%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT327+1 : 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 : n008.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 04:38:07 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 202 ( 0 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 265 ( 95 ~; 92 |; 52 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 1 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> r3_lattices(X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(t64_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r2_hidden(X2,k22_filter_2(X1,X2,X3))
& r2_hidden(X3,k22_filter_2(X1,X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_filter_2) ).
fof(cc1_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(t63_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r2_hidden(X4,k22_filter_2(X1,X2,X3))
<=> ( r3_lattices(X1,X2,X4)
& r3_lattices(X1,X4,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v6_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1)
& l3_lattices(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> r3_lattices(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r2_hidden(X2,k22_filter_2(X1,X2,X3))
& r2_hidden(X3,k22_filter_2(X1,X2,X3)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t64_filter_2])]) ).
fof(c_0_6,plain,
! [X114,X115,X116] :
( v3_struct_0(X114)
| ~ v6_lattices(X114)
| ~ v8_lattices(X114)
| ~ v9_lattices(X114)
| ~ l3_lattices(X114)
| ~ m1_subset_1(X115,u1_struct_0(X114))
| ~ m1_subset_1(X116,u1_struct_0(X114))
| r3_lattices(X114,X115,X115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
fof(c_0_7,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))
& m1_subset_1(esk3_0,u1_struct_0(esk1_0))
& r3_lattices(esk1_0,esk2_0,esk3_0)
& ( ~ r2_hidden(esk2_0,k22_filter_2(esk1_0,esk2_0,esk3_0))
| ~ r2_hidden(esk3_0,k22_filter_2(esk1_0,esk2_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v4_lattices(X1)
& v5_lattices(X1)
& v6_lattices(X1)
& v7_lattices(X1)
& v8_lattices(X1)
& v9_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
fof(c_0_9,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( r3_lattices(X1,X2,X3)
=> ( r2_hidden(X4,k22_filter_2(X1,X2,X3))
<=> ( r3_lattices(X1,X2,X4)
& r3_lattices(X1,X4,X3) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t63_filter_2]) ).
cnf(c_0_10,plain,
( v3_struct_0(X1)
| r3_lattices(X1,X2,X2)
| ~ v6_lattices(X1)
| ~ v8_lattices(X1)
| ~ v9_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_14,plain,
! [X127] :
( ( ~ v3_struct_0(X127)
| v3_struct_0(X127)
| ~ v10_lattices(X127)
| ~ l3_lattices(X127) )
& ( v4_lattices(X127)
| v3_struct_0(X127)
| ~ v10_lattices(X127)
| ~ l3_lattices(X127) )
& ( v5_lattices(X127)
| v3_struct_0(X127)
| ~ v10_lattices(X127)
| ~ l3_lattices(X127) )
& ( v6_lattices(X127)
| v3_struct_0(X127)
| ~ v10_lattices(X127)
| ~ l3_lattices(X127) )
& ( v7_lattices(X127)
| v3_struct_0(X127)
| ~ v10_lattices(X127)
| ~ l3_lattices(X127) )
& ( v8_lattices(X127)
| v3_struct_0(X127)
| ~ v10_lattices(X127)
| ~ l3_lattices(X127) )
& ( v9_lattices(X127)
| v3_struct_0(X127)
| ~ v10_lattices(X127)
| ~ l3_lattices(X127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_15,plain,
! [X132,X133,X134,X135] :
( ( r3_lattices(X132,X133,X135)
| ~ r2_hidden(X135,k22_filter_2(X132,X133,X134))
| ~ r3_lattices(X132,X133,X134)
| ~ m1_subset_1(X135,u1_struct_0(X132))
| ~ m1_subset_1(X134,u1_struct_0(X132))
| ~ m1_subset_1(X133,u1_struct_0(X132))
| v3_struct_0(X132)
| ~ v10_lattices(X132)
| ~ l3_lattices(X132) )
& ( r3_lattices(X132,X135,X134)
| ~ r2_hidden(X135,k22_filter_2(X132,X133,X134))
| ~ r3_lattices(X132,X133,X134)
| ~ m1_subset_1(X135,u1_struct_0(X132))
| ~ m1_subset_1(X134,u1_struct_0(X132))
| ~ m1_subset_1(X133,u1_struct_0(X132))
| v3_struct_0(X132)
| ~ v10_lattices(X132)
| ~ l3_lattices(X132) )
& ( ~ r3_lattices(X132,X133,X135)
| ~ r3_lattices(X132,X135,X134)
| r2_hidden(X135,k22_filter_2(X132,X133,X134))
| ~ r3_lattices(X132,X133,X134)
| ~ m1_subset_1(X135,u1_struct_0(X132))
| ~ m1_subset_1(X134,u1_struct_0(X132))
| ~ m1_subset_1(X133,u1_struct_0(X132))
| v3_struct_0(X132)
| ~ v10_lattices(X132)
| ~ l3_lattices(X132) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_16,negated_conjecture,
( r3_lattices(esk1_0,X1,X1)
| ~ v9_lattices(esk1_0)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_17,plain,
( v9_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( ~ r2_hidden(esk2_0,k22_filter_2(esk1_0,esk2_0,esk3_0))
| ~ r2_hidden(esk3_0,k22_filter_2(esk1_0,esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,plain,
( r2_hidden(X3,k22_filter_2(X1,X2,X4))
| v3_struct_0(X1)
| ~ r3_lattices(X1,X2,X3)
| ~ r3_lattices(X1,X3,X4)
| ~ r3_lattices(X1,X2,X4)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
r3_lattices(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( r3_lattices(esk1_0,X1,X1)
| ~ v8_lattices(esk1_0)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,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_16,c_0_17]),c_0_12]),c_0_18])]),c_0_13]) ).
cnf(c_0_24,plain,
( v8_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
( ~ r2_hidden(esk2_0,k22_filter_2(esk1_0,esk2_0,esk3_0))
| ~ r3_lattices(esk1_0,esk3_0,esk3_0) ),
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(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_11]),c_0_22]),c_0_12]),c_0_18])]),c_0_13]) ).
cnf(c_0_26,negated_conjecture,
( r3_lattices(esk1_0,X1,X1)
| ~ v6_lattices(esk1_0)
| ~ m1_subset_1(X1,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_23,c_0_24]),c_0_12]),c_0_18])]),c_0_13]) ).
cnf(c_0_27,plain,
( v6_lattices(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,negated_conjecture,
( ~ r3_lattices(esk1_0,esk3_0,esk3_0)
| ~ r3_lattices(esk1_0,esk2_0,esk2_0) ),
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(spm,[status(thm)],[c_0_25,c_0_20]),c_0_21]),c_0_11]),c_0_22]),c_0_12]),c_0_18])]),c_0_13]) ).
cnf(c_0_29,negated_conjecture,
( r3_lattices(esk1_0,X1,X1)
| ~ m1_subset_1(X1,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_26,c_0_27]),c_0_12]),c_0_18])]),c_0_13]) ).
cnf(c_0_30,negated_conjecture,
~ r3_lattices(esk1_0,esk2_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_11])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT327+1 : 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
% 0.15/0.33 % Computer : n008.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 21:19:58 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------