%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT301+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:04:47 PM UTC 2026
% Result : Theorem 0.08s 0.47s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 353 ( 16 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 424 ( 142 ~; 137 |; 99 &)
% ( 4 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t25_filter_2,conjecture,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> r2_hidden(k5_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_filter_2) ).
fof(dt_m2_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( m2_lattice4(X2,X1)
& ~ v1_xboole_0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(redefinition_k15_filter_2,axiom,
! [X1,X2] :
( ( m2_filter_2(X2,X1)
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k15_filter_2(X1,X2) = k7_filter_2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
fof(d6_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).
fof(dt_k15_filter_2,axiom,
! [X1,X2] :
( ( m2_filter_2(X2,X1)
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_filter_2(k15_filter_2(X1,X2),k1_lattice2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_filter_2) ).
fof(fc6_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v10_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(t12_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( l3_lattices(X1)
& v14_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> r2_hidden(k6_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_filter_0) ).
fof(redefinition_m1_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l3_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(t78_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v13_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k5_lattices(X1) = k6_lattices(k1_lattice2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_lattice2) ).
fof(t63_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).
fof(fc1_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> r2_hidden(k5_lattices(X1),X2) ) ) ),
inference(assume_negation,[status(cth)],[t25_filter_2]) ).
fof(c_0_14,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( m2_lattice4(X2,X1)
& ~ v1_xboole_0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> r2_hidden(k5_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_lattice4]) ).
fof(c_0_17,plain,
! [X41,X42] :
( ( ~ l3_lattices(X41)
| ~ v10_lattices(X41)
| v3_struct_0(X41)
| ~ m2_filter_2(X42,X41)
| m2_lattice4(X42,X41) )
& ( ~ l3_lattices(X41)
| ~ v10_lattices(X41)
| v3_struct_0(X41)
| ~ m2_filter_2(X42,X41)
| ~ v1_xboole_0(X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
fof(c_0_18,negated_conjecture,
( ~ r2_hidden(k5_lattices(esk1_0),esk2_0)
& v13_lattices(esk1_0)
& m2_filter_2(esk2_0,esk1_0)
& l3_lattices(esk1_0)
& v10_lattices(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_19,plain,
! [X1,X2] :
( ( m2_filter_2(X2,X1)
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k15_filter_2(X1,X2) = k7_filter_2(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k15_filter_2]) ).
fof(c_0_20,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d6_filter_2]) ).
fof(c_0_21,plain,
! [X43,X44] :
( m1_subset_1(X44,k1_zfmisc_1(u1_struct_0(X43)))
| ~ m2_lattice4(X44,X43)
| ~ l3_lattices(X43)
| ~ v10_lattices(X43)
| v3_struct_0(X43) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_22,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m2_filter_2(X1,X2)
| v3_struct_0(X2)
| m2_lattice4(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X109,X110] :
( k15_filter_2(X109,X110) = k7_filter_2(X109,X110)
| ~ m2_filter_2(X110,X109)
| ~ l3_lattices(X109)
| ~ v10_lattices(X109)
| v3_struct_0(X109) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_28,plain,
! [X22,X23] :
( k7_filter_2(X22,X23) = X23
| ~ m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))
| ~ l3_lattices(X22)
| ~ v10_lattices(X22)
| v3_struct_0(X22) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_29,plain,
( ~ m2_lattice4(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
m2_lattice4(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
fof(c_0_31,plain,
! [X1,X2] :
( ( m2_filter_2(X2,X1)
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_filter_2(k15_filter_2(X1,X2),k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k15_filter_2]) ).
cnf(c_0_32,plain,
( ~ m2_filter_2(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k15_filter_2(X1,X2) = k7_filter_2(X1,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k7_filter_2(X1,X2) = X2
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24]),c_0_25])]),c_0_26]) ).
fof(c_0_35,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v10_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).
fof(c_0_36,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( l3_lattices(X1)
& v14_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> r2_hidden(k6_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t12_filter_0]) ).
fof(c_0_37,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_filter_2]) ).
fof(c_0_38,plain,
! [X27,X28] :
( m1_filter_2(k15_filter_2(X27,X28),k1_lattice2(X27))
| ~ m2_filter_2(X28,X27)
| ~ l3_lattices(X27)
| ~ v10_lattices(X27)
| v3_struct_0(X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_39,negated_conjecture,
k15_filter_2(esk1_0,esk2_0) = k7_filter_2(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_40,negated_conjecture,
k7_filter_2(esk1_0,esk2_0) = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_24]),c_0_25])]),c_0_26]) ).
fof(c_0_41,plain,
! [X29] :
( ( ~ l3_lattices(X29)
| l3_lattices(k1_lattice2(X29)) )
& ( ~ l3_lattices(X29)
| v3_lattices(k1_lattice2(X29)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])])]) ).
fof(c_0_42,plain,
! [X84] :
( ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| v10_lattices(k1_lattice2(X84)) )
& ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| v9_lattices(k1_lattice2(X84)) )
& ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| v8_lattices(k1_lattice2(X84)) )
& ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| v7_lattices(k1_lattice2(X84)) )
& ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| v6_lattices(k1_lattice2(X84)) )
& ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| v5_lattices(k1_lattice2(X84)) )
& ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| v4_lattices(k1_lattice2(X84)) )
& ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| v3_lattices(k1_lattice2(X84)) )
& ( ~ l3_lattices(X84)
| ~ v10_lattices(X84)
| v3_struct_0(X84)
| ~ v3_struct_0(k1_lattice2(X84)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).
fof(c_0_43,plain,
! [X1] :
( ( l3_lattices(X1)
& v13_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k5_lattices(X1) = k6_lattices(k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[t78_lattice2]) ).
fof(c_0_44,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t63_lattice2]) ).
fof(c_0_45,plain,
! [X117,X118] :
( r2_hidden(k6_lattices(X117),X118)
| ~ l3_lattices(X117)
| ~ v14_lattices(X117)
| ~ v10_lattices(X117)
| v3_struct_0(X117)
| ~ m1_filter_0(X118,X117)
| ~ l3_lattices(X117)
| ~ v10_lattices(X117)
| v3_struct_0(X117) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).
fof(c_0_46,plain,
! [X111,X112] :
( ( ~ l3_lattices(X111)
| ~ v10_lattices(X111)
| v3_struct_0(X111)
| m1_filter_2(X112,X111)
| ~ m1_filter_0(X112,X111) )
& ( ~ l3_lattices(X111)
| ~ v10_lattices(X111)
| v3_struct_0(X111)
| m1_filter_0(X112,X111)
| ~ m1_filter_2(X112,X111) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])]) ).
cnf(c_0_47,plain,
( ~ m2_filter_2(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_filter_2(k15_filter_2(X1,X2),k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,negated_conjecture,
k15_filter_2(esk1_0,esk2_0) = esk2_0,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
( ~ l3_lattices(X1)
| l3_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v10_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_51,plain,
! [X133] :
( k5_lattices(X133) = k6_lattices(k1_lattice2(X133))
| ~ l3_lattices(X133)
| ~ v13_lattices(X133)
| ~ v10_lattices(X133)
| v3_struct_0(X133) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
fof(c_0_52,plain,
! [X131] :
( ( ~ l3_lattices(X131)
| ~ v10_lattices(X131)
| v3_struct_0(X131)
| v13_lattices(X131)
| ~ v14_lattices(k1_lattice2(X131)) )
& ( ~ l3_lattices(X131)
| ~ v10_lattices(X131)
| v3_struct_0(X131)
| v14_lattices(k1_lattice2(X131))
| ~ v13_lattices(X131) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
fof(c_0_53,plain,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc1_lattice2]) ).
cnf(c_0_54,plain,
( ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_0(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r2_hidden(k6_lattices(X1),X2)
| v3_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m1_filter_2(X1,X2)
| v3_struct_0(X2)
| m1_filter_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,negated_conjecture,
m1_filter_2(esk2_0,k1_lattice2(esk1_0)),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_23]),c_0_24]),c_0_25])]),c_0_26]),c_0_48]) ).
cnf(c_0_57,negated_conjecture,
l3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_49,c_0_24]) ).
cnf(c_0_58,negated_conjecture,
v10_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_25]),c_0_24])]),c_0_26]) ).
cnf(c_0_59,plain,
( ~ l3_lattices(X1)
| ~ v13_lattices(X1)
| ~ v10_lattices(X1)
| k5_lattices(X1) = k6_lattices(k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,negated_conjecture,
v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_61,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| v3_struct_0(X1)
| v14_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_62,plain,
! [X72] :
( ( ~ l3_lattices(X72)
| v3_struct_0(X72)
| v3_lattices(k1_lattice2(X72)) )
& ( ~ l3_lattices(X72)
| v3_struct_0(X72)
| ~ v3_struct_0(k1_lattice2(X72)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
cnf(c_0_63,plain,
( ~ m1_filter_0(X2,X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r2_hidden(k6_lattices(X1),X2)
| v3_struct_0(X1) ),
inference(cn,[status(thm)],[c_0_54]) ).
cnf(c_0_64,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| m1_filter_0(esk2_0,k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_65,negated_conjecture,
k6_lattices(k1_lattice2(esk1_0)) = k5_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_66,negated_conjecture,
v14_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_60]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_67,negated_conjecture,
~ r2_hidden(k5_lattices(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_68,plain,
( ~ l3_lattices(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66]),c_0_57]),c_0_58])]),c_0_67]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_24])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT301+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 23:30:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.47 % Version: 3.5.1
% 0.08/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.47 % Starting sh5l with 300s (1) cores
% 0.08/0.47 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1489397 completed with status 0
% 0.08/0.47 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.08/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.47 % No SInE strategy applied
% 0.08/0.47 % Search class: FGHSM-FSMM31-MFFFFFNN
% 0.08/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.08/0.47 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.08/0.47 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.08/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.08/0.47 % G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 1489407 completed with status 0
% 0.08/0.47 % Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 0.08/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.47 % No SInE strategy applied
% 0.08/0.47 % Search class: FGHSM-FSMM31-MFFFFFNN
% 0.08/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.08/0.47 % Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 136s (1) cores
% 0.08/0.47 % Preprocessing time : 0.003 s
% 0.08/0.47
% 0.08/0.47 % Proof found!
% 0.08/0.47 % SZS status Theorem
% 0.08/0.47 % SZS output start CNFRefutation
% See solution above
% 0.08/0.47 % Parsed axioms : 88
% 0.08/0.47 % Removed by relevancy pruning/SinE : 0
% 0.08/0.47 % Initial clauses : 181
% 0.08/0.47 % Removed in clause preprocessing : 13
% 0.08/0.47 % Initial clauses in saturation : 168
% 0.08/0.47 % Processed clauses : 445
% 0.08/0.47 % ...of these trivial : 18
% 0.08/0.47 % ...subsumed : 45
% 0.08/0.47 % ...remaining for further processing : 382
% 0.08/0.47 % Other redundant clauses eliminated : 0
% 0.08/0.47 % Clauses deleted for lack of memory : 0
% 0.08/0.47 % Backward-subsumed : 1
% 0.08/0.47 % Backward-rewritten : 12
% 0.08/0.47 % Generated clauses : 691
% 0.08/0.47 % ...of the previous two non-redundant : 633
% 0.08/0.47 % ...aggressively subsumed : 0
% 0.08/0.47 % Contextual simplify-reflections : 1
% 0.08/0.47 % Paramodulations : 688
% 0.08/0.47 % Factorizations : 0
% 0.08/0.47 % NegExts : 0
% 0.08/0.47 % Equation resolutions : 3
% 0.08/0.47 % Disequality decompositions : 0
% 0.08/0.47 % Total rewrite steps : 408
% 0.08/0.47 % ...of those cached : 296
% 0.08/0.47 % Propositional unsat checks : 0
% 0.08/0.47 % Propositional check models : 0
% 0.08/0.47 % Propositional check unsatisfiable : 0
% 0.08/0.47 % Propositional clauses : 0
% 0.08/0.47 % Propositional clauses after purity: 0
% 0.08/0.47 % Propositional unsat core size : 0
% 0.08/0.47 % Propositional preprocessing time : 0.000
% 0.08/0.47 % Propositional encoding time : 0.000
% 0.08/0.47 % Propositional solver time : 0.000
% 0.08/0.47 % Success case prop preproc time : 0.000
% 0.08/0.47 % Success case prop encoding time : 0.000
% 0.08/0.47 % Success case prop solver time : 0.000
% 0.08/0.47 % Current number of processed clauses : 369
% 0.08/0.47 % Positive orientable unit clauses : 215
% 0.08/0.47 % Positive unorientable unit clauses: 0
% 0.08/0.47 % Negative unit clauses : 27
% 0.08/0.47 % Non-unit-clauses : 127
% 0.08/0.47 % Current number of unprocessed clauses: 341
% 0.08/0.47 % ...number of literals in the above : 765
% 0.08/0.47 % Current number of archived formulas : 0
% 0.08/0.47 % Current number of archived clauses : 13
% 0.08/0.47 % Clause-clause subsumption calls (NU) : 4603
% 0.08/0.47 % Rec. Clause-clause subsumption calls : 1209
% 0.08/0.47 % Non-unit clause-clause subsumptions : 23
% 0.08/0.47 % Unit Clause-clause subsumption calls : 5234
% 0.08/0.47 % Rewrite failures with RHS unbound : 0
% 0.08/0.47 % BW rewrite match attempts : 18
% 0.08/0.47 % BW rewrite match successes : 6
% 0.08/0.47 % Condensation attempts : 0
% 0.08/0.47 % Condensation successes : 0
% 0.08/0.47 % Termbank termtop insertions : 21122
% 0.08/0.47 % Search garbage collected termcells : 1751
% 0.08/0.47
% 0.08/0.47 % -------------------------------------------------
% 0.08/0.47 % User time : 0.034 s
% 0.08/0.47 % System time : 0.010 s
% 0.08/0.47 % Total time : 0.044 s
% 0.08/0.47 % Maximum resident set size: 3976 pages
% 0.08/0.47
% 0.08/0.47 % -------------------------------------------------
% 0.08/0.47 % User time : 0.164 s
% 0.08/0.47 % System time : 0.025 s
% 0.08/0.47 % Total time : 0.189 s
% 0.08/0.47 % Maximum resident set size: 4608 pages
% 0.08/0.47 % E exiting
%------------------------------------------------------------------------------