%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT305+1 : 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 : n013.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 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 10 unt; 0 def)
% Number of atoms : 394 ( 13 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 532 ( 202 ~; 196 |; 99 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 111 ( 1 sgn 74 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t31_filter_2,conjecture,
! [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,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_2) ).
fof(d9_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_2) ).
fof(fraenkel_a_2_0_filter_2,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2)
& m1_subset_1(X3,u1_struct_0(X2)) )
=> ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
& X1 = X4
& r3_lattices(X2,X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_2) ).
fof(commutativity_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( r3_lattices(X1,X2,X3)
<=> r1_lattices(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(t23_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> r1_lattices(X1,k4_lattices(X1,X2,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
fof(dt_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
fof(reflexivity_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> r3_lattices(X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(cc1_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(c_0_11,negated_conjecture,
~ ! [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,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t31_filter_2])]) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d9_filter_2]) ).
fof(c_0_13,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2)
& m1_subset_1(X3,u1_struct_0(X2)) )
=> ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
& X1 = X4
& r3_lattices(X2,X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_filter_2]) ).
fof(c_0_14,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& m1_subset_1(esk3_0,u1_struct_0(esk1_0))
& ( ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_15,plain,
! [X175,X176] :
( v3_struct_0(X175)
| ~ v10_lattices(X175)
| ~ l3_lattices(X175)
| ~ m1_subset_1(X176,u1_struct_0(X175))
| k18_filter_2(X175,X176) = a_2_0_filter_2(X175,X176) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_16,plain,
! [X228,X229,X230,X232] :
( ( m1_subset_1(esk13_3(X228,X229,X230),u1_struct_0(X229))
| ~ r2_hidden(X228,a_2_0_filter_2(X229,X230))
| v3_struct_0(X229)
| ~ v10_lattices(X229)
| ~ l3_lattices(X229)
| ~ m1_subset_1(X230,u1_struct_0(X229)) )
& ( X228 = esk13_3(X228,X229,X230)
| ~ r2_hidden(X228,a_2_0_filter_2(X229,X230))
| v3_struct_0(X229)
| ~ v10_lattices(X229)
| ~ l3_lattices(X229)
| ~ m1_subset_1(X230,u1_struct_0(X229)) )
& ( r3_lattices(X229,esk13_3(X228,X229,X230),X230)
| ~ r2_hidden(X228,a_2_0_filter_2(X229,X230))
| v3_struct_0(X229)
| ~ v10_lattices(X229)
| ~ l3_lattices(X229)
| ~ m1_subset_1(X230,u1_struct_0(X229)) )
& ( ~ m1_subset_1(X232,u1_struct_0(X229))
| X228 != X232
| ~ r3_lattices(X229,X232,X230)
| r2_hidden(X228,a_2_0_filter_2(X229,X230))
| v3_struct_0(X229)
| ~ v10_lattices(X229)
| ~ l3_lattices(X229)
| ~ m1_subset_1(X230,u1_struct_0(X229)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( v3_struct_0(X1)
| k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( r2_hidden(X3,a_2_0_filter_2(X2,X4))
| v3_struct_0(X2)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| X3 != X1
| ~ r3_lattices(X2,X1,X4)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X4,u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(esk2_0,a_2_0_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_17,c_0_18]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_25,plain,
( r2_hidden(X1,a_2_0_filter_2(X2,X3))
| v3_struct_0(X2)
| ~ r3_lattices(X2,X1,X3)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ l3_lattices(X2)
| ~ v10_lattices(X2) ),
inference(er,[status(thm)],[c_0_23]) ).
fof(c_0_26,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
fof(c_0_27,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( r3_lattices(X1,X2,X3)
<=> r1_lattices(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> r1_lattices(X1,k4_lattices(X1,X2,X3),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t23_lattices]) ).
cnf(c_0_29,negated_conjecture,
( ~ r3_lattices(esk1_0,k4_lattices(esk1_0,esk3_0,esk2_0),esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0))
| ~ m1_subset_1(k4_lattices(esk1_0,esk3_0,esk2_0),u1_struct_0(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_24,c_0_25]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
fof(c_0_30,plain,
! [X164,X165,X166] :
( v3_struct_0(X164)
| ~ v6_lattices(X164)
| ~ l1_lattices(X164)
| ~ m1_subset_1(X165,u1_struct_0(X164))
| ~ m1_subset_1(X166,u1_struct_0(X164))
| k4_lattices(X164,X165,X166) = k4_lattices(X164,X166,X165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_31,plain,
! [X261,X262,X263] :
( ( ~ r3_lattices(X261,X262,X263)
| r1_lattices(X261,X262,X263)
| v3_struct_0(X261)
| ~ v6_lattices(X261)
| ~ v8_lattices(X261)
| ~ v9_lattices(X261)
| ~ l3_lattices(X261)
| ~ m1_subset_1(X262,u1_struct_0(X261))
| ~ m1_subset_1(X263,u1_struct_0(X261)) )
& ( ~ r1_lattices(X261,X262,X263)
| r3_lattices(X261,X262,X263)
| v3_struct_0(X261)
| ~ v6_lattices(X261)
| ~ v8_lattices(X261)
| ~ v9_lattices(X261)
| ~ l3_lattices(X261)
| ~ m1_subset_1(X262,u1_struct_0(X261))
| ~ m1_subset_1(X263,u1_struct_0(X261)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_32,plain,
! [X270,X271,X272] :
( v3_struct_0(X270)
| ~ v6_lattices(X270)
| ~ v8_lattices(X270)
| ~ l3_lattices(X270)
| ~ m1_subset_1(X271,u1_struct_0(X270))
| ~ m1_subset_1(X272,u1_struct_0(X270))
| r1_lattices(X270,k4_lattices(X270,X271,X272),X271) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_33,negated_conjecture,
( ~ r3_lattices(esk1_0,k4_lattices(esk1_0,esk3_0,esk2_0),esk2_0)
| ~ r3_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,esk3_0),esk2_0)
| ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0))
| ~ m1_subset_1(k4_lattices(esk1_0,esk3_0,esk2_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(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_29,c_0_25]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_34,plain,
( v3_struct_0(X1)
| k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2)
| ~ v6_lattices(X1)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,plain,
( r3_lattices(X1,X2,X3)
| v3_struct_0(X1)
| ~ r1_lattices(X1,X2,X3)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| r1_lattices(X1,k4_lattices(X1,X2,X3),X2)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_38,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k4_lattices]) ).
cnf(c_0_39,negated_conjecture,
( ~ r3_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,esk3_0),esk2_0)
| ~ l1_lattices(esk1_0)
| ~ v6_lattices(esk1_0)
| ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0))
| ~ m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_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_33,c_0_34]),c_0_35]),c_0_19])]),c_0_22]) ).
cnf(c_0_40,plain,
( r3_lattices(X1,k4_lattices(X1,X2,X3),X2)
| v3_struct_0(X1)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| ~ m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_41,plain,
! [X188,X189,X190] :
( v3_struct_0(X188)
| ~ v6_lattices(X188)
| ~ l1_lattices(X188)
| ~ m1_subset_1(X189,u1_struct_0(X188))
| ~ m1_subset_1(X190,u1_struct_0(X188))
| m1_subset_1(k4_lattices(X188,X189,X190),u1_struct_0(X188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
fof(c_0_42,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> r3_lattices(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
cnf(c_0_43,negated_conjecture,
( ~ l1_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(esk1_0)
| ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0))
| ~ m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(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_39,c_0_40]),c_0_19]),c_0_35]),c_0_20])]),c_0_22]) ).
cnf(c_0_44,plain,
( v3_struct_0(X1)
| m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1))
| ~ v6_lattices(X1)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_45,plain,
! [X265,X266,X267] :
( v3_struct_0(X265)
| ~ v6_lattices(X265)
| ~ v8_lattices(X265)
| ~ v9_lattices(X265)
| ~ l3_lattices(X265)
| ~ m1_subset_1(X266,u1_struct_0(X265))
| ~ m1_subset_1(X267,u1_struct_0(X265))
| r3_lattices(X265,X266,X266) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])]) ).
fof(c_0_46,plain,
! [X209] : m1_subset_1(esk9_1(X209),X209),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_47,negated_conjecture,
( ~ l1_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(esk1_0)
| ~ r2_hidden(esk2_0,a_2_0_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_43,c_0_44]),c_0_35]),c_0_19])]),c_0_22]) ).
cnf(c_0_48,plain,
( v3_struct_0(X1)
| r3_lattices(X1,X2,X2)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_50,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
cnf(c_0_51,negated_conjecture,
( ~ r3_lattices(esk1_0,esk2_0,esk2_0)
| ~ l1_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v6_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_47,c_0_25]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_52,plain,
( r3_lattices(X1,X2,X2)
| v3_struct_0(X1)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_53,plain,
! [X155] :
( ( ~ v3_struct_0(X155)
| v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ l3_lattices(X155) )
& ( v4_lattices(X155)
| v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ l3_lattices(X155) )
& ( v5_lattices(X155)
| v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ l3_lattices(X155) )
& ( v6_lattices(X155)
| v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ l3_lattices(X155) )
& ( v7_lattices(X155)
| v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ l3_lattices(X155) )
& ( v8_lattices(X155)
| v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ l3_lattices(X155) )
& ( v9_lattices(X155)
| v3_struct_0(X155)
| ~ v10_lattices(X155)
| ~ l3_lattices(X155) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])]) ).
cnf(c_0_54,negated_conjecture,
( ~ l1_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v6_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_51,c_0_52]),c_0_19]),c_0_20])]),c_0_22]) ).
cnf(c_0_55,plain,
( v9_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( ~ l1_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v6_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_54,c_0_55]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_57,plain,
( v8_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( ~ l1_lattices(esk1_0)
| ~ v6_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_56,c_0_57]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_59,plain,
( v6_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_60,plain,
! [X193] :
( ( l1_lattices(X193)
| ~ l3_lattices(X193) )
& ( l2_lattices(X193)
| ~ l3_lattices(X193) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_61,negated_conjecture,
~ l1_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_58,c_0_59]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_62,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT305+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n013.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 21:09:11 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Theorem for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------