TSTP Solution File: LAT301+3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : LAT301+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 : Sat May 4 08:14:54 EDT 2024
% Result : Theorem 8.56s 4.24s
% Output : CNFRefutation 8.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 82 ( 21 unt; 0 def)
% Number of atoms : 417 ( 16 equ)
% Maximal formula atoms : 87 ( 5 avg)
% Number of connectives : 481 ( 146 ~; 180 |; 100 &)
% ( 5 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-3 aty)
% Number of variables : 119 ( 0 sgn 84 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_m2_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',dt_m2_filter_2) ).
fof(t25_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> r2_hidden(k5_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',t25_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',dt_m2_lattice4) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',t3_subset) ).
fof(t24_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
& r2_hidden(X3,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',t24_filter_2) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',d3_tarski) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',dt_k1_lattice2) ).
fof(t78_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1) )
=> k5_lattices(X1) = k6_lattices(k1_lattice2(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',t78_lattice2) ).
fof(t18_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1))
& u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
& u1_lattices(X1) = u2_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',t18_lattice2) ).
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/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',fc1_lattice2) ).
fof(t41_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r3_lattices(X1,k5_lattices(X1),X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',t41_lattices) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',t1_subset) ).
fof(dt_k6_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',dt_k6_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',dt_l3_lattices) ).
fof(t22_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( m2_filter_2(X2,X1)
<=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
=> r2_hidden(k3_lattices(X1,X3,X4),X2) ) ) )
& ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r3_lattices(X1,X4,X3) )
=> r2_hidden(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BPWNALqi3M/E---3.1_28425.p',t22_filter_2) ).
fof(c_0_15,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_filter_2]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> r2_hidden(k5_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t25_filter_2])]) ).
fof(c_0_17,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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]) ).
fof(c_0_18,plain,
! [X101,X102] :
( ( ~ v1_xboole_0(X102)
| ~ m2_filter_2(X102,X101)
| v3_struct_0(X101)
| ~ v10_lattices(X101)
| ~ l3_lattices(X101) )
& ( m2_lattice4(X102,X101)
| ~ m2_filter_2(X102,X101)
| v3_struct_0(X101)
| ~ v10_lattices(X101)
| ~ l3_lattices(X101) ) ),
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_15])])])])]) ).
fof(c_0_19,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m2_filter_2(esk2_0,esk1_0)
& v13_lattices(esk1_0)
& ~ r2_hidden(k5_lattices(esk1_0),esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_20,plain,
! [X481,X482] :
( v3_struct_0(X481)
| ~ v10_lattices(X481)
| ~ l3_lattices(X481)
| ~ m2_lattice4(X482,X481)
| m1_subset_1(X482,k1_zfmisc_1(u1_struct_0(X481))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_21,plain,
( m2_lattice4(X1,X2)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,plain,
! [X161,X162] :
( ( ~ m1_subset_1(X161,k1_zfmisc_1(X162))
| r1_tarski(X161,X162) )
& ( ~ r1_tarski(X161,X162)
| m1_subset_1(X161,k1_zfmisc_1(X162)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_27,plain,
( v3_struct_0(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
m2_lattice4(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_21,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).
fof(c_0_29,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
& r2_hidden(X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[t24_filter_2]) ).
fof(c_0_30,plain,
! [X500,X501,X502,X503,X504] :
( ( ~ r1_tarski(X500,X501)
| ~ r2_hidden(X502,X500)
| r2_hidden(X502,X501) )
& ( r2_hidden(esk62_2(X503,X504),X503)
| r1_tarski(X503,X504) )
& ( ~ r2_hidden(esk62_2(X503,X504),X504)
| r1_tarski(X503,X504) ) ),
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)],[d3_tarski])])])])])])]) ).
cnf(c_0_31,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
m1_subset_1(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_27,c_0_28]),c_0_23]),c_0_24])]),c_0_25]) ).
fof(c_0_33,plain,
! [X124,X125] :
( ( m1_subset_1(esk15_2(X124,X125),u1_struct_0(X124))
| ~ m2_filter_2(X125,X124)
| v3_struct_0(X124)
| ~ v10_lattices(X124)
| ~ l3_lattices(X124) )
& ( r2_hidden(esk15_2(X124,X125),X125)
| ~ m2_filter_2(X125,X124)
| v3_struct_0(X124)
| ~ v10_lattices(X124)
| ~ l3_lattices(X124) ) ),
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_29])])])])])]) ).
cnf(c_0_34,plain,
( r2_hidden(X3,X2)
| ~ r1_tarski(X1,X2)
| ~ r2_hidden(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
r1_tarski(esk2_0,u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( r2_hidden(esk15_2(X1,X2),X2)
| v3_struct_0(X1)
| ~ m2_filter_2(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_37,plain,
! [X355] :
( ( v3_lattices(k1_lattice2(X355))
| ~ l3_lattices(X355) )
& ( l3_lattices(k1_lattice2(X355))
| ~ l3_lattices(X355) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])])]) ).
fof(c_0_38,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1) )
=> k5_lattices(X1) = k6_lattices(k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[t78_lattice2]) ).
fof(c_0_39,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1))
& u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
& u1_lattices(X1) = u2_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t18_lattice2]) ).
fof(c_0_40,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]) ).
fof(c_0_41,plain,
! [X1,X2] :
( epred1_2(X2,X1)
<=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r2_hidden(X4,X2) )
=> r2_hidden(k3_lattices(X1,X3,X4),X2) ) ) )
& ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r3_lattices(X1,X4,X3) )
=> r2_hidden(X4,X2) ) ) ) ) ),
introduced(definition) ).
fof(c_0_42,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v13_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r3_lattices(X1,k5_lattices(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[t41_lattices]) ).
fof(c_0_43,plain,
! [X41,X42] :
( ~ r2_hidden(X41,X42)
| m1_subset_1(X41,X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_44,negated_conjecture,
( r2_hidden(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_45,negated_conjecture,
r2_hidden(esk15_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_36,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).
fof(c_0_46,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_lattices(X1) )
=> m1_subset_1(k6_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k6_lattices]) ).
fof(c_0_47,plain,
! [X1147] :
( ( l1_lattices(X1147)
| ~ l3_lattices(X1147) )
& ( l2_lattices(X1147)
| ~ l3_lattices(X1147) ) ),
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_48,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_49,plain,
! [X91] :
( v3_struct_0(X91)
| ~ v10_lattices(X91)
| ~ v13_lattices(X91)
| ~ l3_lattices(X91)
| k5_lattices(X91) = k6_lattices(k1_lattice2(X91)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
fof(c_0_50,plain,
! [X267] :
( ( u1_struct_0(X267) = u1_struct_0(k1_lattice2(X267))
| v3_struct_0(X267)
| ~ l3_lattices(X267) )
& ( u2_lattices(X267) = u1_lattices(k1_lattice2(X267))
| v3_struct_0(X267)
| ~ l3_lattices(X267) )
& ( u1_lattices(X267) = u2_lattices(k1_lattice2(X267))
| v3_struct_0(X267)
| ~ l3_lattices(X267) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).
fof(c_0_51,plain,
! [X340] :
( ( ~ v3_struct_0(k1_lattice2(X340))
| v3_struct_0(X340)
| ~ l3_lattices(X340) )
& ( v3_lattices(k1_lattice2(X340))
| v3_struct_0(X340)
| ~ l3_lattices(X340) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
fof(c_0_52,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
=> ( m2_filter_2(X2,X1)
<=> epred1_2(X2,X1) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[t22_filter_2]),c_0_41]) ).
fof(c_0_53,plain,
! [X73,X74] :
( v3_struct_0(X73)
| ~ v10_lattices(X73)
| ~ v13_lattices(X73)
| ~ l3_lattices(X73)
| ~ m1_subset_1(X74,u1_struct_0(X73))
| r3_lattices(X73,k5_lattices(X73),X74) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
cnf(c_0_54,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,negated_conjecture,
r2_hidden(esk15_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_56,plain,
! [X324] :
( v3_struct_0(X324)
| ~ l2_lattices(X324)
| m1_subset_1(k6_lattices(X324),u1_struct_0(X324)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
cnf(c_0_57,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,negated_conjecture,
l3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_48,c_0_24]) ).
cnf(c_0_59,plain,
( v3_struct_0(X1)
| k5_lattices(X1) = k6_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,negated_conjecture,
v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_61,plain,
( u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_62,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_63,plain,
! [X118,X119] :
( ( ~ m2_filter_2(X119,X118)
| epred1_2(X119,X118)
| v1_xboole_0(X119)
| ~ m1_subset_1(X119,k1_zfmisc_1(u1_struct_0(X118)))
| v3_struct_0(X118)
| ~ v10_lattices(X118)
| ~ l3_lattices(X118) )
& ( ~ epred1_2(X119,X118)
| m2_filter_2(X119,X118)
| v1_xboole_0(X119)
| ~ m1_subset_1(X119,k1_zfmisc_1(u1_struct_0(X118)))
| v3_struct_0(X118)
| ~ v10_lattices(X118)
| ~ l3_lattices(X118) ) ),
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_52])])])])]) ).
fof(c_0_64,plain,
! [X1351,X1352,X1353,X1354,X1355,X1356,X1357,X1358] :
( ( ~ m1_subset_1(X1353,u1_struct_0(X1351))
| ~ m1_subset_1(X1354,u1_struct_0(X1351))
| ~ r2_hidden(X1353,X1352)
| ~ r2_hidden(X1354,X1352)
| r2_hidden(k3_lattices(X1351,X1353,X1354),X1352)
| ~ epred1_2(X1352,X1351) )
& ( ~ m1_subset_1(X1355,u1_struct_0(X1351))
| ~ m1_subset_1(X1356,u1_struct_0(X1351))
| ~ r2_hidden(X1355,X1352)
| ~ r3_lattices(X1351,X1356,X1355)
| r2_hidden(X1356,X1352)
| ~ epred1_2(X1352,X1351) )
& ( m1_subset_1(esk186_2(X1357,X1358),u1_struct_0(X1357))
| m1_subset_1(esk184_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk187_2(X1357,X1358),u1_struct_0(X1357))
| m1_subset_1(esk184_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( r2_hidden(esk186_2(X1357,X1358),X1358)
| m1_subset_1(esk184_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( r3_lattices(X1357,esk187_2(X1357,X1358),esk186_2(X1357,X1358))
| m1_subset_1(esk184_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( ~ r2_hidden(esk187_2(X1357,X1358),X1358)
| m1_subset_1(esk184_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk186_2(X1357,X1358),u1_struct_0(X1357))
| m1_subset_1(esk185_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk187_2(X1357,X1358),u1_struct_0(X1357))
| m1_subset_1(esk185_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( r2_hidden(esk186_2(X1357,X1358),X1358)
| m1_subset_1(esk185_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( r3_lattices(X1357,esk187_2(X1357,X1358),esk186_2(X1357,X1358))
| m1_subset_1(esk185_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( ~ r2_hidden(esk187_2(X1357,X1358),X1358)
| m1_subset_1(esk185_2(X1357,X1358),u1_struct_0(X1357))
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk186_2(X1357,X1358),u1_struct_0(X1357))
| r2_hidden(esk184_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk187_2(X1357,X1358),u1_struct_0(X1357))
| r2_hidden(esk184_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( r2_hidden(esk186_2(X1357,X1358),X1358)
| r2_hidden(esk184_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( r3_lattices(X1357,esk187_2(X1357,X1358),esk186_2(X1357,X1358))
| r2_hidden(esk184_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( ~ r2_hidden(esk187_2(X1357,X1358),X1358)
| r2_hidden(esk184_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk186_2(X1357,X1358),u1_struct_0(X1357))
| r2_hidden(esk185_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk187_2(X1357,X1358),u1_struct_0(X1357))
| r2_hidden(esk185_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( r2_hidden(esk186_2(X1357,X1358),X1358)
| r2_hidden(esk185_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( r3_lattices(X1357,esk187_2(X1357,X1358),esk186_2(X1357,X1358))
| r2_hidden(esk185_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( ~ r2_hidden(esk187_2(X1357,X1358),X1358)
| r2_hidden(esk185_2(X1357,X1358),X1358)
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk186_2(X1357,X1358),u1_struct_0(X1357))
| ~ r2_hidden(k3_lattices(X1357,esk184_2(X1357,X1358),esk185_2(X1357,X1358)),X1358)
| epred1_2(X1358,X1357) )
& ( m1_subset_1(esk187_2(X1357,X1358),u1_struct_0(X1357))
| ~ r2_hidden(k3_lattices(X1357,esk184_2(X1357,X1358),esk185_2(X1357,X1358)),X1358)
| epred1_2(X1358,X1357) )
& ( r2_hidden(esk186_2(X1357,X1358),X1358)
| ~ r2_hidden(k3_lattices(X1357,esk184_2(X1357,X1358),esk185_2(X1357,X1358)),X1358)
| epred1_2(X1358,X1357) )
& ( r3_lattices(X1357,esk187_2(X1357,X1358),esk186_2(X1357,X1358))
| ~ r2_hidden(k3_lattices(X1357,esk184_2(X1357,X1358),esk185_2(X1357,X1358)),X1358)
| epred1_2(X1358,X1357) )
& ( ~ r2_hidden(esk187_2(X1357,X1358),X1358)
| ~ r2_hidden(k3_lattices(X1357,esk184_2(X1357,X1358),esk185_2(X1357,X1358)),X1358)
| epred1_2(X1358,X1357) ) ),
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)],[c_0_41])])])])])])]) ).
cnf(c_0_65,plain,
( v3_struct_0(X1)
| r3_lattices(X1,k5_lattices(X1),X2)
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,negated_conjecture,
m1_subset_1(esk15_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,plain,
( v3_struct_0(X1)
| m1_subset_1(k6_lattices(X1),u1_struct_0(X1))
| ~ l2_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,negated_conjecture,
l2_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,negated_conjecture,
k6_lattices(k1_lattice2(esk1_0)) = k5_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_59,c_0_24]),c_0_60]),c_0_23])]),c_0_25]) ).
cnf(c_0_70,negated_conjecture,
u1_struct_0(k1_lattice2(esk1_0)) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_24]),c_0_25]) ).
cnf(c_0_71,negated_conjecture,
~ v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_24]),c_0_25]) ).
cnf(c_0_72,plain,
( epred1_2(X1,X2)
| v1_xboole_0(X1)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_74,plain,
( r2_hidden(X3,X4)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ r2_hidden(X1,X4)
| ~ r3_lattices(X2,X3,X1)
| ~ epred1_2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_75,negated_conjecture,
r3_lattices(esk1_0,k5_lattices(esk1_0),esk15_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_65,c_0_66]),c_0_60]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_76,negated_conjecture,
m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70]),c_0_71]) ).
cnf(c_0_77,plain,
( epred1_2(X1,X2)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2))) ),
inference(csr,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( r2_hidden(k5_lattices(esk1_0),X1)
| ~ epred1_2(X1,esk1_0)
| ~ r2_hidden(esk15_2(esk1_0,esk2_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_66])]) ).
cnf(c_0_79,negated_conjecture,
epred1_2(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_32]),c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_80,negated_conjecture,
~ r2_hidden(k5_lattices(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_45])]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.81/0.86 % Problem : LAT301+3 : TPTP v8.1.2. Released v3.4.0.
% 0.81/0.88 % Command : run_E %s %d THM
% 0.87/1.07 % Computer : n032.cluster.edu
% 0.87/1.07 % Model : x86_64 x86_64
% 0.87/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.87/1.07 % Memory : 8042.1875MB
% 0.87/1.07 % OS : Linux 3.10.0-693.el7.x86_64
% 0.87/1.07 % CPULimit : 300
% 0.87/1.07 % WCLimit : 300
% 0.87/1.07 % DateTime : Fri May 3 08:26:11 EDT 2024
% 0.87/1.07 % CPUTime :
% 3.05/3.22 Running first-order theorem proving
% 3.05/3.22 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/tmp/tmp.BPWNALqi3M/E---3.1_28425.p
% 8.56/4.24 # Version: 3.1.0
% 8.56/4.24 # Preprocessing class: FMLLSMLLSSSNFFN.
% 8.56/4.24 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.56/4.24 # Starting new_bool_3 with 900s (3) cores
% 8.56/4.24 # Starting new_bool_1 with 900s (3) cores
% 8.56/4.24 # Starting sh5l with 300s (1) cores
% 8.56/4.24 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 8.56/4.24 # new_bool_3 with pid 29853 completed with status 0
% 8.56/4.24 # Result found by new_bool_3
% 8.56/4.24 # Preprocessing class: FMLLSMLLSSSNFFN.
% 8.56/4.24 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.56/4.24 # Starting new_bool_3 with 900s (3) cores
% 8.56/4.24 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 8.56/4.24 # Search class: FGHSM-SMLM32-MFFFFFNN
% 8.56/4.24 # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 8.56/4.24 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 8.56/4.24 # Starting new_bool_3 with 91s (1) cores
% 8.56/4.24 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 68s (1) cores
% 8.56/4.24 # G-E--_208_C18_F1_SE_CS_SP_PS_S2g with pid 29861 completed with status 0
% 8.56/4.24 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S2g
% 8.56/4.24 # Preprocessing class: FMLLSMLLSSSNFFN.
% 8.56/4.24 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.56/4.24 # Starting new_bool_3 with 900s (3) cores
% 8.56/4.24 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 8.56/4.24 # Search class: FGHSM-SMLM32-MFFFFFNN
% 8.56/4.24 # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 8.56/4.24 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 8.56/4.24 # Starting new_bool_3 with 91s (1) cores
% 8.56/4.24 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 68s (1) cores
% 8.56/4.24 # Preprocessing time : 0.021 s
% 8.56/4.24 # Presaturation interreduction done
% 8.56/4.24
% 8.56/4.24 # Proof found!
% 8.56/4.24 # SZS status Theorem
% 8.56/4.24 # SZS output start CNFRefutation
% See solution above
% 8.56/4.24 # Parsed axioms : 13608
% 8.56/4.24 # Removed by relevancy pruning/SinE : 13125
% 8.56/4.24 # Initial clauses : 1182
% 8.56/4.24 # Removed in clause preprocessing : 60
% 8.56/4.24 # Initial clauses in saturation : 1122
% 8.56/4.24 # Processed clauses : 5494
% 8.56/4.24 # ...of these trivial : 74
% 8.56/4.24 # ...subsumed : 1235
% 8.56/4.24 # ...remaining for further processing : 4185
% 8.56/4.24 # Other redundant clauses eliminated : 120
% 8.56/4.24 # Clauses deleted for lack of memory : 0
% 8.56/4.24 # Backward-subsumed : 5
% 8.56/4.24 # Backward-rewritten : 198
% 8.56/4.24 # Generated clauses : 19396
% 8.56/4.24 # ...of the previous two non-redundant : 18537
% 8.56/4.24 # ...aggressively subsumed : 0
% 8.56/4.24 # Contextual simplify-reflections : 49
% 8.56/4.24 # Paramodulations : 19283
% 8.56/4.24 # Factorizations : 2
% 8.56/4.24 # NegExts : 0
% 8.56/4.24 # Equation resolutions : 126
% 8.56/4.24 # Disequality decompositions : 0
% 8.56/4.24 # Total rewrite steps : 4917
% 8.56/4.24 # ...of those cached : 4232
% 8.56/4.24 # Propositional unsat checks : 0
% 8.56/4.24 # Propositional check models : 0
% 8.56/4.24 # Propositional check unsatisfiable : 0
% 8.56/4.24 # Propositional clauses : 0
% 8.56/4.24 # Propositional clauses after purity: 0
% 8.56/4.24 # Propositional unsat core size : 0
% 8.56/4.24 # Propositional preprocessing time : 0.000
% 8.56/4.24 # Propositional encoding time : 0.000
% 8.56/4.24 # Propositional solver time : 0.000
% 8.56/4.24 # Success case prop preproc time : 0.000
% 8.56/4.24 # Success case prop encoding time : 0.000
% 8.56/4.24 # Success case prop solver time : 0.000
% 8.56/4.24 # Current number of processed clauses : 2856
% 8.56/4.24 # Positive orientable unit clauses : 1108
% 8.56/4.24 # Positive unorientable unit clauses: 0
% 8.56/4.24 # Negative unit clauses : 457
% 8.56/4.24 # Non-unit-clauses : 1291
% 8.56/4.24 # Current number of unprocessed clauses: 15157
% 8.56/4.24 # ...number of literals in the above : 31432
% 8.56/4.24 # Current number of archived formulas : 0
% 8.56/4.24 # Current number of archived clauses : 1239
% 8.56/4.24 # Clause-clause subsumption calls (NU) : 976088
% 8.56/4.24 # Rec. Clause-clause subsumption calls : 240045
% 8.56/4.24 # Non-unit clause-clause subsumptions : 344
% 8.56/4.24 # Unit Clause-clause subsumption calls : 233289
% 8.56/4.24 # Rewrite failures with RHS unbound : 0
% 8.56/4.24 # BW rewrite match attempts : 1008
% 8.56/4.24 # BW rewrite match successes : 63
% 8.56/4.24 # Condensation attempts : 0
% 8.56/4.24 # Condensation successes : 0
% 8.56/4.24 # Termbank termtop insertions : 701582
% 8.56/4.24 # Search garbage collected termcells : 134799
% 8.56/4.24
% 8.56/4.24 # -------------------------------------------------
% 8.56/4.24 # User time : 0.669 s
% 8.56/4.24 # System time : 0.042 s
% 8.56/4.24 # Total time : 0.712 s
% 8.56/4.24 # Maximum resident set size: 26332 pages
% 8.56/4.24
% 8.56/4.24 # -------------------------------------------------
% 8.56/4.24 # User time : 2.100 s
% 8.56/4.24 # System time : 0.083 s
% 8.56/4.24 # Total time : 2.183 s
% 8.56/4.24 # Maximum resident set size: 20004 pages
% 8.56/4.24 % E---3.1 exiting
% 8.56/4.24 % E exiting
%------------------------------------------------------------------------------