TSTP Solution File: SEU293+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU293+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/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 : n001.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 10:58:18 EDT 2023
% Result : Theorem 11.64s 3.84s
% Output : CNFRefutation 11.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 62
% Syntax : Number of formulae : 282 ( 122 unt; 43 typ; 0 def)
% Number of atoms : 432 ( 66 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 368 ( 175 ~; 153 |; 17 &)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 26 >; 22 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 17 con; 0-3 aty)
% Number of variables : 233 (; 229 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ relation_of2_as_subset > relation_of2 > quasi_total > subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > relation_dom_as_subset > relation_inverse_image > cartesian_product2 > apply > #nlpp > relation_dom > powerset > empty_set > #skF_1 > #skF_20 > #skF_4 > #skF_18 > #skF_17 > #skF_11 > #skF_25 > #skF_19 > #skF_3 > #skF_13 > #skF_16 > #skF_15 > #skF_14 > #skF_10 > #skF_6 > #skF_2 > #skF_21 > #skF_9 > #skF_8 > #skF_22 > #skF_24 > #skF_23 > #skF_7 > #skF_5 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation,type,
relation: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(quasi_total,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(relation_inverse_image,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(relation_dom_as_subset,type,
relation_dom_as_subset: ( $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(relation_dom,type,
relation_dom: $i > $i ).
tff(relation_of2,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(relation_of2_as_subset,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_182,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
tff(f_276,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_199,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
tff(f_272,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
tff(f_140,axiom,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
tff(f_161,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
tff(f_238,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
tff(f_259,negated_conjecture,
~ ! [A,B,C,D] :
( ( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B) )
=> ( ( B != empty_set )
=> ! [E] :
( in(E,relation_inverse_image(D,C))
<=> ( in(E,A)
& in(apply(D,E),C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).
tff(f_96,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
tff(f_43,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
tff(f_69,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B,C] :
( ( C = relation_inverse_image(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,relation_dom(A))
& in(apply(A,D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
tff(f_226,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
tff(f_222,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> ( relation_dom_as_subset(A,B,C) = relation_dom(C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
tff(f_92,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_dom_as_subset(A,B,C),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
tff(f_265,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_102,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
tff(f_134,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
tff(f_242,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_87,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( quasi_total(C,A,B)
<=> ( A = relation_dom_as_subset(A,B,C) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( quasi_total(C,A,B)
<=> ( C = empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
tff(c_126,plain,
empty('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_217,plain,
! [A_88] :
( ( empty_set = A_88 )
| ~ empty(A_88) ),
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_240,plain,
empty_set = '#skF_12',
inference(resolution,[status(thm)],[c_126,c_217]) ).
tff(c_140,plain,
! [A_51] : empty('#skF_15'(A_51)),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_236,plain,
! [A_51] : ( '#skF_15'(A_51) = empty_set ),
inference(resolution,[status(thm)],[c_140,c_217]) ).
tff(c_4404,plain,
! [A_51] : ( '#skF_15'(A_51) = '#skF_12' ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_236]) ).
tff(c_142,plain,
! [A_51] : element('#skF_15'(A_51),powerset(A_51)),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_4431,plain,
! [A_51] : element('#skF_12',powerset(A_51)),
inference(demodulation,[status(thm),theory(equality)],[c_4404,c_142]) ).
tff(c_5371,plain,
! [C_988,B_989,A_990] :
( ~ empty(C_988)
| ~ element(B_989,powerset(C_988))
| ~ in(A_990,B_989) ),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_5383,plain,
! [A_51,A_990] :
( ~ empty(A_51)
| ~ in(A_990,'#skF_12') ),
inference(resolution,[status(thm)],[c_4431,c_5371]) ).
tff(c_5391,plain,
! [A_990] : ~ in(A_990,'#skF_12'),
inference(splitLeft,[status(thm)],[c_5383]) ).
tff(c_128,plain,
relation('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_124,plain,
function('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_4425,plain,
! [A_795] :
( empty(relation_dom(A_795))
| ~ empty(A_795) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_106,plain,
empty('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_237,plain,
empty_set = '#skF_8',
inference(resolution,[status(thm)],[c_106,c_217]) ).
tff(c_264,plain,
'#skF_8' = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_240,c_237]) ).
tff(c_202,plain,
! [A_74] :
( ( empty_set = A_74 )
| ~ empty(A_74) ),
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_243,plain,
! [A_74] :
( ( A_74 = '#skF_8' )
| ~ empty(A_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_237,c_202]) ).
tff(c_4417,plain,
! [A_74] :
( ( A_74 = '#skF_12' )
| ~ empty(A_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_264,c_243]) ).
tff(c_4454,plain,
! [A_802] :
( ( relation_dom(A_802) = '#skF_12' )
| ~ empty(A_802) ),
inference(resolution,[status(thm)],[c_4425,c_4417]) ).
tff(c_4462,plain,
relation_dom('#skF_12') = '#skF_12',
inference(resolution,[status(thm)],[c_126,c_4454]) ).
tff(c_4669,plain,
! [A_846,B_847] :
( in(A_846,B_847)
| empty(B_847)
| ~ element(A_846,B_847) ),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_190,plain,
( in('#skF_24','#skF_20')
| ~ in(apply('#skF_23','#skF_25'),'#skF_22')
| ~ in('#skF_25','#skF_20') ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_4438,plain,
~ in('#skF_25','#skF_20'),
inference(splitLeft,[status(thm)],[c_190]) ).
tff(c_4691,plain,
( empty('#skF_20')
| ~ element('#skF_25','#skF_20') ),
inference(resolution,[status(thm)],[c_4669,c_4438]) ).
tff(c_4693,plain,
~ element('#skF_25','#skF_20'),
inference(splitLeft,[status(thm)],[c_4691]) ).
tff(c_180,plain,
relation_of2_as_subset('#skF_23','#skF_20','#skF_21'),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_4793,plain,
! [C_872,A_873,B_874] :
( element(C_872,powerset(cartesian_product2(A_873,B_874)))
| ~ relation_of2_as_subset(C_872,A_873,B_874) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_8,plain,
! [C_7,A_5,B_6] :
( relation(C_7)
| ~ element(C_7,powerset(cartesian_product2(A_5,B_6))) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_4808,plain,
! [C_875,A_876,B_877] :
( relation(C_875)
| ~ relation_of2_as_subset(C_875,A_876,B_877) ),
inference(resolution,[status(thm)],[c_4793,c_8]) ).
tff(c_4820,plain,
relation('#skF_23'),
inference(resolution,[status(thm)],[c_180,c_4808]) ).
tff(c_184,plain,
function('#skF_23'),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_194,plain,
( in(apply('#skF_23','#skF_24'),'#skF_22')
| in('#skF_25',relation_inverse_image('#skF_23','#skF_22')) ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_4414,plain,
in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
inference(splitLeft,[status(thm)],[c_194]) ).
tff(c_5268,plain,
! [D_985,A_986,B_987] :
( in(D_985,relation_dom(A_986))
| ~ in(D_985,relation_inverse_image(A_986,B_987))
| ~ function(A_986)
| ~ relation(A_986) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_5278,plain,
( in('#skF_25',relation_dom('#skF_23'))
| ~ function('#skF_23')
| ~ relation('#skF_23') ),
inference(resolution,[status(thm)],[c_4414,c_5268]) ).
tff(c_5285,plain,
in('#skF_25',relation_dom('#skF_23')),
inference(demodulation,[status(thm),theory(equality)],[c_4820,c_184,c_5278]) ).
tff(c_4566,plain,
! [C_827,A_828,B_829] :
( relation_of2(C_827,A_828,B_829)
| ~ relation_of2_as_subset(C_827,A_828,B_829) ),
inference(cnfTransformation,[status(thm)],[f_226]) ).
tff(c_4574,plain,
relation_of2('#skF_23','#skF_20','#skF_21'),
inference(resolution,[status(thm)],[c_180,c_4566]) ).
tff(c_4822,plain,
! [A_880,B_881,C_882] :
( ( relation_dom_as_subset(A_880,B_881,C_882) = relation_dom(C_882) )
| ~ relation_of2(C_882,A_880,B_881) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_4839,plain,
relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = relation_dom('#skF_23'),
inference(resolution,[status(thm)],[c_4574,c_4822]) ).
tff(c_4959,plain,
! [A_909,B_910,C_911] :
( element(relation_dom_as_subset(A_909,B_910,C_911),powerset(A_909))
| ~ relation_of2(C_911,A_909,B_910) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_4973,plain,
( element(relation_dom('#skF_23'),powerset('#skF_20'))
| ~ relation_of2('#skF_23','#skF_20','#skF_21') ),
inference(superposition,[status(thm),theory(equality)],[c_4839,c_4959]) ).
tff(c_4979,plain,
element(relation_dom('#skF_23'),powerset('#skF_20')),
inference(demodulation,[status(thm),theory(equality)],[c_4574,c_4973]) ).
tff(c_198,plain,
! [A_68,C_70,B_69] :
( element(A_68,C_70)
| ~ element(B_69,powerset(C_70))
| ~ in(A_68,B_69) ),
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_4987,plain,
! [A_68] :
( element(A_68,'#skF_20')
| ~ in(A_68,relation_dom('#skF_23')) ),
inference(resolution,[status(thm)],[c_4979,c_198]) ).
tff(c_5317,plain,
element('#skF_25','#skF_20'),
inference(resolution,[status(thm)],[c_5285,c_4987]) ).
tff(c_5336,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4693,c_5317]) ).
tff(c_5337,plain,
empty('#skF_20'),
inference(splitRight,[status(thm)],[c_4691]) ).
tff(c_5352,plain,
'#skF_20' = '#skF_12',
inference(resolution,[status(thm)],[c_5337,c_4417]) ).
tff(c_5356,plain,
relation_of2_as_subset('#skF_23','#skF_12','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_5352,c_180]) ).
tff(c_5554,plain,
! [C_1029,A_1030,B_1031] :
( element(C_1029,powerset(cartesian_product2(A_1030,B_1031)))
| ~ relation_of2_as_subset(C_1029,A_1030,B_1031) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_5569,plain,
! [C_1032,A_1033,B_1034] :
( relation(C_1032)
| ~ relation_of2_as_subset(C_1032,A_1033,B_1034) ),
inference(resolution,[status(thm)],[c_5554,c_8]) ).
tff(c_5579,plain,
relation('#skF_23'),
inference(resolution,[status(thm)],[c_5356,c_5569]) ).
tff(c_68,plain,
! [A_33] : element('#skF_4'(A_33),A_33),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_172,plain,
! [A_63,B_64] :
( in(A_63,B_64)
| empty(B_64)
| ~ element(A_63,B_64) ),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_5354,plain,
relation_of2('#skF_23','#skF_12','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_5352,c_4574]) ).
tff(c_5461,plain,
! [A_1008,B_1009,C_1010] :
( ( relation_dom_as_subset(A_1008,B_1009,C_1010) = relation_dom(C_1010) )
| ~ relation_of2(C_1010,A_1008,B_1009) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_5477,plain,
relation_dom_as_subset('#skF_12','#skF_21','#skF_23') = relation_dom('#skF_23'),
inference(resolution,[status(thm)],[c_5354,c_5461]) ).
tff(c_5609,plain,
! [A_1042,B_1043,C_1044] :
( element(relation_dom_as_subset(A_1042,B_1043,C_1044),powerset(A_1042))
| ~ relation_of2(C_1044,A_1042,B_1043) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_5623,plain,
( element(relation_dom('#skF_23'),powerset('#skF_12'))
| ~ relation_of2('#skF_23','#skF_12','#skF_21') ),
inference(superposition,[status(thm),theory(equality)],[c_5477,c_5609]) ).
tff(c_5629,plain,
element(relation_dom('#skF_23'),powerset('#skF_12')),
inference(demodulation,[status(thm),theory(equality)],[c_5354,c_5623]) ).
tff(c_200,plain,
! [C_73,B_72,A_71] :
( ~ empty(C_73)
| ~ element(B_72,powerset(C_73))
| ~ in(A_71,B_72) ),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_5633,plain,
! [A_71] :
( ~ empty('#skF_12')
| ~ in(A_71,relation_dom('#skF_23')) ),
inference(resolution,[status(thm)],[c_5629,c_200]) ).
tff(c_5642,plain,
! [A_1045] : ~ in(A_1045,relation_dom('#skF_23')),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_5633]) ).
tff(c_5647,plain,
! [A_63] :
( empty(relation_dom('#skF_23'))
| ~ element(A_63,relation_dom('#skF_23')) ),
inference(resolution,[status(thm)],[c_172,c_5642]) ).
tff(c_5649,plain,
! [A_1046] : ~ element(A_1046,relation_dom('#skF_23')),
inference(splitLeft,[status(thm)],[c_5647]) ).
tff(c_5654,plain,
$false,
inference(resolution,[status(thm)],[c_68,c_5649]) ).
tff(c_5655,plain,
empty(relation_dom('#skF_23')),
inference(splitRight,[status(thm)],[c_5647]) ).
tff(c_88,plain,
! [A_41] :
( ~ empty(relation_dom(A_41))
| ~ relation(A_41)
| empty(A_41) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_5662,plain,
( ~ relation('#skF_23')
| empty('#skF_23') ),
inference(resolution,[status(thm)],[c_5655,c_88]) ).
tff(c_5675,plain,
empty('#skF_23'),
inference(demodulation,[status(thm),theory(equality)],[c_5579,c_5662]) ).
tff(c_5695,plain,
'#skF_23' = '#skF_12',
inference(resolution,[status(thm)],[c_5675,c_4417]) ).
tff(c_192,plain,
( ~ in('#skF_24',relation_inverse_image('#skF_23','#skF_22'))
| in('#skF_25',relation_inverse_image('#skF_23','#skF_22')) ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_295,plain,
~ in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
inference(splitLeft,[status(thm)],[c_192]) ).
tff(c_3227,plain,
! [C_614,A_615,B_616] :
( element(C_614,powerset(cartesian_product2(A_615,B_616)))
| ~ relation_of2_as_subset(C_614,A_615,B_616) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_3239,plain,
! [C_617,A_618,B_619] :
( relation(C_617)
| ~ relation_of2_as_subset(C_617,A_618,B_619) ),
inference(resolution,[status(thm)],[c_3227,c_8]) ).
tff(c_3251,plain,
relation('#skF_23'),
inference(resolution,[status(thm)],[c_180,c_3239]) ).
tff(c_2175,plain,
! [C_419,A_420,B_421] :
( element(C_419,powerset(cartesian_product2(A_420,B_421)))
| ~ relation_of2_as_subset(C_419,A_420,B_421) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_2218,plain,
! [C_427,A_428,B_429] :
( relation(C_427)
| ~ relation_of2_as_subset(C_427,A_428,B_429) ),
inference(resolution,[status(thm)],[c_2175,c_8]) ).
tff(c_2230,plain,
relation('#skF_23'),
inference(resolution,[status(thm)],[c_180,c_2218]) ).
tff(c_196,plain,
( in('#skF_24','#skF_20')
| in('#skF_25',relation_inverse_image('#skF_23','#skF_22')) ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_254,plain,
in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
inference(splitLeft,[status(thm)],[c_196]) ).
tff(c_2803,plain,
! [A_560,D_561,B_562] :
( in(apply(A_560,D_561),B_562)
| ~ in(D_561,relation_inverse_image(A_560,B_562))
| ~ function(A_560)
| ~ relation(A_560) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_296,plain,
! [A_51] : ( '#skF_15'(A_51) = '#skF_12' ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_236]) ).
tff(c_308,plain,
! [A_51] : element('#skF_12',powerset(A_51)),
inference(demodulation,[status(thm),theory(equality)],[c_296,c_142]) ).
tff(c_1178,plain,
! [C_255,B_256,A_257] :
( ~ empty(C_255)
| ~ element(B_256,powerset(C_255))
| ~ in(A_257,B_256) ),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_1190,plain,
! [A_51,A_257] :
( ~ empty(A_51)
| ~ in(A_257,'#skF_12') ),
inference(resolution,[status(thm)],[c_308,c_1178]) ).
tff(c_1192,plain,
! [A_257] : ~ in(A_257,'#skF_12'),
inference(splitLeft,[status(thm)],[c_1190]) ).
tff(c_318,plain,
! [A_98] :
( empty(relation_dom(A_98))
| ~ empty(A_98) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_310,plain,
! [A_74] :
( ( A_74 = '#skF_12' )
| ~ empty(A_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_264,c_243]) ).
tff(c_331,plain,
! [A_102] :
( ( relation_dom(A_102) = '#skF_12' )
| ~ empty(A_102) ),
inference(resolution,[status(thm)],[c_318,c_310]) ).
tff(c_339,plain,
relation_dom('#skF_12') = '#skF_12',
inference(resolution,[status(thm)],[c_126,c_331]) ).
tff(c_514,plain,
! [A_151,B_152] :
( in(A_151,B_152)
| empty(B_152)
| ~ element(A_151,B_152) ),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_359,plain,
~ in('#skF_25','#skF_20'),
inference(splitLeft,[status(thm)],[c_190]) ).
tff(c_534,plain,
( empty('#skF_20')
| ~ element('#skF_25','#skF_20') ),
inference(resolution,[status(thm)],[c_514,c_359]) ).
tff(c_540,plain,
~ element('#skF_25','#skF_20'),
inference(splitLeft,[status(thm)],[c_534]) ).
tff(c_498,plain,
! [C_141,A_142,B_143] :
( relation_of2(C_141,A_142,B_143)
| ~ relation_of2_as_subset(C_141,A_142,B_143) ),
inference(cnfTransformation,[status(thm)],[f_226]) ).
tff(c_506,plain,
relation_of2('#skF_23','#skF_20','#skF_21'),
inference(resolution,[status(thm)],[c_180,c_498]) ).
tff(c_644,plain,
! [A_165,B_166,C_167] :
( ( relation_dom_as_subset(A_165,B_166,C_167) = relation_dom(C_167) )
| ~ relation_of2(C_167,A_165,B_166) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_661,plain,
relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = relation_dom('#skF_23'),
inference(resolution,[status(thm)],[c_506,c_644]) ).
tff(c_850,plain,
! [A_216,B_217,C_218] :
( element(relation_dom_as_subset(A_216,B_217,C_218),powerset(A_216))
| ~ relation_of2(C_218,A_216,B_217) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_873,plain,
( element(relation_dom('#skF_23'),powerset('#skF_20'))
| ~ relation_of2('#skF_23','#skF_20','#skF_21') ),
inference(superposition,[status(thm),theory(equality)],[c_661,c_850]) ).
tff(c_885,plain,
element(relation_dom('#skF_23'),powerset('#skF_20')),
inference(demodulation,[status(thm),theory(equality)],[c_506,c_873]) ).
tff(c_174,plain,
! [A_65,B_66] :
( subset(A_65,B_66)
| ~ element(A_65,powerset(B_66)) ),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_895,plain,
subset(relation_dom('#skF_23'),'#skF_20'),
inference(resolution,[status(thm)],[c_885,c_174]) ).
tff(c_691,plain,
! [C_176,A_177,B_178] :
( element(C_176,powerset(cartesian_product2(A_177,B_178)))
| ~ relation_of2_as_subset(C_176,A_177,B_178) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_703,plain,
! [C_179,A_180,B_181] :
( relation(C_179)
| ~ relation_of2_as_subset(C_179,A_180,B_181) ),
inference(resolution,[status(thm)],[c_691,c_8]) ).
tff(c_715,plain,
relation('#skF_23'),
inference(resolution,[status(thm)],[c_180,c_703]) ).
tff(c_988,plain,
! [D_246,A_247,B_248] :
( in(D_246,relation_dom(A_247))
| ~ in(D_246,relation_inverse_image(A_247,B_248))
| ~ function(A_247)
| ~ relation(A_247) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_995,plain,
( in('#skF_25',relation_dom('#skF_23'))
| ~ function('#skF_23')
| ~ relation('#skF_23') ),
inference(resolution,[status(thm)],[c_254,c_988]) ).
tff(c_999,plain,
in('#skF_25',relation_dom('#skF_23')),
inference(demodulation,[status(thm),theory(equality)],[c_715,c_184,c_995]) ).
tff(c_176,plain,
! [A_65,B_66] :
( element(A_65,powerset(B_66))
| ~ subset(A_65,B_66) ),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_717,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_265]) ).
tff(c_731,plain,
! [A_184,B_66,A_65] :
( element(A_184,B_66)
| ~ in(A_184,A_65)
| ~ subset(A_65,B_66) ),
inference(resolution,[status(thm)],[c_176,c_717]) ).
tff(c_1057,plain,
! [B_252] :
( element('#skF_25',B_252)
| ~ subset(relation_dom('#skF_23'),B_252) ),
inference(resolution,[status(thm)],[c_999,c_731]) ).
tff(c_1060,plain,
element('#skF_25','#skF_20'),
inference(resolution,[status(thm)],[c_895,c_1057]) ).
tff(c_1072,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_540,c_1060]) ).
tff(c_1073,plain,
empty('#skF_20'),
inference(splitRight,[status(thm)],[c_534]) ).
tff(c_1088,plain,
'#skF_20' = '#skF_12',
inference(resolution,[status(thm)],[c_1073,c_310]) ).
tff(c_1092,plain,
relation_of2_as_subset('#skF_23','#skF_12','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_1088,c_180]) ).
tff(c_1251,plain,
! [C_276,A_277,B_278] :
( element(C_276,powerset(cartesian_product2(A_277,B_278)))
| ~ relation_of2_as_subset(C_276,A_277,B_278) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_1266,plain,
! [C_279,A_280,B_281] :
( relation(C_279)
| ~ relation_of2_as_subset(C_279,A_280,B_281) ),
inference(resolution,[status(thm)],[c_1251,c_8]) ).
tff(c_1276,plain,
relation('#skF_23'),
inference(resolution,[status(thm)],[c_1092,c_1266]) ).
tff(c_182,plain,
quasi_total('#skF_23','#skF_20','#skF_21'),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_1093,plain,
quasi_total('#skF_23','#skF_12','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_1088,c_182]) ).
tff(c_1090,plain,
relation_of2('#skF_23','#skF_12','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_1088,c_506]) ).
tff(c_1306,plain,
! [A_289,B_290,C_291] :
( ( relation_dom_as_subset(A_289,B_290,C_291) = relation_dom(C_291) )
| ~ relation_of2(C_291,A_289,B_290) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_1322,plain,
relation_dom_as_subset('#skF_12','#skF_21','#skF_23') = relation_dom('#skF_23'),
inference(resolution,[status(thm)],[c_1090,c_1306]) ).
tff(c_42,plain,
! [B_22,C_23] :
( ( relation_dom_as_subset(empty_set,B_22,C_23) = empty_set )
| ~ quasi_total(C_23,empty_set,B_22)
| ~ relation_of2_as_subset(C_23,empty_set,B_22) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1716,plain,
! [B_362,C_363] :
( ( relation_dom_as_subset('#skF_12',B_362,C_363) = '#skF_12' )
| ~ quasi_total(C_363,'#skF_12',B_362)
| ~ relation_of2_as_subset(C_363,'#skF_12',B_362) ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_240,c_240,c_240,c_42]) ).
tff(c_1719,plain,
( ( relation_dom_as_subset('#skF_12','#skF_21','#skF_23') = '#skF_12' )
| ~ quasi_total('#skF_23','#skF_12','#skF_21') ),
inference(resolution,[status(thm)],[c_1092,c_1716]) ).
tff(c_1730,plain,
relation_dom('#skF_23') = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_1093,c_1322,c_1719]) ).
tff(c_1743,plain,
( ~ empty('#skF_12')
| ~ relation('#skF_23')
| empty('#skF_23') ),
inference(superposition,[status(thm),theory(equality)],[c_1730,c_88]) ).
tff(c_1756,plain,
empty('#skF_23'),
inference(demodulation,[status(thm),theory(equality)],[c_1276,c_126,c_1743]) ).
tff(c_1783,plain,
'#skF_23' = '#skF_12',
inference(resolution,[status(thm)],[c_1756,c_310]) ).
tff(c_1802,plain,
in('#skF_25',relation_inverse_image('#skF_12','#skF_22')),
inference(demodulation,[status(thm),theory(equality)],[c_1783,c_254]) ).
tff(c_20,plain,
! [D_20,A_9,B_16] :
( in(D_20,relation_dom(A_9))
| ~ in(D_20,relation_inverse_image(A_9,B_16))
| ~ function(A_9)
| ~ relation(A_9) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_1862,plain,
( in('#skF_25',relation_dom('#skF_12'))
| ~ function('#skF_12')
| ~ relation('#skF_12') ),
inference(resolution,[status(thm)],[c_1802,c_20]) ).
tff(c_1880,plain,
in('#skF_25','#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_124,c_339,c_1862]) ).
tff(c_1882,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1192,c_1880]) ).
tff(c_1883,plain,
! [A_51] : ~ empty(A_51),
inference(splitRight,[status(thm)],[c_1190]) ).
tff(c_1892,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1883,c_126]) ).
tff(c_1894,plain,
in('#skF_25','#skF_20'),
inference(splitRight,[status(thm)],[c_190]) ).
tff(c_188,plain,
( in(apply('#skF_23','#skF_24'),'#skF_22')
| ~ in(apply('#skF_23','#skF_25'),'#skF_22')
| ~ in('#skF_25','#skF_20') ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_1985,plain,
( in(apply('#skF_23','#skF_24'),'#skF_22')
| ~ in(apply('#skF_23','#skF_25'),'#skF_22') ),
inference(demodulation,[status(thm),theory(equality)],[c_1894,c_188]) ).
tff(c_1986,plain,
~ in(apply('#skF_23','#skF_25'),'#skF_22'),
inference(splitLeft,[status(thm)],[c_1985]) ).
tff(c_2861,plain,
( ~ in('#skF_25',relation_inverse_image('#skF_23','#skF_22'))
| ~ function('#skF_23')
| ~ relation('#skF_23') ),
inference(resolution,[status(thm)],[c_2803,c_1986]) ).
tff(c_2888,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2230,c_184,c_254,c_2861]) ).
tff(c_2890,plain,
in(apply('#skF_23','#skF_25'),'#skF_22'),
inference(splitRight,[status(thm)],[c_1985]) ).
tff(c_1893,plain,
( ~ in(apply('#skF_23','#skF_25'),'#skF_22')
| in('#skF_24','#skF_20') ),
inference(splitRight,[status(thm)],[c_190]) ).
tff(c_2903,plain,
~ in(apply('#skF_23','#skF_25'),'#skF_22'),
inference(splitLeft,[status(thm)],[c_1893]) ).
tff(c_2916,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2890,c_2903]) ).
tff(c_2917,plain,
in('#skF_24','#skF_20'),
inference(splitRight,[status(thm)],[c_1893]) ).
tff(c_178,plain,
empty_set != '#skF_21',
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_245,plain,
'#skF_21' != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_237,c_178]) ).
tff(c_277,plain,
'#skF_21' != '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_264,c_245]) ).
tff(c_3110,plain,
! [C_589,A_590,B_591] :
( relation_of2(C_589,A_590,B_591)
| ~ relation_of2_as_subset(C_589,A_590,B_591) ),
inference(cnfTransformation,[status(thm)],[f_226]) ).
tff(c_3122,plain,
relation_of2('#skF_23','#skF_20','#skF_21'),
inference(resolution,[status(thm)],[c_180,c_3110]) ).
tff(c_3306,plain,
! [A_633,B_634,C_635] :
( ( relation_dom_as_subset(A_633,B_634,C_635) = relation_dom(C_635) )
| ~ relation_of2(C_635,A_633,B_634) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_3323,plain,
relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = relation_dom('#skF_23'),
inference(resolution,[status(thm)],[c_3122,c_3306]) ).
tff(c_44,plain,
! [B_22,A_21,C_23] :
( ( empty_set = B_22 )
| ( relation_dom_as_subset(A_21,B_22,C_23) = A_21 )
| ~ quasi_total(C_23,A_21,B_22)
| ~ relation_of2_as_subset(C_23,A_21,B_22) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_4145,plain,
! [B_774,A_775,C_776] :
( ( B_774 = '#skF_12' )
| ( relation_dom_as_subset(A_775,B_774,C_776) = A_775 )
| ~ quasi_total(C_776,A_775,B_774)
| ~ relation_of2_as_subset(C_776,A_775,B_774) ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_44]) ).
tff(c_4154,plain,
( ( '#skF_21' = '#skF_12' )
| ( relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = '#skF_20' )
| ~ quasi_total('#skF_23','#skF_20','#skF_21') ),
inference(resolution,[status(thm)],[c_180,c_4145]) ).
tff(c_4160,plain,
( ( '#skF_21' = '#skF_12' )
| ( relation_dom('#skF_23') = '#skF_20' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_3323,c_4154]) ).
tff(c_4161,plain,
relation_dom('#skF_23') = '#skF_20',
inference(negUnitSimplification,[status(thm)],[c_277,c_4160]) ).
tff(c_2889,plain,
in(apply('#skF_23','#skF_24'),'#skF_22'),
inference(splitRight,[status(thm)],[c_1985]) ).
tff(c_4378,plain,
! [D_785,A_786,B_787] :
( in(D_785,relation_inverse_image(A_786,B_787))
| ~ in(apply(A_786,D_785),B_787)
| ~ in(D_785,relation_dom(A_786))
| ~ function(A_786)
| ~ relation(A_786) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_4391,plain,
( in('#skF_24',relation_inverse_image('#skF_23','#skF_22'))
| ~ in('#skF_24',relation_dom('#skF_23'))
| ~ function('#skF_23')
| ~ relation('#skF_23') ),
inference(resolution,[status(thm)],[c_2889,c_4378]) ).
tff(c_4399,plain,
in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
inference(demodulation,[status(thm),theory(equality)],[c_3251,c_184,c_2917,c_4161,c_4391]) ).
tff(c_4401,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_295,c_4399]) ).
tff(c_4403,plain,
in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
inference(splitRight,[status(thm)],[c_192]) ).
tff(c_5715,plain,
in('#skF_24',relation_inverse_image('#skF_12','#skF_22')),
inference(demodulation,[status(thm),theory(equality)],[c_5695,c_4403]) ).
tff(c_5841,plain,
! [D_1051,A_1052,B_1053] :
( in(D_1051,relation_dom(A_1052))
| ~ in(D_1051,relation_inverse_image(A_1052,B_1053))
| ~ function(A_1052)
| ~ relation(A_1052) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_5844,plain,
( in('#skF_24',relation_dom('#skF_12'))
| ~ function('#skF_12')
| ~ relation('#skF_12') ),
inference(resolution,[status(thm)],[c_5715,c_5841]) ).
tff(c_5854,plain,
in('#skF_24','#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_124,c_4462,c_5844]) ).
tff(c_5856,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5391,c_5854]) ).
tff(c_5857,plain,
! [A_51] : ~ empty(A_51),
inference(splitRight,[status(thm)],[c_5383]) ).
tff(c_5866,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5857,c_126]) ).
tff(c_5868,plain,
in('#skF_25','#skF_20'),
inference(splitRight,[status(thm)],[c_190]) ).
tff(c_186,plain,
( ~ in('#skF_24',relation_inverse_image('#skF_23','#skF_22'))
| ~ in(apply('#skF_23','#skF_25'),'#skF_22')
| ~ in('#skF_25','#skF_20') ),
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_6851,plain,
~ in(apply('#skF_23','#skF_25'),'#skF_22'),
inference(demodulation,[status(thm),theory(equality)],[c_5868,c_4403,c_186]) ).
tff(c_6258,plain,
! [C_1127,A_1128,B_1129] :
( element(C_1127,powerset(cartesian_product2(A_1128,B_1129)))
| ~ relation_of2_as_subset(C_1127,A_1128,B_1129) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_6273,plain,
! [C_1130,A_1131,B_1132] :
( relation(C_1130)
| ~ relation_of2_as_subset(C_1130,A_1131,B_1132) ),
inference(resolution,[status(thm)],[c_6258,c_8]) ).
tff(c_6285,plain,
relation('#skF_23'),
inference(resolution,[status(thm)],[c_180,c_6273]) ).
tff(c_6765,plain,
! [A_1223,D_1224,B_1225] :
( in(apply(A_1223,D_1224),B_1225)
| ~ in(D_1224,relation_inverse_image(A_1223,B_1225))
| ~ function(A_1223)
| ~ relation(A_1223) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_5874,plain,
( in(apply('#skF_23','#skF_24'),'#skF_22')
| ~ in(apply('#skF_23','#skF_25'),'#skF_22') ),
inference(demodulation,[status(thm),theory(equality)],[c_5868,c_188]) ).
tff(c_5875,plain,
~ in(apply('#skF_23','#skF_25'),'#skF_22'),
inference(splitLeft,[status(thm)],[c_5874]) ).
tff(c_6820,plain,
( ~ in('#skF_25',relation_inverse_image('#skF_23','#skF_22'))
| ~ function('#skF_23')
| ~ relation('#skF_23') ),
inference(resolution,[status(thm)],[c_6765,c_5875]) ).
tff(c_6842,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6285,c_184,c_4414,c_6820]) ).
tff(c_6844,plain,
in(apply('#skF_23','#skF_25'),'#skF_22'),
inference(splitRight,[status(thm)],[c_5874]) ).
tff(c_6852,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6851,c_6844]) ).
tff(c_6854,plain,
~ in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
inference(splitRight,[status(thm)],[c_194]) ).
tff(c_6879,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6854,c_254]) ).
tff(c_6881,plain,
~ in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
inference(splitRight,[status(thm)],[c_196]) ).
tff(c_6889,plain,
~ in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
inference(splitLeft,[status(thm)],[c_192]) ).
tff(c_7364,plain,
! [C_1337,A_1338,B_1339] :
( element(C_1337,powerset(cartesian_product2(A_1338,B_1339)))
| ~ relation_of2_as_subset(C_1337,A_1338,B_1339) ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_7376,plain,
! [C_1340,A_1341,B_1342] :
( relation(C_1340)
| ~ relation_of2_as_subset(C_1340,A_1341,B_1342) ),
inference(resolution,[status(thm)],[c_7364,c_8]) ).
tff(c_7388,plain,
relation('#skF_23'),
inference(resolution,[status(thm)],[c_180,c_7376]) ).
tff(c_6880,plain,
in('#skF_24','#skF_20'),
inference(splitRight,[status(thm)],[c_196]) ).
tff(c_6890,plain,
'#skF_8' = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_240,c_237]) ).
tff(c_6905,plain,
'#skF_21' != '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_6890,c_245]) ).
tff(c_7116,plain,
! [C_1289,A_1290,B_1291] :
( relation_of2(C_1289,A_1290,B_1291)
| ~ relation_of2_as_subset(C_1289,A_1290,B_1291) ),
inference(cnfTransformation,[status(thm)],[f_226]) ).
tff(c_7124,plain,
relation_of2('#skF_23','#skF_20','#skF_21'),
inference(resolution,[status(thm)],[c_180,c_7116]) ).
tff(c_7432,plain,
! [A_1351,B_1352,C_1353] :
( ( relation_dom_as_subset(A_1351,B_1352,C_1353) = relation_dom(C_1353) )
| ~ relation_of2(C_1353,A_1351,B_1352) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_7449,plain,
relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = relation_dom('#skF_23'),
inference(resolution,[status(thm)],[c_7124,c_7432]) ).
tff(c_8487,plain,
! [B_1501,A_1502,C_1503] :
( ( B_1501 = '#skF_12' )
| ( relation_dom_as_subset(A_1502,B_1501,C_1503) = A_1502 )
| ~ quasi_total(C_1503,A_1502,B_1501)
| ~ relation_of2_as_subset(C_1503,A_1502,B_1501) ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_44]) ).
tff(c_8496,plain,
( ( '#skF_21' = '#skF_12' )
| ( relation_dom_as_subset('#skF_20','#skF_21','#skF_23') = '#skF_20' )
| ~ quasi_total('#skF_23','#skF_20','#skF_21') ),
inference(resolution,[status(thm)],[c_180,c_8487]) ).
tff(c_8502,plain,
( ( '#skF_21' = '#skF_12' )
| ( relation_dom('#skF_23') = '#skF_20' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_7449,c_8496]) ).
tff(c_8503,plain,
relation_dom('#skF_23') = '#skF_20',
inference(negUnitSimplification,[status(thm)],[c_6905,c_8502]) ).
tff(c_6933,plain,
in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
inference(splitLeft,[status(thm)],[c_194]) ).
tff(c_6958,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6881,c_6933]) ).
tff(c_6959,plain,
in(apply('#skF_23','#skF_24'),'#skF_22'),
inference(splitRight,[status(thm)],[c_194]) ).
tff(c_8715,plain,
! [D_1521,A_1522,B_1523] :
( in(D_1521,relation_inverse_image(A_1522,B_1523))
| ~ in(apply(A_1522,D_1521),B_1523)
| ~ in(D_1521,relation_dom(A_1522))
| ~ function(A_1522)
| ~ relation(A_1522) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_8725,plain,
( in('#skF_24',relation_inverse_image('#skF_23','#skF_22'))
| ~ in('#skF_24',relation_dom('#skF_23'))
| ~ function('#skF_23')
| ~ relation('#skF_23') ),
inference(resolution,[status(thm)],[c_6959,c_8715]) ).
tff(c_8730,plain,
in('#skF_24',relation_inverse_image('#skF_23','#skF_22')),
inference(demodulation,[status(thm),theory(equality)],[c_7388,c_184,c_6880,c_8503,c_8725]) ).
tff(c_8732,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6889,c_8730]) ).
tff(c_8733,plain,
in('#skF_25',relation_inverse_image('#skF_23','#skF_22')),
inference(splitRight,[status(thm)],[c_192]) ).
tff(c_8789,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6881,c_8733]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n001.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 12:45:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 11.64/3.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.64/3.87
% 11.64/3.87 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.83/3.92
% 11.83/3.92 Inference rules
% 11.83/3.92 ----------------------
% 11.83/3.92 #Ref : 0
% 11.83/3.92 #Sup : 1795
% 11.83/3.92 #Fact : 0
% 11.83/3.92 #Define : 0
% 11.83/3.92 #Split : 77
% 11.83/3.92 #Chain : 0
% 11.83/3.92 #Close : 0
% 11.83/3.92
% 11.83/3.92 Ordering : KBO
% 11.83/3.92
% 11.83/3.92 Simplification rules
% 11.83/3.92 ----------------------
% 11.83/3.92 #Subsume : 295
% 11.83/3.92 #Demod : 853
% 11.83/3.92 #Tautology : 500
% 11.83/3.92 #SimpNegUnit : 93
% 11.83/3.92 #BackRed : 138
% 11.83/3.92
% 11.83/3.92 #Partial instantiations: 0
% 11.83/3.92 #Strategies tried : 1
% 11.83/3.92
% 11.83/3.92 Timing (in seconds)
% 11.83/3.92 ----------------------
% 11.83/3.92 Preprocessing : 0.67
% 11.83/3.92 Parsing : 0.33
% 11.83/3.92 CNF conversion : 0.06
% 11.83/3.92 Main loop : 2.06
% 11.83/3.92 Inferencing : 0.73
% 11.83/3.92 Reduction : 0.70
% 11.83/3.92 Demodulation : 0.48
% 11.83/3.92 BG Simplification : 0.06
% 11.83/3.92 Subsumption : 0.39
% 11.83/3.92 Abstraction : 0.05
% 11.83/3.92 MUC search : 0.00
% 11.83/3.92 Cooper : 0.00
% 11.83/3.92 Total : 2.82
% 11.83/3.92 Index Insertion : 0.00
% 11.83/3.92 Index Deletion : 0.00
% 11.83/3.92 Index Matching : 0.00
% 11.83/3.92 BG Taut test : 0.00
%------------------------------------------------------------------------------