%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT323+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 04:38:06 PM UTC 2026
% Result : Theorem 9.10s 6.49s
% Output : CNFRefutation 9.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 94 ( 20 unt; 0 def)
% Number of atoms : 579 ( 20 equ)
% Maximal formula atoms : 80 ( 6 avg)
% Number of connectives : 733 ( 248 ~; 262 |; 160 &)
% ( 8 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(t59_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( r2_filter_2(X1,X2)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X3,X2)
<=> ~ r2_hidden(k7_lattices(X1,X3),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_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/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(d6_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).
fof(d4_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k5_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
fof(redefinition_k15_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m2_filter_2(X2,X1) )
=> k15_filter_2(X1,X2) = k7_filter_2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).
fof(dt_k5_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(l70_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k7_lattices(k1_lattice2(X1),k5_filter_2(X1,X2)) = k7_lattices(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l70_filter_2) ).
fof(fc4_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_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))
& v11_lattices(k1_lattice2(X1))
& v12_lattices(k1_lattice2(X1))
& v13_lattices(k1_lattice2(X1))
& v14_lattices(k1_lattice2(X1))
& v15_lattices(k1_lattice2(X1))
& v16_lattices(k1_lattice2(X1))
& v17_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_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/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(dt_k15_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m2_filter_2(X2,X1) )
=> m1_filter_2(k15_filter_2(X1,X2),k1_lattice2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_filter_2) ).
fof(t59_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( v1_filter_0(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X3,X2)
<=> ~ r2_hidden(k7_lattices(X1,X3),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_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/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(t33_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( r2_filter_2(X1,X2)
<=> v1_filter_0(k15_filter_2(X1,X2),k1_lattice2(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_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/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_16,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_17,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( r2_filter_2(X1,X2)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X3,X2)
<=> ~ r2_hidden(k7_lattices(X1,X3),X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t59_filter_2])]) ).
fof(c_0_18,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_19,plain,
! [X196,X197] :
( ( ~ v1_xboole_0(X197)
| ~ m2_filter_2(X197,X196)
| v3_struct_0(X196)
| ~ v10_lattices(X196)
| ~ l3_lattices(X196) )
& ( m2_lattice4(X197,X196)
| ~ m2_filter_2(X197,X196)
| v3_struct_0(X196)
| ~ v10_lattices(X196)
| ~ l3_lattices(X196) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_20,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& v17_lattices(esk1_0)
& l3_lattices(esk1_0)
& m2_filter_2(esk2_0,esk1_0)
& r2_filter_2(esk1_0,esk2_0)
& m1_subset_1(esk3_0,u1_struct_0(esk1_0))
& ( ~ r2_hidden(esk3_0,esk2_0)
| r2_hidden(k7_lattices(esk1_0,esk3_0),esk2_0) )
& ( r2_hidden(esk3_0,esk2_0)
| ~ r2_hidden(k7_lattices(esk1_0,esk3_0),esk2_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_21,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> k7_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d6_filter_2]) ).
fof(c_0_22,plain,
! [X198,X199] :
( v3_struct_0(X198)
| ~ v10_lattices(X198)
| ~ l3_lattices(X198)
| ~ m2_lattice4(X199,X198)
| m1_subset_1(X199,k1_zfmisc_1(u1_struct_0(X198))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_23,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_19]) ).
cnf(c_0_24,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k5_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_filter_2]) ).
fof(c_0_29,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m2_filter_2(X2,X1) )
=> k15_filter_2(X1,X2) = k7_filter_2(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k15_filter_2]) ).
fof(c_0_30,plain,
! [X175,X176] :
( v3_struct_0(X175)
| ~ v10_lattices(X175)
| ~ l3_lattices(X175)
| ~ m1_subset_1(X176,k1_zfmisc_1(u1_struct_0(X175)))
| k7_filter_2(X175,X176) = X176 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_31,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_22]) ).
cnf(c_0_32,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_23,c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).
fof(c_0_33,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k5_filter_2]) ).
fof(c_0_34,plain,
! [X173,X174] :
( v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ l3_lattices(X173)
| ~ m1_subset_1(X174,u1_struct_0(X173))
| k5_filter_2(X173,X174) = X174 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k7_lattices(k1_lattice2(X1),k5_filter_2(X1,X2)) = k7_lattices(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[l70_filter_2]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_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))
& v11_lattices(k1_lattice2(X1))
& v12_lattices(k1_lattice2(X1))
& v13_lattices(k1_lattice2(X1))
& v14_lattices(k1_lattice2(X1))
& v15_lattices(k1_lattice2(X1))
& v16_lattices(k1_lattice2(X1))
& v17_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc4_filter_2]) ).
fof(c_0_37,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_38,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m2_filter_2(X2,X1) )
=> m1_filter_2(k15_filter_2(X1,X2),k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k15_filter_2]) ).
fof(c_0_39,plain,
! [X270,X271] :
( v3_struct_0(X270)
| ~ v10_lattices(X270)
| ~ l3_lattices(X270)
| ~ m2_filter_2(X271,X270)
| k15_filter_2(X270,X271) = k7_filter_2(X270,X271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])]) ).
cnf(c_0_40,plain,
( v3_struct_0(X1)
| k7_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25]),c_0_26])]),c_0_27]) ).
fof(c_0_42,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( v1_filter_0(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X3,X2)
<=> ~ r2_hidden(k7_lattices(X1,X3),X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t59_filter_0]) ).
fof(c_0_43,plain,
! [X183,X184] :
( v3_struct_0(X183)
| ~ v10_lattices(X183)
| ~ l3_lattices(X183)
| ~ m1_subset_1(X184,u1_struct_0(X183))
| m1_subset_1(k5_filter_2(X183,X184),u1_struct_0(k1_lattice2(X183))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_44,plain,
( v3_struct_0(X1)
| k5_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_46,plain,
! [X247,X248] :
( v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ v17_lattices(X247)
| ~ l3_lattices(X247)
| ~ m1_subset_1(X248,u1_struct_0(X247))
| k7_lattices(k1_lattice2(X247),k5_filter_2(X247,X248)) = k7_lattices(X247,X248) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_47,plain,
! [X235] :
( ( ~ v3_struct_0(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v3_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v4_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v5_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v6_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v7_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v8_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v9_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v10_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v11_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v12_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v13_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v14_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v15_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v16_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) )
& ( v17_lattices(k1_lattice2(X235))
| v3_struct_0(X235)
| ~ v10_lattices(X235)
| ~ v17_lattices(X235)
| ~ l3_lattices(X235) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_48,plain,
! [X240] :
( ( ~ v3_struct_0(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( v3_lattices(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( v4_lattices(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( v5_lattices(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( v6_lattices(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( v7_lattices(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( v8_lattices(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( v9_lattices(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) )
& ( v10_lattices(k1_lattice2(X240))
| v3_struct_0(X240)
| ~ v10_lattices(X240)
| ~ l3_lattices(X240) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
fof(c_0_49,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_50,plain,
! [X180,X181] :
( v3_struct_0(X180)
| ~ v10_lattices(X180)
| ~ l3_lattices(X180)
| ~ m2_filter_2(X181,X180)
| m1_filter_2(k15_filter_2(X180,X181),k1_lattice2(X180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
cnf(c_0_51,plain,
( v3_struct_0(X1)
| k15_filter_2(X1,X2) = k7_filter_2(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_filter_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,negated_conjecture,
k7_filter_2(esk1_0,esk2_0) = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_25]),c_0_26])]),c_0_27]) ).
fof(c_0_53,plain,
! [X289,X290,X291] :
( ( ~ r2_hidden(X291,X290)
| ~ r2_hidden(k7_lattices(X289,X291),X290)
| ~ m1_subset_1(X291,u1_struct_0(X289))
| ~ v1_filter_0(X290,X289)
| ~ m1_filter_0(X290,X289)
| v3_struct_0(X289)
| ~ v10_lattices(X289)
| ~ v17_lattices(X289)
| ~ l3_lattices(X289) )
& ( r2_hidden(k7_lattices(X289,X291),X290)
| r2_hidden(X291,X290)
| ~ m1_subset_1(X291,u1_struct_0(X289))
| ~ v1_filter_0(X290,X289)
| ~ m1_filter_0(X290,X289)
| v3_struct_0(X289)
| ~ v10_lattices(X289)
| ~ v17_lattices(X289)
| ~ l3_lattices(X289) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
cnf(c_0_54,plain,
( v3_struct_0(X1)
| m1_subset_1(k5_filter_2(X1,X2),u1_struct_0(k1_lattice2(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,negated_conjecture,
k5_filter_2(esk1_0,esk3_0) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_56,plain,
( v3_struct_0(X1)
| k7_lattices(k1_lattice2(X1),k5_filter_2(X1,X2)) = k7_lattices(X1,X2)
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,negated_conjecture,
v17_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_58,plain,
( v17_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_60,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( r2_filter_2(X1,X2)
<=> v1_filter_0(k15_filter_2(X1,X2),k1_lattice2(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[t33_filter_2]) ).
fof(c_0_61,plain,
! [X272,X273] :
( ( ~ m1_filter_2(X273,X272)
| m1_filter_0(X273,X272)
| v3_struct_0(X272)
| ~ v10_lattices(X272)
| ~ l3_lattices(X272) )
& ( ~ m1_filter_0(X273,X272)
| m1_filter_2(X273,X272)
| v3_struct_0(X272)
| ~ v10_lattices(X272)
| ~ l3_lattices(X272) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
cnf(c_0_62,plain,
( v3_struct_0(X1)
| m1_filter_2(k15_filter_2(X1,X2),k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_filter_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_63,negated_conjecture,
k15_filter_2(esk1_0,esk2_0) = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_24]),c_0_52]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_64,plain,
( r2_hidden(k7_lattices(X1,X2),X3)
| r2_hidden(X2,X3)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v1_filter_0(X3,X1)
| ~ m1_filter_0(X3,X1)
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,negated_conjecture,
m1_subset_1(esk3_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_54,c_0_45]),c_0_55]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_66,negated_conjecture,
k7_lattices(k1_lattice2(esk1_0),esk3_0) = k7_lattices(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_45]),c_0_55]),c_0_25]),c_0_57]),c_0_26])]),c_0_27]) ).
cnf(c_0_67,negated_conjecture,
v17_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_58,c_0_25]),c_0_57]),c_0_26])]),c_0_27]) ).
cnf(c_0_68,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_59,c_0_25]),c_0_26])]),c_0_27]) ).
fof(c_0_69,plain,
! [X182] :
( ( v3_lattices(k1_lattice2(X182))
| ~ l3_lattices(X182) )
& ( l3_lattices(k1_lattice2(X182))
| ~ l3_lattices(X182) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_70,plain,
! [X282,X283] :
( ( ~ r2_filter_2(X282,X283)
| v1_filter_0(k15_filter_2(X282,X283),k1_lattice2(X282))
| ~ m2_filter_2(X283,X282)
| v3_struct_0(X282)
| ~ v10_lattices(X282)
| ~ l3_lattices(X282) )
& ( ~ v1_filter_0(k15_filter_2(X282,X283),k1_lattice2(X282))
| r2_filter_2(X282,X283)
| ~ m2_filter_2(X283,X282)
| v3_struct_0(X282)
| ~ v10_lattices(X282)
| ~ l3_lattices(X282) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])]) ).
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_61]) ).
cnf(c_0_72,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_24]),c_0_63]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_73,negated_conjecture,
( r2_hidden(k7_lattices(esk1_0,esk3_0),X1)
| r2_hidden(esk3_0,X1)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ v1_filter_0(X1,k1_lattice2(esk1_0))
| ~ m1_filter_0(X1,k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]),c_0_68])]) ).
cnf(c_0_74,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,plain,
( v1_filter_0(k15_filter_2(X1,X2),k1_lattice2(X1))
| v3_struct_0(X1)
| ~ r2_filter_2(X1,X2)
| ~ m2_filter_2(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_76,negated_conjecture,
r2_filter_2(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_77,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_71,c_0_72]),c_0_68])]) ).
cnf(c_0_78,plain,
( v3_struct_0(X3)
| ~ r2_hidden(X1,X2)
| ~ r2_hidden(k7_lattices(X3,X1),X2)
| ~ m1_subset_1(X1,u1_struct_0(X3))
| ~ v1_filter_0(X2,X3)
| ~ m1_filter_0(X2,X3)
| ~ v10_lattices(X3)
| ~ v17_lattices(X3)
| ~ l3_lattices(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_79,negated_conjecture,
( r2_hidden(k7_lattices(esk1_0,esk3_0),X1)
| r2_hidden(esk3_0,X1)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ v1_filter_0(X1,k1_lattice2(esk1_0))
| ~ m1_filter_0(X1,k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_25])]) ).
cnf(c_0_80,negated_conjecture,
v1_filter_0(esk2_0,k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_63]),c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_81,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_77,c_0_74]),c_0_25])]) ).
cnf(c_0_82,negated_conjecture,
( r2_hidden(k7_lattices(esk1_0,esk3_0),esk2_0)
| ~ r2_hidden(esk3_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_83,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_84,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ v1_filter_0(X1,k1_lattice2(esk1_0))
| ~ m1_filter_0(X1,k1_lattice2(esk1_0))
| ~ r2_hidden(k7_lattices(esk1_0,esk3_0),X1)
| ~ r2_hidden(esk3_0,X1)
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_66]),c_0_65]),c_0_67]),c_0_68])]) ).
cnf(c_0_85,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| ~ r2_hidden(k7_lattices(esk1_0,esk3_0),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_86,negated_conjecture,
( r2_hidden(k7_lattices(esk1_0,esk3_0),esk2_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]) ).
fof(c_0_87,plain,
! [X227] :
( ( ~ v3_struct_0(k1_lattice2(X227))
| v3_struct_0(X227)
| ~ l3_lattices(X227) )
& ( v3_lattices(k1_lattice2(X227))
| v3_struct_0(X227)
| ~ l3_lattices(X227) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])]) ).
cnf(c_0_88,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ r2_hidden(esk3_0,esk2_0)
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_82]),c_0_80])]),c_0_81]) ).
cnf(c_0_89,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,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_90,c_0_91]),c_0_25])]),c_0_27]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_74]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT323+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n029.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 21:17:29 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 9.10/6.49 % Version : CSE_E---1.7
% 9.10/6.49 % Problem : theBenchmark.p
% 9.10/6.49 % SZS status Theorem for theBenchmark.p
% 9.10/6.49 % SZS output start CNFRefutation
% See solution above
% 9.20/6.51 % Total time : 5.372s
%------------------------------------------------------------------------------