%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT333+3 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 May 5 04:38:10 PM UTC 2026
% Result : Theorem 19.60s 15.74s
% Output : CNFRefutation 19.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 182 ( 49 unt; 0 def)
% Number of atoms : 937 ( 92 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 1145 ( 390 ~; 441 |; 234 &)
% ( 8 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 179 ( 0 sgn 118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(u1_struct_0(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_2) ).
fof(t76_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> v13_lattices(k23_filter_2(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_filter_2) ).
fof(d16_nat_lat,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ( m2_nat_lat(X2,X1)
<=> ( r1_tarski(u1_struct_0(X2),u1_struct_0(X1))
& u2_lattices(X2) = k1_realset1(u2_lattices(X1),u1_struct_0(X2))
& u1_lattices(X2) = k1_realset1(u1_lattices(X1),u1_struct_0(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+297.ax',d16_nat_lat) ).
fof(dt_m2_nat_lat,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_nat_lat(X2,X1)
=> ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+297.ax',dt_m2_nat_lat) ).
fof(t75_nat_lat,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_nat_lat(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+297.ax',t75_nat_lat) ).
fof(dt_m2_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(t19_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_lattices(X1)
& l3_lattices(X1) )
=> k1_lattice2(k1_lattice2(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t19_lattice2) ).
fof(dt_k23_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k23_filter_2) ).
fof(t21_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',fc6_lattice2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',dt_k1_lattice2) ).
fof(t73_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( u1_struct_0(k23_filter_2(X1,X2)) = X2
& u2_lattices(k23_filter_2(X1,X2)) = k1_realset1(u2_lattices(X1),X2)
& u1_lattices(k23_filter_2(X1,X2)) = k1_realset1(u1_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_filter_2) ).
fof(fc5_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( ~ v3_struct_0(k23_filter_2(X1,X2))
& v3_lattices(k23_filter_2(X1,X2))
& v4_lattices(k23_filter_2(X1,X2))
& v5_lattices(k23_filter_2(X1,X2))
& v6_lattices(k23_filter_2(X1,X2))
& v7_lattices(k23_filter_2(X1,X2))
& v8_lattices(k23_filter_2(X1,X2))
& v9_lattices(k23_filter_2(X1,X2))
& v10_lattices(k23_filter_2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_filter_2) ).
fof(t7_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_lattice2(k1_lattice2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_filter_2) ).
fof(dt_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_2) ).
fof(fc1_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',fc1_lattice2) ).
fof(redefinition_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(t18_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1))
& u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
& u1_lattices(X1) = u2_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t18_lattice2) ).
fof(t70_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
=> k8_filter_0(X1,X2) = k23_filter_2(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_filter_2) ).
fof(abstractness_v3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(X1)
=> X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',abstractness_v3_lattices) ).
fof(t63_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( u1_struct_0(k8_filter_0(X1,X2)) = X2
& u2_lattices(k8_filter_0(X1,X2)) = k1_realset1(u2_lattices(X1),X2)
& u1_lattices(k8_filter_0(X1,X2)) = k1_realset1(u1_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t63_filter_0) ).
fof(fc2_filter_0,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,X1) )
=> ( ~ v3_struct_0(k8_filter_0(X1,X2))
& v3_lattices(k8_filter_0(X1,X2))
& v4_lattices(k8_filter_0(X1,X2))
& v5_lattices(k8_filter_0(X1,X2))
& v6_lattices(k8_filter_0(X1,X2))
& v7_lattices(k8_filter_0(X1,X2))
& v8_lattices(k8_filter_0(X1,X2))
& v9_lattices(k8_filter_0(X1,X2))
& v10_lattices(k8_filter_0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',fc2_filter_0) ).
fof(dt_k8_filter_0,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,X1) )
=> ( ~ v3_struct_0(k8_filter_0(X1,X2))
& v10_lattices(k8_filter_0(X1,X2))
& l3_lattices(k8_filter_0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',dt_k8_filter_0) ).
fof(t63_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t63_lattice2) ).
fof(t66_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( v14_lattices(X1)
=> v14_lattices(k8_filter_0(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t66_filter_0) ).
fof(d2_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> k1_lattice2(X1) = g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',d2_lattice2) ).
fof(c_0_26,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(u1_struct_0(X1),X1) ),
inference(fof_simplification,[status(thm)],[t28_filter_2]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> v13_lattices(k23_filter_2(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t76_filter_2])]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ( m2_nat_lat(X2,X1)
<=> ( r1_tarski(u1_struct_0(X2),u1_struct_0(X1))
& u2_lattices(X2) = k1_realset1(u2_lattices(X1),u1_struct_0(X2))
& u1_lattices(X2) = k1_realset1(u1_lattices(X1),u1_struct_0(X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[d16_nat_lat]) ).
fof(c_0_29,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_nat_lat(X2,X1)
=> ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_nat_lat]) ).
fof(c_0_30,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_nat_lat(X1,X1) ),
inference(fof_simplification,[status(thm)],[t75_nat_lat]) ).
fof(c_0_31,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).
fof(c_0_32,plain,
! [X537] :
( v3_struct_0(X537)
| ~ v10_lattices(X537)
| ~ l3_lattices(X537)
| m2_filter_2(u1_struct_0(X537),X537) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_33,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m2_filter_2(esk2_0,esk1_0)
& v13_lattices(esk1_0)
& ~ v13_lattices(k23_filter_2(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_34,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_lattices(X1)
& l3_lattices(X1) )
=> k1_lattice2(k1_lattice2(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[t19_lattice2]) ).
fof(c_0_35,plain,
! [X566,X567] :
( ( r1_tarski(u1_struct_0(X567),u1_struct_0(X566))
| ~ m2_nat_lat(X567,X566)
| v3_struct_0(X567)
| ~ v10_lattices(X567)
| ~ l3_lattices(X567)
| v3_struct_0(X566)
| ~ v10_lattices(X566)
| ~ l3_lattices(X566) )
& ( u2_lattices(X567) = k1_realset1(u2_lattices(X566),u1_struct_0(X567))
| ~ m2_nat_lat(X567,X566)
| v3_struct_0(X567)
| ~ v10_lattices(X567)
| ~ l3_lattices(X567)
| v3_struct_0(X566)
| ~ v10_lattices(X566)
| ~ l3_lattices(X566) )
& ( u1_lattices(X567) = k1_realset1(u1_lattices(X566),u1_struct_0(X567))
| ~ m2_nat_lat(X567,X566)
| v3_struct_0(X567)
| ~ v10_lattices(X567)
| ~ l3_lattices(X567)
| v3_struct_0(X566)
| ~ v10_lattices(X566)
| ~ l3_lattices(X566) )
& ( ~ r1_tarski(u1_struct_0(X567),u1_struct_0(X566))
| u2_lattices(X567) != k1_realset1(u2_lattices(X566),u1_struct_0(X567))
| u1_lattices(X567) != k1_realset1(u1_lattices(X566),u1_struct_0(X567))
| m2_nat_lat(X567,X566)
| v3_struct_0(X567)
| ~ v10_lattices(X567)
| ~ l3_lattices(X567)
| v3_struct_0(X566)
| ~ v10_lattices(X566)
| ~ l3_lattices(X566) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
fof(c_0_36,plain,
! [X569,X570] :
( ( ~ v3_struct_0(X570)
| ~ m2_nat_lat(X570,X569)
| v3_struct_0(X569)
| ~ v10_lattices(X569)
| ~ l3_lattices(X569) )
& ( v10_lattices(X570)
| ~ m2_nat_lat(X570,X569)
| v3_struct_0(X569)
| ~ v10_lattices(X569)
| ~ l3_lattices(X569) )
& ( l3_lattices(X570)
| ~ m2_nat_lat(X570,X569)
| v3_struct_0(X569)
| ~ v10_lattices(X569)
| ~ l3_lattices(X569) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
fof(c_0_37,plain,
! [X568] :
( v3_struct_0(X568)
| ~ v10_lattices(X568)
| ~ l3_lattices(X568)
| m2_nat_lat(X568,X568) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])]) ).
fof(c_0_38,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> m2_nat_lat(k23_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k23_filter_2]) ).
fof(c_0_39,plain,
! [X506,X507] :
( ( ~ v1_xboole_0(X507)
| ~ m2_filter_2(X507,X506)
| v3_struct_0(X506)
| ~ v10_lattices(X506)
| ~ l3_lattices(X506) )
& ( m2_lattice4(X507,X506)
| ~ m2_filter_2(X507,X506)
| v3_struct_0(X506)
| ~ v10_lattices(X506)
| ~ l3_lattices(X506) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_40,plain,
( v3_struct_0(X1)
| m2_filter_2(u1_struct_0(X1),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_44,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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_45,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).
fof(c_0_46,plain,
! [X751] :
( v3_struct_0(X751)
| ~ v3_lattices(X751)
| ~ l3_lattices(X751)
| k1_lattice2(k1_lattice2(X751)) = X751 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])]) ).
fof(c_0_47,plain,
! [X752] :
( ( v3_lattices(k1_lattice2(X752))
| ~ l3_lattices(X752) )
& ( l3_lattices(k1_lattice2(X752))
| ~ l3_lattices(X752) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_48,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( u1_struct_0(k23_filter_2(X1,X2)) = X2
& u2_lattices(k23_filter_2(X1,X2)) = k1_realset1(u2_lattices(X1),X2)
& u1_lattices(k23_filter_2(X1,X2)) = k1_realset1(u1_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t73_filter_2]) ).
cnf(c_0_49,plain,
( u1_lattices(X1) = k1_realset1(u1_lattices(X2),u1_struct_0(X1))
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ m2_nat_lat(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_50,plain,
( l3_lattices(X1)
| v3_struct_0(X2)
| ~ m2_nat_lat(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_51,plain,
( v10_lattices(X1)
| v3_struct_0(X2)
| ~ m2_nat_lat(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_52,plain,
( v3_struct_0(X2)
| ~ v3_struct_0(X1)
| ~ m2_nat_lat(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_53,plain,
( v3_struct_0(X1)
| m2_nat_lat(X1,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_54,plain,
( u2_lattices(X1) = k1_realset1(u2_lattices(X2),u1_struct_0(X1))
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ m2_nat_lat(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_55,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) )
=> ( ~ v3_struct_0(k23_filter_2(X1,X2))
& v3_lattices(k23_filter_2(X1,X2))
& v4_lattices(k23_filter_2(X1,X2))
& v5_lattices(k23_filter_2(X1,X2))
& v6_lattices(k23_filter_2(X1,X2))
& v7_lattices(k23_filter_2(X1,X2))
& v8_lattices(k23_filter_2(X1,X2))
& v9_lattices(k23_filter_2(X1,X2))
& v10_lattices(k23_filter_2(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc5_filter_2]) ).
fof(c_0_56,plain,
! [X479,X480] :
( v3_struct_0(X479)
| ~ v10_lattices(X479)
| ~ l3_lattices(X479)
| v1_xboole_0(X480)
| ~ m2_lattice4(X480,X479)
| m2_nat_lat(k23_filter_2(X479,X480),X479) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
cnf(c_0_57,plain,
( m2_lattice4(X1,X2)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_58,negated_conjecture,
m2_filter_2(u1_struct_0(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_59,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_60,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_lattice2(k1_lattice2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) ),
inference(fof_simplification,[status(thm)],[t7_filter_2]) ).
fof(c_0_61,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_filter_2]) ).
fof(c_0_62,plain,
! [X803,X804] :
( ( ~ m2_filter_2(X804,X803)
| m1_filter_2(X804,k1_lattice2(X803))
| v3_struct_0(X803)
| ~ v10_lattices(X803)
| ~ l3_lattices(X803) )
& ( ~ m1_filter_2(X804,k1_lattice2(X803))
| m2_filter_2(X804,X803)
| v3_struct_0(X803)
| ~ v10_lattices(X803)
| ~ l3_lattices(X803) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
fof(c_0_63,plain,
! [X738] :
( ( ~ v3_struct_0(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) )
& ( v3_lattices(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) )
& ( v4_lattices(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) )
& ( v5_lattices(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) )
& ( v6_lattices(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) )
& ( v7_lattices(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) )
& ( v8_lattices(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) )
& ( v9_lattices(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) )
& ( v10_lattices(k1_lattice2(X738))
| v3_struct_0(X738)
| ~ v10_lattices(X738)
| ~ l3_lattices(X738) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
fof(c_0_64,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc1_lattice2]) ).
cnf(c_0_65,plain,
( v3_struct_0(X1)
| k1_lattice2(k1_lattice2(X1)) = X1
| ~ v3_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_66,plain,
( v3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_67,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_68,plain,
! [X492,X493] :
( ( u1_struct_0(k23_filter_2(X492,X493)) = X493
| v1_xboole_0(X493)
| ~ m2_lattice4(X493,X492)
| v3_struct_0(X492)
| ~ v10_lattices(X492)
| ~ l3_lattices(X492) )
& ( u2_lattices(k23_filter_2(X492,X493)) = k1_realset1(u2_lattices(X492),X493)
| v1_xboole_0(X493)
| ~ m2_lattice4(X493,X492)
| v3_struct_0(X492)
| ~ v10_lattices(X492)
| ~ l3_lattices(X492) )
& ( u1_lattices(k23_filter_2(X492,X493)) = k1_realset1(u1_lattices(X492),X493)
| v1_xboole_0(X493)
| ~ m2_lattice4(X493,X492)
| v3_struct_0(X492)
| ~ v10_lattices(X492)
| ~ l3_lattices(X492) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
cnf(c_0_69,plain,
( k1_realset1(u1_lattices(X1),u1_struct_0(X2)) = u1_lattices(X2)
| v3_struct_0(X1)
| ~ m2_nat_lat(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]) ).
cnf(c_0_70,negated_conjecture,
m2_nat_lat(esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_71,plain,
( k1_realset1(u2_lattices(X1),u1_struct_0(X2)) = u2_lattices(X2)
| v3_struct_0(X1)
| ~ m2_nat_lat(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_54,c_0_50]),c_0_51]),c_0_52]) ).
fof(c_0_72,plain,
! [X488,X489] :
( ( ~ v3_struct_0(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) )
& ( v3_lattices(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) )
& ( v4_lattices(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) )
& ( v5_lattices(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) )
& ( v6_lattices(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) )
& ( v7_lattices(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) )
& ( v8_lattices(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) )
& ( v9_lattices(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) )
& ( v10_lattices(k23_filter_2(X488,X489))
| v3_struct_0(X488)
| ~ v10_lattices(X488)
| ~ l3_lattices(X488)
| v1_xboole_0(X489)
| ~ m2_lattice4(X489,X488) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
cnf(c_0_73,plain,
( v3_struct_0(X1)
| v1_xboole_0(X2)
| m2_nat_lat(k23_filter_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_74,negated_conjecture,
m2_lattice4(u1_struct_0(esk1_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_57,c_0_58]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_75,negated_conjecture,
~ v1_xboole_0(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_59,c_0_58]),c_0_41]),c_0_42])]),c_0_43]) ).
fof(c_0_76,plain,
! [X562] :
( v3_struct_0(X562)
| ~ v10_lattices(X562)
| ~ l3_lattices(X562)
| k1_lattice2(k1_lattice2(X562)) = g3_lattices(u1_struct_0(X562),u2_lattices(X562),u1_lattices(X562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])]) ).
fof(c_0_77,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_filter_2]) ).
fof(c_0_78,plain,
! [X794,X795] :
( ( ~ v1_xboole_0(X795)
| ~ m1_filter_2(X795,X794)
| v3_struct_0(X794)
| ~ v10_lattices(X794)
| ~ l3_lattices(X794) )
& ( m2_lattice4(X795,X794)
| ~ m1_filter_2(X795,X794)
| v3_struct_0(X794)
| ~ v10_lattices(X794)
| ~ l3_lattices(X794) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
cnf(c_0_79,plain,
( m1_filter_2(X1,k1_lattice2(X2))
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_80,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_81,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_82,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1))
& u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
& u1_lattices(X1) = u2_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t18_lattice2]) ).
fof(c_0_83,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
=> k8_filter_0(X1,X2) = k23_filter_2(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t70_filter_2]) ).
fof(c_0_84,plain,
! [X750] :
( ( ~ v3_struct_0(k1_lattice2(X750))
| v3_struct_0(X750)
| ~ l3_lattices(X750) )
& ( v3_lattices(k1_lattice2(X750))
| v3_struct_0(X750)
| ~ l3_lattices(X750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
cnf(c_0_85,plain,
( k1_lattice2(k1_lattice2(k1_lattice2(X1))) = k1_lattice2(X1)
| v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
fof(c_0_86,plain,
! [X746] :
( ~ l3_lattices(X746)
| ~ v3_lattices(X746)
| X746 = g3_lattices(u1_struct_0(X746),u2_lattices(X746),u1_lattices(X746)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])]) ).
cnf(c_0_87,plain,
( u1_lattices(k23_filter_2(X1,X2)) = k1_realset1(u1_lattices(X1),X2)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m2_lattice4(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_88,negated_conjecture,
k1_realset1(u1_lattices(esk1_0),u1_struct_0(esk1_0)) = u1_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_69,c_0_70]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_89,plain,
( u1_struct_0(k23_filter_2(X1,X2)) = X2
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m2_lattice4(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_90,plain,
( u2_lattices(k23_filter_2(X1,X2)) = k1_realset1(u2_lattices(X1),X2)
| v1_xboole_0(X2)
| v3_struct_0(X1)
| ~ m2_lattice4(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_91,negated_conjecture,
k1_realset1(u2_lattices(esk1_0),u1_struct_0(esk1_0)) = u2_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_71,c_0_70]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_92,plain,
( v3_lattices(k23_filter_2(X1,X2))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_93,negated_conjecture,
m2_nat_lat(k23_filter_2(esk1_0,u1_struct_0(esk1_0)),esk1_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_41]),c_0_42])]),c_0_43]),c_0_75]) ).
cnf(c_0_94,plain,
( v3_struct_0(X1)
| k1_lattice2(k1_lattice2(X1)) = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_95,plain,
! [X798,X799] :
( ( ~ m1_filter_2(X799,X798)
| m1_filter_0(X799,X798)
| v3_struct_0(X798)
| ~ v10_lattices(X798)
| ~ l3_lattices(X798) )
& ( ~ m1_filter_0(X799,X798)
| m1_filter_2(X799,X798)
| v3_struct_0(X798)
| ~ v10_lattices(X798)
| ~ l3_lattices(X798) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])])]) ).
cnf(c_0_96,plain,
( m2_lattice4(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_97,negated_conjecture,
m1_filter_2(esk2_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_79,c_0_80]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_98,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_81,c_0_41]),c_0_42])]),c_0_43]) ).
fof(c_0_99,plain,
! [X543] :
( ( u1_struct_0(X543) = u1_struct_0(k1_lattice2(X543))
| v3_struct_0(X543)
| ~ l3_lattices(X543) )
& ( u2_lattices(X543) = u1_lattices(k1_lattice2(X543))
| v3_struct_0(X543)
| ~ l3_lattices(X543) )
& ( u1_lattices(X543) = u2_lattices(k1_lattice2(X543))
| v3_struct_0(X543)
| ~ l3_lattices(X543) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])]) ).
cnf(c_0_100,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_57,c_0_80]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_101,negated_conjecture,
~ v1_xboole_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_59,c_0_80]),c_0_41]),c_0_42])]),c_0_43]) ).
fof(c_0_102,plain,
! [X490,X491] :
( v3_struct_0(X490)
| ~ v10_lattices(X490)
| ~ l3_lattices(X490)
| ~ m1_filter_2(X491,X490)
| k8_filter_0(X490,X491) = k23_filter_2(X490,X491) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])]) ).
cnf(c_0_103,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_104,negated_conjecture,
( k1_lattice2(k1_lattice2(k1_lattice2(esk1_0))) = k1_lattice2(esk1_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_85,c_0_42]) ).
cnf(c_0_105,plain,
( X1 = g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1))
| ~ l3_lattices(X1)
| ~ v3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_106,negated_conjecture,
u1_lattices(k23_filter_2(esk1_0,u1_struct_0(esk1_0))) = u1_lattices(esk1_0),
inference(sr,[status(thm)],[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_87,c_0_74]),c_0_88]),c_0_41]),c_0_42])]),c_0_43]),c_0_75]) ).
cnf(c_0_107,negated_conjecture,
u1_struct_0(k23_filter_2(esk1_0,u1_struct_0(esk1_0))) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_74]),c_0_41]),c_0_42])]),c_0_43]),c_0_75]) ).
cnf(c_0_108,negated_conjecture,
u2_lattices(k23_filter_2(esk1_0,u1_struct_0(esk1_0))) = u2_lattices(esk1_0),
inference(sr,[status(thm)],[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_90,c_0_74]),c_0_91]),c_0_41]),c_0_42])]),c_0_43]),c_0_75]) ).
cnf(c_0_109,negated_conjecture,
v3_lattices(k23_filter_2(esk1_0,u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_74]),c_0_41]),c_0_42])]),c_0_43]),c_0_75]) ).
cnf(c_0_110,negated_conjecture,
l3_lattices(k23_filter_2(esk1_0,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_50,c_0_93]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_111,negated_conjecture,
g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) = k1_lattice2(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_41]),c_0_42])]),c_0_43]) ).
fof(c_0_112,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( u1_struct_0(k8_filter_0(X1,X2)) = X2
& u2_lattices(k8_filter_0(X1,X2)) = k1_realset1(u2_lattices(X1),X2)
& u1_lattices(k8_filter_0(X1,X2)) = k1_realset1(u1_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t63_filter_0]) ).
cnf(c_0_113,plain,
( m1_filter_0(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
fof(c_0_114,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,X1) )
=> ( ~ v3_struct_0(k8_filter_0(X1,X2))
& v3_lattices(k8_filter_0(X1,X2))
& v4_lattices(k8_filter_0(X1,X2))
& v5_lattices(k8_filter_0(X1,X2))
& v6_lattices(k8_filter_0(X1,X2))
& v7_lattices(k8_filter_0(X1,X2))
& v8_lattices(k8_filter_0(X1,X2))
& v9_lattices(k8_filter_0(X1,X2))
& v10_lattices(k8_filter_0(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc2_filter_0]) ).
fof(c_0_115,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,X1) )
=> ( ~ v3_struct_0(k8_filter_0(X1,X2))
& v10_lattices(k8_filter_0(X1,X2))
& l3_lattices(k8_filter_0(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[dt_k8_filter_0]) ).
fof(c_0_116,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t63_lattice2]) ).
cnf(c_0_117,negated_conjecture,
( m2_lattice4(esk2_0,k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])]) ).
cnf(c_0_118,plain,
( u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_119,negated_conjecture,
m2_nat_lat(k23_filter_2(esk1_0,esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_100]),c_0_41]),c_0_42])]),c_0_43]),c_0_101]) ).
cnf(c_0_120,negated_conjecture,
u1_struct_0(k23_filter_2(esk1_0,esk2_0)) = esk2_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_100]),c_0_41]),c_0_42])]),c_0_43]),c_0_101]) ).
cnf(c_0_121,plain,
( v3_struct_0(X1)
| k8_filter_0(X1,X2) = k23_filter_2(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_122,negated_conjecture,
k1_lattice2(k1_lattice2(k1_lattice2(esk1_0))) = k1_lattice2(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_42])]),c_0_43]) ).
cnf(c_0_123,negated_conjecture,
k23_filter_2(esk1_0,u1_struct_0(esk1_0)) = k1_lattice2(k1_lattice2(esk1_0)),
inference(rw,[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_105,c_0_106]),c_0_107]),c_0_108]),c_0_109]),c_0_110])]),c_0_111]) ).
cnf(c_0_124,negated_conjecture,
~ v3_struct_0(k23_filter_2(esk1_0,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_52,c_0_93]),c_0_41]),c_0_42])]),c_0_43]) ).
fof(c_0_125,plain,
! [X762,X763] :
( ( u1_struct_0(k8_filter_0(X762,X763)) = X763
| ~ m1_filter_0(X763,X762)
| v3_struct_0(X762)
| ~ v10_lattices(X762)
| ~ l3_lattices(X762) )
& ( u2_lattices(k8_filter_0(X762,X763)) = k1_realset1(u2_lattices(X762),X763)
| ~ m1_filter_0(X763,X762)
| v3_struct_0(X762)
| ~ v10_lattices(X762)
| ~ l3_lattices(X762) )
& ( u1_lattices(k8_filter_0(X762,X763)) = k1_realset1(u1_lattices(X762),X763)
| ~ m1_filter_0(X763,X762)
| v3_struct_0(X762)
| ~ v10_lattices(X762)
| ~ l3_lattices(X762) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])])])]) ).
cnf(c_0_126,negated_conjecture,
( m1_filter_0(esk2_0,k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_97]),c_0_98])]) ).
cnf(c_0_127,plain,
( u1_lattices(X1) = u2_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
fof(c_0_128,plain,
! [X753,X754] :
( ( ~ v3_struct_0(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) )
& ( v3_lattices(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) )
& ( v4_lattices(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) )
& ( v5_lattices(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) )
& ( v6_lattices(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) )
& ( v7_lattices(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) )
& ( v8_lattices(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) )
& ( v9_lattices(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) )
& ( v10_lattices(k8_filter_0(X753,X754))
| v3_struct_0(X753)
| ~ v10_lattices(X753)
| ~ l3_lattices(X753)
| ~ m1_filter_0(X754,X753) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_114])])]) ).
fof(c_0_129,plain,
! [X792,X793] :
( ( ~ v3_struct_0(k8_filter_0(X792,X793))
| v3_struct_0(X792)
| ~ v10_lattices(X792)
| ~ l3_lattices(X792)
| ~ m1_filter_0(X793,X792) )
& ( v10_lattices(k8_filter_0(X792,X793))
| v3_struct_0(X792)
| ~ v10_lattices(X792)
| ~ l3_lattices(X792)
| ~ m1_filter_0(X793,X792) )
& ( l3_lattices(k8_filter_0(X792,X793))
| v3_struct_0(X792)
| ~ v10_lattices(X792)
| ~ l3_lattices(X792)
| ~ m1_filter_0(X793,X792) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])]) ).
fof(c_0_130,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( v14_lattices(X1)
=> v14_lattices(k8_filter_0(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[t66_filter_0]) ).
fof(c_0_131,plain,
! [X477] :
( ( ~ v13_lattices(X477)
| v14_lattices(k1_lattice2(X477))
| v3_struct_0(X477)
| ~ v10_lattices(X477)
| ~ l3_lattices(X477) )
& ( ~ v14_lattices(k1_lattice2(X477))
| v13_lattices(X477)
| v3_struct_0(X477)
| ~ v10_lattices(X477)
| ~ l3_lattices(X477) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_116])])]) ).
cnf(c_0_132,negated_conjecture,
( m2_lattice4(esk2_0,k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_67]),c_0_42])]) ).
cnf(c_0_133,negated_conjecture,
u1_lattices(k1_lattice2(esk1_0)) = u2_lattices(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_42]),c_0_43]) ).
cnf(c_0_134,negated_conjecture,
k1_realset1(u2_lattices(esk1_0),esk2_0) = u2_lattices(k23_filter_2(esk1_0,esk2_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_71,c_0_119]),c_0_120]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_135,negated_conjecture,
( k23_filter_2(k1_lattice2(esk1_0),esk2_0) = k8_filter_0(k1_lattice2(esk1_0),esk2_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_97]),c_0_98])]) ).
cnf(c_0_136,negated_conjecture,
( v3_struct_0(k1_lattice2(k1_lattice2(esk1_0)))
| ~ l3_lattices(k1_lattice2(k1_lattice2(esk1_0)))
| ~ v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_103,c_0_122]) ).
cnf(c_0_137,negated_conjecture,
l3_lattices(k1_lattice2(k1_lattice2(esk1_0))),
inference(rw,[status(thm)],[c_0_110,c_0_123]) ).
cnf(c_0_138,negated_conjecture,
~ v3_struct_0(k1_lattice2(k1_lattice2(esk1_0))),
inference(rw,[status(thm)],[c_0_124,c_0_123]) ).
cnf(c_0_139,plain,
( u1_struct_0(k8_filter_0(X1,X2)) = X2
| v3_struct_0(X1)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_140,negated_conjecture,
( m1_filter_0(esk2_0,k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_67]),c_0_42])]) ).
cnf(c_0_141,negated_conjecture,
u2_lattices(k1_lattice2(esk1_0)) = u1_lattices(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_42]),c_0_43]) ).
cnf(c_0_142,negated_conjecture,
k1_realset1(u1_lattices(esk1_0),esk2_0) = u1_lattices(k23_filter_2(esk1_0,esk2_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_69,c_0_119]),c_0_120]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_143,plain,
( v3_lattices(k8_filter_0(X1,X2))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_144,plain,
( l3_lattices(k8_filter_0(X1,X2))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
fof(c_0_145,plain,
! [X776,X777] :
( v3_struct_0(X776)
| ~ v10_lattices(X776)
| ~ l3_lattices(X776)
| ~ m1_filter_0(X777,X776)
| ~ v14_lattices(X776)
| v14_lattices(k8_filter_0(X776,X777)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])]) ).
cnf(c_0_146,plain,
( v14_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v13_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_147,negated_conjecture,
v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_148,negated_conjecture,
( u1_lattices(k23_filter_2(k1_lattice2(esk1_0),esk2_0)) = u2_lattices(k23_filter_2(esk1_0,esk2_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(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_87,c_0_132]),c_0_133]),c_0_134]),c_0_98])]),c_0_101]) ).
cnf(c_0_149,negated_conjecture,
( k23_filter_2(k1_lattice2(esk1_0),esk2_0) = k8_filter_0(k1_lattice2(esk1_0),esk2_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_67]),c_0_42])]) ).
cnf(c_0_150,negated_conjecture,
~ v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137])]),c_0_138]) ).
cnf(c_0_151,negated_conjecture,
( u1_struct_0(k8_filter_0(k1_lattice2(esk1_0),esk2_0)) = esk2_0
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_98])]) ).
cnf(c_0_152,negated_conjecture,
( u2_lattices(k23_filter_2(k1_lattice2(esk1_0),esk2_0)) = u1_lattices(k23_filter_2(esk1_0,esk2_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(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_90,c_0_132]),c_0_141]),c_0_142]),c_0_98])]),c_0_101]) ).
fof(c_0_153,plain,
! [X542] :
( ~ l3_lattices(X542)
| k1_lattice2(X542) = g3_lattices(u1_struct_0(X542),u1_lattices(X542),u2_lattices(X542)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_lattice2])]) ).
cnf(c_0_154,negated_conjecture,
( v3_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_140]),c_0_98])]) ).
cnf(c_0_155,negated_conjecture,
( l3_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_140]),c_0_98])]) ).
cnf(c_0_156,plain,
( v3_struct_0(X1)
| v14_lattices(k8_filter_0(X1,X2))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1)
| ~ v14_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_157,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_146,c_0_147]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_158,negated_conjecture,
( u1_lattices(k23_filter_2(k1_lattice2(esk1_0),esk2_0)) = u2_lattices(k23_filter_2(esk1_0,esk2_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_67]),c_0_42])]) ).
cnf(c_0_159,negated_conjecture,
k23_filter_2(k1_lattice2(esk1_0),esk2_0) = k8_filter_0(k1_lattice2(esk1_0),esk2_0),
inference(sr,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_160,negated_conjecture,
( u1_struct_0(k8_filter_0(k1_lattice2(esk1_0),esk2_0)) = esk2_0
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_67]),c_0_42])]) ).
cnf(c_0_161,negated_conjecture,
( u2_lattices(k23_filter_2(k1_lattice2(esk1_0),esk2_0)) = u1_lattices(k23_filter_2(esk1_0,esk2_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_67]),c_0_42])]) ).
cnf(c_0_162,plain,
( k1_lattice2(X1) = g3_lattices(u1_struct_0(X1),u1_lattices(X1),u2_lattices(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_163,negated_conjecture,
l3_lattices(k23_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_50,c_0_119]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_164,negated_conjecture,
( v3_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_67]),c_0_42])]) ).
cnf(c_0_165,negated_conjecture,
( l3_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_67]),c_0_42])]) ).
cnf(c_0_166,negated_conjecture,
( v14_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_140]),c_0_157]),c_0_98])]) ).
cnf(c_0_167,negated_conjecture,
u1_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0)) = u2_lattices(k23_filter_2(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_158,c_0_150]),c_0_159]) ).
cnf(c_0_168,negated_conjecture,
u1_struct_0(k8_filter_0(k1_lattice2(esk1_0),esk2_0)) = esk2_0,
inference(sr,[status(thm)],[c_0_160,c_0_150]) ).
cnf(c_0_169,negated_conjecture,
u2_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0)) = u1_lattices(k23_filter_2(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_161,c_0_150]),c_0_159]) ).
cnf(c_0_170,negated_conjecture,
g3_lattices(esk2_0,u1_lattices(k23_filter_2(esk1_0,esk2_0)),u2_lattices(k23_filter_2(esk1_0,esk2_0))) = k1_lattice2(k23_filter_2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_120]),c_0_163])]) ).
cnf(c_0_171,negated_conjecture,
v3_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0)),
inference(sr,[status(thm)],[c_0_164,c_0_150]) ).
cnf(c_0_172,negated_conjecture,
l3_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0)),
inference(sr,[status(thm)],[c_0_165,c_0_150]) ).
cnf(c_0_173,negated_conjecture,
( v14_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_67]),c_0_42])]) ).
cnf(c_0_174,plain,
( v10_lattices(k23_filter_2(X1,X2))
| v3_struct_0(X1)
| v1_xboole_0(X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_175,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| ~ v14_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_176,negated_conjecture,
k1_lattice2(k23_filter_2(esk1_0,esk2_0)) = k8_filter_0(k1_lattice2(esk1_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_167]),c_0_168]),c_0_169]),c_0_170]),c_0_171]),c_0_172])]) ).
cnf(c_0_177,negated_conjecture,
v14_lattices(k8_filter_0(k1_lattice2(esk1_0),esk2_0)),
inference(sr,[status(thm)],[c_0_173,c_0_150]) ).
cnf(c_0_178,negated_conjecture,
v10_lattices(k23_filter_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_100]),c_0_41]),c_0_42])]),c_0_43]),c_0_101]) ).
cnf(c_0_179,negated_conjecture,
~ v13_lattices(k23_filter_2(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_180,negated_conjecture,
~ v3_struct_0(k23_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_52,c_0_119]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_181,negated_conjecture,
$false,
inference(sr,[status(thm)],[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_175,c_0_176]),c_0_177]),c_0_178]),c_0_163])]),c_0_179]),c_0_180]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT333+3 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 21:23:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 19.60/15.74 % Version : CSE_E---1.7
% 19.60/15.74 % Problem : theBenchmark.p
% 19.60/15.74 % SZS status Theorem for theBenchmark.p
% 19.60/15.74 % SZS output start CNFRefutation
% See solution above
% 19.60/15.77 % Total time : 13.760s
%------------------------------------------------------------------------------