%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT305+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 : n005.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 01:04:48 PM UTC 2026
% Result : Theorem 20.02s 3.44s
% Output : CNFRefutation 20.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 10 unt; 0 def)
% Number of atoms : 398 ( 13 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 534 ( 200 ~; 193 |; 103 &)
% ( 4 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 114 ( 1 sgn 77 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t31_filter_2,conjecture,
! [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))
=> ( r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(X2,k18_filter_2(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_2) ).
fof(d9_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_2) ).
fof(commutativity_k4_lattices,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l1_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(fraenkel_a_2_0_filter_2,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X2))
& l3_lattices(X2)
& v10_lattices(X2)
& ~ v3_struct_0(X2) )
=> ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
<=> ? [X4] :
( r3_lattices(X2,X4,X3)
& X1 = X4
& m1_subset_1(X4,u1_struct_0(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_2) ).
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(t23_lattices,axiom,
! [X1] :
( ( l3_lattices(X1)
& v8_lattices(X1)
& v6_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,k4_lattices(X1,X2,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
fof(dt_k4_lattices,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l1_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
fof(reflexivity_r3_lattices,axiom,
! [X1,X2,X3] :
( ( 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(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(cc1_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( 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(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(c_0_11,negated_conjecture,
~ ! [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))
=> ( r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(X2,k18_filter_2(X1,X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[t31_filter_2]) ).
fof(c_0_12,negated_conjecture,
~ ! [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))
=> ( r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2))
& r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
& r2_hidden(X2,k18_filter_2(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_13,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d9_filter_2]) ).
fof(c_0_14,negated_conjecture,
( ( ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0)) )
& m1_subset_1(esk3_0,u1_struct_0(esk1_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_12])])])]) ).
fof(c_0_15,plain,
! [X33,X34] :
( k18_filter_2(X33,X34) = a_2_0_filter_2(X33,X34)
| ~ m1_subset_1(X34,u1_struct_0(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_13])])])]) ).
fof(c_0_16,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l1_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
fof(c_0_17,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X2))
& l3_lattices(X2)
& v10_lattices(X2)
& ~ v3_struct_0(X2) )
=> ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
<=> ? [X4] :
( r3_lattices(X2,X4,X3)
& X1 = X4
& m1_subset_1(X4,u1_struct_0(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_filter_2]) ).
cnf(c_0_18,negated_conjecture,
( ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_24,plain,
! [X22,X23,X24] :
( k4_lattices(X22,X23,X24) = k4_lattices(X22,X24,X23)
| ~ m1_subset_1(X24,u1_struct_0(X22))
| ~ m1_subset_1(X23,u1_struct_0(X22))
| ~ l1_lattices(X22)
| ~ v6_lattices(X22)
| v3_struct_0(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_25,plain,
! [X86,X87,X88,X90] :
( ( ~ m1_subset_1(X88,u1_struct_0(X87))
| ~ l3_lattices(X87)
| ~ v10_lattices(X87)
| v3_struct_0(X87)
| r2_hidden(X86,a_2_0_filter_2(X87,X88))
| ~ r3_lattices(X87,X90,X88)
| X86 != X90
| ~ m1_subset_1(X90,u1_struct_0(X87)) )
& ( ~ m1_subset_1(X88,u1_struct_0(X87))
| ~ l3_lattices(X87)
| ~ v10_lattices(X87)
| v3_struct_0(X87)
| ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
| r3_lattices(X87,esk13_3(X86,X87,X88),X88) )
& ( ~ m1_subset_1(X88,u1_struct_0(X87))
| ~ l3_lattices(X87)
| ~ v10_lattices(X87)
| v3_struct_0(X87)
| ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
| X86 = esk13_3(X86,X87,X88) )
& ( ~ m1_subset_1(X88,u1_struct_0(X87))
| ~ l3_lattices(X87)
| ~ v10_lattices(X87)
| v3_struct_0(X87)
| ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
| m1_subset_1(esk13_3(X86,X87,X88),u1_struct_0(X87)) ) ),
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_17])])])])])]) ).
fof(c_0_26,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_27,plain,
! [X1] :
( ( l3_lattices(X1)
& v8_lattices(X1)
& v6_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,k4_lattices(X1,X2,X3),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t23_lattices]) ).
cnf(c_0_28,negated_conjecture,
( ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_29,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_lattices(X1)
| ~ v6_lattices(X1)
| k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,plain,
( ~ m1_subset_1(X4,u1_struct_0(X2))
| ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ r3_lattices(X2,X1,X4)
| X3 != X1
| ~ m1_subset_1(X1,u1_struct_0(X2))
| v3_struct_0(X2)
| r2_hidden(X3,a_2_0_filter_2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X119,X120,X121] :
( ( ~ m1_subset_1(X121,u1_struct_0(X119))
| ~ m1_subset_1(X120,u1_struct_0(X119))
| ~ l3_lattices(X119)
| ~ v9_lattices(X119)
| ~ v8_lattices(X119)
| ~ v6_lattices(X119)
| v3_struct_0(X119)
| r3_lattices(X119,X120,X121)
| ~ r1_lattices(X119,X120,X121) )
& ( ~ m1_subset_1(X121,u1_struct_0(X119))
| ~ m1_subset_1(X120,u1_struct_0(X119))
| ~ l3_lattices(X119)
| ~ v9_lattices(X119)
| ~ v8_lattices(X119)
| ~ v6_lattices(X119)
| v3_struct_0(X119)
| r1_lattices(X119,X120,X121)
| ~ r3_lattices(X119,X120,X121) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
fof(c_0_33,plain,
! [X128,X129,X130] :
( r1_lattices(X128,k4_lattices(X128,X129,X130),X129)
| ~ m1_subset_1(X130,u1_struct_0(X128))
| ~ m1_subset_1(X129,u1_struct_0(X128))
| ~ l3_lattices(X128)
| ~ v8_lattices(X128)
| ~ v6_lattices(X128)
| v3_struct_0(X128) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_34,negated_conjecture,
( ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0))
| ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0))
| ~ v6_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]),c_0_30])]),c_0_23]) ).
cnf(c_0_35,plain,
( ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ r3_lattices(X2,X1,X3)
| v3_struct_0(X2)
| r2_hidden(X1,a_2_0_filter_2(X2,X3)) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_36,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)
| ~ r1_lattices(X1,X2,X3)
| v3_struct_0(X1)
| r3_lattices(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| r1_lattices(X1,k4_lattices(X1,X2,X3),X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( ~ m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0))
| ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0))
| ~ v6_lattices(esk1_0)
| ~ l1_lattices(esk1_0)
| ~ r3_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,esk3_0),esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_39,plain,
( ~ l3_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1))
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| v3_struct_0(X1)
| r3_lattices(X1,k4_lattices(X1,X2,X3),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_40,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l1_lattices(X1)
& v6_lattices(X1)
& ~ v3_struct_0(X1) )
=> m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k4_lattices]) ).
fof(c_0_41,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]) ).
cnf(c_0_42,negated_conjecture,
( ~ m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0))
| ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0))
| ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_20]),c_0_30]),c_0_21])]),c_0_23]) ).
fof(c_0_43,plain,
! [X46,X47,X48] :
( m1_subset_1(k4_lattices(X46,X47,X48),u1_struct_0(X46))
| ~ m1_subset_1(X48,u1_struct_0(X46))
| ~ m1_subset_1(X47,u1_struct_0(X46))
| ~ l1_lattices(X46)
| ~ v6_lattices(X46)
| v3_struct_0(X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
fof(c_0_44,plain,
! [X123,X124,X125] :
( r3_lattices(X123,X124,X124)
| ~ m1_subset_1(X125,u1_struct_0(X123))
| ~ m1_subset_1(X124,u1_struct_0(X123))
| ~ l3_lattices(X123)
| ~ v9_lattices(X123)
| ~ v8_lattices(X123)
| ~ v6_lattices(X123)
| v3_struct_0(X123) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
fof(c_0_45,plain,
! [X67] : m1_subset_1(esk9_1(X67),X67),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_46,negated_conjecture,
( ~ m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0))
| ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| ~ l1_lattices(esk1_0)
| ~ r3_lattices(esk1_0,esk2_0,esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_35]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_47,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_lattices(X1)
| ~ v6_lattices(X1)
| m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,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_49,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_50,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]) ).
cnf(c_0_51,negated_conjecture,
( ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| ~ l1_lattices(esk1_0)
| ~ r3_lattices(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_46,c_0_47]),c_0_30]),c_0_20])]),c_0_23]) ).
cnf(c_0_52,plain,
( ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| v3_struct_0(X1)
| r3_lattices(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_53,plain,
! [X13] :
( ( ~ l3_lattices(X13)
| ~ v10_lattices(X13)
| v3_struct_0(X13)
| v9_lattices(X13) )
& ( ~ l3_lattices(X13)
| ~ v10_lattices(X13)
| v3_struct_0(X13)
| v8_lattices(X13) )
& ( ~ l3_lattices(X13)
| ~ v10_lattices(X13)
| v3_struct_0(X13)
| v7_lattices(X13) )
& ( ~ l3_lattices(X13)
| ~ v10_lattices(X13)
| v3_struct_0(X13)
| v6_lattices(X13) )
& ( ~ l3_lattices(X13)
| ~ v10_lattices(X13)
| v3_struct_0(X13)
| v5_lattices(X13) )
& ( ~ l3_lattices(X13)
| ~ v10_lattices(X13)
| v3_struct_0(X13)
| v4_lattices(X13) )
& ( ~ l3_lattices(X13)
| ~ v10_lattices(X13)
| v3_struct_0(X13)
| ~ v3_struct_0(X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])]) ).
cnf(c_0_54,negated_conjecture,
( ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v9_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_20]),c_0_21])]),c_0_23]) ).
cnf(c_0_55,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v9_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( ~ v6_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_57,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v8_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( ~ v6_lattices(esk1_0)
| ~ l1_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_59,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v6_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_60,plain,
! [X51] :
( ( ~ l3_lattices(X51)
| l2_lattices(X51) )
& ( ~ l3_lattices(X51)
| l1_lattices(X51) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
cnf(c_0_61,negated_conjecture,
~ l1_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_62,plain,
( ~ l3_lattices(X1)
| l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT305+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 20 23:31:18 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 20.02/3.44 % Version: 3.5.1
% 20.02/3.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 20.02/3.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.02/3.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 20.02/3.44 % Starting new_bool_3 with 300s (1) cores
% 20.02/3.44 % Starting new_bool_1 with 300s (1) cores
% 20.02/3.44 % Starting sh5l with 300s (1) cores
% 20.02/3.44 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1997493 completed with status 0
% 20.02/3.44 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 20.02/3.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 20.02/3.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.02/3.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 20.02/3.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 20.02/3.44 % No SInE strategy applied
% 20.02/3.44 % Search class: FGHSM-FFMM31-MFFFFFNN
% 20.02/3.44 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 20.02/3.44 % Starting SubtermCWHack with 136s (1) cores
% 20.02/3.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 20.02/3.44 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 20.02/3.44 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 20.02/3.44 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 20.02/3.44 % G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with pid 1997503 completed with status 0
% 20.02/3.44 % Result found by G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y
% 20.02/3.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 20.02/3.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 20.02/3.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 20.02/3.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 20.02/3.44 % No SInE strategy applied
% 20.02/3.44 % Search class: FGHSM-FFMM31-MFFFFFNN
% 20.02/3.44 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 20.02/3.44 % Starting SubtermCWHack with 136s (1) cores
% 20.02/3.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 20.02/3.44 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 20.02/3.44 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 20.02/3.44 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 20.02/3.44 % Preprocessing time : 0.004 s
% 20.02/3.44
% 20.02/3.44 % Proof found!
% 20.02/3.44 % SZS status Theorem
% 20.02/3.44 % SZS output start CNFRefutation
% See solution above
% 20.02/3.44 % Parsed axioms : 84
% 20.02/3.44 % Removed by relevancy pruning/SinE : 0
% 20.02/3.44 % Initial clauses : 131
% 20.02/3.44 % Removed in clause preprocessing : 17
% 20.02/3.44 % Initial clauses in saturation : 114
% 20.02/3.44 % Processed clauses : 6033
% 20.02/3.44 % ...of these trivial : 1
% 20.02/3.44 % ...subsumed : 4655
% 20.02/3.44 % ...remaining for further processing : 1377
% 20.02/3.44 % Other redundant clauses eliminated : 1
% 20.02/3.44 % Clauses deleted for lack of memory : 0
% 20.02/3.44 % Backward-subsumed : 86
% 20.02/3.44 % Backward-rewritten : 11
% 20.02/3.44 % Generated clauses : 52359
% 20.02/3.44 % ...of the previous two non-redundant : 51700
% 20.02/3.44 % ...aggressively subsumed : 0
% 20.02/3.44 % Contextual simplify-reflections : 97
% 20.02/3.44 % Paramodulations : 52229
% 20.02/3.44 % Factorizations : 104
% 20.02/3.44 % NegExts : 0
% 20.02/3.44 % Equation resolutions : 1
% 20.02/3.44 % Disequality decompositions : 0
% 20.02/3.44 % Total rewrite steps : 1878
% 20.02/3.44 % ...of those cached : 1853
% 20.02/3.44 % Propositional unsat checks : 0
% 20.02/3.44 % Propositional check models : 0
% 20.02/3.44 % Propositional check unsatisfiable : 0
% 20.02/3.44 % Propositional clauses : 0
% 20.02/3.44 % Propositional clauses after purity: 0
% 20.02/3.44 % Propositional unsat core size : 0
% 20.02/3.44 % Propositional preprocessing time : 0.000
% 20.02/3.44 % Propositional encoding time : 0.000
% 20.02/3.44 % Propositional solver time : 0.000
% 20.02/3.44 % Success case prop preproc time : 0.000
% 20.02/3.44 % Success case prop encoding time : 0.000
% 20.02/3.44 % Success case prop solver time : 0.000
% 20.02/3.44 % Current number of processed clauses : 1262
% 20.02/3.44 % Positive orientable unit clauses : 37
% 20.02/3.44 % Positive unorientable unit clauses: 1
% 20.02/3.44 % Negative unit clauses : 16
% 20.02/3.44 % Non-unit-clauses : 1208
% 20.02/3.44 % Current number of unprocessed clauses: 45540
% 20.02/3.44 % ...number of literals in the above : 352237
% 20.02/3.44 % Current number of archived formulas : 0
% 20.02/3.44 % Current number of archived clauses : 98
% 20.02/3.44 % Clause-clause subsumption calls (NU) : 470223
% 20.02/3.44 % Rec. Clause-clause subsumption calls : 47690
% 20.02/3.44 % Non-unit clause-clause subsumptions : 4447
% 20.02/3.44 % Unit Clause-clause subsumption calls : 1161
% 20.02/3.44 % Rewrite failures with RHS unbound : 16
% 20.02/3.44 % BW rewrite match attempts : 19
% 20.02/3.44 % BW rewrite match successes : 11
% 20.02/3.44 % Condensation attempts : 0
% 20.02/3.44 % Condensation successes : 0
% 20.02/3.44 % Termbank termtop insertions : 1828277
% 20.02/3.44 % Search garbage collected termcells : 1559
% 20.02/3.44
% 20.02/3.44 % -------------------------------------------------
% 20.02/3.44 % User time : 2.757 s
% 20.02/3.44 % System time : 0.089 s
% 20.02/3.44 % Total time : 2.846 s
% 20.02/3.44 % Maximum resident set size: 3968 pages
% 20.02/3.44
% 20.02/3.44 % -------------------------------------------------
% 20.02/3.44 % User time : 13.802 s
% 20.02/3.44 % System time : 0.492 s
% 20.02/3.44 % Total time : 14.294 s
% 20.02/3.44 % Maximum resident set size: 4864 pages
% 20.02/3.44 % E exiting
%------------------------------------------------------------------------------