%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT301+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:04:47 PM UTC 2026
% Result : Theorem 50.92s 14.03s
% Output : CNFRefutation 50.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 76 ( 15 unt; 0 def)
% Number of atoms : 348 ( 16 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 421 ( 149 ~; 140 |; 90 &)
% ( 7 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-1 aty)
% Number of variables : 72 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+200.ax',fc1_struct_0) ).
fof(t25_filter_2,conjecture,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> r2_hidden(k5_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_filter_2) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( l1_lattices(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+205.ax',dt_l1_lattices) ).
fof(t18_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( u1_lattices(X1) = u2_lattices(k1_lattice2(X1))
& u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
& u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',t18_lattice2) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l2_lattices(X1)
& l1_lattices(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+205.ax',dt_l3_lattices) ).
fof(d1_struct_0,axiom,
! [X1] :
( l1_struct_0(X1)
=> ( v3_struct_0(X1)
<=> v1_xboole_0(u1_struct_0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+200.ax',d1_struct_0) ).
fof(fc1_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',fc1_lattice2) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( l3_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',dt_k1_lattice2) ).
fof(t21_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_filter_2) ).
fof(fc6_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v10_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',fc6_lattice2) ).
fof(t12_filter_0,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( l3_lattices(X1)
& v14_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> r2_hidden(k6_lattices(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+242.ax',t12_filter_0) ).
fof(redefinition_m1_filter_2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(t78_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v13_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k5_lattices(X1) = k6_lattices(k1_lattice2(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',t78_lattice2) ).
fof(t63_lattice2,axiom,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',t63_lattice2) ).
fof(c_0_14,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_15,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> r2_hidden(k5_lattices(X1),X2) ) ) ),
inference(assume_negation,[status(cth)],[t25_filter_2]) ).
fof(c_0_16,plain,
! [X5313] :
( ~ v1_xboole_0(u1_struct_0(X5313))
| ~ l1_struct_0(X5313)
| v3_struct_0(X5313) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_17,plain,
! [X2555] :
( l1_struct_0(X2555)
| ~ l1_lattices(X2555) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])])]) ).
fof(c_0_18,plain,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( u1_lattices(X1) = u2_lattices(k1_lattice2(X1))
& u2_lattices(X1) = u1_lattices(k1_lattice2(X1))
& u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t18_lattice2]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( v13_lattices(X1)
=> r2_hidden(k5_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( ~ l1_lattices(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X2557] :
( ( ~ l3_lattices(X2557)
| l2_lattices(X2557) )
& ( ~ l3_lattices(X2557)
| l1_lattices(X2557) ) ),
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,plain,
! [X3104] :
( ( ~ l3_lattices(X3104)
| v3_struct_0(X3104)
| u1_lattices(X3104) = u2_lattices(k1_lattice2(X3104)) )
& ( ~ l3_lattices(X3104)
| v3_struct_0(X3104)
| u2_lattices(X3104) = u1_lattices(k1_lattice2(X3104)) )
& ( ~ l3_lattices(X3104)
| v3_struct_0(X3104)
| u1_struct_0(X3104) = u1_struct_0(k1_lattice2(X3104)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_24,negated_conjecture,
( ~ r2_hidden(k5_lattices(esk1_0),esk2_0)
& v13_lattices(esk1_0)
& m2_filter_2(esk2_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_19])])])]) ).
cnf(c_0_25,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_lattices(X1)
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ l3_lattices(X1)
| l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ l3_lattices(X1)
| v3_struct_0(X1)
| u1_struct_0(X1) = u1_struct_0(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X5316] :
( ( ~ l1_struct_0(X5316)
| v3_struct_0(X5316)
| ~ v1_xboole_0(u1_struct_0(X5316)) )
& ( ~ l1_struct_0(X5316)
| v1_xboole_0(u1_struct_0(X5316))
| ~ v3_struct_0(X5316) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_struct_0])])])]) ).
fof(c_0_31,plain,
! [X1] :
( ( l3_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc1_lattice2]) ).
cnf(c_0_32,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l3_lattices(X1)
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
u1_struct_0(k1_lattice2(esk1_0)) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
fof(c_0_34,plain,
! [X3186] :
( ( ~ l3_lattices(X3186)
| l3_lattices(k1_lattice2(X3186)) )
& ( ~ l3_lattices(X3186)
| v3_lattices(k1_lattice2(X3186)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])])]) ).
cnf(c_0_35,plain,
( ~ l1_struct_0(X1)
| ~ v3_struct_0(X1)
| v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X3177] :
( ( ~ l3_lattices(X3177)
| v3_struct_0(X3177)
| v3_lattices(k1_lattice2(X3177)) )
& ( ~ l3_lattices(X3177)
| v3_struct_0(X3177)
| ~ v3_struct_0(k1_lattice2(X3177)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_37,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( ~ l3_lattices(X1)
| l3_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_39,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t21_filter_2]) ).
fof(c_0_40,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v10_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& ~ v3_struct_0(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).
cnf(c_0_41,plain,
( ~ v3_struct_0(X1)
| ~ l1_lattices(X1)
| v1_xboole_0(u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_42,plain,
( ~ l3_lattices(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk1_0))
| v3_struct_0(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28])]) ).
fof(c_0_44,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( l3_lattices(X1)
& v14_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> r2_hidden(k6_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t12_filter_0]) ).
fof(c_0_45,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_filter_2]) ).
fof(c_0_46,plain,
! [X603,X604] :
( ( ~ l3_lattices(X603)
| ~ v10_lattices(X603)
| v3_struct_0(X603)
| m2_filter_2(X604,X603)
| ~ m1_filter_2(X604,k1_lattice2(X603)) )
& ( ~ l3_lattices(X603)
| ~ v10_lattices(X603)
| v3_struct_0(X603)
| m1_filter_2(X604,k1_lattice2(X603))
| ~ m2_filter_2(X604,X603) ) ),
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_39])])])])]) ).
fof(c_0_47,plain,
! [X3178] :
( ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| v10_lattices(k1_lattice2(X3178)) )
& ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| v9_lattices(k1_lattice2(X3178)) )
& ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| v8_lattices(k1_lattice2(X3178)) )
& ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| v7_lattices(k1_lattice2(X3178)) )
& ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| v6_lattices(k1_lattice2(X3178)) )
& ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| v5_lattices(k1_lattice2(X3178)) )
& ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| v4_lattices(k1_lattice2(X3178)) )
& ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| v3_lattices(k1_lattice2(X3178)) )
& ( ~ l3_lattices(X3178)
| ~ v10_lattices(X3178)
| v3_struct_0(X3178)
| ~ v3_struct_0(k1_lattice2(X3178)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
cnf(c_0_48,plain,
( ~ v3_struct_0(X1)
| ~ l3_lattices(X1)
| v1_xboole_0(u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_49,negated_conjecture,
~ v1_xboole_0(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_28])]),c_0_29]) ).
fof(c_0_50,plain,
! [X1] :
( ( l3_lattices(X1)
& v13_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> k5_lattices(X1) = k6_lattices(k1_lattice2(X1)) ),
inference(fof_simplification,[status(thm)],[t78_lattice2]) ).
fof(c_0_51,plain,
! [X1] :
( ( l3_lattices(X1)
& v10_lattices(X1)
& ~ v3_struct_0(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t63_lattice2]) ).
fof(c_0_52,plain,
! [X2936,X2937] :
( r2_hidden(k6_lattices(X2936),X2937)
| ~ l3_lattices(X2936)
| ~ v14_lattices(X2936)
| ~ v10_lattices(X2936)
| v3_struct_0(X2936)
| ~ m1_filter_0(X2937,X2936)
| ~ l3_lattices(X2936)
| ~ v10_lattices(X2936)
| v3_struct_0(X2936) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).
fof(c_0_53,plain,
! [X3516,X3517] :
( ( ~ l3_lattices(X3516)
| ~ v10_lattices(X3516)
| v3_struct_0(X3516)
| m1_filter_2(X3517,X3516)
| ~ m1_filter_0(X3517,X3516) )
& ( ~ l3_lattices(X3516)
| ~ v10_lattices(X3516)
| v3_struct_0(X3516)
| m1_filter_0(X3517,X3516)
| ~ m1_filter_2(X3517,X3516) ) ),
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_45])])])])]) ).
cnf(c_0_54,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m2_filter_2(X1,X2)
| v3_struct_0(X2)
| m1_filter_2(X1,k1_lattice2(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_56,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_57,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| v10_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,negated_conjecture,
( ~ v3_struct_0(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_49]) ).
fof(c_0_59,plain,
! [X532] :
( k5_lattices(X532) = k6_lattices(k1_lattice2(X532))
| ~ l3_lattices(X532)
| ~ v13_lattices(X532)
| ~ v10_lattices(X532)
| v3_struct_0(X532) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])]) ).
fof(c_0_60,plain,
! [X559] :
( ( ~ l3_lattices(X559)
| ~ v10_lattices(X559)
| v3_struct_0(X559)
| v13_lattices(X559)
| ~ v14_lattices(k1_lattice2(X559)) )
& ( ~ l3_lattices(X559)
| ~ v10_lattices(X559)
| v3_struct_0(X559)
| v14_lattices(k1_lattice2(X559))
| ~ v13_lattices(X559) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])]) ).
cnf(c_0_61,plain,
( ~ l3_lattices(X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_filter_0(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r2_hidden(k6_lattices(X1),X2)
| v3_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,plain,
( ~ l3_lattices(X2)
| ~ v10_lattices(X2)
| ~ m1_filter_2(X1,X2)
| v3_struct_0(X2)
| m1_filter_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,negated_conjecture,
m1_filter_2(esk2_0,k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_28])]),c_0_29]) ).
cnf(c_0_64,negated_conjecture,
v10_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_56]),c_0_28])]),c_0_29]) ).
cnf(c_0_65,negated_conjecture,
~ v3_struct_0(k1_lattice2(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_38]),c_0_28])]) ).
cnf(c_0_66,plain,
( ~ l3_lattices(X1)
| ~ v13_lattices(X1)
| ~ v10_lattices(X1)
| k5_lattices(X1) = k6_lattices(k1_lattice2(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,negated_conjecture,
v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_68,plain,
( ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v13_lattices(X1)
| v3_struct_0(X1)
| v14_lattices(k1_lattice2(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_69,plain,
( ~ m1_filter_0(X2,X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| r2_hidden(k6_lattices(X1),X2)
| v3_struct_0(X1) ),
inference(cn,[status(thm)],[c_0_61]) ).
cnf(c_0_70,negated_conjecture,
( ~ l3_lattices(k1_lattice2(esk1_0))
| m1_filter_0(esk2_0,k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]),c_0_65]) ).
cnf(c_0_71,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_66,c_0_67]),c_0_56]),c_0_28])]),c_0_29]) ).
cnf(c_0_72,negated_conjecture,
v14_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_67]),c_0_56]),c_0_28])]),c_0_29]) ).
cnf(c_0_73,negated_conjecture,
~ r2_hidden(k5_lattices(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_74,negated_conjecture,
~ l3_lattices(k1_lattice2(esk1_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(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_72]),c_0_64])]),c_0_65]),c_0_73]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_38]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT301+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.50 % Computer : n015.cluster.edu
% 0.18/5.50 % Model : x86_64 x86_64
% 0.18/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.50 % Memory : 8046.5625MB
% 0.18/5.50 % OS : Linux 6.8.0-71-generic
% 0.18/5.50 % CPULimit : 300
% 0.18/5.50 % WCLimit : 300
% 0.18/5.50 % DateTime : Sun Sep 20 23:33:56 UTC 2026
% 0.18/5.51 % CPUTime :
% 0.18/5.51 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.57 Running first-order theorem proving
% 0.18/5.57 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 50.92/14.03 % Version: 3.5.1
% 50.92/14.03 % Preprocessing class: FMLMSMSLSSSNFFN.
% 50.92/14.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.92/14.03 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 50.92/14.03 % Starting new_bool_3 with 600s (2) cores
% 50.92/14.03 % Starting new_bool_1 with 600s (2) cores
% 50.92/14.03 % Starting sh5l with 300s (1) cores
% 50.92/14.03 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 4191901 completed with status 0
% 50.92/14.03 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 50.92/14.03 % Preprocessing class: FMLMSMSLSSSNFFN.
% 50.92/14.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.92/14.03 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 50.92/14.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 50.92/14.03 % SinE strategy is gf600_h_gu_R05_F100_L20000
% 50.92/14.03 % Search class: FGHSM-SMLM32-DFFFFFNN
% 50.92/14.03 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 50.92/14.03 % Starting SubtermCWHack with 82s (1) cores
% 50.92/14.03 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 91s (1) cores
% 50.92/14.03 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 50.92/14.03 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 4191911 completed with status 0
% 50.92/14.03 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 50.92/14.03 % Preprocessing class: FMLMSMSLSSSNFFN.
% 50.92/14.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.92/14.03 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 50.92/14.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 50.92/14.03 % SinE strategy is gf600_h_gu_R05_F100_L20000
% 50.92/14.03 % Search class: FGHSM-SMLM32-DFFFFFNN
% 50.92/14.03 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 50.92/14.03 % Starting SubtermCWHack with 82s (1) cores
% 50.92/14.03 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 91s (1) cores
% 50.92/14.03 % Preprocessing time : 0.155 s
% 50.92/14.03 % Presaturation interreduction done
% 50.92/14.03
% 50.92/14.03 % Proof found!
% 50.92/14.03 % SZS status Theorem
% 50.92/14.03 % SZS output start CNFRefutation
% See solution above
% 50.92/14.03 % Parsed axioms : 2949
% 50.92/14.03 % Removed by relevancy pruning/SinE : 853
% 50.92/14.03 % Initial clauses : 4522
% 50.92/14.03 % Removed in clause preprocessing : 139
% 50.92/14.03 % Initial clauses in saturation : 4383
% 50.92/14.03 % Processed clauses : 11734
% 50.92/14.03 % ...of these trivial : 137
% 50.92/14.03 % ...subsumed : 3160
% 50.92/14.03 % ...remaining for further processing : 8437
% 50.92/14.03 % Other redundant clauses eliminated : 671
% 50.92/14.03 % Clauses deleted for lack of memory : 0
% 50.92/14.03 % Backward-subsumed : 120
% 50.92/14.03 % Backward-rewritten : 154
% 50.92/14.03 % Generated clauses : 62580
% 50.92/14.03 % ...of the previous two non-redundant : 52530
% 50.92/14.03 % ...aggressively subsumed : 0
% 50.92/14.03 % Contextual simplify-reflections : 314
% 50.92/14.03 % Paramodulations : 62002
% 50.92/14.03 % Factorizations : 0
% 50.92/14.03 % NegExts : 0
% 50.92/14.03 % Equation resolutions : 679
% 50.92/14.03 % Disequality decompositions : 0
% 50.92/14.03 % Total rewrite steps : 138029
% 50.92/14.03 % ...of those cached : 130672
% 50.92/14.03 % Propositional unsat checks : 1
% 50.92/14.03 % Propositional check models : 1
% 50.92/14.03 % Propositional check unsatisfiable : 0
% 50.92/14.03 % Propositional clauses : 0
% 50.92/14.03 % Propositional clauses after purity: 0
% 50.92/14.03 % Propositional unsat core size : 0
% 50.92/14.03 % Propositional preprocessing time : 0.000
% 50.92/14.03 % Propositional encoding time : 0.024
% 50.92/14.03 % Propositional solver time : 0.010
% 50.92/14.03 % Success case prop preproc time : 0.000
% 50.92/14.03 % Success case prop encoding time : 0.000
% 50.92/14.03 % Success case prop solver time : 0.000
% 50.92/14.03 % Current number of processed clauses : 3626
% 50.92/14.03 % Positive orientable unit clauses : 1236
% 50.92/14.03 % Positive unorientable unit clauses: 57
% 50.92/14.03 % Negative unit clauses : 587
% 50.92/14.03 % Non-unit-clauses : 1746
% 50.92/14.03 % Current number of unprocessed clauses: 49073
% 50.92/14.03 % ...number of literals in the above : 88866
% 50.92/14.03 % Current number of archived formulas : 0
% 50.92/14.03 % Current number of archived clauses : 4282
% 50.92/14.03 % Clause-clause subsumption calls (NU) : 5433244
% 50.92/14.03 % Rec. Clause-clause subsumption calls : 638108
% 50.92/14.03 % Non-unit clause-clause subsumptions : 1500
% 50.92/14.03 % Unit Clause-clause subsumption calls : 318689
% 50.92/14.03 % Rewrite failures with RHS unbound : 0
% 50.92/14.03 % BW rewrite match attempts : 14878
% 50.92/14.03 % BW rewrite match successes : 8843
% 50.92/14.03 % Condensation attempts : 0
% 50.92/14.03 % Condensation successes : 0
% 50.92/14.03 % Termbank termtop insertions : 2964906
% 50.92/14.03 % Search garbage collected termcells : 91789
% 50.92/14.03
% 50.92/14.03 % -------------------------------------------------
% 50.92/14.03 % User time : 6.902 s
% 50.92/14.03 % System time : 0.167 s
% 50.92/14.03 % Total time : 7.069 s
% 50.92/14.03 % Maximum resident set size: 24272 pages
% 50.92/14.03
% 50.92/14.03 % -------------------------------------------------
% 50.92/14.03 % User time : 19.511 s
% 50.92/14.03 % System time : 0.568 s
% 50.92/14.03 % Total time : 20.079 s
% 50.92/14.03 % Maximum resident set size: 8448 pages
% 50.92/14.03 % E exiting
%------------------------------------------------------------------------------