TSTP Solution File: LAT305+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LAT305+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n015.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 10:46:45 EDT 2023
% Result : Theorem 13.30s 4.44s
% Output : CNFRefutation 13.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 84
% Syntax : Number of formulae : 250 ( 73 unt; 73 typ; 0 def)
% Number of atoms : 547 ( 57 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 649 ( 279 ~; 305 |; 46 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 99 ( 57 >; 42 *; 0 +; 0 <<)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 16 con; 0-6 aty)
% Number of variables : 126 (; 125 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ v1_partfun1 > v1_funct_2 > r3_lattices > r1_lattices > m2_relset_1 > m1_relset_1 > v2_binop_1 > v1_binop_1 > r2_hidden > r1_tarski > m2_lattice4 > m2_filter_2 > m1_subset_1 > v9_lattices > v8_lattices > v7_lattices > v6_lattices > v5_lattices > v4_lattices > v3_struct_0 > v2_funct_1 > v1_xboole_0 > v1_relat_1 > v1_realset1 > v1_funct_1 > v1_finset_1 > v10_lattices > l3_lattices > l2_lattices > l1_struct_0 > l1_lattices > k2_binop_1 > k4_lattices > k2_lattices > k1_binop_1 > k4_tarski > k2_zfmisc_1 > k2_tarski > k1_funct_1 > k18_filter_2 > a_2_0_filter_2 > #nlpp > u1_struct_0 > u1_lattices > k1_zfmisc_1 > k1_tarski > k1_xboole_0 > #skF_13 > #skF_9 > #skF_25 > #skF_21 > #skF_20 > #skF_18 > #skF_26 > #skF_19 > #skF_7 > #skF_16 > #skF_15 > #skF_12 > #skF_14 > #skF_5 > #skF_10 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_4 > #skF_17 > #skF_11 > #skF_22 > #skF_24 > #skF_23 > #skF_27
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(l3_lattices,type,
l3_lattices: $i > $o ).
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff(k2_lattices,type,
k2_lattices: ( $i * $i * $i ) > $i ).
tff(m2_relset_1,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff(l2_lattices,type,
l2_lattices: $i > $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(v1_funct_1,type,
v1_funct_1: $i > $o ).
tff(v1_realset1,type,
v1_realset1: $i > $o ).
tff(v2_funct_1,type,
v2_funct_1: $i > $o ).
tff(r3_lattices,type,
r3_lattices: ( $i * $i * $i ) > $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(r2_hidden,type,
r2_hidden: ( $i * $i ) > $o ).
tff('#skF_26',type,
'#skF_26': ( $i * $i ) > $i ).
tff(k4_lattices,type,
k4_lattices: ( $i * $i * $i ) > $i ).
tff(k1_tarski,type,
k1_tarski: $i > $i ).
tff(k4_tarski,type,
k4_tarski: ( $i * $i ) > $i ).
tff(v1_partfun1,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(k1_xboole_0,type,
k1_xboole_0: $i ).
tff(m2_lattice4,type,
m2_lattice4: ( $i * $i ) > $o ).
tff(m2_filter_2,type,
m2_filter_2: ( $i * $i ) > $o ).
tff(l1_lattices,type,
l1_lattices: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(r1_lattices,type,
r1_lattices: ( $i * $i * $i ) > $o ).
tff(r1_tarski,type,
r1_tarski: ( $i * $i ) > $o ).
tff(m1_relset_1,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(k2_tarski,type,
k2_tarski: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(v1_funct_2,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
tff(v4_lattices,type,
v4_lattices: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff(a_2_0_filter_2,type,
a_2_0_filter_2: ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(v6_lattices,type,
v6_lattices: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(v9_lattices,type,
v9_lattices: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(u1_lattices,type,
u1_lattices: $i > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(v5_lattices,type,
v5_lattices: $i > $o ).
tff(v10_lattices,type,
v10_lattices: $i > $o ).
tff(k2_binop_1,type,
k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(k1_binop_1,type,
k1_binop_1: ( $i * $i * $i ) > $i ).
tff(k1_zfmisc_1,type,
k1_zfmisc_1: $i > $i ).
tff(l1_struct_0,type,
l1_struct_0: $i > $o ).
tff(k1_funct_1,type,
k1_funct_1: ( $i * $i ) > $i ).
tff(v1_binop_1,type,
v1_binop_1: ( $i * $i ) > $o ).
tff(v2_binop_1,type,
v2_binop_1: ( $i * $i ) > $o ).
tff(v1_relat_1,type,
v1_relat_1: $i > $o ).
tff(k2_zfmisc_1,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(v8_lattices,type,
v8_lattices: $i > $o ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(u1_struct_0,type,
u1_struct_0: $i > $i ).
tff(v1_xboole_0,type,
v1_xboole_0: $i > $o ).
tff(v1_finset_1,type,
v1_finset_1: $i > $o ).
tff(k18_filter_2,type,
k18_filter_2: ( $i * $i ) > $i ).
tff(v3_struct_0,type,
v3_struct_0: $i > $o ).
tff(m1_subset_1,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(v7_lattices,type,
v7_lattices: $i > $o ).
tff(f_49,negated_conjecture,
~ ! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(B,k18_filter_2(A,B))
& r2_hidden(k4_lattices(A,B,C),k18_filter_2(A,B))
& r2_hidden(k4_lattices(A,C,B),k18_filter_2(A,B)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_2) ).
tff(f_80,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
tff(f_551,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r3_lattices(A,B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
tff(f_241,axiom,
! [A] :
( l3_lattices(A)
=> ( l1_lattices(A)
& l2_lattices(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
tff(f_509,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l1_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( k4_lattices(A,B,C) = k2_lattices(A,B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
tff(f_173,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k18_filter_2(A,B) = a_2_0_filter_2(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
tff(f_139,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l1_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( k4_lattices(A,B,C) = k4_lattices(A,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
tff(f_227,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l1_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).
tff(f_403,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_filter_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& ( A = D )
& r3_lattices(B,D,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_2) ).
tff(f_572,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& v8_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_lattices(A,k4_lattices(A,B,C),B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).
tff(f_532,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r3_lattices(A,B,C)
<=> r1_lattices(A,B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
tff(c_4,plain,
m1_subset_1('#skF_3',u1_struct_0('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_12,plain,
~ v3_struct_0('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_8,plain,
l3_lattices('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_10,plain,
v10_lattices('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_24,plain,
! [A_8] :
( v6_lattices(A_8)
| ~ v10_lattices(A_8)
| v3_struct_0(A_8)
| ~ l3_lattices(A_8) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_11819,plain,
! [A_1130,B_1131,C_1132] :
( r3_lattices(A_1130,B_1131,B_1131)
| ~ m1_subset_1(C_1132,u1_struct_0(A_1130))
| ~ m1_subset_1(B_1131,u1_struct_0(A_1130))
| ~ l3_lattices(A_1130)
| ~ v9_lattices(A_1130)
| ~ v8_lattices(A_1130)
| ~ v6_lattices(A_1130)
| v3_struct_0(A_1130) ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_11878,plain,
! [B_1131] :
( r3_lattices('#skF_1',B_1131,B_1131)
| ~ m1_subset_1(B_1131,u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_4,c_11819]) ).
tff(c_11903,plain,
! [B_1131] :
( r3_lattices('#skF_1',B_1131,B_1131)
| ~ m1_subset_1(B_1131,u1_struct_0('#skF_1'))
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_11878]) ).
tff(c_11904,plain,
! [B_1131] :
( r3_lattices('#skF_1',B_1131,B_1131)
| ~ m1_subset_1(B_1131,u1_struct_0('#skF_1'))
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| ~ v6_lattices('#skF_1') ),
inference(negUnitSimplification,[status(thm)],[c_12,c_11903]) ).
tff(c_12014,plain,
~ v6_lattices('#skF_1'),
inference(splitLeft,[status(thm)],[c_11904]) ).
tff(c_12017,plain,
( ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1')
| ~ l3_lattices('#skF_1') ),
inference(resolution,[status(thm)],[c_24,c_12014]) ).
tff(c_12020,plain,
v3_struct_0('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10,c_12017]) ).
tff(c_12022,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_12020]) ).
tff(c_12024,plain,
v6_lattices('#skF_1'),
inference(splitRight,[status(thm)],[c_11904]) ).
tff(c_8412,plain,
! [A_807] :
( l1_lattices(A_807)
| ~ l3_lattices(A_807) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_8420,plain,
l1_lattices('#skF_1'),
inference(resolution,[status(thm)],[c_8,c_8412]) ).
tff(c_6,plain,
m1_subset_1('#skF_2',u1_struct_0('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_12285,plain,
! [A_1142,B_1143,C_1144] :
( ( k4_lattices(A_1142,B_1143,C_1144) = k2_lattices(A_1142,B_1143,C_1144) )
| ~ m1_subset_1(C_1144,u1_struct_0(A_1142))
| ~ m1_subset_1(B_1143,u1_struct_0(A_1142))
| ~ l1_lattices(A_1142)
| ~ v6_lattices(A_1142)
| v3_struct_0(A_1142) ),
inference(cnfTransformation,[status(thm)],[f_509]) ).
tff(c_12350,plain,
! [B_1143] :
( ( k4_lattices('#skF_1',B_1143,'#skF_2') = k2_lattices('#skF_1',B_1143,'#skF_2') )
| ~ m1_subset_1(B_1143,u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_12285]) ).
tff(c_12378,plain,
! [B_1143] :
( ( k4_lattices('#skF_1',B_1143,'#skF_2') = k2_lattices('#skF_1',B_1143,'#skF_2') )
| ~ m1_subset_1(B_1143,u1_struct_0('#skF_1'))
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_12024,c_8420,c_12350]) ).
tff(c_12655,plain,
! [B_1149] :
( ( k4_lattices('#skF_1',B_1149,'#skF_2') = k2_lattices('#skF_1',B_1149,'#skF_2') )
| ~ m1_subset_1(B_1149,u1_struct_0('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_12378]) ).
tff(c_12793,plain,
k4_lattices('#skF_1','#skF_3','#skF_2') = k2_lattices('#skF_1','#skF_3','#skF_2'),
inference(resolution,[status(thm)],[c_4,c_12655]) ).
tff(c_10948,plain,
! [A_1090,B_1091] :
( ( k18_filter_2(A_1090,B_1091) = a_2_0_filter_2(A_1090,B_1091) )
| ~ m1_subset_1(B_1091,u1_struct_0(A_1090))
| ~ l3_lattices(A_1090)
| ~ v10_lattices(A_1090)
| v3_struct_0(A_1090) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_11014,plain,
( ( k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2') )
| ~ l3_lattices('#skF_1')
| ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_10948]) ).
tff(c_11036,plain,
( ( k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2') )
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_11014]) ).
tff(c_11037,plain,
k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_12,c_11036]) ).
tff(c_4444,plain,
! [A_486] :
( l1_lattices(A_486)
| ~ l3_lattices(A_486) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_4452,plain,
l1_lattices('#skF_1'),
inference(resolution,[status(thm)],[c_8,c_4444]) ).
tff(c_6878,plain,
! [A_767,C_768,B_769] :
( ( k4_lattices(A_767,C_768,B_769) = k4_lattices(A_767,B_769,C_768) )
| ~ m1_subset_1(C_768,u1_struct_0(A_767))
| ~ m1_subset_1(B_769,u1_struct_0(A_767))
| ~ l1_lattices(A_767)
| ~ v6_lattices(A_767)
| v3_struct_0(A_767) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_6916,plain,
! [B_769] :
( ( k4_lattices('#skF_1',B_769,'#skF_3') = k4_lattices('#skF_1','#skF_3',B_769) )
| ~ m1_subset_1(B_769,u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_4,c_6878]) ).
tff(c_6934,plain,
! [B_769] :
( ( k4_lattices('#skF_1',B_769,'#skF_3') = k4_lattices('#skF_1','#skF_3',B_769) )
| ~ m1_subset_1(B_769,u1_struct_0('#skF_1'))
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_4452,c_6916]) ).
tff(c_6935,plain,
! [B_769] :
( ( k4_lattices('#skF_1',B_769,'#skF_3') = k4_lattices('#skF_1','#skF_3',B_769) )
| ~ m1_subset_1(B_769,u1_struct_0('#skF_1'))
| ~ v6_lattices('#skF_1') ),
inference(negUnitSimplification,[status(thm)],[c_12,c_6934]) ).
tff(c_7023,plain,
~ v6_lattices('#skF_1'),
inference(splitLeft,[status(thm)],[c_6935]) ).
tff(c_7026,plain,
( ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1')
| ~ l3_lattices('#skF_1') ),
inference(resolution,[status(thm)],[c_24,c_7023]) ).
tff(c_7029,plain,
v3_struct_0('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10,c_7026]) ).
tff(c_7031,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_7029]) ).
tff(c_7033,plain,
v6_lattices('#skF_1'),
inference(splitRight,[status(thm)],[c_6935]) ).
tff(c_7158,plain,
! [A_777,B_778,C_779] :
( ( k4_lattices(A_777,B_778,C_779) = k2_lattices(A_777,B_778,C_779) )
| ~ m1_subset_1(C_779,u1_struct_0(A_777))
| ~ m1_subset_1(B_778,u1_struct_0(A_777))
| ~ l1_lattices(A_777)
| ~ v6_lattices(A_777)
| v3_struct_0(A_777) ),
inference(cnfTransformation,[status(thm)],[f_509]) ).
tff(c_7206,plain,
! [B_778] :
( ( k4_lattices('#skF_1',B_778,'#skF_2') = k2_lattices('#skF_1',B_778,'#skF_2') )
| ~ m1_subset_1(B_778,u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_7158]) ).
tff(c_7232,plain,
! [B_778] :
( ( k4_lattices('#skF_1',B_778,'#skF_2') = k2_lattices('#skF_1',B_778,'#skF_2') )
| ~ m1_subset_1(B_778,u1_struct_0('#skF_1'))
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_7033,c_4452,c_7206]) ).
tff(c_7513,plain,
! [B_784] :
( ( k4_lattices('#skF_1',B_784,'#skF_2') = k2_lattices('#skF_1',B_784,'#skF_2') )
| ~ m1_subset_1(B_784,u1_struct_0('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_7232]) ).
tff(c_7612,plain,
k4_lattices('#skF_1','#skF_3','#skF_2') = k2_lattices('#skF_1','#skF_3','#skF_2'),
inference(resolution,[status(thm)],[c_4,c_7513]) ).
tff(c_78,plain,
! [A_48,B_49,C_50] :
( m1_subset_1(k4_lattices(A_48,B_49,C_50),u1_struct_0(A_48))
| ~ m1_subset_1(C_50,u1_struct_0(A_48))
| ~ m1_subset_1(B_49,u1_struct_0(A_48))
| ~ l1_lattices(A_48)
| ~ v6_lattices(A_48)
| v3_struct_0(A_48) ),
inference(cnfTransformation,[status(thm)],[f_227]) ).
tff(c_7618,plain,
( m1_subset_1(k2_lattices('#skF_1','#skF_3','#skF_2'),u1_struct_0('#skF_1'))
| ~ m1_subset_1('#skF_2',u1_struct_0('#skF_1'))
| ~ m1_subset_1('#skF_3',u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_7612,c_78]) ).
tff(c_7622,plain,
( m1_subset_1(k2_lattices('#skF_1','#skF_3','#skF_2'),u1_struct_0('#skF_1'))
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_7033,c_4452,c_4,c_6,c_7618]) ).
tff(c_7623,plain,
m1_subset_1(k2_lattices('#skF_1','#skF_3','#skF_2'),u1_struct_0('#skF_1')),
inference(negUnitSimplification,[status(thm)],[c_12,c_7622]) ).
tff(c_7745,plain,
! [D_785,B_786,C_787] :
( r2_hidden(D_785,a_2_0_filter_2(B_786,C_787))
| ~ r3_lattices(B_786,D_785,C_787)
| ~ m1_subset_1(D_785,u1_struct_0(B_786))
| ~ m1_subset_1(C_787,u1_struct_0(B_786))
| ~ l3_lattices(B_786)
| ~ v10_lattices(B_786)
| v3_struct_0(B_786) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_7204,plain,
! [B_778] :
( ( k4_lattices('#skF_1',B_778,'#skF_3') = k2_lattices('#skF_1',B_778,'#skF_3') )
| ~ m1_subset_1(B_778,u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_4,c_7158]) ).
tff(c_7228,plain,
! [B_778] :
( ( k4_lattices('#skF_1',B_778,'#skF_3') = k2_lattices('#skF_1',B_778,'#skF_3') )
| ~ m1_subset_1(B_778,u1_struct_0('#skF_1'))
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_7033,c_4452,c_7204]) ).
tff(c_7234,plain,
! [B_780] :
( ( k4_lattices('#skF_1',B_780,'#skF_3') = k2_lattices('#skF_1',B_780,'#skF_3') )
| ~ m1_subset_1(B_780,u1_struct_0('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_7228]) ).
tff(c_7330,plain,
k4_lattices('#skF_1','#skF_2','#skF_3') = k2_lattices('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_6,c_7234]) ).
tff(c_7034,plain,
! [B_776] :
( ( k4_lattices('#skF_1',B_776,'#skF_3') = k4_lattices('#skF_1','#skF_3',B_776) )
| ~ m1_subset_1(B_776,u1_struct_0('#skF_1')) ),
inference(splitRight,[status(thm)],[c_6935]) ).
tff(c_7127,plain,
k4_lattices('#skF_1','#skF_2','#skF_3') = k4_lattices('#skF_1','#skF_3','#skF_2'),
inference(resolution,[status(thm)],[c_6,c_7034]) ).
tff(c_7371,plain,
k4_lattices('#skF_1','#skF_3','#skF_2') = k2_lattices('#skF_1','#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_7330,c_7127]) ).
tff(c_7614,plain,
k2_lattices('#skF_1','#skF_2','#skF_3') = k2_lattices('#skF_1','#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_7612,c_7371]) ).
tff(c_5853,plain,
! [A_701,B_702] :
( ( k18_filter_2(A_701,B_702) = a_2_0_filter_2(A_701,B_702) )
| ~ m1_subset_1(B_702,u1_struct_0(A_701))
| ~ l3_lattices(A_701)
| ~ v10_lattices(A_701)
| v3_struct_0(A_701) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_5875,plain,
( ( k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2') )
| ~ l3_lattices('#skF_1')
| ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_5853]) ).
tff(c_5886,plain,
( ( k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2') )
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_5875]) ).
tff(c_5887,plain,
k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_12,c_5886]) ).
tff(c_18,plain,
! [A_8] :
( v9_lattices(A_8)
| ~ v10_lattices(A_8)
| v3_struct_0(A_8)
| ~ l3_lattices(A_8) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_20,plain,
! [A_8] :
( v8_lattices(A_8)
| ~ v10_lattices(A_8)
| v3_struct_0(A_8)
| ~ l3_lattices(A_8) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_366,plain,
! [A_163] :
( l1_lattices(A_163)
| ~ l3_lattices(A_163) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_374,plain,
l1_lattices('#skF_1'),
inference(resolution,[status(thm)],[c_8,c_366]) ).
tff(c_2783,plain,
! [A_440,B_441,C_442] :
( ( k4_lattices(A_440,B_441,C_442) = k2_lattices(A_440,B_441,C_442) )
| ~ m1_subset_1(C_442,u1_struct_0(A_440))
| ~ m1_subset_1(B_441,u1_struct_0(A_440))
| ~ l1_lattices(A_440)
| ~ v6_lattices(A_440)
| v3_struct_0(A_440) ),
inference(cnfTransformation,[status(thm)],[f_509]) ).
tff(c_2827,plain,
! [B_441] :
( ( k4_lattices('#skF_1',B_441,'#skF_2') = k2_lattices('#skF_1',B_441,'#skF_2') )
| ~ m1_subset_1(B_441,u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_2783]) ).
tff(c_2848,plain,
! [B_441] :
( ( k4_lattices('#skF_1',B_441,'#skF_2') = k2_lattices('#skF_1',B_441,'#skF_2') )
| ~ m1_subset_1(B_441,u1_struct_0('#skF_1'))
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_374,c_2827]) ).
tff(c_2849,plain,
! [B_441] :
( ( k4_lattices('#skF_1',B_441,'#skF_2') = k2_lattices('#skF_1',B_441,'#skF_2') )
| ~ m1_subset_1(B_441,u1_struct_0('#skF_1'))
| ~ v6_lattices('#skF_1') ),
inference(negUnitSimplification,[status(thm)],[c_12,c_2848]) ).
tff(c_2950,plain,
~ v6_lattices('#skF_1'),
inference(splitLeft,[status(thm)],[c_2849]) ).
tff(c_2953,plain,
( ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1')
| ~ l3_lattices('#skF_1') ),
inference(resolution,[status(thm)],[c_24,c_2950]) ).
tff(c_2956,plain,
v3_struct_0('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10,c_2953]) ).
tff(c_2958,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_2956]) ).
tff(c_2960,plain,
v6_lattices('#skF_1'),
inference(splitRight,[status(thm)],[c_2849]) ).
tff(c_3781,plain,
! [A_462,B_463,C_464] :
( r3_lattices(A_462,B_463,B_463)
| ~ m1_subset_1(C_464,u1_struct_0(A_462))
| ~ m1_subset_1(B_463,u1_struct_0(A_462))
| ~ l3_lattices(A_462)
| ~ v9_lattices(A_462)
| ~ v8_lattices(A_462)
| ~ v6_lattices(A_462)
| v3_struct_0(A_462) ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_3839,plain,
! [B_463] :
( r3_lattices('#skF_1',B_463,B_463)
| ~ m1_subset_1(B_463,u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_4,c_3781]) ).
tff(c_3874,plain,
! [B_463] :
( r3_lattices('#skF_1',B_463,B_463)
| ~ m1_subset_1(B_463,u1_struct_0('#skF_1'))
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_2960,c_8,c_3839]) ).
tff(c_3875,plain,
! [B_463] :
( r3_lattices('#skF_1',B_463,B_463)
| ~ m1_subset_1(B_463,u1_struct_0('#skF_1'))
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1') ),
inference(negUnitSimplification,[status(thm)],[c_12,c_3874]) ).
tff(c_4002,plain,
~ v8_lattices('#skF_1'),
inference(splitLeft,[status(thm)],[c_3875]) ).
tff(c_4005,plain,
( ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1')
| ~ l3_lattices('#skF_1') ),
inference(resolution,[status(thm)],[c_20,c_4002]) ).
tff(c_4008,plain,
v3_struct_0('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10,c_4005]) ).
tff(c_4010,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_4008]) ).
tff(c_4011,plain,
! [B_463] :
( ~ v9_lattices('#skF_1')
| r3_lattices('#skF_1',B_463,B_463)
| ~ m1_subset_1(B_463,u1_struct_0('#skF_1')) ),
inference(splitRight,[status(thm)],[c_3875]) ).
tff(c_4019,plain,
~ v9_lattices('#skF_1'),
inference(splitLeft,[status(thm)],[c_4011]) ).
tff(c_4077,plain,
( ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1')
| ~ l3_lattices('#skF_1') ),
inference(resolution,[status(thm)],[c_18,c_4019]) ).
tff(c_4080,plain,
v3_struct_0('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10,c_4077]) ).
tff(c_4082,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_4080]) ).
tff(c_4092,plain,
! [B_469] :
( r3_lattices('#skF_1',B_469,B_469)
| ~ m1_subset_1(B_469,u1_struct_0('#skF_1')) ),
inference(splitRight,[status(thm)],[c_4011]) ).
tff(c_4188,plain,
r3_lattices('#skF_1','#skF_2','#skF_2'),
inference(resolution,[status(thm)],[c_6,c_4092]) ).
tff(c_4362,plain,
! [D_476,B_477,C_478] :
( r2_hidden(D_476,a_2_0_filter_2(B_477,C_478))
| ~ r3_lattices(B_477,D_476,C_478)
| ~ m1_subset_1(D_476,u1_struct_0(B_477))
| ~ m1_subset_1(C_478,u1_struct_0(B_477))
| ~ l3_lattices(B_477)
| ~ v10_lattices(B_477)
| v3_struct_0(B_477) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_1959,plain,
! [A_386,B_387] :
( ( k18_filter_2(A_386,B_387) = a_2_0_filter_2(A_386,B_387) )
| ~ m1_subset_1(B_387,u1_struct_0(A_386))
| ~ l3_lattices(A_386)
| ~ v10_lattices(A_386)
| v3_struct_0(A_386) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_1993,plain,
( ( k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2') )
| ~ l3_lattices('#skF_1')
| ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_1959]) ).
tff(c_2007,plain,
( ( k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2') )
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_1993]) ).
tff(c_2008,plain,
k18_filter_2('#skF_1','#skF_2') = a_2_0_filter_2('#skF_1','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_12,c_2007]) ).
tff(c_2,plain,
( ~ r2_hidden(k4_lattices('#skF_1','#skF_3','#skF_2'),k18_filter_2('#skF_1','#skF_2'))
| ~ r2_hidden(k4_lattices('#skF_1','#skF_2','#skF_3'),k18_filter_2('#skF_1','#skF_2'))
| ~ r2_hidden('#skF_2',k18_filter_2('#skF_1','#skF_2')) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_334,plain,
~ r2_hidden('#skF_2',k18_filter_2('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_2]) ).
tff(c_2027,plain,
~ r2_hidden('#skF_2',a_2_0_filter_2('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_2008,c_334]) ).
tff(c_4378,plain,
( ~ r3_lattices('#skF_1','#skF_2','#skF_2')
| ~ m1_subset_1('#skF_2',u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_4362,c_2027]) ).
tff(c_4407,plain,
v3_struct_0('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_6,c_4188,c_4378]) ).
tff(c_4409,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_4407]) ).
tff(c_4410,plain,
( ~ r2_hidden(k4_lattices('#skF_1','#skF_2','#skF_3'),k18_filter_2('#skF_1','#skF_2'))
| ~ r2_hidden(k4_lattices('#skF_1','#skF_3','#skF_2'),k18_filter_2('#skF_1','#skF_2')) ),
inference(splitRight,[status(thm)],[c_2]) ).
tff(c_4442,plain,
~ r2_hidden(k4_lattices('#skF_1','#skF_3','#skF_2'),k18_filter_2('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_4410]) ).
tff(c_5913,plain,
~ r2_hidden(k4_lattices('#skF_1','#skF_3','#skF_2'),a_2_0_filter_2('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_5887,c_4442]) ).
tff(c_7413,plain,
~ r2_hidden(k2_lattices('#skF_1','#skF_2','#skF_3'),a_2_0_filter_2('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_7371,c_5913]) ).
tff(c_7716,plain,
~ r2_hidden(k2_lattices('#skF_1','#skF_3','#skF_2'),a_2_0_filter_2('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_7614,c_7413]) ).
tff(c_7748,plain,
( ~ r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2')
| ~ m1_subset_1(k2_lattices('#skF_1','#skF_3','#skF_2'),u1_struct_0('#skF_1'))
| ~ m1_subset_1('#skF_2',u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_7745,c_7716]) ).
tff(c_7786,plain,
( ~ r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_6,c_7623,c_7748]) ).
tff(c_7787,plain,
~ r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_12,c_7786]) ).
tff(c_7432,plain,
! [A_781,B_782,C_783] :
( r3_lattices(A_781,B_782,B_782)
| ~ m1_subset_1(C_783,u1_struct_0(A_781))
| ~ m1_subset_1(B_782,u1_struct_0(A_781))
| ~ l3_lattices(A_781)
| ~ v9_lattices(A_781)
| ~ v8_lattices(A_781)
| ~ v6_lattices(A_781)
| v3_struct_0(A_781) ),
inference(cnfTransformation,[status(thm)],[f_551]) ).
tff(c_7479,plain,
! [B_782] :
( r3_lattices('#skF_1',B_782,B_782)
| ~ m1_subset_1(B_782,u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_4,c_7432]) ).
tff(c_7507,plain,
! [B_782] :
( r3_lattices('#skF_1',B_782,B_782)
| ~ m1_subset_1(B_782,u1_struct_0('#skF_1'))
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_7033,c_8,c_7479]) ).
tff(c_7508,plain,
! [B_782] :
( r3_lattices('#skF_1',B_782,B_782)
| ~ m1_subset_1(B_782,u1_struct_0('#skF_1'))
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1') ),
inference(negUnitSimplification,[status(thm)],[c_12,c_7507]) ).
tff(c_7800,plain,
~ v8_lattices('#skF_1'),
inference(splitLeft,[status(thm)],[c_7508]) ).
tff(c_7803,plain,
( ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1')
| ~ l3_lattices('#skF_1') ),
inference(resolution,[status(thm)],[c_20,c_7800]) ).
tff(c_7806,plain,
v3_struct_0('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10,c_7803]) ).
tff(c_7808,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_7806]) ).
tff(c_7810,plain,
v8_lattices('#skF_1'),
inference(splitRight,[status(thm)],[c_7508]) ).
tff(c_7718,plain,
k4_lattices('#skF_1','#skF_2','#skF_3') = k2_lattices('#skF_1','#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_7614,c_7330]) ).
tff(c_7948,plain,
! [A_792,B_793,C_794] :
( r1_lattices(A_792,k4_lattices(A_792,B_793,C_794),B_793)
| ~ m1_subset_1(C_794,u1_struct_0(A_792))
| ~ m1_subset_1(B_793,u1_struct_0(A_792))
| ~ l3_lattices(A_792)
| ~ v8_lattices(A_792)
| ~ v6_lattices(A_792)
| v3_struct_0(A_792) ),
inference(cnfTransformation,[status(thm)],[f_572]) ).
tff(c_7951,plain,
( r1_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2')
| ~ m1_subset_1('#skF_3',u1_struct_0('#skF_1'))
| ~ m1_subset_1('#skF_2',u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_7718,c_7948]) ).
tff(c_7962,plain,
( r1_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_7033,c_7810,c_8,c_6,c_4,c_7951]) ).
tff(c_7963,plain,
r1_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_12,c_7962]) ).
tff(c_7809,plain,
! [B_782] :
( ~ v9_lattices('#skF_1')
| r3_lattices('#skF_1',B_782,B_782)
| ~ m1_subset_1(B_782,u1_struct_0('#skF_1')) ),
inference(splitRight,[status(thm)],[c_7508]) ).
tff(c_7817,plain,
~ v9_lattices('#skF_1'),
inference(splitLeft,[status(thm)],[c_7809]) ).
tff(c_7845,plain,
( ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1')
| ~ l3_lattices('#skF_1') ),
inference(resolution,[status(thm)],[c_18,c_7817]) ).
tff(c_7848,plain,
v3_struct_0('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_10,c_7845]) ).
tff(c_7850,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12,c_7848]) ).
tff(c_7852,plain,
v9_lattices('#skF_1'),
inference(splitRight,[status(thm)],[c_7809]) ).
tff(c_8112,plain,
! [A_801,B_802,C_803] :
( r3_lattices(A_801,B_802,C_803)
| ~ r1_lattices(A_801,B_802,C_803)
| ~ m1_subset_1(C_803,u1_struct_0(A_801))
| ~ m1_subset_1(B_802,u1_struct_0(A_801))
| ~ l3_lattices(A_801)
| ~ v9_lattices(A_801)
| ~ v8_lattices(A_801)
| ~ v6_lattices(A_801)
| v3_struct_0(A_801) ),
inference(cnfTransformation,[status(thm)],[f_532]) ).
tff(c_8166,plain,
! [B_802] :
( r3_lattices('#skF_1',B_802,'#skF_2')
| ~ r1_lattices('#skF_1',B_802,'#skF_2')
| ~ m1_subset_1(B_802,u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v9_lattices('#skF_1')
| ~ v8_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_8112]) ).
tff(c_8204,plain,
! [B_802] :
( r3_lattices('#skF_1',B_802,'#skF_2')
| ~ r1_lattices('#skF_1',B_802,'#skF_2')
| ~ m1_subset_1(B_802,u1_struct_0('#skF_1'))
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_7033,c_7810,c_7852,c_8,c_8166]) ).
tff(c_8321,plain,
! [B_805] :
( r3_lattices('#skF_1',B_805,'#skF_2')
| ~ r1_lattices('#skF_1',B_805,'#skF_2')
| ~ m1_subset_1(B_805,u1_struct_0('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_8204]) ).
tff(c_8330,plain,
( r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2')
| ~ r1_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2') ),
inference(resolution,[status(thm)],[c_7623,c_8321]) ).
tff(c_8406,plain,
r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_7963,c_8330]) ).
tff(c_8408,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7787,c_8406]) ).
tff(c_8410,plain,
r2_hidden(k4_lattices('#skF_1','#skF_3','#skF_2'),k18_filter_2('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_4410]) ).
tff(c_11067,plain,
r2_hidden(k4_lattices('#skF_1','#skF_3','#skF_2'),a_2_0_filter_2('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_11037,c_8410]) ).
tff(c_11237,plain,
! [A_1100,B_1101,C_1102] :
( ( '#skF_13'(A_1100,B_1101,C_1102) = A_1100 )
| ~ r2_hidden(A_1100,a_2_0_filter_2(B_1101,C_1102))
| ~ m1_subset_1(C_1102,u1_struct_0(B_1101))
| ~ l3_lattices(B_1101)
| ~ v10_lattices(B_1101)
| v3_struct_0(B_1101) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_11240,plain,
( ( '#skF_13'(k4_lattices('#skF_1','#skF_3','#skF_2'),'#skF_1','#skF_2') = k4_lattices('#skF_1','#skF_3','#skF_2') )
| ~ m1_subset_1('#skF_2',u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_11067,c_11237]) ).
tff(c_11282,plain,
( ( '#skF_13'(k4_lattices('#skF_1','#skF_3','#skF_2'),'#skF_1','#skF_2') = k4_lattices('#skF_1','#skF_3','#skF_2') )
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_6,c_11240]) ).
tff(c_11283,plain,
'#skF_13'(k4_lattices('#skF_1','#skF_3','#skF_2'),'#skF_1','#skF_2') = k4_lattices('#skF_1','#skF_3','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_12,c_11282]) ).
tff(c_11597,plain,
! [B_1122,A_1123,C_1124] :
( r3_lattices(B_1122,'#skF_13'(A_1123,B_1122,C_1124),C_1124)
| ~ r2_hidden(A_1123,a_2_0_filter_2(B_1122,C_1124))
| ~ m1_subset_1(C_1124,u1_struct_0(B_1122))
| ~ l3_lattices(B_1122)
| ~ v10_lattices(B_1122)
| v3_struct_0(B_1122) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_11600,plain,
( r3_lattices('#skF_1',k4_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2')
| ~ r2_hidden(k4_lattices('#skF_1','#skF_3','#skF_2'),a_2_0_filter_2('#skF_1','#skF_2'))
| ~ m1_subset_1('#skF_2',u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_11283,c_11597]) ).
tff(c_11605,plain,
( r3_lattices('#skF_1',k4_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_6,c_11067,c_11600]) ).
tff(c_11606,plain,
r3_lattices('#skF_1',k4_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_12,c_11605]) ).
tff(c_12797,plain,
r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_12793,c_11606]) ).
tff(c_12348,plain,
! [B_1143] :
( ( k4_lattices('#skF_1',B_1143,'#skF_3') = k2_lattices('#skF_1',B_1143,'#skF_3') )
| ~ m1_subset_1(B_1143,u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_4,c_12285]) ).
tff(c_12374,plain,
! [B_1143] :
( ( k4_lattices('#skF_1',B_1143,'#skF_3') = k2_lattices('#skF_1',B_1143,'#skF_3') )
| ~ m1_subset_1(B_1143,u1_struct_0('#skF_1'))
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_12024,c_8420,c_12348]) ).
tff(c_12380,plain,
! [B_1145] :
( ( k4_lattices('#skF_1',B_1145,'#skF_3') = k2_lattices('#skF_1',B_1145,'#skF_3') )
| ~ m1_subset_1(B_1145,u1_struct_0('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_12374]) ).
tff(c_12499,plain,
k4_lattices('#skF_1','#skF_2','#skF_3') = k2_lattices('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_6,c_12380]) ).
tff(c_12884,plain,
! [A_1150,C_1151,B_1152] :
( ( k4_lattices(A_1150,C_1151,B_1152) = k4_lattices(A_1150,B_1152,C_1151) )
| ~ m1_subset_1(C_1151,u1_struct_0(A_1150))
| ~ m1_subset_1(B_1152,u1_struct_0(A_1150))
| ~ l1_lattices(A_1150)
| ~ v6_lattices(A_1150)
| v3_struct_0(A_1150) ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_12957,plain,
! [B_1152] :
( ( k4_lattices('#skF_1',B_1152,'#skF_2') = k4_lattices('#skF_1','#skF_2',B_1152) )
| ~ m1_subset_1(B_1152,u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_6,c_12884]) ).
tff(c_12998,plain,
! [B_1152] :
( ( k4_lattices('#skF_1',B_1152,'#skF_2') = k4_lattices('#skF_1','#skF_2',B_1152) )
| ~ m1_subset_1(B_1152,u1_struct_0('#skF_1'))
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_12024,c_8420,c_12957]) ).
tff(c_13109,plain,
! [B_1157] :
( ( k4_lattices('#skF_1',B_1157,'#skF_2') = k4_lattices('#skF_1','#skF_2',B_1157) )
| ~ m1_subset_1(B_1157,u1_struct_0('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_12,c_12998]) ).
tff(c_13212,plain,
k4_lattices('#skF_1','#skF_2','#skF_3') = k4_lattices('#skF_1','#skF_3','#skF_2'),
inference(resolution,[status(thm)],[c_4,c_13109]) ).
tff(c_13252,plain,
k2_lattices('#skF_1','#skF_2','#skF_3') = k2_lattices('#skF_1','#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_12793,c_12499,c_13212]) ).
tff(c_12544,plain,
( m1_subset_1(k2_lattices('#skF_1','#skF_2','#skF_3'),u1_struct_0('#skF_1'))
| ~ m1_subset_1('#skF_3',u1_struct_0('#skF_1'))
| ~ m1_subset_1('#skF_2',u1_struct_0('#skF_1'))
| ~ l1_lattices('#skF_1')
| ~ v6_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_12499,c_78]) ).
tff(c_12548,plain,
( m1_subset_1(k2_lattices('#skF_1','#skF_2','#skF_3'),u1_struct_0('#skF_1'))
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_12024,c_8420,c_6,c_4,c_12544]) ).
tff(c_12549,plain,
m1_subset_1(k2_lattices('#skF_1','#skF_2','#skF_3'),u1_struct_0('#skF_1')),
inference(negUnitSimplification,[status(thm)],[c_12,c_12548]) ).
tff(c_13255,plain,
! [D_1158,B_1159,C_1160] :
( r2_hidden(D_1158,a_2_0_filter_2(B_1159,C_1160))
| ~ r3_lattices(B_1159,D_1158,C_1160)
| ~ m1_subset_1(D_1158,u1_struct_0(B_1159))
| ~ m1_subset_1(C_1160,u1_struct_0(B_1159))
| ~ l3_lattices(B_1159)
| ~ v10_lattices(B_1159)
| v3_struct_0(B_1159) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_8409,plain,
~ r2_hidden(k4_lattices('#skF_1','#skF_2','#skF_3'),k18_filter_2('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_4410]) ).
tff(c_11068,plain,
~ r2_hidden(k4_lattices('#skF_1','#skF_2','#skF_3'),a_2_0_filter_2('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_11037,c_8409]) ).
tff(c_12540,plain,
~ r2_hidden(k2_lattices('#skF_1','#skF_2','#skF_3'),a_2_0_filter_2('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_12499,c_11068]) ).
tff(c_13258,plain,
( ~ r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_2','#skF_3'),'#skF_2')
| ~ m1_subset_1(k2_lattices('#skF_1','#skF_2','#skF_3'),u1_struct_0('#skF_1'))
| ~ m1_subset_1('#skF_2',u1_struct_0('#skF_1'))
| ~ l3_lattices('#skF_1')
| ~ v10_lattices('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_13255,c_12540]) ).
tff(c_13296,plain,
( ~ r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_2','#skF_3'),'#skF_2')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_8,c_6,c_12549,c_13258]) ).
tff(c_13297,plain,
~ r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_2','#skF_3'),'#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_12,c_13296]) ).
tff(c_13310,plain,
~ r3_lattices('#skF_1',k2_lattices('#skF_1','#skF_3','#skF_2'),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_13252,c_13297]) ).
tff(c_13319,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12797,c_13310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LAT305+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.15 % 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 : n015.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 12:54:14 EDT 2023
% 0.14/0.36 % CPUTime :
% 13.30/4.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.30/4.46
% 13.30/4.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.30/4.50
% 13.30/4.50 Inference rules
% 13.30/4.50 ----------------------
% 13.30/4.50 #Ref : 0
% 13.30/4.50 #Sup : 2934
% 13.30/4.50 #Fact : 0
% 13.30/4.50 #Define : 0
% 13.30/4.50 #Split : 34
% 13.30/4.50 #Chain : 0
% 13.30/4.50 #Close : 0
% 13.30/4.50
% 13.30/4.50 Ordering : KBO
% 13.30/4.50
% 13.30/4.50 Simplification rules
% 13.30/4.50 ----------------------
% 13.30/4.50 #Subsume : 623
% 13.30/4.50 #Demod : 867
% 13.30/4.50 #Tautology : 435
% 13.30/4.50 #SimpNegUnit : 358
% 13.30/4.50 #BackRed : 99
% 13.30/4.50
% 13.30/4.50 #Partial instantiations: 0
% 13.30/4.50 #Strategies tried : 1
% 13.30/4.50
% 13.30/4.50 Timing (in seconds)
% 13.30/4.50 ----------------------
% 13.30/4.51 Preprocessing : 0.80
% 13.30/4.51 Parsing : 0.40
% 13.30/4.51 CNF conversion : 0.07
% 13.30/4.51 Main loop : 2.59
% 13.30/4.51 Inferencing : 0.82
% 13.30/4.51 Reduction : 0.91
% 13.30/4.51 Demodulation : 0.63
% 13.30/4.51 BG Simplification : 0.09
% 13.30/4.51 Subsumption : 0.56
% 13.30/4.51 Abstraction : 0.08
% 13.30/4.51 MUC search : 0.00
% 13.30/4.51 Cooper : 0.00
% 13.30/4.51 Total : 3.47
% 13.30/4.51 Index Insertion : 0.00
% 13.30/4.51 Index Deletion : 0.00
% 13.30/4.51 Index Matching : 0.00
% 13.30/4.51 BG Taut test : 0.00
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