%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT301+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 : n007.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 04:37:59 PM UTC 2026
% Result : Theorem 27.65s 18.61s
% Output : CNFRefutation 27.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 14 unt; 0 def)
% Number of atoms : 259 ( 5 equ)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 316 ( 106 ~; 104 |; 75 &)
% ( 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 : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 49 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/sandbox2/benchmark/theBenchmark.p',t25_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(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(t12_filter_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(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] :
( ( ~ 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(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(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/sandbox2/benchmark/Axioms/SET007/SET007+253.ax',t78_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(c_0_9,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_10,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_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) )
=> ! [X2] :
( m1_filter_0(X2,X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v14_lattices(X1)
& l3_lattices(X1) )
=> r2_hidden(k6_lattices(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t12_filter_0]) ).
fof(c_0_14,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_15,plain,
! [X6794,X6795] :
( ( ~ m2_filter_2(X6795,X6794)
| m1_filter_2(X6795,k1_lattice2(X6794))
| v3_struct_0(X6794)
| ~ v10_lattices(X6794)
| ~ l3_lattices(X6794) )
& ( ~ m1_filter_2(X6795,k1_lattice2(X6794))
| m2_filter_2(X6795,X6794)
| v3_struct_0(X6794)
| ~ v10_lattices(X6794)
| ~ l3_lattices(X6794) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_16,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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X9369] :
( ( ~ v3_struct_0(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) )
& ( v3_lattices(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) )
& ( v4_lattices(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) )
& ( v5_lattices(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) )
& ( v6_lattices(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) )
& ( v7_lattices(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) )
& ( v8_lattices(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) )
& ( v9_lattices(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) )
& ( v10_lattices(k1_lattice2(X9369))
| v3_struct_0(X9369)
| ~ v10_lattices(X9369)
| ~ l3_lattices(X9369) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_18,plain,
! [X9377] :
( ( v3_lattices(k1_lattice2(X9377))
| ~ l3_lattices(X9377) )
& ( l3_lattices(k1_lattice2(X9377))
| ~ l3_lattices(X9377) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_19,plain,
! [X9368] :
( ( ~ v3_struct_0(k1_lattice2(X9368))
| v3_struct_0(X9368)
| ~ l3_lattices(X9368) )
& ( v3_lattices(k1_lattice2(X9368))
| v3_struct_0(X9368)
| ~ l3_lattices(X9368) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_20,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_21,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_22,plain,
! [X9127,X9128] :
( v3_struct_0(X9127)
| ~ v10_lattices(X9127)
| ~ l3_lattices(X9127)
| ~ m1_filter_0(X9128,X9127)
| v3_struct_0(X9127)
| ~ v10_lattices(X9127)
| ~ v14_lattices(X9127)
| ~ l3_lattices(X9127)
| r2_hidden(k6_lattices(X9127),X9128) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_23,plain,
! [X9707,X9708] :
( ( ~ m1_filter_2(X9708,X9707)
| m1_filter_0(X9708,X9707)
| v3_struct_0(X9707)
| ~ v10_lattices(X9707)
| ~ l3_lattices(X9707) )
& ( ~ m1_filter_0(X9708,X9707)
| m1_filter_2(X9708,X9707)
| v3_struct_0(X9707)
| ~ v10_lattices(X9707)
| ~ l3_lattices(X9707) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_24,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_15]) ).
cnf(c_0_25,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,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_30,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_32,plain,
! [X6723] :
( v3_struct_0(X6723)
| ~ v10_lattices(X6723)
| ~ v13_lattices(X6723)
| ~ l3_lattices(X6723)
| k5_lattices(X6723) = k6_lattices(k1_lattice2(X6723)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
fof(c_0_33,plain,
! [X6750] :
( ( ~ v13_lattices(X6750)
| v14_lattices(k1_lattice2(X6750))
| v3_struct_0(X6750)
| ~ v10_lattices(X6750)
| ~ l3_lattices(X6750) )
& ( ~ v14_lattices(k1_lattice2(X6750))
| v13_lattices(X6750)
| v3_struct_0(X6750)
| ~ v10_lattices(X6750)
| ~ l3_lattices(X6750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_34,plain,
( v3_struct_0(X1)
| v3_struct_0(X1)
| r2_hidden(k6_lattices(X1),X2)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_filter_0(X2,X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,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_23]) ).
cnf(c_0_36,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_24,c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_37,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_29,c_0_27]),c_0_26])]),c_0_28]) ).
cnf(c_0_38,negated_conjecture,
l3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_39,negated_conjecture,
~ v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_28]) ).
cnf(c_0_40,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_32]) ).
cnf(c_0_41,negated_conjecture,
v13_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_42,plain,
( v14_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v13_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
( v3_struct_0(X1)
| r2_hidden(k6_lattices(X1),X2)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v14_lattices(X1)
| ~ m1_filter_0(X2,X1) ),
inference(cn,[status(thm)],[c_0_34]) ).
cnf(c_0_44,negated_conjecture,
m1_filter_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_37]),c_0_38])]),c_0_39]) ).
cnf(c_0_45,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_40,c_0_27]),c_0_41]),c_0_26])]),c_0_28]) ).
cnf(c_0_46,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_42,c_0_27]),c_0_41]),c_0_26])]),c_0_28]) ).
cnf(c_0_47,negated_conjecture,
~ r2_hidden(k5_lattices(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_48,negated_conjecture,
$false,
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(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]),c_0_37]),c_0_38])]),c_0_39]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT301+2 : 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
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 21:07:54 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 27.65/18.61 % Version : CSE_E---1.7
% 27.65/18.61 % Problem : theBenchmark.p
% 27.65/18.61 % SZS status Theorem for theBenchmark.p
% 27.65/18.61 % SZS output start CNFRefutation
% See solution above
% 27.65/18.68 % Total time : 15.222s
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