%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT331+3 : 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 : n011.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 04:38:09 PM UTC 2026
% Result : Theorem 13.73s 11.87s
% Output : CNFRefutation 13.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 91 ( 39 unt; 0 def)
% Number of atoms : 359 ( 74 equ)
% Maximal formula atoms : 45 ( 3 avg)
% Number of connectives : 398 ( 130 ~; 141 |; 96 &)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',t7_filter_2) ).
fof(t68_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ! [X3] :
( m1_filter_2(X3,X1)
=> ! [X4] :
( m1_filter_2(X4,X2)
=> ( ( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = g3_lattices(u1_struct_0(X2),u2_lattices(X2),u1_lattices(X2))
& X3 = X4 )
=> k8_filter_0(X1,X3) = k8_filter_0(X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_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/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',t18_lattice2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',dt_k1_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/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+242.ax',t63_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/sandbox2/benchmark/Axioms/SET007/SET007+242.ax',dt_k8_filter_0) ).
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/Axioms/SET007/SET007+253.ax',fc1_lattice2) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+242.ax',fc2_filter_0) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+205.ax',abstractness_v3_lattices) ).
fof(c_0_10,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_11,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ! [X3] :
( m1_filter_2(X3,X1)
=> ! [X4] :
( m1_filter_2(X4,X2)
=> ( ( g3_lattices(u1_struct_0(X1),u2_lattices(X1),u1_lattices(X1)) = g3_lattices(u1_struct_0(X2),u2_lattices(X2),u1_lattices(X2))
& X3 = X4 )
=> k8_filter_0(X1,X3) = k8_filter_0(X2,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t68_filter_2])]) ).
fof(c_0_12,plain,
! [X539] :
( v3_struct_0(X539)
| ~ v10_lattices(X539)
| ~ l3_lattices(X539)
| k1_lattice2(k1_lattice2(X539)) = g3_lattices(u1_struct_0(X539),u2_lattices(X539),u1_lattices(X539)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
fof(c_0_13,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& ~ v3_struct_0(esk2_0)
& v10_lattices(esk2_0)
& l3_lattices(esk2_0)
& m1_filter_2(esk3_0,esk1_0)
& m1_filter_2(esk4_0,esk2_0)
& g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) = g3_lattices(u1_struct_0(esk2_0),u2_lattices(esk2_0),u1_lattices(esk2_0))
& esk3_0 = esk4_0
& k8_filter_0(esk1_0,esk3_0) != k8_filter_0(esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,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]) ).
cnf(c_0_15,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_12]) ).
cnf(c_0_16,negated_conjecture,
v10_lattices(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) = g3_lattices(u1_struct_0(esk2_0),u2_lattices(esk2_0),u1_lattices(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
l3_lattices(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X540] :
( ( u1_struct_0(X540) = u1_struct_0(k1_lattice2(X540))
| v3_struct_0(X540)
| ~ l3_lattices(X540) )
& ( u2_lattices(X540) = u1_lattices(k1_lattice2(X540))
| v3_struct_0(X540)
| ~ l3_lattices(X540) )
& ( u1_lattices(X540) = u2_lattices(k1_lattice2(X540))
| v3_struct_0(X540)
| ~ l3_lattices(X540) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_21,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,negated_conjecture,
g3_lattices(u1_struct_0(esk1_0),u2_lattices(esk1_0),u1_lattices(esk1_0)) = k1_lattice2(k1_lattice2(esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_25,plain,
( u1_lattices(X1) = u2_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
k1_lattice2(k1_lattice2(esk2_0)) = k1_lattice2(k1_lattice2(esk1_0)),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_21]),c_0_22])]),c_0_23]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
u2_lattices(k1_lattice2(esk2_0)) = u1_lattices(esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_19]) ).
fof(c_0_29,plain,
! [X577] :
( ( v3_lattices(k1_lattice2(X577))
| ~ l3_lattices(X577) )
& ( l3_lattices(k1_lattice2(X577))
| ~ l3_lattices(X577) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_30,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]) ).
cnf(c_0_31,negated_conjecture,
( u1_lattices(k1_lattice2(k1_lattice2(esk1_0))) = u1_lattices(esk2_0)
| v3_struct_0(k1_lattice2(esk2_0))
| ~ l3_lattices(k1_lattice2(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_32,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
u1_lattices(k1_lattice2(esk2_0)) = u2_lattices(esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_19]) ).
fof(c_0_34,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]) ).
fof(c_0_35,plain,
! [X545,X546] :
( ( ~ m1_filter_2(X546,X545)
| m1_filter_0(X546,X545)
| v3_struct_0(X545)
| ~ v10_lattices(X545)
| ~ l3_lattices(X545) )
& ( ~ m1_filter_0(X546,X545)
| m1_filter_2(X546,X545)
| v3_struct_0(X545)
| ~ v10_lattices(X545)
| ~ l3_lattices(X545) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_36,negated_conjecture,
m1_filter_2(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,negated_conjecture,
esk3_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_38,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_39,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_40,negated_conjecture,
( u1_lattices(k1_lattice2(k1_lattice2(esk1_0))) = u1_lattices(esk2_0)
| v3_struct_0(k1_lattice2(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_18])]) ).
cnf(c_0_41,negated_conjecture,
u2_lattices(k1_lattice2(esk1_0)) = u1_lattices(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_23]) ).
cnf(c_0_42,negated_conjecture,
( u2_lattices(k1_lattice2(k1_lattice2(esk1_0))) = u2_lattices(esk2_0)
| v3_struct_0(k1_lattice2(esk2_0))
| ~ l3_lattices(k1_lattice2(esk2_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_33]) ).
fof(c_0_43,plain,
! [X498,X499] :
( ( u1_struct_0(k8_filter_0(X498,X499)) = X499
| ~ m1_filter_0(X499,X498)
| v3_struct_0(X498)
| ~ v10_lattices(X498)
| ~ l3_lattices(X498) )
& ( u2_lattices(k8_filter_0(X498,X499)) = k1_realset1(u2_lattices(X498),X499)
| ~ m1_filter_0(X499,X498)
| v3_struct_0(X498)
| ~ v10_lattices(X498)
| ~ l3_lattices(X498) )
& ( u1_lattices(k8_filter_0(X498,X499)) = k1_realset1(u1_lattices(X498),X499)
| ~ m1_filter_0(X499,X498)
| v3_struct_0(X498)
| ~ v10_lattices(X498)
| ~ l3_lattices(X498) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
cnf(c_0_44,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_35]) ).
cnf(c_0_45,negated_conjecture,
m1_filter_2(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_46,plain,
! [X528,X529] :
( ( ~ v3_struct_0(k8_filter_0(X528,X529))
| v3_struct_0(X528)
| ~ v10_lattices(X528)
| ~ l3_lattices(X528)
| ~ m1_filter_0(X529,X528) )
& ( v10_lattices(k8_filter_0(X528,X529))
| v3_struct_0(X528)
| ~ v10_lattices(X528)
| ~ l3_lattices(X528)
| ~ m1_filter_0(X529,X528) )
& ( l3_lattices(k8_filter_0(X528,X529))
| v3_struct_0(X528)
| ~ v10_lattices(X528)
| ~ l3_lattices(X528)
| ~ m1_filter_0(X529,X528) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
fof(c_0_47,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_48,plain,
! [X575] :
( ( ~ v3_struct_0(k1_lattice2(X575))
| v3_struct_0(X575)
| ~ l3_lattices(X575) )
& ( v3_lattices(k1_lattice2(X575))
| v3_struct_0(X575)
| ~ l3_lattices(X575) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
cnf(c_0_49,negated_conjecture,
( u1_lattices(esk2_0) = u1_lattices(esk1_0)
| v3_struct_0(k1_lattice2(esk2_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_40]),c_0_41]) ).
cnf(c_0_50,negated_conjecture,
( u2_lattices(k1_lattice2(k1_lattice2(esk1_0))) = u2_lattices(esk2_0)
| v3_struct_0(k1_lattice2(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_18])]) ).
cnf(c_0_51,negated_conjecture,
u1_lattices(k1_lattice2(esk1_0)) = u2_lattices(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_23]) ).
fof(c_0_52,plain,
! [X571] :
( ~ l3_lattices(X571)
| ~ v3_lattices(X571)
| X571 = g3_lattices(u1_struct_0(X571),u2_lattices(X571),u1_lattices(X571)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_lattices])]) ).
cnf(c_0_53,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_43]) ).
cnf(c_0_54,negated_conjecture,
m1_filter_0(esk3_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_44,c_0_45]),c_0_16]),c_0_18])]),c_0_19]) ).
cnf(c_0_55,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_46]) ).
fof(c_0_56,plain,
! [X489,X490] :
( ( ~ v3_struct_0(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) )
& ( v3_lattices(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) )
& ( v4_lattices(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) )
& ( v5_lattices(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) )
& ( v6_lattices(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) )
& ( v7_lattices(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) )
& ( v8_lattices(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) )
& ( v9_lattices(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) )
& ( v10_lattices(k8_filter_0(X489,X490))
| v3_struct_0(X489)
| ~ v10_lattices(X489)
| ~ l3_lattices(X489)
| ~ m1_filter_0(X490,X489) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
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_48]) ).
cnf(c_0_58,negated_conjecture,
( u1_lattices(esk2_0) = u1_lattices(esk1_0)
| v3_struct_0(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_32]),c_0_22])]) ).
cnf(c_0_59,negated_conjecture,
m1_filter_2(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_60,negated_conjecture,
( u2_lattices(esk2_0) = u2_lattices(esk1_0)
| v3_struct_0(k1_lattice2(esk2_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_50]),c_0_51]) ).
cnf(c_0_61,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_52]) ).
cnf(c_0_62,negated_conjecture,
u1_struct_0(k8_filter_0(esk2_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_53,c_0_54]),c_0_16]),c_0_18])]),c_0_19]) ).
cnf(c_0_63,negated_conjecture,
l3_lattices(k8_filter_0(esk2_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_55,c_0_54]),c_0_16]),c_0_18])]),c_0_19]) ).
cnf(c_0_64,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_56]) ).
cnf(c_0_65,plain,
( u1_lattices(k8_filter_0(X1,X2)) = k1_realset1(u1_lattices(X1),X2)
| v3_struct_0(X1)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_66,negated_conjecture,
( u1_lattices(esk2_0) = u1_lattices(esk1_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_18])]),c_0_19]) ).
cnf(c_0_67,negated_conjecture,
m1_filter_0(esk3_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_44,c_0_59]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_68,negated_conjecture,
( u2_lattices(esk2_0) = u2_lattices(esk1_0)
| v3_struct_0(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_32]),c_0_22])]) ).
cnf(c_0_69,negated_conjecture,
( g3_lattices(esk3_0,u2_lattices(k8_filter_0(esk2_0,esk3_0)),u1_lattices(k8_filter_0(esk2_0,esk3_0))) = k8_filter_0(esk2_0,esk3_0)
| ~ v3_lattices(k8_filter_0(esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_70,negated_conjecture,
v3_lattices(k8_filter_0(esk2_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_64,c_0_54]),c_0_16]),c_0_18])]),c_0_19]) ).
cnf(c_0_71,negated_conjecture,
k1_realset1(u1_lattices(esk2_0),esk3_0) = u1_lattices(k8_filter_0(esk2_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_65,c_0_54]),c_0_16]),c_0_18])]),c_0_19]) ).
cnf(c_0_72,negated_conjecture,
u1_lattices(esk2_0) = u1_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_66]),c_0_22])]),c_0_23]) ).
cnf(c_0_73,negated_conjecture,
k1_realset1(u1_lattices(esk1_0),esk3_0) = u1_lattices(k8_filter_0(esk1_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_65,c_0_67]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_74,plain,
( u2_lattices(k8_filter_0(X1,X2)) = k1_realset1(u2_lattices(X1),X2)
| v3_struct_0(X1)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_75,negated_conjecture,
( u2_lattices(esk2_0) = u2_lattices(esk1_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_68]),c_0_18])]),c_0_19]) ).
cnf(c_0_76,negated_conjecture,
u1_struct_0(k8_filter_0(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_53,c_0_67]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_77,negated_conjecture,
l3_lattices(k8_filter_0(esk1_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_55,c_0_67]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_78,negated_conjecture,
g3_lattices(esk3_0,u2_lattices(k8_filter_0(esk2_0,esk3_0)),u1_lattices(k8_filter_0(esk2_0,esk3_0))) = k8_filter_0(esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_79,negated_conjecture,
u1_lattices(k8_filter_0(esk2_0,esk3_0)) = u1_lattices(k8_filter_0(esk1_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_80,negated_conjecture,
k1_realset1(u2_lattices(esk2_0),esk3_0) = u2_lattices(k8_filter_0(esk2_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_74,c_0_54]),c_0_16]),c_0_18])]),c_0_19]) ).
cnf(c_0_81,negated_conjecture,
u2_lattices(esk2_0) = u2_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_75]),c_0_22])]),c_0_23]) ).
cnf(c_0_82,negated_conjecture,
k1_realset1(u2_lattices(esk1_0),esk3_0) = u2_lattices(k8_filter_0(esk1_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_74,c_0_67]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_83,negated_conjecture,
( g3_lattices(esk3_0,u2_lattices(k8_filter_0(esk1_0,esk3_0)),u1_lattices(k8_filter_0(esk1_0,esk3_0))) = k8_filter_0(esk1_0,esk3_0)
| ~ v3_lattices(k8_filter_0(esk1_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_76]),c_0_77])]) ).
cnf(c_0_84,negated_conjecture,
v3_lattices(k8_filter_0(esk1_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_64,c_0_67]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_85,negated_conjecture,
k8_filter_0(esk1_0,esk3_0) != k8_filter_0(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_86,negated_conjecture,
g3_lattices(esk3_0,u2_lattices(k8_filter_0(esk2_0,esk3_0)),u1_lattices(k8_filter_0(esk1_0,esk3_0))) = k8_filter_0(esk2_0,esk3_0),
inference(rw,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
u2_lattices(k8_filter_0(esk2_0,esk3_0)) = u2_lattices(k8_filter_0(esk1_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_88,negated_conjecture,
g3_lattices(esk3_0,u2_lattices(k8_filter_0(esk1_0,esk3_0)),u1_lattices(k8_filter_0(esk1_0,esk3_0))) = k8_filter_0(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
cnf(c_0_89,negated_conjecture,
k8_filter_0(esk2_0,esk3_0) != k8_filter_0(esk1_0,esk3_0),
inference(rw,[status(thm)],[c_0_85,c_0_37]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_88]),c_0_89]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT331+3 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % 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
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 21:21:49 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 13.73/11.87 % Version : CSE_E---1.7
% 13.73/11.87 % Problem : theBenchmark.p
% 13.73/11.87 % SZS status Theorem for theBenchmark.p
% 13.73/11.87 % SZS output start CNFRefutation
% See solution above
% 13.73/11.88 % Total time : 10.703s
%------------------------------------------------------------------------------