%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT309+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 : n028.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 04:38:02 PM UTC 2026
% Result : Theorem 2.21s 1.95s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 104 ( 13 unt; 0 def)
% Number of atoms : 543 ( 46 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 669 ( 230 ~; 250 |; 134 &)
% ( 4 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 89 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',d4_filter_2) ).
fof(t36_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ~ ( v14_lattices(X1)
& X2 != k6_lattices(X1)
& ! [X3] :
( m2_filter_2(X3,X1)
=> ~ ( r2_hidden(X2,X3)
& r2_filter_2(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_filter_2) ).
fof(t24_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ~ ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1)
& X2 != k5_lattices(X1)
& ! [X3] :
( m1_filter_0(X3,X1)
=> ~ ( r2_hidden(X2,X3)
& v1_filter_0(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_0) ).
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/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).
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/theBenchmark.p',t79_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/theBenchmark.p',t64_lattice2) ).
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/theBenchmark.p',fc6_lattice2) ).
fof(dt_m1_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_0) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(dt_k8_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) )
=> m1_subset_1(k8_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_2) ).
fof(d7_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(k1_lattice2(X1))))
=> k8_filter_2(X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_filter_2) ).
fof(dt_k14_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,k1_lattice2(X1)) )
=> m2_filter_2(k14_filter_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_filter_2) ).
fof(redefinition_k14_filter_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,k1_lattice2(X1)) )
=> k14_filter_2(X1,X2) = k8_filter_2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).
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/sandbox/benchmark/theBenchmark.p',d6_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/sandbox/benchmark/theBenchmark.p',redefinition_k15_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/sandbox/benchmark/theBenchmark.p',t33_filter_2) ).
fof(fc1_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_17,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_18,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ~ ( v14_lattices(X1)
& X2 != k6_lattices(X1)
& ! [X3] :
( m2_filter_2(X3,X1)
=> ~ ( r2_hidden(X2,X3)
& r2_filter_2(X1,X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t36_filter_2])]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ~ ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1)
& X2 != k5_lattices(X1)
& ! [X3] :
( m1_filter_0(X3,X1)
=> ~ ( r2_hidden(X2,X3)
& v1_filter_0(X3,X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t24_filter_0]) ).
fof(c_0_20,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_21,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_17])])]) ).
fof(c_0_22,negated_conjecture,
! [X159] :
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& v14_lattices(esk1_0)
& esk2_0 != k6_lattices(esk1_0)
& ( ~ m2_filter_2(X159,esk1_0)
| ~ r2_hidden(esk2_0,X159)
| ~ r2_filter_2(esk1_0,X159) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_23,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_24,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_25,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_26,plain,
! [X284,X285] :
( ( m1_filter_0(esk28_2(X284,X285),X284)
| v3_struct_0(X284)
| ~ v10_lattices(X284)
| ~ v13_lattices(X284)
| ~ l3_lattices(X284)
| X285 = k5_lattices(X284)
| ~ m1_subset_1(X285,u1_struct_0(X284))
| v3_struct_0(X284)
| ~ v10_lattices(X284)
| ~ l3_lattices(X284) )
& ( r2_hidden(X285,esk28_2(X284,X285))
| v3_struct_0(X284)
| ~ v10_lattices(X284)
| ~ v13_lattices(X284)
| ~ l3_lattices(X284)
| X285 = k5_lattices(X284)
| ~ m1_subset_1(X285,u1_struct_0(X284))
| v3_struct_0(X284)
| ~ v10_lattices(X284)
| ~ l3_lattices(X284) )
& ( v1_filter_0(esk28_2(X284,X285),X284)
| v3_struct_0(X284)
| ~ v10_lattices(X284)
| ~ v13_lattices(X284)
| ~ l3_lattices(X284)
| X285 = k5_lattices(X284)
| ~ m1_subset_1(X285,u1_struct_0(X284))
| v3_struct_0(X284)
| ~ v10_lattices(X284)
| ~ l3_lattices(X284) ) ),
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_19])])])])]) ).
fof(c_0_27,plain,
! [X187,X188] :
( v3_struct_0(X187)
| ~ v10_lattices(X187)
| ~ l3_lattices(X187)
| ~ m1_subset_1(X188,u1_struct_0(X187))
| m1_subset_1(k5_filter_2(X187,X188),u1_struct_0(k1_lattice2(X187))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
cnf(c_0_28,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_21]) ).
cnf(c_0_29,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_33,plain,
! [X301] :
( v3_struct_0(X301)
| ~ v10_lattices(X301)
| ~ v14_lattices(X301)
| ~ l3_lattices(X301)
| k6_lattices(X301) = k5_lattices(k1_lattice2(X301)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
fof(c_0_34,plain,
! [X299] :
( ( ~ v14_lattices(X299)
| v13_lattices(k1_lattice2(X299))
| v3_struct_0(X299)
| ~ v10_lattices(X299)
| ~ l3_lattices(X299) )
& ( ~ v13_lattices(k1_lattice2(X299))
| v14_lattices(X299)
| v3_struct_0(X299)
| ~ v10_lattices(X299)
| ~ l3_lattices(X299) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_35,plain,
! [X247] :
( ( ~ v3_struct_0(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( v3_lattices(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( v4_lattices(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( v5_lattices(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( v6_lattices(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( v7_lattices(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( v8_lattices(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( v9_lattices(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) )
& ( v10_lattices(k1_lattice2(X247))
| v3_struct_0(X247)
| ~ v10_lattices(X247)
| ~ l3_lattices(X247) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_36,plain,
( m1_filter_0(esk28_2(X1,X2),X1)
| v3_struct_0(X1)
| X2 = k5_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,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_27]) ).
cnf(c_0_38,negated_conjecture,
k5_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_28,c_0_29]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_39,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_33]) ).
cnf(c_0_40,negated_conjecture,
v14_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_41,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_34]) ).
cnf(c_0_42,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_43,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_filter_0]) ).
cnf(c_0_44,plain,
( X2 = k5_lattices(X1)
| v3_struct_0(X1)
| m1_filter_0(esk28_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v13_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(cn,[status(thm)],[c_0_36]) ).
cnf(c_0_45,negated_conjecture,
m1_subset_1(esk2_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_37,c_0_29]),c_0_38]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_46,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_39,c_0_40]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_47,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_41,c_0_40]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_48,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_42,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_49,negated_conjecture,
esk2_0 != k6_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_50,plain,
! [X186] :
( ( v3_lattices(k1_lattice2(X186))
| ~ l3_lattices(X186) )
& ( l3_lattices(k1_lattice2(X186))
| ~ l3_lattices(X186) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_51,plain,
! [X198,X199] :
( ( ~ v1_xboole_0(X199)
| ~ m1_filter_0(X199,X198)
| v3_struct_0(X198)
| ~ v10_lattices(X198)
| ~ l3_lattices(X198) )
& ( m1_subset_1(X199,k1_zfmisc_1(u1_struct_0(X198)))
| ~ m1_filter_0(X199,X198)
| v3_struct_0(X198)
| ~ v10_lattices(X198)
| ~ l3_lattices(X198) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).
cnf(c_0_52,negated_conjecture,
( m1_filter_0(esk28_2(k1_lattice2(esk1_0),esk2_0),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]),c_0_48])]),c_0_49]) ).
cnf(c_0_53,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_54,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) )
=> m1_subset_1(k8_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k8_filter_2]) ).
cnf(c_0_55,plain,
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X2)
| ~ m1_filter_0(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( m1_filter_0(esk28_2(k1_lattice2(esk1_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_52,c_0_53]),c_0_30])]) ).
fof(c_0_57,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
=> k8_filter_2(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d7_filter_2]) ).
fof(c_0_58,plain,
! [X193,X194] :
( v3_struct_0(X193)
| ~ v10_lattices(X193)
| ~ l3_lattices(X193)
| ~ m1_subset_1(X194,k1_zfmisc_1(u1_struct_0(k1_lattice2(X193))))
| m1_subset_1(k8_filter_2(X193,X194),k1_zfmisc_1(u1_struct_0(X193))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])]) ).
cnf(c_0_59,negated_conjecture,
( m1_subset_1(esk28_2(k1_lattice2(esk1_0),esk2_0),k1_zfmisc_1(u1_struct_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_55,c_0_56]),c_0_48])]) ).
fof(c_0_60,plain,
! [X177,X178] :
( v3_struct_0(X177)
| ~ v10_lattices(X177)
| ~ l3_lattices(X177)
| ~ m1_subset_1(X178,k1_zfmisc_1(u1_struct_0(k1_lattice2(X177))))
| k8_filter_2(X177,X178) = X178 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
fof(c_0_61,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,k1_lattice2(X1)) )
=> m2_filter_2(k14_filter_2(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[dt_k14_filter_2]) ).
fof(c_0_62,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& m1_filter_0(X2,k1_lattice2(X1)) )
=> k14_filter_2(X1,X2) = k8_filter_2(X1,X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k14_filter_2]) ).
fof(c_0_63,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]) ).
cnf(c_0_64,plain,
( v3_struct_0(X1)
| m1_subset_1(k8_filter_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( m1_subset_1(esk28_2(k1_lattice2(esk1_0),esk2_0),k1_zfmisc_1(u1_struct_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_59,c_0_53]),c_0_30])]) ).
cnf(c_0_66,plain,
( v3_struct_0(X1)
| k8_filter_2(X1,X2) = X2
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_67,plain,
! [X182,X183] :
( v3_struct_0(X182)
| ~ v10_lattices(X182)
| ~ l3_lattices(X182)
| ~ m1_filter_0(X183,k1_lattice2(X182))
| m2_filter_2(k14_filter_2(X182,X183),X182) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])]) ).
fof(c_0_68,plain,
! [X272,X273] :
( v3_struct_0(X272)
| ~ v10_lattices(X272)
| ~ l3_lattices(X272)
| ~ m1_filter_0(X273,k1_lattice2(X272))
| k14_filter_2(X272,X273) = k8_filter_2(X272,X273) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])]) ).
fof(c_0_69,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_70,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_63])])]) ).
cnf(c_0_71,negated_conjecture,
( m1_subset_1(k8_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0)),k1_zfmisc_1(u1_struct_0(esk1_0)))
| v3_struct_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_64,c_0_65]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_72,negated_conjecture,
( k8_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0)) = esk28_2(k1_lattice2(esk1_0),esk2_0)
| v3_struct_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_66,c_0_65]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_73,plain,
( v3_struct_0(X1)
| m2_filter_2(k14_filter_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,plain,
( v3_struct_0(X1)
| k14_filter_2(X1,X2) = k8_filter_2(X1,X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_75,plain,
! [X274,X275] :
( v3_struct_0(X274)
| ~ v10_lattices(X274)
| ~ l3_lattices(X274)
| ~ m2_filter_2(X275,X274)
| k15_filter_2(X274,X275) = k7_filter_2(X274,X275) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])]) ).
cnf(c_0_76,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_70]) ).
cnf(c_0_77,negated_conjecture,
( m1_subset_1(esk28_2(k1_lattice2(esk1_0),esk2_0),k1_zfmisc_1(u1_struct_0(esk1_0)))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( m2_filter_2(k14_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0)),esk1_0)
| v3_struct_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_73,c_0_56]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_79,negated_conjecture,
( k14_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0)) = k8_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0))
| v3_struct_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_74,c_0_56]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_80,plain,
( v1_filter_0(esk28_2(X1,X2),X1)
| v3_struct_0(X1)
| X2 = k5_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_81,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]) ).
cnf(c_0_82,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_75]) ).
cnf(c_0_83,negated_conjecture,
( k7_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0)) = esk28_2(k1_lattice2(esk1_0),esk2_0)
| v3_struct_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_76,c_0_77]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_84,negated_conjecture,
( m2_filter_2(k8_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0)),esk1_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,plain,
( X2 = k5_lattices(X1)
| v3_struct_0(X1)
| v1_filter_0(esk28_2(X1,X2),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v13_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(cn,[status(thm)],[c_0_80]) ).
cnf(c_0_86,plain,
( r2_hidden(X1,esk28_2(X2,X1))
| v3_struct_0(X2)
| X1 = k5_lattices(X2)
| v3_struct_0(X2)
| ~ v10_lattices(X2)
| ~ v13_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_87,plain,
! [X289,X290] :
( ( ~ r2_filter_2(X289,X290)
| v1_filter_0(k15_filter_2(X289,X290),k1_lattice2(X289))
| ~ m2_filter_2(X290,X289)
| v3_struct_0(X289)
| ~ v10_lattices(X289)
| ~ l3_lattices(X289) )
& ( ~ v1_filter_0(k15_filter_2(X289,X290),k1_lattice2(X289))
| r2_filter_2(X289,X290)
| ~ m2_filter_2(X290,X289)
| v3_struct_0(X289)
| ~ v10_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_81])])])]) ).
cnf(c_0_88,negated_conjecture,
( k15_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0)) = esk28_2(k1_lattice2(esk1_0),esk2_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ m2_filter_2(esk28_2(k1_lattice2(esk1_0),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_82,c_0_83]),c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_89,negated_conjecture,
( m2_filter_2(esk28_2(k1_lattice2(esk1_0),esk2_0),esk1_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_84,c_0_72]) ).
cnf(c_0_90,negated_conjecture,
( v1_filter_0(esk28_2(k1_lattice2(esk1_0),esk2_0),k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_45]),c_0_46]),c_0_47]),c_0_48])]),c_0_49]) ).
cnf(c_0_91,plain,
( X1 = k5_lattices(X2)
| v3_struct_0(X2)
| r2_hidden(X1,esk28_2(X2,X1))
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ v13_lattices(X2)
| ~ m1_subset_1(X1,u1_struct_0(X2)) ),
inference(cn,[status(thm)],[c_0_86]) ).
fof(c_0_92,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_93,plain,
( r2_filter_2(X1,X2)
| v3_struct_0(X1)
| ~ v1_filter_0(k15_filter_2(X1,X2),k1_lattice2(X1))
| ~ m2_filter_2(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( k15_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0)) = esk28_2(k1_lattice2(esk1_0),esk2_0)
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( v1_filter_0(esk28_2(k1_lattice2(esk1_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_90,c_0_53]),c_0_30])]) ).
cnf(c_0_96,negated_conjecture,
( r2_hidden(esk2_0,esk28_2(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_45]),c_0_46]),c_0_47]),c_0_48])]),c_0_49]) ).
fof(c_0_97,plain,
! [X233] :
( ( ~ v3_struct_0(k1_lattice2(X233))
| v3_struct_0(X233)
| ~ l3_lattices(X233) )
& ( v3_lattices(k1_lattice2(X233))
| v3_struct_0(X233)
| ~ l3_lattices(X233) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])])]) ).
cnf(c_0_98,negated_conjecture,
( ~ m2_filter_2(X1,esk1_0)
| ~ r2_hidden(esk2_0,X1)
| ~ r2_filter_2(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_99,negated_conjecture,
( r2_filter_2(esk1_0,esk28_2(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_30]),c_0_31])]),c_0_32]),c_0_89]),c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( r2_hidden(esk2_0,esk28_2(k1_lattice2(esk1_0),esk2_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_53]),c_0_30])]) ).
cnf(c_0_101,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_102,negated_conjecture,
v3_struct_0(k1_lattice2(esk1_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_89]),c_0_100]) ).
cnf(c_0_103,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_30])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT309+1 : 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
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 21:11:15 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 2.21/1.95 % Version : CSE_E---1.7
% 2.21/1.95 % Problem : theBenchmark.p
% 2.21/1.95 % SZS status Theorem for theBenchmark.p
% 2.21/1.95 % SZS output start CNFRefutation
% See solution above
% 2.21/1.96 % Total time : 1.375s
%------------------------------------------------------------------------------