%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT304+2 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 04:38:01 PM UTC 2026
% Result : Theorem 21.78s 13.43s
% Output : CNFRefutation 21.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 209 ( 21 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 243 ( 80 ~; 77 |; 67 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 37 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(u1_struct_0(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_2) ).
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/benchmark/Axioms/SET007/SET007+253.ax',t18_lattice2) ).
fof(fc6_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',fc6_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/benchmark/Axioms/SET007/SET007+253.ax',fc1_lattice2) ).
fof(d2_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+242.ax',d2_filter_0) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',dt_k1_lattice2) ).
fof(redefinition_k1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_2(X1) = k1_filter_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).
fof(dt_k1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m1_filter_2(k1_filter_2(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_2) ).
fof(t21_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
<=> m1_filter_2(X2,k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m2_filter_2(u1_struct_0(X1),X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t28_filter_2])]) ).
fof(c_0_10,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_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ~ v3_struct_0(k1_lattice2(X1))
& v3_lattices(k1_lattice2(X1))
& v4_lattices(k1_lattice2(X1))
& v5_lattices(k1_lattice2(X1))
& v6_lattices(k1_lattice2(X1))
& v7_lattices(k1_lattice2(X1))
& v8_lattices(k1_lattice2(X1))
& v9_lattices(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc6_lattice2]) ).
fof(c_0_12,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_13,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_0(X1) = u1_struct_0(X1) ),
inference(fof_simplification,[status(thm)],[d2_filter_0]) ).
fof(c_0_14,plain,
! [X6993] :
( ( v3_lattices(k1_lattice2(X6993))
| ~ l3_lattices(X6993) )
& ( l3_lattices(k1_lattice2(X6993))
| ~ l3_lattices(X6993) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_15,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& ~ m2_filter_2(u1_struct_0(esk1_0),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_16,plain,
! [X6926] :
( ( u1_struct_0(X6926) = u1_struct_0(k1_lattice2(X6926))
| v3_struct_0(X6926)
| ~ l3_lattices(X6926) )
& ( u2_lattices(X6926) = u1_lattices(k1_lattice2(X6926))
| v3_struct_0(X6926)
| ~ l3_lattices(X6926) )
& ( u1_lattices(X6926) = u2_lattices(k1_lattice2(X6926))
| v3_struct_0(X6926)
| ~ l3_lattices(X6926) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X6971] :
( ( ~ v3_struct_0(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) )
& ( v3_lattices(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) )
& ( v4_lattices(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) )
& ( v5_lattices(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) )
& ( v6_lattices(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) )
& ( v7_lattices(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) )
& ( v8_lattices(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) )
& ( v9_lattices(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) )
& ( v10_lattices(k1_lattice2(X6971))
| v3_struct_0(X6971)
| ~ v10_lattices(X6971)
| ~ l3_lattices(X6971) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_18,plain,
! [X6970] :
( ( ~ v3_struct_0(k1_lattice2(X6970))
| v3_struct_0(X6970)
| ~ l3_lattices(X6970) )
& ( v3_lattices(k1_lattice2(X6970))
| v3_struct_0(X6970)
| ~ l3_lattices(X6970) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> k1_filter_2(X1) = k1_filter_0(X1) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_filter_2]) ).
fof(c_0_20,plain,
! [X10190] :
( v3_struct_0(X10190)
| ~ v10_lattices(X10190)
| ~ l3_lattices(X10190)
| k1_filter_0(X10190) = u1_struct_0(X10190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
cnf(c_0_21,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,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_16]) ).
cnf(c_0_24,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> m1_filter_2(k1_filter_2(X1),X1) ),
inference(fof_simplification,[status(thm)],[dt_k1_filter_2]) ).
fof(c_0_29,plain,
! [X10123] :
( v3_struct_0(X10123)
| ~ v10_lattices(X10123)
| ~ l3_lattices(X10123)
| k1_filter_2(X10123) = k1_filter_0(X10123) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
cnf(c_0_30,plain,
( v3_struct_0(X1)
| k1_filter_0(X1) = u1_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,negated_conjecture,
l3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
u1_struct_0(k1_lattice2(esk1_0)) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24]) ).
cnf(c_0_33,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_25,c_0_22]),c_0_26])]),c_0_24]) ).
cnf(c_0_34,negated_conjecture,
~ v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_24]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(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_36,plain,
! [X6958] :
( v3_struct_0(X6958)
| ~ v10_lattices(X6958)
| ~ l3_lattices(X6958)
| m1_filter_2(k1_filter_2(X6958),X6958) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| k1_filter_2(X1) = k1_filter_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
k1_filter_0(k1_lattice2(esk1_0)) = 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_30,c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).
fof(c_0_39,plain,
! [X6109,X6110] :
( ( ~ m2_filter_2(X6110,X6109)
| m1_filter_2(X6110,k1_lattice2(X6109))
| v3_struct_0(X6109)
| ~ v10_lattices(X6109)
| ~ l3_lattices(X6109) )
& ( ~ m1_filter_2(X6110,k1_lattice2(X6109))
| m2_filter_2(X6110,X6109)
| v3_struct_0(X6109)
| ~ v10_lattices(X6109)
| ~ l3_lattices(X6109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).
cnf(c_0_40,plain,
( v3_struct_0(X1)
| m1_filter_2(k1_filter_2(X1),X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,negated_conjecture,
k1_filter_2(k1_lattice2(esk1_0)) = 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_37,c_0_31]),c_0_38]),c_0_33])]),c_0_34]) ).
cnf(c_0_42,plain,
( m2_filter_2(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,k1_lattice2(X2))
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
m1_filter_2(u1_struct_0(esk1_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_40,c_0_31]),c_0_41]),c_0_33])]),c_0_34]) ).
cnf(c_0_44,negated_conjecture,
~ m2_filter_2(u1_struct_0(esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_45,negated_conjecture,
$false,
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_42,c_0_43]),c_0_26]),c_0_22])]),c_0_44]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT304+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n026.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 21:09:39 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 21.78/13.43 % Version : CSE_E---1.7
% 21.78/13.43 % Problem : theBenchmark.p
% 21.78/13.43 % SZS status Theorem for theBenchmark.p
% 21.78/13.43 % SZS output start CNFRefutation
% See solution above
% 21.88/13.50 % Total time : 10.263s
%------------------------------------------------------------------------------