%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT328+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:04:56 PM UTC 2026
% Result : Theorem 110.11s 21.69s
% Output : CNFRefutation 110.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 127 ( 28 unt; 0 def)
% Number of atoms : 573 ( 32 equ)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 709 ( 263 ~; 278 |; 102 &)
% ( 10 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 208 ( 4 sgn 123 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t65_filter_2,conjecture,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r1_filter_2(u1_struct_0(X1),k22_filter_2(X1,X2,X2),k6_domain_1(u1_struct_0(X1),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_filter_2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l2_lattices(X1)
& l1_lattices(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(dt_k22_filter_2,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( m2_lattice4(k22_filter_2(X1,X2,X3),X1)
& ~ v1_xboole_0(k22_filter_2(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k22_filter_2) ).
fof(cc1_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v9_lattices(X1)
& v8_lattices(X1)
& v7_lattices(X1)
& v6_lattices(X1)
& v5_lattices(X1)
& v4_lattices(X1)
& ~ v3_struct_0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(redefinition_k6_domain_1,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,X1)
& ~ v1_xboole_0(X1) )
=> k6_domain_1(X1,X2) = k1_tarski(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
fof(reflexivity_r3_lattices,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v9_lattices(X1)
& v8_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> r3_lattices(X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(dt_k6_domain_1,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,X1)
& ~ v1_xboole_0(X1) )
=> m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).
fof(d1_filter_2,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ( r1_filter_2(X1,X2,X3)
<=> ! [X4] :
( m1_subset_1(X4,X1)
=> ( r2_hidden(X4,X2)
<=> r2_hidden(X4,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).
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(t63_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r2_hidden(X4,k22_filter_2(X1,X2,X3))
<=> ( r3_lattices(X1,X4,X3)
& r3_lattices(X1,X2,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = k1_tarski(X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(redefinition_r3_lattices,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v9_lattices(X1)
& v8_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( r3_lattices(X1,X2,X3)
<=> r1_lattices(X1,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( r2_hidden(X1,X2)
| v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t26_lattices,axiom,
! [X1] :
( ( l2_lattices(X1)
& v4_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ( r1_lattices(X1,X3,X2)
& r1_lattices(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( v1_xboole_0(X3)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r1_filter_2(u1_struct_0(X1),k22_filter_2(X1,X2,X2),k6_domain_1(u1_struct_0(X1),X2)) ) ),
inference(assume_negation,[status(cth)],[t65_filter_2]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r1_filter_2(u1_struct_0(X1),k22_filter_2(X1,X2,X2),k6_domain_1(u1_struct_0(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_22,plain,
! [X32] :
( ( ~ l3_lattices(X32)
| l2_lattices(X32) )
& ( ~ l3_lattices(X32)
| l1_lattices(X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
fof(c_0_23,negated_conjecture,
( ~ r1_filter_2(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k6_domain_1(u1_struct_0(esk1_0),esk2_0))
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& l3_lattices(esk1_0)
& v10_lattices(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
fof(c_0_24,plain,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_25,plain,
! [X30] :
( l1_struct_0(X30)
| ~ l1_lattices(X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])])]) ).
cnf(c_0_26,plain,
( ~ l3_lattices(X1)
| l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( m2_lattice4(k22_filter_2(X1,X2,X3),X1)
& ~ v1_xboole_0(k22_filter_2(X1,X2,X3)) ) ),
inference(fof_simplification,[status(thm)],[dt_k22_filter_2]) ).
fof(c_0_29,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v9_lattices(X1)
& v8_lattices(X1)
& v7_lattices(X1)
& v6_lattices(X1)
& v5_lattices(X1)
& v4_lattices(X1)
& ~ v3_struct_0(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
fof(c_0_30,plain,
! [X1,X2] :
( ( m1_subset_1(X2,X1)
& ~ v1_xboole_0(X1) )
=> k6_domain_1(X1,X2) = k1_tarski(X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k6_domain_1]) ).
fof(c_0_31,plain,
! [X43] :
( ~ v1_xboole_0(u1_struct_0(X43))
| ~ l1_struct_0(X43)
| v3_struct_0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_32,plain,
( ~ l1_lattices(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,negated_conjecture,
l1_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_34,plain,
! [X25,X26,X27] :
( ( ~ m1_subset_1(X27,u1_struct_0(X25))
| ~ m1_subset_1(X26,u1_struct_0(X25))
| ~ l3_lattices(X25)
| ~ v10_lattices(X25)
| v3_struct_0(X25)
| m2_lattice4(k22_filter_2(X25,X26,X27),X25) )
& ( ~ m1_subset_1(X27,u1_struct_0(X25))
| ~ m1_subset_1(X26,u1_struct_0(X25))
| ~ l3_lattices(X25)
| ~ v10_lattices(X25)
| v3_struct_0(X25)
| ~ v1_xboole_0(k22_filter_2(X25,X26,X27)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
fof(c_0_35,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v9_lattices(X1)
& v8_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> r3_lattices(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
fof(c_0_36,plain,
! [X10] :
( ( ~ l3_lattices(X10)
| ~ v10_lattices(X10)
| v3_struct_0(X10)
| v9_lattices(X10) )
& ( ~ l3_lattices(X10)
| ~ v10_lattices(X10)
| v3_struct_0(X10)
| v8_lattices(X10) )
& ( ~ l3_lattices(X10)
| ~ v10_lattices(X10)
| v3_struct_0(X10)
| v7_lattices(X10) )
& ( ~ l3_lattices(X10)
| ~ v10_lattices(X10)
| v3_struct_0(X10)
| v6_lattices(X10) )
& ( ~ l3_lattices(X10)
| ~ v10_lattices(X10)
| v3_struct_0(X10)
| v5_lattices(X10) )
& ( ~ l3_lattices(X10)
| ~ v10_lattices(X10)
| v3_struct_0(X10)
| v4_lattices(X10) )
& ( ~ l3_lattices(X10)
| ~ v10_lattices(X10)
| v3_struct_0(X10)
| ~ v3_struct_0(X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
fof(c_0_37,plain,
! [X1,X2] :
( ( m1_subset_1(X2,X1)
& ~ v1_xboole_0(X1) )
=> m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_domain_1]) ).
fof(c_0_38,plain,
! [X60,X61] :
( k6_domain_1(X60,X61) = k1_tarski(X61)
| ~ m1_subset_1(X61,X60)
| v1_xboole_0(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_39,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_42,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| m2_lattice4(k22_filter_2(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_44,plain,
! [X72,X73,X74] :
( r3_lattices(X72,X73,X73)
| ~ m1_subset_1(X74,u1_struct_0(X72))
| ~ m1_subset_1(X73,u1_struct_0(X72))
| ~ l3_lattices(X72)
| ~ v9_lattices(X72)
| ~ v8_lattices(X72)
| ~ v6_lattices(X72)
| v3_struct_0(X72) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_45,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v9_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v8_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v6_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_48,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ( r1_filter_2(X1,X2,X3)
<=> ! [X4] :
( m1_subset_1(X4,X1)
=> ( r2_hidden(X4,X2)
<=> r2_hidden(X4,X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_filter_2]) ).
fof(c_0_49,plain,
! [X28,X29] :
( m1_subset_1(k6_domain_1(X28,X29),k1_zfmisc_1(X28))
| ~ m1_subset_1(X29,X28)
| v1_xboole_0(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
cnf(c_0_50,plain,
( ~ m1_subset_1(X2,X1)
| k6_domain_1(X1,X2) = k1_tarski(X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_52,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
fof(c_0_53,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(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]) ).
cnf(c_0_54,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| m2_lattice4(k22_filter_2(esk1_0,X1,X2),esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_27])]),c_0_41]) ).
cnf(c_0_55,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| r3_lattices(X1,X2,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,negated_conjecture,
v9_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_43]),c_0_27])]),c_0_41]) ).
cnf(c_0_57,negated_conjecture,
v8_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_27])]),c_0_41]) ).
cnf(c_0_58,negated_conjecture,
v6_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_43]),c_0_27])]),c_0_41]) ).
fof(c_0_59,plain,
! [X39] : m1_subset_1(esk9_1(X39),X39),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_60,plain,
! [X13,X14,X15,X16] :
( ( v1_xboole_0(X13)
| ~ m1_subset_1(X14,k1_zfmisc_1(X13))
| ~ m1_subset_1(X15,k1_zfmisc_1(X13))
| r1_filter_2(X13,X14,X15)
| r2_hidden(esk3_3(X13,X14,X15),X15)
| r2_hidden(esk3_3(X13,X14,X15),X14) )
& ( v1_xboole_0(X13)
| ~ m1_subset_1(X14,k1_zfmisc_1(X13))
| ~ m1_subset_1(X15,k1_zfmisc_1(X13))
| r1_filter_2(X13,X14,X15)
| ~ r2_hidden(esk3_3(X13,X14,X15),X15)
| ~ r2_hidden(esk3_3(X13,X14,X15),X14) )
& ( v1_xboole_0(X13)
| ~ m1_subset_1(X14,k1_zfmisc_1(X13))
| ~ m1_subset_1(X15,k1_zfmisc_1(X13))
| r1_filter_2(X13,X14,X15)
| m1_subset_1(esk3_3(X13,X14,X15),X13) )
& ( v1_xboole_0(X13)
| ~ m1_subset_1(X14,k1_zfmisc_1(X13))
| ~ m1_subset_1(X15,k1_zfmisc_1(X13))
| ~ r1_filter_2(X13,X14,X15)
| ~ m1_subset_1(X16,X13)
| r2_hidden(X16,X14)
| ~ r2_hidden(X16,X15) )
& ( v1_xboole_0(X13)
| ~ m1_subset_1(X14,k1_zfmisc_1(X13))
| ~ m1_subset_1(X15,k1_zfmisc_1(X13))
| ~ r1_filter_2(X13,X14,X15)
| ~ m1_subset_1(X16,X13)
| r2_hidden(X16,X15)
| ~ r2_hidden(X16,X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])])])]) ).
cnf(c_0_61,plain,
( ~ m1_subset_1(X2,X1)
| m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_62,negated_conjecture,
k6_domain_1(u1_struct_0(esk1_0),esk2_0) = k1_tarski(esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
fof(c_0_63,plain,
! [X33,X34] :
( m1_subset_1(X34,k1_zfmisc_1(u1_struct_0(X33)))
| ~ m2_lattice4(X34,X33)
| ~ l3_lattices(X33)
| ~ v10_lattices(X33)
| v3_struct_0(X33) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
cnf(c_0_64,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| m2_lattice4(k22_filter_2(esk1_0,X1,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
fof(c_0_65,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r2_hidden(X4,k22_filter_2(X1,X2,X3))
<=> ( r3_lattices(X1,X4,X3)
& r3_lattices(X1,X2,X4) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t63_filter_2]) ).
cnf(c_0_66,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| r3_lattices(esk1_0,X1,X1) ),
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_55,c_0_56]),c_0_57]),c_0_58]),c_0_27])]),c_0_41]) ).
cnf(c_0_67,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1)
| r1_filter_2(X1,X2,X3)
| r2_hidden(esk3_3(X1,X2,X3),X3)
| r2_hidden(esk3_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_69,negated_conjecture,
m1_subset_1(k1_tarski(esk2_0),k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_51]),c_0_62]),c_0_52]) ).
cnf(c_0_70,plain,
( ~ m2_lattice4(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,negated_conjecture,
m2_lattice4(k22_filter_2(esk1_0,esk2_0,esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_64,c_0_51]) ).
cnf(c_0_72,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k6_domain_1(u1_struct_0(esk1_0),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_73,plain,
! [X93,X94,X95,X96] :
( ( ~ l3_lattices(X93)
| ~ v10_lattices(X93)
| v3_struct_0(X93)
| ~ m1_subset_1(X94,u1_struct_0(X93))
| ~ m1_subset_1(X95,u1_struct_0(X93))
| ~ m1_subset_1(X96,u1_struct_0(X93))
| ~ r3_lattices(X93,X94,X95)
| r2_hidden(X96,k22_filter_2(X93,X94,X95))
| ~ r3_lattices(X93,X96,X95)
| ~ r3_lattices(X93,X94,X96) )
& ( ~ l3_lattices(X93)
| ~ v10_lattices(X93)
| v3_struct_0(X93)
| ~ m1_subset_1(X94,u1_struct_0(X93))
| ~ m1_subset_1(X95,u1_struct_0(X93))
| ~ m1_subset_1(X96,u1_struct_0(X93))
| ~ r3_lattices(X93,X94,X95)
| ~ r2_hidden(X96,k22_filter_2(X93,X94,X95))
| r3_lattices(X93,X96,X95) )
& ( ~ l3_lattices(X93)
| ~ v10_lattices(X93)
| v3_struct_0(X93)
| ~ m1_subset_1(X94,u1_struct_0(X93))
| ~ m1_subset_1(X95,u1_struct_0(X93))
| ~ m1_subset_1(X96,u1_struct_0(X93))
| ~ r3_lattices(X93,X94,X95)
| ~ r2_hidden(X96,k22_filter_2(X93,X94,X95))
| r3_lattices(X93,X94,X96) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])]) ).
cnf(c_0_74,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| r3_lattices(esk1_0,X1,X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
fof(c_0_75,plain,
! [X18,X19,X20,X21,X22,X23] :
( ( X23 = k1_tarski(X22)
| esk4_2(X22,X23) = X22
| r2_hidden(esk4_2(X22,X23),X23) )
& ( X23 = k1_tarski(X22)
| esk4_2(X22,X23) != X22
| ~ r2_hidden(esk4_2(X22,X23),X23) )
& ( X19 != k1_tarski(X18)
| r2_hidden(X21,X19)
| X21 != X18 )
& ( X19 != k1_tarski(X18)
| X20 = X18
| ~ r2_hidden(X20,X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])])]) ).
fof(c_0_76,plain,
! [X78,X79] :
( m1_subset_1(X78,X79)
| ~ r2_hidden(X78,X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_77,negated_conjecture,
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))
| r1_filter_2(u1_struct_0(esk1_0),X1,k1_tarski(esk2_0))
| r2_hidden(esk3_3(u1_struct_0(esk1_0),X1,k1_tarski(esk2_0)),X1)
| r2_hidden(esk3_3(u1_struct_0(esk1_0),X1,k1_tarski(esk2_0)),k1_tarski(esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_52]) ).
cnf(c_0_78,negated_conjecture,
m1_subset_1(k22_filter_2(esk1_0,esk2_0,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_70,c_0_71]),c_0_27]),c_0_43])]),c_0_41]) ).
cnf(c_0_79,negated_conjecture,
~ r1_filter_2(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),
inference(rw,[status(thm)],[c_0_72,c_0_62]) ).
cnf(c_0_80,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ r3_lattices(X1,X2,X4)
| ~ r3_lattices(X1,X3,X4)
| ~ r3_lattices(X1,X2,X3)
| v3_struct_0(X1)
| r2_hidden(X3,k22_filter_2(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,negated_conjecture,
r3_lattices(esk1_0,esk2_0,esk2_0),
inference(spm,[status(thm)],[c_0_74,c_0_51]) ).
cnf(c_0_82,plain,
( X2 != k1_tarski(X3)
| ~ r2_hidden(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),k1_tarski(esk2_0))
| r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),k22_filter_2(esk1_0,esk2_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
fof(c_0_85,plain,
! [X98,X99] :
( ~ v1_xboole_0(X99)
| ~ r2_hidden(X98,X99) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_86,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r3_lattices(esk1_0,X1,esk2_0)
| r2_hidden(esk2_0,k22_filter_2(esk1_0,X1,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_80,c_0_81]),c_0_51]),c_0_27]),c_0_43])]),c_0_41]) ).
fof(c_0_87,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l3_lattices(X1)
& v9_lattices(X1)
& v8_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( r3_lattices(X1,X2,X3)
<=> r1_lattices(X1,X2,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).
fof(c_0_88,plain,
! [X83,X84] :
( r2_hidden(X83,X84)
| v1_xboole_0(X84)
| ~ m1_subset_1(X83,X84) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_89,plain,
( ~ r2_hidden(X1,k1_tarski(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_90,negated_conjecture,
( m1_subset_1(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),k22_filter_2(esk1_0,esk2_0,esk2_0))
| r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),k1_tarski(esk2_0)) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_92,negated_conjecture,
r2_hidden(esk2_0,k22_filter_2(esk1_0,esk2_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_81]),c_0_51])]) ).
cnf(c_0_93,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1)
| r1_filter_2(X1,X2,X3)
| m1_subset_1(esk3_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_94,plain,
! [X1] :
( ( l2_lattices(X1)
& v4_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ( r1_lattices(X1,X3,X2)
& r1_lattices(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[t26_lattices]) ).
fof(c_0_95,plain,
! [X65,X66,X67] :
( ( ~ m1_subset_1(X67,u1_struct_0(X65))
| ~ m1_subset_1(X66,u1_struct_0(X65))
| ~ l3_lattices(X65)
| ~ v9_lattices(X65)
| ~ v8_lattices(X65)
| ~ v6_lattices(X65)
| v3_struct_0(X65)
| r3_lattices(X65,X66,X67)
| ~ r1_lattices(X65,X66,X67) )
& ( ~ m1_subset_1(X67,u1_struct_0(X65))
| ~ m1_subset_1(X66,u1_struct_0(X65))
| ~ l3_lattices(X65)
| ~ v9_lattices(X65)
| ~ v8_lattices(X65)
| ~ v6_lattices(X65)
| v3_struct_0(X65)
| r1_lattices(X65,X66,X67)
| ~ r3_lattices(X65,X66,X67) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])])]) ).
cnf(c_0_96,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r3_lattices(X1,X4,X3)
| ~ r2_hidden(X2,k22_filter_2(X1,X4,X3))
| v3_struct_0(X1)
| r3_lattices(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_97,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_98,negated_conjecture,
( m1_subset_1(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),k22_filter_2(esk1_0,esk2_0,esk2_0))
| esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_99,negated_conjecture,
~ v1_xboole_0(k22_filter_2(esk1_0,esk2_0,esk2_0)),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,negated_conjecture,
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))
| m1_subset_1(esk3_3(u1_struct_0(esk1_0),X1,k1_tarski(esk2_0)),u1_struct_0(esk1_0))
| r1_filter_2(u1_struct_0(esk1_0),X1,k1_tarski(esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_69]),c_0_52]) ).
cnf(c_0_101,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ r3_lattices(X1,X2,X4)
| ~ r2_hidden(X3,k22_filter_2(X1,X2,X4))
| v3_struct_0(X1)
| r3_lattices(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
fof(c_0_102,plain,
! [X80,X81,X82] :
( X81 = X82
| ~ r1_lattices(X80,X82,X81)
| ~ r1_lattices(X80,X81,X82)
| ~ m1_subset_1(X82,u1_struct_0(X80))
| ~ m1_subset_1(X81,u1_struct_0(X80))
| ~ l2_lattices(X80)
| ~ v4_lattices(X80)
| v3_struct_0(X80) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])])]) ).
cnf(c_0_103,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v4_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_104,plain,
( ~ l3_lattices(X1)
| l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_105,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| ~ r3_lattices(X1,X2,X3)
| v3_struct_0(X1)
| r1_lattices(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_106,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,k22_filter_2(esk1_0,esk2_0,esk2_0))
| r3_lattices(esk1_0,X1,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_96,c_0_81]),c_0_51]),c_0_27]),c_0_43])]),c_0_41]) ).
cnf(c_0_107,negated_conjecture,
( r2_hidden(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),k22_filter_2(esk1_0,esk2_0,esk2_0))
| esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)) = esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_108,negated_conjecture,
m1_subset_1(esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_78]),c_0_79]) ).
cnf(c_0_109,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,k22_filter_2(esk1_0,esk2_0,esk2_0))
| r3_lattices(esk1_0,esk2_0,X1) ),
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_101,c_0_81]),c_0_51]),c_0_27]),c_0_43])]),c_0_41]) ).
fof(c_0_110,plain,
! [X90,X91,X92] :
( ~ v1_xboole_0(X92)
| ~ m1_subset_1(X91,k1_zfmisc_1(X92))
| ~ r2_hidden(X90,X91) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
cnf(c_0_111,plain,
( ~ r1_lattices(X1,X3,X2)
| ~ r1_lattices(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l2_lattices(X1)
| ~ v4_lattices(X1)
| X2 = X3
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_112,negated_conjecture,
v4_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_43]),c_0_27])]),c_0_41]) ).
cnf(c_0_113,negated_conjecture,
l2_lattices(esk1_0),
inference(spm,[status(thm)],[c_0_104,c_0_27]) ).
cnf(c_0_114,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ r3_lattices(esk1_0,X1,X2)
| r1_lattices(esk1_0,X1,X2) ),
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_105,c_0_56]),c_0_57]),c_0_58]),c_0_27])]),c_0_41]) ).
cnf(c_0_115,negated_conjecture,
( r3_lattices(esk1_0,esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),esk2_0)
| esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108])]) ).
cnf(c_0_116,negated_conjecture,
( r3_lattices(esk1_0,esk2_0,esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)))
| esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_107]),c_0_108])]) ).
cnf(c_0_117,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ r2_hidden(esk3_3(X1,X2,X3),X3)
| ~ r2_hidden(esk3_3(X1,X2,X3),X2)
| v1_xboole_0(X1)
| r1_filter_2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_118,plain,
( ~ v1_xboole_0(X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_119,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ r1_lattices(esk1_0,X1,X2)
| ~ r1_lattices(esk1_0,X2,X1)
| X1 = X2 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113])]),c_0_41]) ).
cnf(c_0_120,negated_conjecture,
( r1_lattices(esk1_0,esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)),esk2_0)
| esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_51]),c_0_108])]) ).
cnf(c_0_121,negated_conjecture,
( r1_lattices(esk1_0,esk2_0,esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)))
| esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_116]),c_0_108]),c_0_51])]) ).
cnf(c_0_122,plain,
( X3 != k1_tarski(X2)
| X1 != X2
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_123,plain,
( ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ r2_hidden(esk3_3(X1,X2,X3),X2)
| ~ r2_hidden(esk3_3(X1,X2,X3),X3)
| r1_filter_2(X1,X2,X3) ),
inference(csr,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_124,negated_conjecture,
esk3_3(u1_struct_0(esk1_0),k22_filter_2(esk1_0,esk2_0,esk2_0),k1_tarski(esk2_0)) = esk2_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_108]),c_0_51])]),c_0_121]) ).
cnf(c_0_125,plain,
r2_hidden(X1,k1_tarski(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_122])]) ).
cnf(c_0_126,negated_conjecture,
$false,
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_123,c_0_124]),c_0_125]),c_0_92]),c_0_69]),c_0_78])]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT328+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.45 % Computer : n010.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Sun Sep 20 23:39:15 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/5.52 Running first-order theorem proving
% 0.24/5.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 110.11/21.68 % Version: 3.5.1
% 110.11/21.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 110.11/21.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.11/21.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 110.11/21.68 % Starting new_bool_3 with 300s (1) cores
% 110.11/21.68 % Starting new_bool_1 with 300s (1) cores
% 110.11/21.68 % Starting sh5l with 300s (1) cores
% 110.11/21.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3772894 completed with status 0
% 110.11/21.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 110.11/21.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 110.11/21.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.11/21.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 110.11/21.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 110.11/21.68 % No SInE strategy applied
% 110.11/21.68 % Search class: FGHSM-FFMM31-SFFFFFNN
% 110.11/21.68 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 110.11/21.68 % Starting SubtermCWHack with 136s (1) cores
% 110.11/21.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 110.11/21.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 110.11/21.69 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 110.11/21.69 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 110.11/21.69 % G-E--_208_C18_F1_SE_CS_SP_PS_S4b with pid 3772903 completed with status 0
% 110.11/21.69 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4b
% 110.11/21.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 110.11/21.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 110.11/21.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 110.11/21.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 110.11/21.69 % No SInE strategy applied
% 110.11/21.69 % Search class: FGHSM-FFMM31-SFFFFFNN
% 110.11/21.69 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 110.11/21.69 % Starting SubtermCWHack with 136s (1) cores
% 110.11/21.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 110.11/21.69 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 110.11/21.69 % Preprocessing time : 0.003 s
% 110.11/21.69 % Presaturation interreduction done
% 110.11/21.69
% 110.11/21.69 % Proof found!
% 110.11/21.69 % SZS status Theorem
% 110.11/21.69 % SZS output start CNFRefutation
% See solution above
% 110.11/21.69 % Parsed axioms : 57
% 110.11/21.69 % Removed by relevancy pruning/SinE : 0
% 110.11/21.69 % Initial clauses : 91
% 110.11/21.69 % Removed in clause preprocessing : 8
% 110.11/21.69 % Initial clauses in saturation : 83
% 110.11/21.69 % Processed clauses : 18708
% 110.11/21.69 % ...of these trivial : 215
% 110.11/21.69 % ...subsumed : 8919
% 110.11/21.69 % ...remaining for further processing : 9574
% 110.11/21.69 % Other redundant clauses eliminated : 16
% 110.11/21.69 % Clauses deleted for lack of memory : 0
% 110.11/21.69 % Backward-subsumed : 18
% 110.11/21.69 % Backward-rewritten : 439
% 110.11/21.69 % Generated clauses : 364500
% 110.11/21.69 % ...of the previous two non-redundant : 357962
% 110.11/21.69 % ...aggressively subsumed : 0
% 110.11/21.69 % Contextual simplify-reflections : 164
% 110.11/21.69 % Paramodulations : 364475
% 110.11/21.69 % Factorizations : 10
% 110.11/21.69 % NegExts : 0
% 110.11/21.69 % Equation resolutions : 16
% 110.11/21.69 % Disequality decompositions : 0
% 110.11/21.69 % Total rewrite steps : 41234
% 110.11/21.69 % ...of those cached : 39076
% 110.11/21.69 % Propositional unsat checks : 0
% 110.11/21.69 % Propositional check models : 0
% 110.11/21.69 % Propositional check unsatisfiable : 0
% 110.11/21.69 % Propositional clauses : 0
% 110.11/21.69 % Propositional clauses after purity: 0
% 110.11/21.69 % Propositional unsat core size : 0
% 110.11/21.69 % Propositional preprocessing time : 0.000
% 110.11/21.69 % Propositional encoding time : 0.000
% 110.11/21.69 % Propositional solver time : 0.000
% 110.11/21.69 % Success case prop preproc time : 0.000
% 110.11/21.69 % Success case prop encoding time : 0.000
% 110.11/21.69 % Success case prop solver time : 0.000
% 110.11/21.69 % Current number of processed clauses : 9033
% 110.11/21.69 % Positive orientable unit clauses : 1382
% 110.11/21.69 % Positive unorientable unit clauses: 0
% 110.11/21.69 % Negative unit clauses : 319
% 110.11/21.69 % Non-unit-clauses : 7332
% 110.11/21.69 % Current number of unprocessed clauses: 338942
% 110.11/21.69 % ...number of literals in the above : 1168836
% 110.11/21.69 % Current number of archived formulas : 0
% 110.11/21.69 % Current number of archived clauses : 538
% 110.11/21.69 % Clause-clause subsumption calls (NU) : 13820770
% 110.11/21.69 % Rec. Clause-clause subsumption calls : 9312397
% 110.11/21.69 % Non-unit clause-clause subsumptions : 7129
% 110.11/21.69 % Unit Clause-clause subsumption calls : 1345472
% 110.11/21.69 % Rewrite failures with RHS unbound : 0
% 110.11/21.69 % BW rewrite match attempts : 87840
% 110.11/21.69 % BW rewrite match successes : 57
% 110.11/21.69 % Condensation attempts : 0
% 110.11/21.69 % Condensation successes : 0
% 110.11/21.69 % Termbank termtop insertions : 17893555
% 110.11/21.69 % Search garbage collected termcells : 1319
% 110.11/21.69
% 110.11/21.69 % -------------------------------------------------
% 110.11/21.69 % User time : 14.770 s
% 110.11/21.69 % System time : 0.491 s
% 110.11/21.69 % Total time : 15.261 s
% 110.11/21.69 % Maximum resident set size: 3940 pages
% 110.11/21.69
% 110.11/21.69 % -------------------------------------------------
% 110.11/21.69 % User time : 75.518 s
% 110.11/21.69 % System time : 2.340 s
% 110.11/21.69 % Total time : 77.859 s
% 110.11/21.69 % Maximum resident set size: 4608 pages
% 110.11/21.69 % E exiting
%------------------------------------------------------------------------------