%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT306+2 : 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 : n010.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 04:38:01 PM UTC 2026
% Result : Theorem 35.05s 20.97s
% Output : CNFRefutation 35.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 113 ( 29 unt; 0 def)
% Number of atoms : 523 ( 36 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 629 ( 219 ~; 215 |; 130 &)
% ( 10 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t32_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k17_filter_2(X1),k18_filter_2(X1,k6_lattices(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_2) ).
fof(dt_k6_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',dt_k6_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',dt_l3_lattices) ).
fof(dt_k18_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m2_filter_2(k18_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_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(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(t32_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1)
& r2_hidden(k5_lattices(X1),X2) )
=> ( X2 = k1_filter_0(X1)
& X2 = u1_struct_0(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',t32_filter_0) ).
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(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(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(t64_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
<=> v13_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t64_lattice2) ).
fof(t79_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> k6_lattices(X1) = k5_lattices(k1_lattice2(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t79_lattice2) ).
fof(t45_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r3_lattices(X1,X2,k6_lattices(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',t45_lattices) ).
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(d8_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_2) ).
fof(t29_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X2,k18_filter_2(X1,X3))
<=> r3_lattices(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_2) ).
fof(redefinition_r1_filter_2,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+375.ax',dt_m2_lattice4) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+200.ax',fc1_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',dt_l1_lattices) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
=> r1_filter_2(u1_struct_0(X1),k17_filter_2(X1),k18_filter_2(X1,k6_lattices(X1))) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t32_filter_2])]) ).
fof(c_0_22,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_lattices]) ).
fof(c_0_23,plain,
! [X7310] :
( ( l1_lattices(X7310)
| ~ l3_lattices(X7310) )
& ( l2_lattices(X7310)
| ~ l3_lattices(X7310) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_24,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& v14_lattices(esk1_0)
& ~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_25,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m2_filter_2(k18_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k18_filter_2]) ).
fof(c_0_26,plain,
! [X6227] :
( v3_struct_0(X6227)
| ~ l2_lattices(X6227)
| m1_subset_1(k6_lattices(X6227),u1_struct_0(X6227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
cnf(c_0_27,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,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_30,plain,
! [X6203,X6204] :
( v3_struct_0(X6203)
| ~ v10_lattices(X6203)
| ~ l3_lattices(X6203)
| ~ m1_subset_1(X6204,u1_struct_0(X6203))
| m2_filter_2(k18_filter_2(X6203,X6204),X6203) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
cnf(c_0_31,plain,
( v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
l2_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_34,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_35,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]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1)
& r2_hidden(k5_lattices(X1),X2) )
=> ( X2 = k1_filter_0(X1)
& X2 = u1_struct_0(X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[t32_filter_0]) ).
fof(c_0_37,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_38,plain,
! [X6910,X6911] :
( ( ~ m2_filter_2(X6911,X6910)
| m1_filter_2(X6911,k1_lattice2(X6910))
| v3_struct_0(X6910)
| ~ v10_lattices(X6910)
| ~ l3_lattices(X6910) )
& ( ~ m1_filter_2(X6911,k1_lattice2(X6910))
| m2_filter_2(X6911,X6910)
| v3_struct_0(X6910)
| ~ v10_lattices(X6910)
| ~ l3_lattices(X6910) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
cnf(c_0_39,plain,
( v3_struct_0(X1)
| m2_filter_2(k18_filter_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,negated_conjecture,
m1_subset_1(k6_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_41,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_42,plain,
! [X7110] :
( ( ~ v3_struct_0(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) )
& ( v3_lattices(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) )
& ( v4_lattices(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) )
& ( v5_lattices(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) )
& ( v6_lattices(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) )
& ( v7_lattices(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) )
& ( v8_lattices(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) )
& ( v9_lattices(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) )
& ( v10_lattices(k1_lattice2(X7110))
| v3_struct_0(X7110)
| ~ v10_lattices(X7110)
| ~ l3_lattices(X7110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
fof(c_0_43,plain,
! [X7125] :
( ( v3_lattices(k1_lattice2(X7125))
| ~ l3_lattices(X7125) )
& ( l3_lattices(k1_lattice2(X7125))
| ~ l3_lattices(X7125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_44,plain,
! [X7109] :
( ( ~ v3_struct_0(k1_lattice2(X7109))
| v3_struct_0(X7109)
| ~ l3_lattices(X7109) )
& ( v3_lattices(k1_lattice2(X7109))
| v3_struct_0(X7109)
| ~ l3_lattices(X7109) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_45,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_46,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
<=> v13_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t64_lattice2]) ).
fof(c_0_47,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> k6_lattices(X1) = k5_lattices(k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[t79_lattice2]) ).
fof(c_0_48,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r3_lattices(X1,X2,k6_lattices(X1)) ) ),
inference(fof_simplification,[status(thm)],[t45_lattices]) ).
fof(c_0_49,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_50,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k17_filter_2(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d8_filter_2]) ).
fof(c_0_51,plain,
! [X7685,X7686] :
( ( X7686 = k1_filter_0(X7685)
| v3_struct_0(X7685)
| ~ v10_lattices(X7685)
| ~ v13_lattices(X7685)
| ~ l3_lattices(X7685)
| ~ r2_hidden(k5_lattices(X7685),X7686)
| ~ m1_filter_0(X7686,X7685)
| v3_struct_0(X7685)
| ~ v10_lattices(X7685)
| ~ l3_lattices(X7685) )
& ( X7686 = u1_struct_0(X7685)
| v3_struct_0(X7685)
| ~ v10_lattices(X7685)
| ~ v13_lattices(X7685)
| ~ l3_lattices(X7685)
| ~ r2_hidden(k5_lattices(X7685),X7686)
| ~ m1_filter_0(X7686,X7685)
| v3_struct_0(X7685)
| ~ v10_lattices(X7685)
| ~ l3_lattices(X7685) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).
fof(c_0_52,plain,
! [X10082,X10083] :
( ( ~ m1_filter_2(X10083,X10082)
| m1_filter_0(X10083,X10082)
| v3_struct_0(X10082)
| ~ v10_lattices(X10082)
| ~ l3_lattices(X10082) )
& ( ~ m1_filter_0(X10083,X10082)
| m1_filter_2(X10083,X10082)
| v3_struct_0(X10082)
| ~ v10_lattices(X10082)
| ~ l3_lattices(X10082) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_53,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_38]) ).
cnf(c_0_54,negated_conjecture,
m2_filter_2(k18_filter_2(esk1_0,k6_lattices(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_39,c_0_40]),c_0_41]),c_0_28])]),c_0_33]) ).
cnf(c_0_55,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_56,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_57,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_58,plain,
! [X7112] :
( ( u1_struct_0(X7112) = u1_struct_0(k1_lattice2(X7112))
| v3_struct_0(X7112)
| ~ l3_lattices(X7112) )
& ( u2_lattices(X7112) = u1_lattices(k1_lattice2(X7112))
| v3_struct_0(X7112)
| ~ l3_lattices(X7112) )
& ( u1_lattices(X7112) = u2_lattices(k1_lattice2(X7112))
| v3_struct_0(X7112)
| ~ l3_lattices(X7112) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
fof(c_0_59,plain,
! [X6284] :
( ( ~ v14_lattices(X6284)
| v13_lattices(k1_lattice2(X6284))
| v3_struct_0(X6284)
| ~ v10_lattices(X6284)
| ~ l3_lattices(X6284) )
& ( ~ v13_lattices(k1_lattice2(X6284))
| v14_lattices(X6284)
| v3_struct_0(X6284)
| ~ v10_lattices(X6284)
| ~ l3_lattices(X6284) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
fof(c_0_60,plain,
! [X6244] :
( v3_struct_0(X6244)
| ~ v10_lattices(X6244)
| ~ v14_lattices(X6244)
| ~ l3_lattices(X6244)
| k6_lattices(X6244) = k5_lattices(k1_lattice2(X6244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])]) ).
fof(c_0_61,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X2,k18_filter_2(X1,X3))
<=> r3_lattices(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t29_filter_2]) ).
fof(c_0_62,plain,
! [X6223,X6224] :
( v3_struct_0(X6223)
| ~ v10_lattices(X6223)
| ~ v14_lattices(X6223)
| ~ l3_lattices(X6223)
| ~ m1_subset_1(X6224,u1_struct_0(X6223))
| r3_lattices(X6223,X6224,k6_lattices(X6223)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])]) ).
fof(c_0_63,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> ( r1_filter_2(X1,X2,X3)
<=> X2 = X3 ) ),
inference(fof_simplification,[status(thm)],[redefinition_r1_filter_2]) ).
fof(c_0_64,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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_65,plain,
! [X6893,X6894] :
( ( ~ v1_xboole_0(X6894)
| ~ m2_filter_2(X6894,X6893)
| v3_struct_0(X6893)
| ~ v10_lattices(X6893)
| ~ l3_lattices(X6893) )
& ( m2_lattice4(X6894,X6893)
| ~ m2_filter_2(X6894,X6893)
| v3_struct_0(X6893)
| ~ v10_lattices(X6893)
| ~ l3_lattices(X6893) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
fof(c_0_66,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_67,plain,
! [X10114] :
( ~ l1_lattices(X10114)
| l1_struct_0(X10114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
cnf(c_0_68,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_69,plain,
! [X6257] :
( v3_struct_0(X6257)
| ~ v10_lattices(X6257)
| ~ l3_lattices(X6257)
| k17_filter_2(X6257) = u1_struct_0(X6257) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])]) ).
cnf(c_0_70,plain,
( X1 = u1_struct_0(X2)
| v3_struct_0(X2)
| v3_struct_0(X2)
| ~ v10_lattices(X2)
| ~ v13_lattices(X2)
| ~ l3_lattices(X2)
| ~ r2_hidden(k5_lattices(X2),X1)
| ~ m1_filter_0(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_71,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_52]) ).
cnf(c_0_72,negated_conjecture,
m1_filter_2(k18_filter_2(esk1_0,k6_lattices(esk1_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_53,c_0_54]),c_0_41]),c_0_28])]),c_0_33]) ).
cnf(c_0_73,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_55,c_0_28]),c_0_41])]),c_0_33]) ).
cnf(c_0_74,negated_conjecture,
l3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_56,c_0_28]) ).
cnf(c_0_75,negated_conjecture,
~ v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_28]),c_0_33]) ).
cnf(c_0_76,plain,
( u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_77,plain,
( v13_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_78,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_79,plain,
( v3_struct_0(X1)
| k6_lattices(X1) = k5_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_80,plain,
! [X6207,X6208,X6209] :
( ( ~ r2_hidden(X6208,k18_filter_2(X6207,X6209))
| r3_lattices(X6207,X6208,X6209)
| ~ m1_subset_1(X6209,u1_struct_0(X6207))
| ~ m1_subset_1(X6208,u1_struct_0(X6207))
| v3_struct_0(X6207)
| ~ v10_lattices(X6207)
| ~ l3_lattices(X6207) )
& ( ~ r3_lattices(X6207,X6208,X6209)
| r2_hidden(X6208,k18_filter_2(X6207,X6209))
| ~ m1_subset_1(X6209,u1_struct_0(X6207))
| ~ m1_subset_1(X6208,u1_struct_0(X6207))
| v3_struct_0(X6207)
| ~ v10_lattices(X6207)
| ~ l3_lattices(X6207) ) ),
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_81,plain,
( v3_struct_0(X1)
| r3_lattices(X1,X2,k6_lattices(X1))
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_82,plain,
! [X6195,X6196,X6197] :
( ( ~ r1_filter_2(X6195,X6196,X6197)
| X6196 = X6197
| v1_xboole_0(X6195)
| ~ m1_subset_1(X6196,k1_zfmisc_1(X6195))
| ~ m1_subset_1(X6197,k1_zfmisc_1(X6195)) )
& ( X6196 != X6197
| r1_filter_2(X6195,X6196,X6197)
| v1_xboole_0(X6195)
| ~ m1_subset_1(X6196,k1_zfmisc_1(X6195))
| ~ m1_subset_1(X6197,k1_zfmisc_1(X6195)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])]) ).
fof(c_0_83,plain,
! [X8150,X8151] :
( v3_struct_0(X8150)
| ~ v10_lattices(X8150)
| ~ l3_lattices(X8150)
| ~ m2_lattice4(X8151,X8150)
| m1_subset_1(X8151,k1_zfmisc_1(u1_struct_0(X8150))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
cnf(c_0_84,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_65]) ).
fof(c_0_85,plain,
! [X10219] :
( v3_struct_0(X10219)
| ~ l1_struct_0(X10219)
| ~ v1_xboole_0(u1_struct_0(X10219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])]) ).
cnf(c_0_86,plain,
( l1_struct_0(X1)
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_87,negated_conjecture,
l1_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_68,c_0_28]) ).
cnf(c_0_88,plain,
( v3_struct_0(X1)
| k17_filter_2(X1) = u1_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_89,plain,
( X1 = u1_struct_0(X2)
| v3_struct_0(X2)
| ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ v13_lattices(X2)
| ~ m1_filter_0(X1,X2)
| ~ r2_hidden(k5_lattices(X2),X1) ),
inference(cn,[status(thm)],[c_0_70]) ).
cnf(c_0_90,negated_conjecture,
m1_filter_0(k18_filter_2(esk1_0,k6_lattices(esk1_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_71,c_0_72]),c_0_73]),c_0_74])]),c_0_75]) ).
cnf(c_0_91,negated_conjecture,
u1_struct_0(k1_lattice2(esk1_0)) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_28]),c_0_33]) ).
cnf(c_0_92,negated_conjecture,
v13_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_77,c_0_28]),c_0_78]),c_0_41])]),c_0_33]) ).
cnf(c_0_93,negated_conjecture,
k5_lattices(k1_lattice2(esk1_0)) = k6_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_79,c_0_28]),c_0_78]),c_0_41])]),c_0_33]) ).
cnf(c_0_94,plain,
( r2_hidden(X2,k18_filter_2(X1,X3))
| v3_struct_0(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_95,negated_conjecture,
r3_lattices(esk1_0,k6_lattices(esk1_0),k6_lattices(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_81,c_0_40]),c_0_78]),c_0_41]),c_0_28])]),c_0_33]) ).
cnf(c_0_96,plain,
( r1_filter_2(X3,X1,X2)
| v1_xboole_0(X3)
| X1 != X2
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_97,plain,
( v3_struct_0(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_98,negated_conjecture,
m2_lattice4(k18_filter_2(esk1_0,k6_lattices(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_84,c_0_54]),c_0_41]),c_0_28])]),c_0_33]) ).
cnf(c_0_99,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_100,negated_conjecture,
l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_101,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k17_filter_2(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_102,negated_conjecture,
k17_filter_2(esk1_0) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_28]),c_0_41])]),c_0_33]) ).
cnf(c_0_103,negated_conjecture,
( k18_filter_2(esk1_0,k6_lattices(esk1_0)) = u1_struct_0(esk1_0)
| ~ r2_hidden(k6_lattices(esk1_0),k18_filter_2(esk1_0,k6_lattices(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92]),c_0_73]),c_0_74]),c_0_93])]),c_0_75]) ).
cnf(c_0_104,negated_conjecture,
r2_hidden(k6_lattices(esk1_0),k18_filter_2(esk1_0,k6_lattices(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_94,c_0_95]),c_0_41]),c_0_28]),c_0_40])]),c_0_33]) ).
cnf(c_0_105,plain,
( r1_filter_2(X1,X2,X2)
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(er,[status(thm)],[c_0_96]) ).
cnf(c_0_106,negated_conjecture,
m1_subset_1(k18_filter_2(esk1_0,k6_lattices(esk1_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_97,c_0_98]),c_0_41]),c_0_28])]),c_0_33]) ).
cnf(c_0_107,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_33]) ).
cnf(c_0_108,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0))),
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
k18_filter_2(esk1_0,k6_lattices(esk1_0)) = u1_struct_0(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).
cnf(c_0_110,negated_conjecture,
r1_filter_2(u1_struct_0(esk1_0),k18_filter_2(esk1_0,k6_lattices(esk1_0)),k18_filter_2(esk1_0,k6_lattices(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_111,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
inference(rw,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_109]),c_0_109]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT306+2 : 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 : n010.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 21:10:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 35.05/20.97 % Version : CSE_E---1.7
% 35.05/20.97 % Problem : theBenchmark.p
% 35.05/20.97 % SZS status Theorem for theBenchmark.p
% 35.05/20.97 % SZS output start CNFRefutation
% See solution above
% 35.18/21.08 % Total time : 16.272s
%------------------------------------------------------------------------------