%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT291+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 04:37:56 PM UTC 2026
% Result : Theorem 1.48s 1.78s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 127 ( 21 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 140 ( 49 ~; 39 |; 39 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 29 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k5_lattices,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_lattices(X1) )
=> m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_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(t37_lopclset,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lopclset) ).
fof(t36_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lopclset) ).
fof(t37_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice4) ).
fof(t28_lopclset,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lopclset) ).
fof(t3_boole,axiom,
! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(c_0_7,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_lattices(X1) )
=> m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).
fof(c_0_8,plain,
! [X216] :
( v3_struct_0(X216)
| ~ l1_lattices(X216)
| m1_subset_1(k5_lattices(X216),u1_struct_0(X216)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
fof(c_0_9,plain,
! [X229] :
( ( l1_lattices(X229)
| ~ l3_lattices(X229) )
& ( l2_lattices(X229)
| ~ l3_lattices(X229) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t37_lopclset])]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
inference(fof_simplification,[status(thm)],[t36_lopclset]) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
=> k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
inference(fof_simplification,[status(thm)],[t37_lattice4]) ).
fof(c_0_13,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& ~ v3_realset2(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[t28_lopclset]) ).
cnf(c_0_14,plain,
( v3_struct_0(X1)
| m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
| ~ l1_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( l1_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& v17_lattices(esk1_0)
& ~ v3_realset2(esk1_0)
& l3_lattices(esk1_0)
& k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k6_lattices(esk1_0)) != k7_lopclset(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X304] :
( v3_struct_0(X304)
| ~ v10_lattices(X304)
| ~ v17_lattices(X304)
| v3_realset2(X304)
| ~ l3_lattices(X304)
| k8_funct_2(u1_struct_0(X304),k1_zfmisc_1(k7_lopclset(X304)),k9_lopclset(X304),k5_lattices(X304)) = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_18,plain,
! [X305] :
( v3_struct_0(X305)
| ~ v10_lattices(X305)
| ~ v17_lattices(X305)
| ~ l3_lattices(X305)
| k7_lattices(X305,k5_lattices(X305)) = k6_lattices(X305) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_19,plain,
! [X297,X298] :
( v3_struct_0(X297)
| ~ v10_lattices(X297)
| ~ v17_lattices(X297)
| v3_realset2(X297)
| ~ l3_lattices(X297)
| ~ m1_subset_1(X298,u1_struct_0(X297))
| k4_xboole_0(k7_lopclset(X297),k8_funct_2(u1_struct_0(X297),k1_zfmisc_1(k7_lopclset(X297)),k9_lopclset(X297),X298)) = k8_funct_2(u1_struct_0(X297),k1_zfmisc_1(k7_lopclset(X297)),k9_lopclset(X297),k7_lattices(X297,X298)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_20,plain,
( m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ l3_lattices(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( v3_struct_0(X1)
| v3_realset2(X1)
| k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
v17_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
~ v3_realset2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_27,plain,
! [X306] : k4_xboole_0(X306,k1_xboole_0) = X306,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_28,plain,
( v3_struct_0(X1)
| k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1)
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( v3_struct_0(X1)
| v3_realset2(X1)
| k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2))
| ~ v10_lattices(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k5_lattices(esk1_0)) = k1_xboole_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_23,c_0_21]),c_0_24]),c_0_25])]),c_0_26]),c_0_22]) ).
cnf(c_0_32,plain,
k4_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
k7_lattices(esk1_0,k5_lattices(esk1_0)) = k6_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_28,c_0_21]),c_0_24]),c_0_25])]),c_0_22]) ).
cnf(c_0_34,negated_conjecture,
k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k6_lattices(esk1_0)) != k7_lopclset(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_21]),c_0_24]),c_0_25])]),c_0_34]),c_0_26]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT291+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
% 0.15/0.33 % Computer : n027.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 21:01:05 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.48/1.78 % Version : CSE_E---1.7
% 1.48/1.78 % Problem : theBenchmark.p
% 1.48/1.78 % SZS status Theorem for theBenchmark.p
% 1.48/1.78 % SZS output start CNFRefutation
% See solution above
% 1.48/1.78 % Total time : 1.375s
%------------------------------------------------------------------------------