%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT303+2 : 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 : n006.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 04:38:00 PM UTC 2026
% Result : Theorem 25.73s 15.83s
% Output : CNFRefutation 25.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 14 unt; 0 def)
% Number of atoms : 245 ( 11 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 293 ( 97 ~; 94 |; 71 &)
% ( 6 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',t18_lattice2) ).
fof(t27_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( m2_filter_2(k6_domain_1(u1_struct_0(X1),X2),X1)
=> v13_lattices(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_2) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',fc6_lattice2) ).
fof(t63_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',t63_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/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',fc1_lattice2) ).
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/sandbox2/benchmark/theBenchmark.p',t21_filter_2) ).
fof(t14_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( m1_filter_0(k6_domain_1(u1_struct_0(X1),X2),X1)
=> v14_lattices(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+242.ax',t14_filter_0) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',dt_k1_lattice2) ).
fof(redefinition_m1_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(c_0_9,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_10,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( m2_filter_2(k6_domain_1(u1_struct_0(X1),X2),X1)
=> v13_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t27_filter_2])]) ).
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)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v13_lattices(X1)
<=> v14_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t63_lattice2]) ).
fof(c_0_13,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_14,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_15,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( m1_filter_0(k6_domain_1(u1_struct_0(X1),X2),X1)
=> v14_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[t14_filter_0]) ).
fof(c_0_16,plain,
! [X7530] :
( ( u1_struct_0(X7530) = u1_struct_0(k1_lattice2(X7530))
| v3_struct_0(X7530)
| ~ l3_lattices(X7530) )
& ( u2_lattices(X7530) = u1_lattices(k1_lattice2(X7530))
| v3_struct_0(X7530)
| ~ l3_lattices(X7530) )
& ( u1_lattices(X7530) = u2_lattices(k1_lattice2(X7530))
| v3_struct_0(X7530)
| ~ l3_lattices(X7530) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_17,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& m2_filter_2(k6_domain_1(u1_struct_0(esk1_0),esk2_0),esk1_0)
& ~ v13_lattices(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_18,plain,
! [X6498] :
( ( ~ v3_struct_0(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) )
& ( v3_lattices(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) )
& ( v4_lattices(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) )
& ( v5_lattices(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) )
& ( v6_lattices(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) )
& ( v7_lattices(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) )
& ( v8_lattices(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) )
& ( v9_lattices(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) )
& ( v10_lattices(k1_lattice2(X6498))
| v3_struct_0(X6498)
| ~ v10_lattices(X6498)
| ~ l3_lattices(X6498) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_19,plain,
! [X6587] :
( ( v3_lattices(k1_lattice2(X6587))
| ~ l3_lattices(X6587) )
& ( l3_lattices(k1_lattice2(X6587))
| ~ l3_lattices(X6587) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_20,plain,
! [X6227] :
( ( ~ v13_lattices(X6227)
| v14_lattices(k1_lattice2(X6227))
| v3_struct_0(X6227)
| ~ v10_lattices(X6227)
| ~ l3_lattices(X6227) )
& ( ~ v14_lattices(k1_lattice2(X6227))
| v13_lattices(X6227)
| v3_struct_0(X6227)
| ~ v10_lattices(X6227)
| ~ l3_lattices(X6227) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_21,plain,
! [X6585] :
( ( ~ v3_struct_0(k1_lattice2(X6585))
| v3_struct_0(X6585)
| ~ l3_lattices(X6585) )
& ( v3_lattices(k1_lattice2(X6585))
| v3_struct_0(X6585)
| ~ l3_lattices(X6585) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_22,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_2(X2,X1)
<=> m1_filter_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_filter_2]) ).
fof(c_0_23,plain,
! [X6280,X6281] :
( ( ~ m2_filter_2(X6281,X6280)
| m1_filter_2(X6281,k1_lattice2(X6280))
| v3_struct_0(X6280)
| ~ v10_lattices(X6280)
| ~ l3_lattices(X6280) )
& ( ~ m1_filter_2(X6281,k1_lattice2(X6280))
| m2_filter_2(X6281,X6280)
| v3_struct_0(X6280)
| ~ v10_lattices(X6280)
| ~ l3_lattices(X6280) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_24,plain,
! [X6297,X6298] :
( v3_struct_0(X6297)
| ~ v10_lattices(X6297)
| ~ l3_lattices(X6297)
| ~ m1_subset_1(X6298,u1_struct_0(X6297))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X6297),X6298),X6297)
| v14_lattices(X6297) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_25,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_26,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| ~ v14_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
~ v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_34,plain,
! [X8324,X8325] :
( ( ~ m1_filter_2(X8325,X8324)
| m1_filter_0(X8325,X8324)
| v3_struct_0(X8324)
| ~ v10_lattices(X8324)
| ~ l3_lattices(X8324) )
& ( ~ m1_filter_0(X8325,X8324)
| m1_filter_2(X8325,X8324)
| v3_struct_0(X8324)
| ~ v10_lattices(X8324)
| ~ l3_lattices(X8324) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
cnf(c_0_35,plain,
( m1_filter_2(X1,k1_lattice2(X2))
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_36,negated_conjecture,
m2_filter_2(k6_domain_1(u1_struct_0(esk1_0),esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,negated_conjecture,
u1_struct_0(k1_lattice2(esk1_0)) = u1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_39,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_28,c_0_26]),c_0_29])]),c_0_27]) ).
cnf(c_0_40,negated_conjecture,
l3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_41,negated_conjecture,
~ v14_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_29])]),c_0_32]),c_0_27]) ).
cnf(c_0_42,negated_conjecture,
~ v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_27]) ).
cnf(c_0_43,plain,
( m1_filter_0(X1,X2)
| v3_struct_0(X2)
| ~ m1_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,negated_conjecture,
m1_filter_2(k6_domain_1(u1_struct_0(esk1_0),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_35,c_0_36]),c_0_29]),c_0_26])]),c_0_27]) ).
cnf(c_0_45,negated_conjecture,
( ~ m1_filter_0(k6_domain_1(u1_struct_0(esk1_0),X1),k1_lattice2(esk1_0))
| ~ m1_subset_1(X1,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_37,c_0_38]),c_0_39]),c_0_40])]),c_0_41]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
m1_filter_0(k6_domain_1(u1_struct_0(esk1_0),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_43,c_0_44]),c_0_39]),c_0_40])]),c_0_42]) ).
cnf(c_0_47,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LAT303+2 : TPTP v9.2.1. Released v3.4.0.
% 0.11/0.13 % 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
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 4 21:08:46 EDT 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % start to proof: theBenchmark
% 25.73/15.83 % Version : CSE_E---1.7
% 25.73/15.83 % Problem : theBenchmark.p
% 25.73/15.83 % SZS status Theorem for theBenchmark.p
% 25.73/15.83 % SZS output start CNFRefutation
% See solution above
% 25.83/15.90 % Total time : 12.274s
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