1888) ),
inference(resolution,[status(thm)],[c_66212,c_353]) ).
tff(c_66309,plain,
! [C_1891] :
( element('#skF_8',powerset(C_1891))
| ~ empty(C_1891) ),
inference(superposition,[status(thm),theory(equality)],[c_66220,c_40]) ).
tff(c_66327,plain,
! [A_42,C_1891] :
( ~ in(A_42,'#skF_8')
| ~ empty(C_1891) ),
inference(resolution,[status(thm)],[c_66309,c_170]) ).
tff(c_66329,plain,
! [C_1891] : ~ empty(C_1891),
inference(splitLeft,[status(thm)],[c_66327]) ).
tff(c_66345,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_66329,c_98]) ).
tff(c_66347,plain,
! [A_1892] : ~ in(A_1892,'#skF_8'),
inference(splitRight,[status(thm)],[c_66327]) ).
tff(c_66363,plain,
! [A_27] :
( in('#skF_8',A_27)
| ( A_27 = '#skF_8' )
| ~ ordinal('#skF_8')
| ~ ordinal(A_27) ),
inference(resolution,[status(thm)],[c_148,c_66347]) ).
tff(c_66387,plain,
! [A_27] :
( in('#skF_8',A_27)
| ( A_27 = '#skF_8' )
| ~ ordinal(A_27) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_66363]) ).
tff(c_63112,plain,
! [B_1739,A_1740] :
( in(B_1739,A_1740)
| ( B_1739 = A_1740 )
| in(A_1740,B_1739)
| ~ ordinal(B_1739)
| ~ ordinal(A_1740) ),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_174,plain,
! [B_47,A_46] :
( ~ empty(B_47)
| ~ in(A_46,B_47) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_63202,plain,
! [B_1739,A_1740] :
( ~ empty(B_1739)
| in(B_1739,A_1740)
| ( B_1739 = A_1740 )
| ~ ordinal(B_1739)
| ~ ordinal(A_1740) ),
inference(resolution,[status(thm)],[c_63112,c_174]) ).
tff(c_66043,plain,
! [B_1870,A_1871] :
( ordinal_subset(B_1870,A_1871)
| ~ ordinal(A_1871)
| ~ ordinal(B_1870)
| ~ in(B_1870,A_1871)
| ~ epsilon_transitive(A_1871) ),
inference(resolution,[status(thm)],[c_28,c_576]) ).
tff(c_66056,plain,
! [B_1872] :
( ~ in(B_1872,'#skF_15')
| ~ ordinal('#skF_17'(B_1872))
| ~ ordinal(B_1872)
| ~ in(B_1872,'#skF_17'(B_1872))
| ~ epsilon_transitive('#skF_17'(B_1872)) ),
inference(resolution,[status(thm)],[c_66043,c_158]) ).
tff(c_66135,plain,
! [B_1880] :
( ~ in(B_1880,'#skF_15')
| ~ epsilon_transitive('#skF_17'(B_1880))
| ~ empty(B_1880)
| ( '#skF_17'(B_1880) = B_1880 )
| ~ ordinal(B_1880)
| ~ ordinal('#skF_17'(B_1880)) ),
inference(resolution,[status(thm)],[c_63202,c_66056]) ).
tff(c_66300,plain,
! [C_1890] :
( ~ epsilon_transitive('#skF_17'(C_1890))
| ~ empty(C_1890)
| ( '#skF_17'(C_1890) = C_1890 )
| ~ in(C_1890,'#skF_15')
| ~ ordinal(C_1890) ),
inference(resolution,[status(thm)],[c_162,c_66135]) ).
tff(c_66667,plain,
! [C_1906] :
( ~ empty(C_1906)
| ( '#skF_17'(C_1906) = C_1906 )
| ~ in(C_1906,'#skF_15')
| ~ ordinal(C_1906) ),
inference(resolution,[status(thm)],[c_340,c_66300]) ).
tff(c_66671,plain,
( ~ empty('#skF_8')
| ( '#skF_17'('#skF_8') = '#skF_8' )
| ~ ordinal('#skF_8')
| ( '#skF_15' = '#skF_8' )
| ~ ordinal('#skF_15') ),
inference(resolution,[status(thm)],[c_66387,c_66667]) ).
tff(c_66705,plain,
( ( '#skF_17'('#skF_8') = '#skF_8' )
| ( '#skF_15' = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_62761,c_92,c_98,c_66671]) ).
tff(c_66706,plain,
'#skF_17'('#skF_8') = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_298,c_66705]) ).
tff(c_66274,plain,
! [C_1889] :
( subset('#skF_8',C_1889)
| ~ empty(C_1889) ),
inference(superposition,[status(thm),theory(equality)],[c_66220,c_413]) ).
tff(c_66288,plain,
! [C_1889] :
( ordinal_subset('#skF_8',C_1889)
| ~ ordinal(C_1889)
| ~ ordinal('#skF_8')
| ~ empty(C_1889) ),
inference(resolution,[status(thm)],[c_66274,c_136]) ).
tff(c_66429,plain,
! [C_1896] :
( ordinal_subset('#skF_8',C_1896)
| ~ ordinal(C_1896)
| ~ empty(C_1896) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_66288]) ).
tff(c_66433,plain,
( ~ in('#skF_8','#skF_15')
| ~ ordinal('#skF_8')
| ~ ordinal('#skF_17'('#skF_8'))
| ~ empty('#skF_17'('#skF_8')) ),
inference(resolution,[status(thm)],[c_66429,c_158]) ).
tff(c_66436,plain,
( ~ in('#skF_8','#skF_15')
| ~ ordinal('#skF_17'('#skF_8'))
| ~ empty('#skF_17'('#skF_8')) ),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_66433]) ).
tff(c_66526,plain,
~ empty('#skF_17'('#skF_8')),
inference(splitLeft,[status(thm)],[c_66436]) ).
tff(c_66726,plain,
~ empty('#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_66706,c_66526]) ).
tff(c_66729,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_66726]) ).
tff(c_66731,plain,
empty('#skF_17'('#skF_8')),
inference(splitRight,[status(thm)],[c_66436]) ).
tff(c_66738,plain,
'#skF_17'('#skF_8') = '#skF_8',
inference(resolution,[status(thm)],[c_66731,c_353]) ).
tff(c_66730,plain,
( ~ ordinal('#skF_17'('#skF_8'))
| ~ in('#skF_8','#skF_15') ),
inference(splitRight,[status(thm)],[c_66436]) ).
tff(c_66816,plain,
~ in('#skF_8','#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_66738,c_66730]) ).
tff(c_66819,plain,
( ( '#skF_15' = '#skF_8' )
| ~ ordinal('#skF_15') ),
inference(resolution,[status(thm)],[c_66387,c_66816]) ).
tff(c_66833,plain,
'#skF_15' = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_62761,c_66819]) ).
tff(c_66835,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_298,c_66833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU235+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
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 11:32:33 EDT 2023
% 0.14/0.36 % CPUTime :
% 22.61/10.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.66/10.74
% 22.66/10.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.82/10.79
% 22.82/10.79 Inference rules
% 22.82/10.79 ----------------------
% 22.82/10.79 #Ref : 0
% 22.82/10.79 #Sup : 14103
% 22.82/10.79 #Fact : 24
% 22.82/10.79 #Define : 0
% 22.82/10.79 #Split : 129
% 22.82/10.79 #Chain : 0
% 22.82/10.79 #Close : 0
% 22.82/10.79
% 22.82/10.79 Ordering : KBO
% 22.82/10.79
% 22.82/10.79 Simplification rules
% 22.82/10.79 ----------------------
% 22.82/10.79 #Subsume : 6019
% 22.82/10.79 #Demod : 8824
% 22.82/10.79 #Tautology : 2675
% 22.82/10.79 #SimpNegUnit : 1775
% 22.82/10.79 #BackRed : 497
% 22.82/10.79
% 22.82/10.79 #Partial instantiations: 0
% 22.82/10.79 #Strategies tried : 1
% 22.82/10.79
% 22.82/10.79 Timing (in seconds)
% 22.82/10.79 ----------------------
% 22.82/10.80 Preprocessing : 0.57
% 22.82/10.80 Parsing : 0.29
% 22.82/10.80 CNF conversion : 0.05
% 22.82/10.80 Main loop : 9.11
% 22.82/10.80 Inferencing : 2.22
% 22.82/10.80 Reduction : 3.33
% 22.82/10.80 Demodulation : 2.38
% 22.82/10.80 BG Simplification : 0.12
% 22.82/10.80 Subsumption : 2.83
% 22.82/10.80 Abstraction : 0.18
% 22.82/10.80 MUC search : 0.00
% 22.82/10.80 Cooper : 0.00
% 22.82/10.80 Total : 9.79
% 22.82/10.80 Index Insertion : 0.00
% 22.82/10.80 Index Deletion : 0.00
% 22.82/10.80 Index Matching : 0.00
% 22.82/10.80 BG Taut test : 0.00
%------------------------------------------------------------------------------