%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT346+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 : n002.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 04:38:14 PM UTC 2026
% Result : Theorem 2.36s 2.00s
% Output : CNFRefutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 11 unt; 0 def)
% Number of atoms : 372 ( 0 equ)
% Maximal formula atoms : 39 ( 5 avg)
% Number of connectives : 445 ( 138 ~; 161 |; 119 &)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& v4_lattices(k11_conlat_1(X1))
& v5_lattices(k11_conlat_1(X1))
& v6_lattices(k11_conlat_1(X1))
& v7_lattices(k11_conlat_1(X1))
& v8_lattices(k11_conlat_1(X1))
& v9_lattices(k11_conlat_1(X1))
& v10_lattices(k11_conlat_1(X1))
& v13_lattices(k11_conlat_1(X1))
& v14_lattices(k11_conlat_1(X1))
& v15_lattices(k11_conlat_1(X1))
& v4_lattice3(k11_conlat_1(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_conlat_2) ).
fof(t22_conlat_2,conjecture,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> r1_filter_1(k11_conlat_1(k7_conlat_2(X1)),k1_lattice2(k11_conlat_1(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_conlat_2) ).
fof(dt_k11_conlat_1,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& l3_lattices(k11_conlat_1(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_conlat_1) ).
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/sandbox/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(t21_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> v3_lattice4(k10_conlat_2(X1),k1_lattice2(k11_conlat_1(X1)),k11_conlat_1(k7_conlat_2(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_conlat_2) ).
fof(dt_k10_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> m1_lattice4(k10_conlat_2(X1),k1_lattice2(k11_conlat_1(X1)),k11_conlat_1(k7_conlat_2(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_conlat_2) ).
fof(dt_k7_conlat_2,axiom,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_conlat_1(k7_conlat_2(X1))
& v4_conlat_1(k7_conlat_2(X1))
& l2_conlat_1(k7_conlat_2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_conlat_2) ).
fof(d5_lattice4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ( r1_filter_1(X1,X2)
<=> ? [X3] :
( m1_lattice4(X3,X1,X2)
& v3_lattice4(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_lattice4) ).
fof(symmetry_r1_filter_1,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ( r1_filter_1(X1,X2)
=> r1_filter_1(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_1) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_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/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& v4_lattices(k11_conlat_1(X1))
& v5_lattices(k11_conlat_1(X1))
& v6_lattices(k11_conlat_1(X1))
& v7_lattices(k11_conlat_1(X1))
& v8_lattices(k11_conlat_1(X1))
& v9_lattices(k11_conlat_1(X1))
& v10_lattices(k11_conlat_1(X1))
& v13_lattices(k11_conlat_1(X1))
& v14_lattices(k11_conlat_1(X1))
& v15_lattices(k11_conlat_1(X1))
& v4_lattice3(k11_conlat_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc1_conlat_2]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> r1_filter_1(k11_conlat_1(k7_conlat_2(X1)),k1_lattice2(k11_conlat_1(X1))) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t22_conlat_2])]) ).
fof(c_0_13,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_struct_0(k11_conlat_1(X1))
& v3_lattices(k11_conlat_1(X1))
& l3_lattices(k11_conlat_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k11_conlat_1]) ).
fof(c_0_14,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_15,plain,
! [X237] :
( ( ~ v3_struct_0(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v3_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v4_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v5_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v6_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v7_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v8_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v9_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v10_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v13_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v14_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v15_lattices(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) )
& ( v4_lattice3(k11_conlat_1(X237))
| v3_conlat_1(X237)
| ~ l2_conlat_1(X237) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_16,negated_conjecture,
( ~ v3_conlat_1(esk1_0)
& l2_conlat_1(esk1_0)
& ~ r1_filter_1(k11_conlat_1(k7_conlat_2(esk1_0)),k1_lattice2(k11_conlat_1(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_17,plain,
! [X199] :
( ( ~ v3_struct_0(k11_conlat_1(X199))
| v3_conlat_1(X199)
| ~ l2_conlat_1(X199) )
& ( v3_lattices(k11_conlat_1(X199))
| v3_conlat_1(X199)
| ~ l2_conlat_1(X199) )
& ( l3_lattices(k11_conlat_1(X199))
| v3_conlat_1(X199)
| ~ l2_conlat_1(X199) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_18,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> v3_lattice4(k10_conlat_2(X1),k1_lattice2(k11_conlat_1(X1)),k11_conlat_1(k7_conlat_2(X1))) ),
inference(fof_simplification,[status(thm)],[t21_conlat_2]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> m1_lattice4(k10_conlat_2(X1),k1_lattice2(k11_conlat_1(X1)),k11_conlat_1(k7_conlat_2(X1))) ),
inference(fof_simplification,[status(thm)],[dt_k10_conlat_2]) ).
fof(c_0_20,plain,
! [X254] :
( ( ~ v3_struct_0(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) )
& ( v3_lattices(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) )
& ( v4_lattices(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) )
& ( v5_lattices(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) )
& ( v6_lattices(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) )
& ( v7_lattices(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) )
& ( v8_lattices(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) )
& ( v9_lattices(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) )
& ( v10_lattices(k1_lattice2(X254))
| v3_struct_0(X254)
| ~ v10_lattices(X254)
| ~ l3_lattices(X254) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_21,plain,
( v10_lattices(k11_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
l2_conlat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
~ v3_conlat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( l3_lattices(k11_conlat_1(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X1] :
( ( ~ v3_conlat_1(X1)
& l2_conlat_1(X1) )
=> ( ~ v3_conlat_1(k7_conlat_2(X1))
& v4_conlat_1(k7_conlat_2(X1))
& l2_conlat_1(k7_conlat_2(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k7_conlat_2]) ).
fof(c_0_26,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ( r1_filter_1(X1,X2)
<=> ? [X3] :
( m1_lattice4(X3,X1,X2)
& v3_lattice4(X3,X1,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[d5_lattice4]) ).
fof(c_0_27,plain,
! [X309] :
( v3_conlat_1(X309)
| ~ l2_conlat_1(X309)
| v3_lattice4(k10_conlat_2(X309),k1_lattice2(k11_conlat_1(X309)),k11_conlat_1(k7_conlat_2(X309))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
fof(c_0_28,plain,
! [X198] :
( v3_conlat_1(X198)
| ~ l2_conlat_1(X198)
| m1_lattice4(k10_conlat_2(X198),k1_lattice2(k11_conlat_1(X198)),k11_conlat_1(k7_conlat_2(X198))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
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_20]) ).
cnf(c_0_30,negated_conjecture,
v10_lattices(k11_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_31,negated_conjecture,
l3_lattices(k11_conlat_1(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23]) ).
fof(c_0_32,plain,
! [X205] :
( ( ~ v3_conlat_1(k7_conlat_2(X205))
| v3_conlat_1(X205)
| ~ l2_conlat_1(X205) )
& ( v4_conlat_1(k7_conlat_2(X205))
| v3_conlat_1(X205)
| ~ l2_conlat_1(X205) )
& ( l2_conlat_1(k7_conlat_2(X205))
| v3_conlat_1(X205)
| ~ l2_conlat_1(X205) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_33,plain,
! [X187,X188,X190] :
( ( m1_lattice4(esk2_2(X187,X188),X187,X188)
| ~ r1_filter_1(X187,X188)
| v3_struct_0(X188)
| ~ v10_lattices(X188)
| ~ l3_lattices(X188)
| v3_struct_0(X187)
| ~ v10_lattices(X187)
| ~ l3_lattices(X187) )
& ( v3_lattice4(esk2_2(X187,X188),X187,X188)
| ~ r1_filter_1(X187,X188)
| v3_struct_0(X188)
| ~ v10_lattices(X188)
| ~ l3_lattices(X188)
| v3_struct_0(X187)
| ~ v10_lattices(X187)
| ~ l3_lattices(X187) )
& ( ~ m1_lattice4(X190,X187,X188)
| ~ v3_lattice4(X190,X187,X188)
| r1_filter_1(X187,X188)
| v3_struct_0(X188)
| ~ v10_lattices(X188)
| ~ l3_lattices(X188)
| v3_struct_0(X187)
| ~ v10_lattices(X187)
| ~ l3_lattices(X187) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])]) ).
cnf(c_0_34,plain,
( v3_conlat_1(X1)
| v3_lattice4(k10_conlat_2(X1),k1_lattice2(k11_conlat_1(X1)),k11_conlat_1(k7_conlat_2(X1)))
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
( v3_conlat_1(X1)
| m1_lattice4(k10_conlat_2(X1),k1_lattice2(k11_conlat_1(X1)),k11_conlat_1(k7_conlat_2(X1)))
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( v3_conlat_1(X1)
| ~ v3_struct_0(k11_conlat_1(X1))
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,negated_conjecture,
( v10_lattices(k1_lattice2(k11_conlat_1(esk1_0)))
| v3_struct_0(k11_conlat_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_38,plain,
( l2_conlat_1(k7_conlat_2(X1))
| v3_conlat_1(X1)
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( r1_filter_1(X2,X3)
| v3_struct_0(X3)
| v3_struct_0(X2)
| ~ m1_lattice4(X1,X2,X3)
| ~ v3_lattice4(X1,X2,X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
v3_lattice4(k10_conlat_2(esk1_0),k1_lattice2(k11_conlat_1(esk1_0)),k11_conlat_1(k7_conlat_2(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_22]),c_0_23]) ).
cnf(c_0_41,negated_conjecture,
m1_lattice4(k10_conlat_2(esk1_0),k1_lattice2(k11_conlat_1(esk1_0)),k11_conlat_1(k7_conlat_2(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_23]) ).
cnf(c_0_42,negated_conjecture,
v10_lattices(k1_lattice2(k11_conlat_1(esk1_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_22])]),c_0_23]) ).
cnf(c_0_43,negated_conjecture,
l2_conlat_1(k7_conlat_2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_23]) ).
fof(c_0_44,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ~ v3_struct_0(X2)
& v10_lattices(X2)
& l3_lattices(X2) )
=> ( r1_filter_1(X1,X2)
=> r1_filter_1(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[symmetry_r1_filter_1]) ).
cnf(c_0_45,negated_conjecture,
( v3_struct_0(k1_lattice2(k11_conlat_1(esk1_0)))
| v3_struct_0(k11_conlat_1(k7_conlat_2(esk1_0)))
| r1_filter_1(k1_lattice2(k11_conlat_1(esk1_0)),k11_conlat_1(k7_conlat_2(esk1_0)))
| ~ v10_lattices(k11_conlat_1(k7_conlat_2(esk1_0)))
| ~ l3_lattices(k11_conlat_1(k7_conlat_2(esk1_0)))
| ~ l3_lattices(k1_lattice2(k11_conlat_1(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_46,negated_conjecture,
( v10_lattices(k11_conlat_1(k7_conlat_2(esk1_0)))
| v3_conlat_1(k7_conlat_2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( l3_lattices(k11_conlat_1(k7_conlat_2(esk1_0)))
| v3_conlat_1(k7_conlat_2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
fof(c_0_48,plain,
! [X200] :
( ( v3_lattices(k1_lattice2(X200))
| ~ l3_lattices(X200) )
& ( l3_lattices(k1_lattice2(X200))
| ~ l3_lattices(X200) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_49,plain,
! [X305,X306] :
( v3_struct_0(X305)
| ~ v10_lattices(X305)
| ~ l3_lattices(X305)
| v3_struct_0(X306)
| ~ v10_lattices(X306)
| ~ l3_lattices(X306)
| ~ r1_filter_1(X305,X306)
| r1_filter_1(X306,X305) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])]) ).
cnf(c_0_50,negated_conjecture,
( v3_struct_0(k11_conlat_1(k7_conlat_2(esk1_0)))
| v3_struct_0(k1_lattice2(k11_conlat_1(esk1_0)))
| r1_filter_1(k1_lattice2(k11_conlat_1(esk1_0)),k11_conlat_1(k7_conlat_2(esk1_0)))
| v3_conlat_1(k7_conlat_2(esk1_0))
| ~ l3_lattices(k1_lattice2(k11_conlat_1(esk1_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_51,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_52,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| r1_filter_1(X2,X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X2)
| ~ l3_lattices(X2)
| ~ r1_filter_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( v3_struct_0(k1_lattice2(k11_conlat_1(esk1_0)))
| v3_struct_0(k11_conlat_1(k7_conlat_2(esk1_0)))
| r1_filter_1(k1_lattice2(k11_conlat_1(esk1_0)),k11_conlat_1(k7_conlat_2(esk1_0)))
| v3_conlat_1(k7_conlat_2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_31])]) ).
cnf(c_0_54,negated_conjecture,
~ r1_filter_1(k11_conlat_1(k7_conlat_2(esk1_0)),k1_lattice2(k11_conlat_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_55,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]) ).
cnf(c_0_56,negated_conjecture,
( v3_struct_0(k1_lattice2(k11_conlat_1(esk1_0)))
| v3_struct_0(k11_conlat_1(k7_conlat_2(esk1_0)))
| v3_conlat_1(k7_conlat_2(esk1_0))
| ~ l3_lattices(k1_lattice2(k11_conlat_1(esk1_0))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_42])]),c_0_54]),c_0_47]),c_0_46]) ).
fof(c_0_57,plain,
! [X238] :
( ( ~ v3_struct_0(k1_lattice2(X238))
| v3_struct_0(X238)
| ~ l3_lattices(X238) )
& ( v3_lattices(k1_lattice2(X238))
| v3_struct_0(X238)
| ~ l3_lattices(X238) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
cnf(c_0_58,negated_conjecture,
( v3_struct_0(k11_conlat_1(k7_conlat_2(esk1_0)))
| v3_struct_0(k1_lattice2(k11_conlat_1(esk1_0)))
| v3_conlat_1(k7_conlat_2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_51]),c_0_31])]) ).
cnf(c_0_59,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( v3_struct_0(k1_lattice2(k11_conlat_1(esk1_0)))
| v3_conlat_1(k7_conlat_2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_58]),c_0_43])]) ).
cnf(c_0_61,negated_conjecture,
( v3_struct_0(k11_conlat_1(esk1_0))
| v3_conlat_1(k7_conlat_2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_31])]) ).
cnf(c_0_62,plain,
( v3_conlat_1(X1)
| ~ v3_conlat_1(k7_conlat_2(X1))
| ~ l2_conlat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_63,negated_conjecture,
v3_conlat_1(k7_conlat_2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_61]),c_0_22])]),c_0_23]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT346+1 : TPTP v9.2.1. Released v3.4.0.
% 0.12/0.13 % 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
% 0.16/0.35 % Computer : n002.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Mon May 4 21:28:01 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.21/0.36 % start to proof: theBenchmark
% 2.36/2.00 % Version : CSE_E---1.7
% 2.36/2.00 % Problem : theBenchmark.p
% 2.36/2.00 % SZS status Theorem for theBenchmark.p
% 2.36/2.00 % SZS output start CNFRefutation
% See solution above
% 2.36/2.01 % Total time : 1.378s
%------------------------------------------------------------------------------