%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT297+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:37:58 PM UTC 2026
% Result : Theorem 226.10s 166.84s
% Output : CNFRefutation 227.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 92 ( 16 unt; 0 def)
% Number of atoms : 476 ( 29 equ)
% Maximal formula atoms : 51 ( 5 avg)
% Number of connectives : 606 ( 222 ~; 238 |; 96 &)
% ( 6 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 162 ( 1 sgn 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( m2_lattice4(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(k4_lattices(X1,X3,X4),X2)
& r2_hidden(k3_lattices(X1,X3,X4),X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattice4) ).
fof(t13_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(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(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_2) ).
fof(cc1_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
fof(dt_k3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> m1_subset_1(k3_lattices(X1,X2,X3),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattices) ).
fof(commutativity_k3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k3_lattices(X1,X2,X3) = k3_lattices(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(commutativity_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(d9_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( v9_lattices(X1)
<=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattices) ).
fof(redefinition_k3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(redefinition_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l1_lattices(X1)
& l2_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(c_0_14,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( m2_lattice4(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(k4_lattices(X1,X3,X4),X2)
& r2_hidden(k3_lattices(X1,X3,X4),X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d10_lattice4]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(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(k4_lattices(X1,X3,X4),X2) ) ) )
=> m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t13_filter_2])]) ).
fof(c_0_16,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
fof(c_0_17,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> m1_subset_1(k3_lattices(X1,X2,X3),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k3_lattices]) ).
fof(c_0_18,plain,
! [X173,X174,X175,X176] :
( ( r2_hidden(k4_lattices(X173,X175,X176),X174)
| ~ r2_hidden(X175,X174)
| ~ r2_hidden(X176,X174)
| ~ m1_subset_1(X176,u1_struct_0(X173))
| ~ m1_subset_1(X175,u1_struct_0(X173))
| ~ m2_lattice4(X174,X173)
| ~ m1_subset_1(X174,k1_zfmisc_1(u1_struct_0(X173)))
| v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ l3_lattices(X173) )
& ( r2_hidden(k3_lattices(X173,X175,X176),X174)
| ~ r2_hidden(X175,X174)
| ~ r2_hidden(X176,X174)
| ~ m1_subset_1(X176,u1_struct_0(X173))
| ~ m1_subset_1(X175,u1_struct_0(X173))
| ~ m2_lattice4(X174,X173)
| ~ m1_subset_1(X174,k1_zfmisc_1(u1_struct_0(X173)))
| v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ l3_lattices(X173) )
& ( m1_subset_1(esk3_2(X173,X174),u1_struct_0(X173))
| m2_lattice4(X174,X173)
| ~ m1_subset_1(X174,k1_zfmisc_1(u1_struct_0(X173)))
| v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ l3_lattices(X173) )
& ( m1_subset_1(esk4_2(X173,X174),u1_struct_0(X173))
| m2_lattice4(X174,X173)
| ~ m1_subset_1(X174,k1_zfmisc_1(u1_struct_0(X173)))
| v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ l3_lattices(X173) )
& ( r2_hidden(esk3_2(X173,X174),X174)
| m2_lattice4(X174,X173)
| ~ m1_subset_1(X174,k1_zfmisc_1(u1_struct_0(X173)))
| v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ l3_lattices(X173) )
& ( r2_hidden(esk4_2(X173,X174),X174)
| m2_lattice4(X174,X173)
| ~ m1_subset_1(X174,k1_zfmisc_1(u1_struct_0(X173)))
| v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ l3_lattices(X173) )
& ( ~ r2_hidden(k4_lattices(X173,esk3_2(X173,X174),esk4_2(X173,X174)),X174)
| ~ r2_hidden(k3_lattices(X173,esk3_2(X173,X174),esk4_2(X173,X174)),X174)
| m2_lattice4(X174,X173)
| ~ m1_subset_1(X174,k1_zfmisc_1(u1_struct_0(X173)))
| v3_struct_0(X173)
| ~ v10_lattices(X173)
| ~ l3_lattices(X173) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
fof(c_0_19,negated_conjecture,
! [X153,X154] :
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
& ( ~ r2_hidden(X153,esk2_0)
| ~ r2_hidden(X154,esk2_0)
| r2_hidden(k4_lattices(esk1_0,X153,X154),esk2_0)
| ~ m1_subset_1(X154,u1_struct_0(esk1_0))
| ~ m1_subset_1(X153,u1_struct_0(esk1_0)) )
& ( r2_hidden(X153,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X153,X154),esk2_0)
| ~ m1_subset_1(X154,u1_struct_0(esk1_0))
| ~ m1_subset_1(X153,u1_struct_0(esk1_0)) )
& ( r2_hidden(X154,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X153,X154),esk2_0)
| ~ m1_subset_1(X154,u1_struct_0(esk1_0))
| ~ m1_subset_1(X153,u1_struct_0(esk1_0)) )
& ~ m2_lattice4(esk2_0,esk1_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
fof(c_0_20,plain,
! [X158] :
( ( ~ v3_struct_0(X158)
| v3_struct_0(X158)
| ~ v10_lattices(X158)
| ~ l3_lattices(X158) )
& ( v4_lattices(X158)
| v3_struct_0(X158)
| ~ v10_lattices(X158)
| ~ l3_lattices(X158) )
& ( v5_lattices(X158)
| v3_struct_0(X158)
| ~ v10_lattices(X158)
| ~ l3_lattices(X158) )
& ( v6_lattices(X158)
| v3_struct_0(X158)
| ~ v10_lattices(X158)
| ~ l3_lattices(X158) )
& ( v7_lattices(X158)
| v3_struct_0(X158)
| ~ v10_lattices(X158)
| ~ l3_lattices(X158) )
& ( v8_lattices(X158)
| v3_struct_0(X158)
| ~ v10_lattices(X158)
| ~ l3_lattices(X158) )
& ( v9_lattices(X158)
| v3_struct_0(X158)
| ~ v10_lattices(X158)
| ~ l3_lattices(X158) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_21,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k3_lattices(X1,X2,X3) = k3_lattices(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k3_lattices]) ).
fof(c_0_22,plain,
! [X287,X288,X289] :
( ~ r2_hidden(X287,X288)
| ~ m1_subset_1(X288,k1_zfmisc_1(X289))
| m1_subset_1(X287,X289) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_23,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
fof(c_0_24,plain,
! [X207,X208,X209] :
( v3_struct_0(X207)
| ~ v4_lattices(X207)
| ~ l2_lattices(X207)
| ~ m1_subset_1(X208,u1_struct_0(X207))
| ~ m1_subset_1(X209,u1_struct_0(X207))
| m1_subset_1(k3_lattices(X207,X208,X209),u1_struct_0(X207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
cnf(c_0_25,plain,
( m1_subset_1(esk3_2(X1,X2),u1_struct_0(X1))
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
~ m2_lattice4(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,plain,
( v4_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_32,plain,
! [X167,X168,X169] :
( v3_struct_0(X167)
| ~ v4_lattices(X167)
| ~ l2_lattices(X167)
| ~ m1_subset_1(X168,u1_struct_0(X167))
| ~ m1_subset_1(X169,u1_struct_0(X167))
| k3_lattices(X167,X168,X169) = k3_lattices(X167,X169,X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
cnf(c_0_33,plain,
( m1_subset_1(esk4_2(X1,X2),u1_struct_0(X1))
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_34,plain,
! [X281,X282] :
( ~ r2_hidden(X281,X282)
| m1_subset_1(X281,X282) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_35,plain,
( m1_subset_1(X1,X3)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_36,plain,
! [X294,X295] :
( ~ r2_hidden(X294,X295)
| ~ v1_xboole_0(X295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_37,plain,
( r2_hidden(esk3_2(X1,X2),X2)
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_38,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l3_lattices(X1) )
=> ( v9_lattices(X1)
<=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[d9_lattices]) ).
fof(c_0_39,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& l2_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_lattices]) ).
fof(c_0_40,plain,
! [X170,X171,X172] :
( v3_struct_0(X170)
| ~ v6_lattices(X170)
| ~ l1_lattices(X170)
| ~ m1_subset_1(X171,u1_struct_0(X170))
| ~ m1_subset_1(X172,u1_struct_0(X170))
| k4_lattices(X170,X171,X172) = k4_lattices(X170,X172,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_41,plain,
( v6_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_42,plain,
( v3_struct_0(X1)
| m1_subset_1(k3_lattices(X1,X2,X3),u1_struct_0(X1))
| ~ v4_lattices(X1)
| ~ l2_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_43,negated_conjecture,
m1_subset_1(esk3_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]),c_0_29]),c_0_30]) ).
cnf(c_0_44,negated_conjecture,
v4_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_28])]),c_0_30]) ).
cnf(c_0_45,plain,
( v3_struct_0(X1)
| k3_lattices(X1,X2,X3) = k3_lattices(X1,X3,X2)
| ~ v4_lattices(X1)
| ~ l2_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_46,negated_conjecture,
m1_subset_1(esk4_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_27]),c_0_28])]),c_0_29]),c_0_30]) ).
fof(c_0_47,plain,
! [X283,X284] :
( ~ m1_subset_1(X283,X284)
| v1_xboole_0(X284)
| r2_hidden(X283,X284) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_48,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_49,negated_conjecture,
( r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ r2_hidden(X1,esk2_0)
| ~ r2_hidden(X2,esk2_0)
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_50,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_51,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_52,negated_conjecture,
r2_hidden(esk3_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_27]),c_0_28])]),c_0_29]),c_0_30]) ).
fof(c_0_53,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& l1_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_lattices]) ).
fof(c_0_54,plain,
! [X190,X191,X192] :
( ( ~ v9_lattices(X190)
| ~ m1_subset_1(X191,u1_struct_0(X190))
| ~ m1_subset_1(X192,u1_struct_0(X190))
| k2_lattices(X190,X191,k1_lattices(X190,X191,X192)) = X191
| v3_struct_0(X190)
| ~ l3_lattices(X190) )
& ( m1_subset_1(esk5_1(X190),u1_struct_0(X190))
| v9_lattices(X190)
| v3_struct_0(X190)
| ~ l3_lattices(X190) )
& ( m1_subset_1(esk6_1(X190),u1_struct_0(X190))
| v9_lattices(X190)
| v3_struct_0(X190)
| ~ l3_lattices(X190) )
& ( k2_lattices(X190,esk5_1(X190),k1_lattices(X190,esk5_1(X190),esk6_1(X190))) != esk5_1(X190)
| v9_lattices(X190)
| v3_struct_0(X190)
| ~ l3_lattices(X190) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])]) ).
cnf(c_0_55,plain,
( v9_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_56,plain,
! [X271,X272,X273] :
( v3_struct_0(X271)
| ~ v4_lattices(X271)
| ~ l2_lattices(X271)
| ~ m1_subset_1(X272,u1_struct_0(X271))
| ~ m1_subset_1(X273,u1_struct_0(X271))
| k3_lattices(X271,X272,X273) = k1_lattices(X271,X272,X273) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
cnf(c_0_57,plain,
( v3_struct_0(X1)
| k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2)
| ~ v6_lattices(X1)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
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_41,c_0_27]),c_0_28])]),c_0_30]) ).
cnf(c_0_59,negated_conjecture,
( m1_subset_1(k3_lattices(esk1_0,X1,esk3_2(esk1_0,esk2_0)),u1_struct_0(esk1_0))
| ~ l2_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(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_44])]),c_0_30]) ).
cnf(c_0_60,negated_conjecture,
( k3_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0)) = k3_lattices(esk1_0,esk4_2(esk1_0,esk2_0),X1)
| ~ l2_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_44])]),c_0_30]) ).
cnf(c_0_61,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_62,negated_conjecture,
( m1_subset_1(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ r2_hidden(X2,esk2_0)
| ~ r2_hidden(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_50]) ).
cnf(c_0_63,negated_conjecture,
~ v1_xboole_0(esk2_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_64,plain,
( r2_hidden(esk4_2(X1,X2),X2)
| m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_65,plain,
! [X274,X275,X276] :
( v3_struct_0(X274)
| ~ v6_lattices(X274)
| ~ l1_lattices(X274)
| ~ m1_subset_1(X275,u1_struct_0(X274))
| ~ m1_subset_1(X276,u1_struct_0(X274))
| k4_lattices(X274,X275,X276) = k2_lattices(X274,X275,X276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])]) ).
cnf(c_0_66,plain,
( k2_lattices(X1,X2,k1_lattices(X1,X2,X3)) = X2
| v3_struct_0(X1)
| ~ v9_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,negated_conjecture,
v9_lattices(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_27]),c_0_28])]),c_0_30]) ).
cnf(c_0_68,plain,
( v3_struct_0(X1)
| k3_lattices(X1,X2,X3) = k1_lattices(X1,X2,X3)
| ~ v4_lattices(X1)
| ~ l2_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_69,negated_conjecture,
( r2_hidden(X1,esk2_0)
| ~ r2_hidden(k4_lattices(esk1_0,X2,X1),esk2_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_70,negated_conjecture,
( k4_lattices(esk1_0,X1,esk3_2(esk1_0,esk2_0)) = k4_lattices(esk1_0,esk3_2(esk1_0,esk2_0),X1)
| ~ l1_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_43]),c_0_58])]),c_0_30]) ).
cnf(c_0_71,negated_conjecture,
( m1_subset_1(k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),u1_struct_0(esk1_0))
| ~ l2_lattices(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_46]),c_0_43])]) ).
cnf(c_0_72,plain,
( m2_lattice4(X2,X1)
| v3_struct_0(X1)
| ~ r2_hidden(k4_lattices(X1,esk3_2(X1,X2),esk4_2(X1,X2)),X2)
| ~ r2_hidden(k3_lattices(X1,esk3_2(X1,X2),esk4_2(X1,X2)),X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_73,negated_conjecture,
( r2_hidden(k4_lattices(esk1_0,X1,X2),esk2_0)
| ~ r2_hidden(X2,esk2_0)
| ~ r2_hidden(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_74,negated_conjecture,
r2_hidden(esk4_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_26]),c_0_27]),c_0_28])]),c_0_29]),c_0_30]) ).
cnf(c_0_75,plain,
( v3_struct_0(X1)
| k4_lattices(X1,X2,X3) = k2_lattices(X1,X2,X3)
| ~ v6_lattices(X1)
| ~ l1_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,negated_conjecture,
( m1_subset_1(k3_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0)),u1_struct_0(esk1_0))
| ~ l2_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_46]),c_0_44])]),c_0_30]) ).
cnf(c_0_77,negated_conjecture,
( k2_lattices(esk1_0,X1,k1_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0))) = X1
| ~ m1_subset_1(X1,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_66,c_0_46]),c_0_67]),c_0_27])]),c_0_30]) ).
cnf(c_0_78,negated_conjecture,
( k1_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0)) = k3_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0))
| ~ l2_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_46]),c_0_44])]),c_0_30]) ).
cnf(c_0_79,negated_conjecture,
( r2_hidden(X1,esk2_0)
| ~ l1_lattices(esk1_0)
| ~ r2_hidden(k4_lattices(esk1_0,X1,esk3_2(esk1_0,esk2_0)),esk2_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_43])]) ).
cnf(c_0_80,negated_conjecture,
( k4_lattices(esk1_0,X1,k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0))) = k4_lattices(esk1_0,k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),X1)
| ~ l1_lattices(esk1_0)
| ~ l2_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_71]),c_0_58])]),c_0_30]) ).
cnf(c_0_81,negated_conjecture,
~ r2_hidden(k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0)),esk2_0),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_26]),c_0_27]),c_0_28]),c_0_74]),c_0_52])]),c_0_29]),c_0_30]) ).
cnf(c_0_82,negated_conjecture,
( k2_lattices(esk1_0,X1,k3_lattices(esk1_0,X2,esk4_2(esk1_0,esk2_0))) = k4_lattices(esk1_0,X1,k3_lattices(esk1_0,X2,esk4_2(esk1_0,esk2_0)))
| ~ l1_lattices(esk1_0)
| ~ l2_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_58])]),c_0_30]) ).
cnf(c_0_83,negated_conjecture,
( k2_lattices(esk1_0,X1,k3_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0))) = X1
| ~ l2_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( ~ l1_lattices(esk1_0)
| ~ l2_lattices(esk1_0)
| ~ r2_hidden(k4_lattices(esk1_0,esk3_2(esk1_0,esk2_0),k3_lattices(esk1_0,esk3_2(esk1_0,esk2_0),esk4_2(esk1_0,esk2_0))),esk2_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_43])]),c_0_81]),c_0_71]) ).
cnf(c_0_85,negated_conjecture,
( k4_lattices(esk1_0,X1,k3_lattices(esk1_0,X1,esk4_2(esk1_0,esk2_0))) = X1
| ~ l1_lattices(esk1_0)
| ~ l2_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
fof(c_0_86,plain,
! [X215] :
( ( l1_lattices(X215)
| ~ l3_lattices(X215) )
& ( l2_lattices(X215)
| ~ l3_lattices(X215) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_87,negated_conjecture,
( ~ l1_lattices(esk1_0)
| ~ l2_lattices(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_52]),c_0_43])]) ).
cnf(c_0_88,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_89,negated_conjecture,
~ l2_lattices(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_27])]) ).
cnf(c_0_90,plain,
( l2_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT297+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 21:03:20 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 226.10/166.84 % Version : CSE_E---1.7
% 226.10/166.84 % Problem : theBenchmark.p
% 226.10/166.84 % SZS status Theorem for theBenchmark.p
% 226.10/166.84 % SZS output start CNFRefutation
% See solution above
% 227.33/168.04 % Total time : 119.333s
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