%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT300+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 : n028.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 23.92s 14.77s
% Output : CNFRefutation 24.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 138 ( 9 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 156 ( 63 ~; 46 |; 30 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 72 ( 3 sgn 50 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_m2_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(t24_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
& r2_hidden(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+375.ax',dt_m2_lattice4) ).
fof(t69_xboole_1,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> ~ ( r1_tarski(X2,X1)
& r1_xboole_0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t69_xboole_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t3_subset) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t4_subset) ).
fof(t34_mcart_1,axiom,
! [X1] :
~ ( X1 != k1_xboole_0
& ! [X2] :
~ ( r2_hidden(X2,X1)
& ! [X3,X4,X5,X6] :
~ ( ( r2_hidden(X3,X1)
| r2_hidden(X4,X1) )
& X2 = k4_mcart_1(X3,X4,X5,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+18.ax',t34_mcart_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( r1_xboole_0(X1,X2)
=> r1_xboole_0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',symmetry_r1_xboole_0) ).
fof(t65_xboole_1,axiom,
! [X1] : r1_xboole_0(X1,k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t65_xboole_1) ).
fof(c_0_9,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_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)
=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
& r2_hidden(X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t24_filter_2])]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_lattice4]) ).
fof(c_0_12,plain,
! [X6701,X6702] :
( ( ~ v1_xboole_0(X6702)
| ~ m2_filter_2(X6702,X6701)
| v3_struct_0(X6701)
| ~ v10_lattices(X6701)
| ~ l3_lattices(X6701) )
& ( m2_lattice4(X6702,X6701)
| ~ m2_filter_2(X6702,X6701)
| v3_struct_0(X6701)
| ~ v10_lattices(X6701)
| ~ l3_lattices(X6701) ) ),
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_13,negated_conjecture,
! [X6191] :
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& m2_filter_2(esk2_0,esk1_0)
& ( ~ m1_subset_1(X6191,u1_struct_0(esk1_0))
| ~ r2_hidden(X6191,esk2_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_14,plain,
! [X8643,X8644] :
( v3_struct_0(X8643)
| ~ v10_lattices(X8643)
| ~ l3_lattices(X8643)
| ~ m2_lattice4(X8644,X8643)
| m1_subset_1(X8644,k1_zfmisc_1(u1_struct_0(X8643))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_15,plain,
( m2_lattice4(X1,X2)
| v3_struct_0(X2)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
m2_filter_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> ~ ( r1_tarski(X2,X1)
& r1_xboole_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[t69_xboole_1]) ).
fof(c_0_21,plain,
! [X6680,X6681] :
( ( ~ m1_subset_1(X6680,k1_zfmisc_1(X6681))
| r1_tarski(X6680,X6681) )
& ( ~ r1_tarski(X6680,X6681)
| m1_subset_1(X6680,k1_zfmisc_1(X6681)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_22,plain,
( v3_struct_0(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
m2_lattice4(esk2_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_15,c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
fof(c_0_24,plain,
! [X6406,X6407,X6408] :
( ~ r2_hidden(X6406,X6407)
| ~ m1_subset_1(X6407,k1_zfmisc_1(X6408))
| m1_subset_1(X6406,X6408) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_25,plain,
! [X7041,X7042] :
( v1_xboole_0(X7042)
| ~ r1_tarski(X7042,X7041)
| ~ r1_xboole_0(X7042,X7041) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
cnf(c_0_26,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(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_22,c_0_23]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_28,plain,
( v3_struct_0(X2)
| ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X2)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,plain,
( m1_subset_1(X1,X3)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_31,plain,
! [X10633,X10635,X10636,X10637,X10638] :
( ( r2_hidden(esk437_1(X10633),X10633)
| X10633 = k1_xboole_0 )
& ( ~ r2_hidden(X10635,X10633)
| esk437_1(X10633) != k4_mcart_1(X10635,X10636,X10637,X10638)
| X10633 = k1_xboole_0 )
& ( ~ r2_hidden(X10636,X10633)
| esk437_1(X10633) != k4_mcart_1(X10635,X10636,X10637,X10638)
| X10633 = k1_xboole_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_mcart_1])])])])])]) ).
fof(c_0_32,plain,
! [X9308,X9309] :
( ~ r1_xboole_0(X9308,X9309)
| r1_xboole_0(X9309,X9308) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(c_0_33,plain,
! [X7332] : r1_xboole_0(X7332,k1_xboole_0),
inference(variable_rename,[status(thm)],[t65_xboole_1]) ).
cnf(c_0_34,plain,
( v1_xboole_0(X1)
| ~ r1_tarski(X1,X2)
| ~ r1_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,negated_conjecture,
r1_tarski(esk2_0,u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,negated_conjecture,
~ v1_xboole_0(esk2_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_16]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_37,negated_conjecture,
~ r2_hidden(X1,esk2_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_30]) ).
cnf(c_0_38,plain,
( r2_hidden(esk437_1(X1),X1)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( r1_xboole_0(X2,X1)
| ~ r1_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
r1_xboole_0(X1,k1_xboole_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
~ r1_xboole_0(esk2_0,u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_42,negated_conjecture,
esk2_0 = k1_xboole_0,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
r1_xboole_0(k1_xboole_0,X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT300+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 21:08:46 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 23.92/14.77 % Version : CSE_E---1.7
% 23.92/14.77 % Problem : theBenchmark.p
% 23.92/14.77 % SZS status Theorem for theBenchmark.p
% 23.92/14.77 % SZS output start CNFRefutation
% See solution above
% 24.02/14.85 % Total time : 11.211s
%------------------------------------------------------------------------------