%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT302+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 83 ( 7 unt; 0 def)
% Number of atoms : 386 ( 8 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 476 ( 173 ~; 178 |; 86 &)
% ( 6 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( ( l3_lattices(X1)
& v14_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_filter_0(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_0) ).
fof(t26_filter_2,conjecture,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v13_lattices(X1)
=> m2_filter_2(k6_domain_1(u1_struct_0(X1),k5_lattices(X1)),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_2) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(redefinition_k6_domain_1,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,X1)
& ~ v1_xboole_0(X1) )
=> k6_domain_1(X1,X2) = k1_tarski(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
fof(t21_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_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/sandbox/benchmark/theBenchmark.p',fc6_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/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l3_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).
fof(dt_k6_lattices,axiom,
! [X1] :
( ( l2_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).
fof(dt_k5_lattices,axiom,
! [X1] :
( ( l1_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l2_lattices(X1)
& l1_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(c_0_15,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( ( l3_lattices(X1)
& v14_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_filter_0(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1) ) ),
inference(fof_simplification,[status(thm)],[t13_filter_0]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v13_lattices(X1)
=> m2_filter_2(k6_domain_1(u1_struct_0(X1),k5_lattices(X1)),X1) ) ),
inference(assume_negation,[status(cth)],[t26_filter_2]) ).
fof(c_0_17,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_18,plain,
! [X18] :
( m1_filter_0(k6_domain_1(u1_struct_0(X18),k6_lattices(X18)),X18)
| ~ l3_lattices(X18)
| ~ v14_lattices(X18)
| ~ v10_lattices(X18)
| v3_struct_0(X18)
| ~ l3_lattices(X18)
| ~ v10_lattices(X18)
| v3_struct_0(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v13_lattices(X1)
=> m2_filter_2(k6_domain_1(u1_struct_0(X1),k5_lattices(X1)),X1) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X1,X2] :
( ( m1_subset_1(X2,X1)
& ~ v1_xboole_0(X1) )
=> k6_domain_1(X1,X2) = k1_tarski(X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k6_domain_1]) ).
fof(c_0_21,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t21_filter_2]) ).
fof(c_0_22,plain,
! [X37,X38] :
( ( ~ l3_lattices(X37)
| ~ v10_lattices(X37)
| v3_struct_0(X37)
| m1_filter_2(X38,X37)
| ~ m1_filter_0(X38,X37) )
& ( ~ l3_lattices(X37)
| ~ v10_lattices(X37)
| v3_struct_0(X37)
| m1_filter_0(X38,X37)
| ~ m1_filter_2(X38,X37) ) ),
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_17])])])])]) ).
cnf(c_0_23,plain,
( ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_filter_0(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1)
| v3_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,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_25,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]) ).
fof(c_0_26,negated_conjecture,
( ~ m2_filter_2(k6_domain_1(u1_struct_0(esk1_0),k5_lattices(esk1_0)),esk1_0)
& v13_lattices(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_19])])])]) ).
fof(c_0_27,plain,
! [X16,X17] :
( k6_domain_1(X16,X17) = k1_tarski(X17)
| ~ m1_subset_1(X17,X16)
| v1_xboole_0(X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_28,plain,
! [X12,X13] :
( ( ~ l3_lattices(X12)
| ~ v10_lattices(X12)
| v3_struct_0(X12)
| m2_filter_2(X13,X12)
| ~ m1_filter_2(X13,k1_lattice2(X12)) )
& ( ~ l3_lattices(X12)
| ~ v10_lattices(X12)
| v3_struct_0(X12)
| m1_filter_2(X13,k1_lattice2(X12))
| ~ m2_filter_2(X13,X12) ) ),
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_21])])])])]) ).
cnf(c_0_29,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m1_filter_0(X1,X2)
| v3_struct_0(X2)
| m1_filter_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( ~ v14_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_filter_0(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1)
| v3_struct_0(X1) ),
inference(cn,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X42] :
( ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| v10_lattices(k1_lattice2(X42)) )
& ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| v9_lattices(k1_lattice2(X42)) )
& ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| v8_lattices(k1_lattice2(X42)) )
& ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| v7_lattices(k1_lattice2(X42)) )
& ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| v6_lattices(k1_lattice2(X42)) )
& ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| v5_lattices(k1_lattice2(X42)) )
& ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| v4_lattices(k1_lattice2(X42)) )
& ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| v3_lattices(k1_lattice2(X42)) )
& ( ~ l3_lattices(X42)
| ~ v10_lattices(X42)
| v3_struct_0(X42)
| ~ v3_struct_0(k1_lattice2(X42)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_32,plain,
! [X40] :
( ( ~ l3_lattices(X40)
| l3_lattices(k1_lattice2(X40)) )
& ( ~ l3_lattices(X40)
| v3_lattices(k1_lattice2(X40)) ) ),
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_33,plain,
! [X41] :
( ( ~ l3_lattices(X41)
| v3_struct_0(X41)
| v3_lattices(k1_lattice2(X41)) )
& ( ~ l3_lattices(X41)
| v3_struct_0(X41)
| ~ v3_struct_0(k1_lattice2(X41)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
fof(c_0_34,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_35,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]) ).
cnf(c_0_36,negated_conjecture,
~ m2_filter_2(k6_domain_1(u1_struct_0(esk1_0),k5_lattices(esk1_0)),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
( ~ m1_subset_1(X2,X1)
| k6_domain_1(X1,X2) = k1_tarski(X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m1_filter_2(X1,k1_lattice2(X2))
| v3_struct_0(X2)
| m2_filter_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| v3_struct_0(X1)
| m1_filter_2(k6_domain_1(u1_struct_0(X1),k6_lattices(X1)),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v10_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
( ~ l3_lattices(X1)
| l3_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( ~ l3_lattices(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_43,plain,
! [X20] :
( k5_lattices(X20) = k6_lattices(k1_lattice2(X20))
| ~ l3_lattices(X20)
| ~ v13_lattices(X20)
| ~ v10_lattices(X20)
| v3_struct_0(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
fof(c_0_44,plain,
! [X21] :
( ( ~ l3_lattices(X21)
| ~ v10_lattices(X21)
| v3_struct_0(X21)
| v13_lattices(X21)
| ~ v14_lattices(k1_lattice2(X21)) )
& ( ~ l3_lattices(X21)
| ~ v10_lattices(X21)
| v3_struct_0(X21)
| v14_lattices(k1_lattice2(X21))
| ~ v13_lattices(X21) ) ),
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_45,plain,
! [X1] :
( ( l2_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_lattices]) ).
cnf(c_0_46,negated_conjecture,
( ~ m2_filter_2(k1_tarski(k5_lattices(esk1_0)),esk1_0)
| ~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_47,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v14_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| m2_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(X1)),k6_lattices(k1_lattice2(X1))),X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]),c_0_42]) ).
cnf(c_0_48,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_43]) ).
cnf(c_0_49,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| v13_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_50,plain,
! [X58] :
( m1_subset_1(k6_lattices(X58),u1_struct_0(X58))
| ~ l2_lattices(X58)
| v3_struct_0(X58) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_51,negated_conjecture,
( ~ m2_filter_2(k6_domain_1(X1,k5_lattices(esk1_0)),esk1_0)
| ~ m1_subset_1(k5_lattices(esk1_0),X1)
| ~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0))
| v1_xboole_0(X1)
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_37]) ).
cnf(c_0_52,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v14_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| m2_filter_2(k6_domain_1(u1_struct_0(k1_lattice2(X1)),k5_lattices(X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_53,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_54,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_55,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_56,plain,
( ~ l2_lattices(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_57,plain,
! [X1] :
( ( l1_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).
fof(c_0_58,plain,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_59,negated_conjecture,
( ~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(k1_lattice2(esk1_0)))
| ~ v14_lattices(k1_lattice2(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(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_51,c_0_52]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_60,plain,
( ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v13_lattices(X1)
| ~ l2_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| m1_subset_1(k5_lattices(X1),u1_struct_0(k1_lattice2(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_48]),c_0_42]) ).
cnf(c_0_61,negated_conjecture,
v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_62,plain,
! [X19] :
( m1_subset_1(k5_lattices(X19),u1_struct_0(X19))
| ~ l1_lattices(X19)
| v3_struct_0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
fof(c_0_63,plain,
! [X89] :
( ~ v1_xboole_0(u1_struct_0(X89))
| ~ l1_struct_0(X89)
| v3_struct_0(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
fof(c_0_64,plain,
! [X59] :
( l1_struct_0(X59)
| ~ l1_lattices(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])])]) ).
cnf(c_0_65,negated_conjecture,
( ~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0))
| ~ v14_lattices(k1_lattice2(esk1_0))
| ~ l2_lattices(k1_lattice2(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| v1_xboole_0(u1_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(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_66,plain,
( ~ l1_lattices(X1)
| m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,plain,
( ~ l1_lattices(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_69,plain,
! [X60] :
( ( ~ l3_lattices(X60)
| l2_lattices(X60) )
& ( ~ l3_lattices(X60)
| l1_lattices(X60) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
cnf(c_0_70,negated_conjecture,
( ~ v14_lattices(k1_lattice2(esk1_0))
| ~ l1_lattices(esk1_0)
| ~ l2_lattices(k1_lattice2(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(k1_lattice2(esk1_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_55]) ).
cnf(c_0_71,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_44]) ).
cnf(c_0_72,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_lattices(X1)
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( ~ l3_lattices(X1)
| l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( ~ l1_lattices(esk1_0)
| ~ l2_lattices(k1_lattice2(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| v1_xboole_0(u1_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(spm,[status(thm)],[c_0_70,c_0_71]),c_0_61]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_75,plain,
( ~ l3_lattices(X1)
| l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,plain,
( ~ l3_lattices(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
( ~ l3_lattices(k1_lattice2(esk1_0))
| ~ l1_lattices(esk1_0)
| v1_xboole_0(u1_struct_0(esk1_0))
| v1_xboole_0(u1_struct_0(k1_lattice2(esk1_0))) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( ~ l3_lattices(k1_lattice2(esk1_0))
| ~ l1_lattices(esk1_0)
| v3_struct_0(k1_lattice2(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
( ~ l3_lattices(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_73]),c_0_53])]) ).
cnf(c_0_80,negated_conjecture,
( ~ l3_lattices(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_79]),c_0_53])]),c_0_55]) ).
cnf(c_0_81,negated_conjecture,
~ l3_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_80]),c_0_53])]),c_0_55]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_41]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT302+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Sep 20 23:30:50 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.13/0.46 % Version: 3.5.1
% 0.13/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.46 % Starting sh5l with 300s (1) cores
% 0.13/0.46 % new_bool_3 with pid 2601761 completed with status 0
% 0.13/0.46 % Result found by new_bool_3
% 0.13/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.46 % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.13/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.46 % SubtermCWHack with pid 2601768 completed with status 0
% 0.13/0.46 % Result found by SubtermCWHack
% 0.13/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.46 % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.13/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.46 % Preprocessing time : 0.003 s
% 0.13/0.46
% 0.13/0.46 % Proof found!
% 0.13/0.46 % SZS status Theorem
% 0.13/0.46 % SZS output start CNFRefutation
% See solution above
% 0.13/0.46 % Parsed axioms : 92
% 0.13/0.46 % Removed by relevancy pruning/SinE : 32
% 0.13/0.46 % Initial clauses : 117
% 0.13/0.46 % Removed in clause preprocessing : 2
% 0.13/0.46 % Initial clauses in saturation : 115
% 0.13/0.46 % Processed clauses : 217
% 0.13/0.46 % ...of these trivial : 0
% 0.13/0.46 % ...subsumed : 47
% 0.13/0.46 % ...remaining for further processing : 170
% 0.13/0.46 % Other redundant clauses eliminated : 0
% 0.13/0.46 % Clauses deleted for lack of memory : 0
% 0.13/0.46 % Backward-subsumed : 5
% 0.13/0.46 % Backward-rewritten : 3
% 0.13/0.46 % Generated clauses : 159
% 0.13/0.46 % ...of the previous two non-redundant : 151
% 0.13/0.46 % ...aggressively subsumed : 0
% 0.13/0.46 % Contextual simplify-reflections : 16
% 0.13/0.46 % Paramodulations : 159
% 0.13/0.46 % Factorizations : 0
% 0.13/0.46 % NegExts : 0
% 0.13/0.46 % Equation resolutions : 0
% 0.13/0.46 % Disequality decompositions : 0
% 0.13/0.46 % Total rewrite steps : 26
% 0.13/0.46 % ...of those cached : 11
% 0.13/0.46 % Propositional unsat checks : 0
% 0.13/0.46 % Propositional check models : 0
% 0.13/0.46 % Propositional check unsatisfiable : 0
% 0.13/0.46 % Propositional clauses : 0
% 0.13/0.46 % Propositional clauses after purity: 0
% 0.13/0.46 % Propositional unsat core size : 0
% 0.13/0.46 % Propositional preprocessing time : 0.000
% 0.13/0.46 % Propositional encoding time : 0.000
% 0.13/0.46 % Propositional solver time : 0.000
% 0.13/0.46 % Success case prop preproc time : 0.000
% 0.13/0.46 % Success case prop encoding time : 0.000
% 0.13/0.46 % Success case prop solver time : 0.000
% 0.13/0.46 % Current number of processed clauses : 162
% 0.13/0.46 % Positive orientable unit clauses : 34
% 0.13/0.46 % Positive unorientable unit clauses: 0
% 0.13/0.46 % Negative unit clauses : 10
% 0.13/0.46 % Non-unit-clauses : 118
% 0.13/0.46 % Current number of unprocessed clauses: 47
% 0.13/0.46 % ...number of literals in the above : 392
% 0.13/0.46 % Current number of archived formulas : 0
% 0.13/0.46 % Current number of archived clauses : 8
% 0.13/0.46 % Clause-clause subsumption calls (NU) : 7620
% 0.13/0.46 % Rec. Clause-clause subsumption calls : 1447
% 0.13/0.46 % Non-unit clause-clause subsumptions : 61
% 0.13/0.46 % Unit Clause-clause subsumption calls : 115
% 0.13/0.46 % Rewrite failures with RHS unbound : 0
% 0.13/0.46 % BW rewrite match attempts : 2
% 0.13/0.46 % BW rewrite match successes : 2
% 0.13/0.46 % Condensation attempts : 0
% 0.13/0.46 % Condensation successes : 0
% 0.13/0.46 % Termbank termtop insertions : 12287
% 0.13/0.46 % Search garbage collected termcells : 1373
% 0.13/0.46
% 0.13/0.46 % -------------------------------------------------
% 0.13/0.46 % User time : 0.020 s
% 0.13/0.46 % System time : 0.007 s
% 0.13/0.46 % Total time : 0.027 s
% 0.13/0.46 % Maximum resident set size: 3976 pages
% 0.13/0.46
% 0.13/0.46 % -------------------------------------------------
% 0.13/0.46 % User time : 0.024 s
% 0.13/0.46 % System time : 0.012 s
% 0.13/0.46 % Total time : 0.036 s
% 0.13/0.46 % Maximum resident set size: 4608 pages
% 0.13/0.46 % E exiting
%------------------------------------------------------------------------------