%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT319+2 : 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 : n017.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 04:38:05 PM UTC 2026
% Result : Theorem 32.79s 20.20s
% Output : CNFRefutation 32.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 102 ( 20 unt; 0 def)
% Number of atoms : 666 ( 0 equ)
% Maximal formula atoms : 70 ( 6 avg)
% Number of connectives : 886 ( 322 ~; 351 |; 173 &)
% ( 12 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 55 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t54_filter_2,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
<=> ( ~ v3_struct_0(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1))
& v17_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_filter_2) ).
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/Axioms/SET007/SET007+253.ax',fc1_lattice2) ).
fof(cc5_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v17_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v11_lattices(X1)
& v13_lattices(X1)
& v14_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',cc5_lattices) ).
fof(dt_k1_lattice2,axiom,
! [X1] :
( l3_lattices(X1)
=> ( v3_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',dt_k1_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/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t63_lattice2) ).
fof(t64_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
<=> v13_lattices(k1_lattice2(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t64_lattice2) ).
fof(t65_lattice2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v11_lattices(X1)
& l3_lattices(X1) )
<=> ( ~ v3_struct_0(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1))
& v11_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+253.ax',t65_lattice2) ).
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/Axioms/SET007/SET007+253.ax',fc6_lattice2) ).
fof(cc3_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v13_lattices(X1)
& v14_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v15_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',cc3_lattices) ).
fof(t53_filter_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1)
& l3_lattices(X1) )
<=> ( ~ v3_struct_0(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1))
& v15_lattices(k1_lattice2(X1))
& v16_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_filter_2) ).
fof(cc6_lattices,axiom,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v11_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v17_lattices(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+205.ax',cc6_lattices) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v17_lattices(X1)
& l3_lattices(X1) )
<=> ( ~ v3_struct_0(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1))
& v17_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t54_filter_2])]) ).
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] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v17_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v11_lattices(X1)
& v13_lattices(X1)
& v14_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc5_lattices]) ).
fof(c_0_14,plain,
! [X6288] :
( ( v3_lattices(k1_lattice2(X6288))
| ~ l3_lattices(X6288) )
& ( l3_lattices(k1_lattice2(X6288))
| ~ l3_lattices(X6288) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_lattice2])])]) ).
fof(c_0_15,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v10_lattices(esk1_0)
& l3_lattices(esk1_0)
& ( v3_struct_0(esk1_0)
| ~ v10_lattices(esk1_0)
| ~ v17_lattices(esk1_0)
| ~ l3_lattices(esk1_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ v10_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) )
& ( ~ v3_struct_0(k1_lattice2(esk1_0))
| ~ v3_struct_0(esk1_0) )
& ( v10_lattices(k1_lattice2(esk1_0))
| ~ v3_struct_0(esk1_0) )
& ( v17_lattices(k1_lattice2(esk1_0))
| ~ v3_struct_0(esk1_0) )
& ( l3_lattices(k1_lattice2(esk1_0))
| ~ v3_struct_0(esk1_0) )
& ( ~ v3_struct_0(k1_lattice2(esk1_0))
| v10_lattices(esk1_0) )
& ( v10_lattices(k1_lattice2(esk1_0))
| v10_lattices(esk1_0) )
& ( v17_lattices(k1_lattice2(esk1_0))
| v10_lattices(esk1_0) )
& ( l3_lattices(k1_lattice2(esk1_0))
| v10_lattices(esk1_0) )
& ( ~ v3_struct_0(k1_lattice2(esk1_0))
| v17_lattices(esk1_0) )
& ( v10_lattices(k1_lattice2(esk1_0))
| v17_lattices(esk1_0) )
& ( v17_lattices(k1_lattice2(esk1_0))
| v17_lattices(esk1_0) )
& ( l3_lattices(k1_lattice2(esk1_0))
| v17_lattices(esk1_0) )
& ( ~ v3_struct_0(k1_lattice2(esk1_0))
| l3_lattices(esk1_0) )
& ( v10_lattices(k1_lattice2(esk1_0))
| l3_lattices(esk1_0) )
& ( v17_lattices(k1_lattice2(esk1_0))
| l3_lattices(esk1_0) )
& ( l3_lattices(k1_lattice2(esk1_0))
| l3_lattices(esk1_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_16,plain,
! [X6258] :
( ( ~ v3_struct_0(k1_lattice2(X6258))
| v3_struct_0(X6258)
| ~ l3_lattices(X6258) )
& ( v3_lattices(k1_lattice2(X6258))
| v3_struct_0(X6258)
| ~ l3_lattices(X6258) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_17,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_18,plain,
! [X6308] :
( ( ~ v3_struct_0(X6308)
| v3_struct_0(X6308)
| ~ v17_lattices(X6308)
| ~ l3_lattices(X6308) )
& ( v11_lattices(X6308)
| v3_struct_0(X6308)
| ~ v17_lattices(X6308)
| ~ l3_lattices(X6308) )
& ( v13_lattices(X6308)
| v3_struct_0(X6308)
| ~ v17_lattices(X6308)
| ~ l3_lattices(X6308) )
& ( v14_lattices(X6308)
| v3_struct_0(X6308)
| ~ v17_lattices(X6308)
| ~ l3_lattices(X6308) )
& ( v15_lattices(X6308)
| v3_struct_0(X6308)
| ~ v17_lattices(X6308)
| ~ l3_lattices(X6308) )
& ( v16_lattices(X6308)
| v3_struct_0(X6308)
| ~ v17_lattices(X6308)
| ~ l3_lattices(X6308) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_19,plain,
( l3_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
l3_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k1_lattice2(X1))
| ~ l3_lattices(X1) ),
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_15]) ).
fof(c_0_23,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( v14_lattices(X1)
<=> v13_lattices(k1_lattice2(X1)) ) ),
inference(fof_simplification,[status(thm)],[t64_lattice2]) ).
fof(c_0_24,plain,
! [X6283] :
( ( ~ v13_lattices(X6283)
| v14_lattices(k1_lattice2(X6283))
| v3_struct_0(X6283)
| ~ v10_lattices(X6283)
| ~ l3_lattices(X6283) )
& ( ~ v14_lattices(k1_lattice2(X6283))
| v13_lattices(X6283)
| v3_struct_0(X6283)
| ~ v10_lattices(X6283)
| ~ l3_lattices(X6283) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_25,plain,
( v14_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
l3_lattices(k1_lattice2(esk1_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
~ v3_struct_0(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).
fof(c_0_28,plain,
! [X6284] :
( ( ~ v14_lattices(X6284)
| v13_lattices(k1_lattice2(X6284))
| v3_struct_0(X6284)
| ~ v10_lattices(X6284)
| ~ l3_lattices(X6284) )
& ( ~ v13_lattices(k1_lattice2(X6284))
| v14_lattices(X6284)
| v3_struct_0(X6284)
| ~ v10_lattices(X6284)
| ~ l3_lattices(X6284) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_29,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_30,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v11_lattices(X1)
& l3_lattices(X1) )
<=> ( ~ v3_struct_0(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1))
& v11_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[t65_lattice2]) ).
fof(c_0_31,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_32,plain,
! [X1] :
( epred1_1(X1)
<=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1)
& l3_lattices(X1) )
<=> ( ~ v3_struct_0(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1))
& v15_lattices(k1_lattice2(X1))
& v16_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ) ),
introduced(definition) ).
cnf(c_0_33,plain,
( v13_lattices(X1)
| v3_struct_0(X1)
| ~ v14_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
v10_lattices(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_35,negated_conjecture,
( v14_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( v17_lattices(k1_lattice2(esk1_0))
| v17_lattices(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_37,plain,
( v14_lattices(X1)
| v3_struct_0(X1)
| ~ v13_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( v13_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_27]) ).
fof(c_0_39,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v13_lattices(X1)
& v14_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v15_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc3_lattices]) ).
fof(c_0_40,plain,
! [X6285] :
( ( ~ v3_struct_0(k1_lattice2(X6285))
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ v11_lattices(X6285)
| ~ l3_lattices(X6285)
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ l3_lattices(X6285) )
& ( v10_lattices(k1_lattice2(X6285))
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ v11_lattices(X6285)
| ~ l3_lattices(X6285)
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ l3_lattices(X6285) )
& ( v11_lattices(k1_lattice2(X6285))
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ v11_lattices(X6285)
| ~ l3_lattices(X6285)
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ l3_lattices(X6285) )
& ( l3_lattices(k1_lattice2(X6285))
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ v11_lattices(X6285)
| ~ l3_lattices(X6285)
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ l3_lattices(X6285) )
& ( ~ v3_struct_0(X6285)
| v3_struct_0(k1_lattice2(X6285))
| ~ v10_lattices(k1_lattice2(X6285))
| ~ v11_lattices(k1_lattice2(X6285))
| ~ l3_lattices(k1_lattice2(X6285))
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ l3_lattices(X6285) )
& ( v10_lattices(X6285)
| v3_struct_0(k1_lattice2(X6285))
| ~ v10_lattices(k1_lattice2(X6285))
| ~ v11_lattices(k1_lattice2(X6285))
| ~ l3_lattices(k1_lattice2(X6285))
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ l3_lattices(X6285) )
& ( v11_lattices(X6285)
| v3_struct_0(k1_lattice2(X6285))
| ~ v10_lattices(k1_lattice2(X6285))
| ~ v11_lattices(k1_lattice2(X6285))
| ~ l3_lattices(k1_lattice2(X6285))
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ l3_lattices(X6285) )
& ( l3_lattices(X6285)
| v3_struct_0(k1_lattice2(X6285))
| ~ v10_lattices(k1_lattice2(X6285))
| ~ v11_lattices(k1_lattice2(X6285))
| ~ l3_lattices(k1_lattice2(X6285))
| v3_struct_0(X6285)
| ~ v10_lattices(X6285)
| ~ l3_lattices(X6285) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
fof(c_0_41,plain,
! [X6259] :
( ( ~ v3_struct_0(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) )
& ( v3_lattices(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) )
& ( v4_lattices(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) )
& ( v5_lattices(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) )
& ( v6_lattices(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) )
& ( v7_lattices(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) )
& ( v8_lattices(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) )
& ( v9_lattices(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) )
& ( v10_lattices(k1_lattice2(X6259))
| v3_struct_0(X6259)
| ~ v10_lattices(X6259)
| ~ l3_lattices(X6259) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
fof(c_0_42,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> epred1_1(X1) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[t53_filter_2]),c_0_32]) ).
cnf(c_0_43,negated_conjecture,
( v13_lattices(esk1_0)
| ~ v14_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20]),c_0_34])]),c_0_22]) ).
cnf(c_0_44,negated_conjecture,
( v17_lattices(esk1_0)
| v14_lattices(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,negated_conjecture,
( v13_lattices(esk1_0)
| ~ v17_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_22]) ).
cnf(c_0_46,negated_conjecture,
( v14_lattices(esk1_0)
| ~ v13_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_20]),c_0_34])]),c_0_22]) ).
cnf(c_0_47,negated_conjecture,
( v17_lattices(esk1_0)
| v13_lattices(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_48,negated_conjecture,
( v14_lattices(esk1_0)
| ~ v17_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_22]) ).
fof(c_0_49,plain,
! [X1] :
( l3_lattices(X1)
=> ( ( ~ v3_struct_0(X1)
& v11_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1) )
=> ( ~ v3_struct_0(X1)
& v17_lattices(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc6_lattices]) ).
fof(c_0_50,plain,
! [X7708] :
( ( ~ v3_struct_0(X7708)
| v3_struct_0(X7708)
| ~ v13_lattices(X7708)
| ~ v14_lattices(X7708)
| ~ l3_lattices(X7708) )
& ( v15_lattices(X7708)
| v3_struct_0(X7708)
| ~ v13_lattices(X7708)
| ~ v14_lattices(X7708)
| ~ l3_lattices(X7708) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
cnf(c_0_51,plain,
( v11_lattices(X1)
| v3_struct_0(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(k1_lattice2(X1))
| ~ v11_lattices(k1_lattice2(X1))
| ~ l3_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,plain,
( v10_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_53,plain,
( v11_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_54,plain,
! [X1] :
( epred1_1(X1)
=> ( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& v15_lattices(X1)
& v16_lattices(X1)
& l3_lattices(X1) )
<=> ( ~ v3_struct_0(k1_lattice2(X1))
& v10_lattices(k1_lattice2(X1))
& v15_lattices(k1_lattice2(X1))
& v16_lattices(k1_lattice2(X1))
& l3_lattices(k1_lattice2(X1)) ) ) ),
inference(split_equiv,[status(thm)],[c_0_32]) ).
fof(c_0_55,plain,
! [X6307] :
( v3_struct_0(X6307)
| ~ v10_lattices(X6307)
| ~ l3_lattices(X6307)
| epred1_1(X6307) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])]) ).
cnf(c_0_56,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_24]) ).
cnf(c_0_57,negated_conjecture,
v13_lattices(esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_58,plain,
( v13_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v14_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_59,negated_conjecture,
v14_lattices(esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
fof(c_0_60,plain,
! [X6309] :
( ( ~ v3_struct_0(X6309)
| v3_struct_0(X6309)
| ~ v11_lattices(X6309)
| ~ v15_lattices(X6309)
| ~ v16_lattices(X6309)
| ~ l3_lattices(X6309) )
& ( v17_lattices(X6309)
| v3_struct_0(X6309)
| ~ v11_lattices(X6309)
| ~ v15_lattices(X6309)
| ~ v16_lattices(X6309)
| ~ l3_lattices(X6309) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
cnf(c_0_61,plain,
( v15_lattices(X1)
| v3_struct_0(X1)
| ~ v13_lattices(X1)
| ~ v14_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_62,plain,
( v11_lattices(X1)
| v3_struct_0(X1)
| ~ v11_lattices(k1_lattice2(X1))
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_51,c_0_19]),c_0_52]),c_0_21]) ).
cnf(c_0_63,negated_conjecture,
( v11_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_26]),c_0_27]) ).
fof(c_0_64,plain,
! [X13029] :
( ( ~ v3_struct_0(k1_lattice2(X13029))
| v3_struct_0(X13029)
| ~ v10_lattices(X13029)
| ~ v15_lattices(X13029)
| ~ v16_lattices(X13029)
| ~ l3_lattices(X13029)
| ~ epred1_1(X13029) )
& ( v10_lattices(k1_lattice2(X13029))
| v3_struct_0(X13029)
| ~ v10_lattices(X13029)
| ~ v15_lattices(X13029)
| ~ v16_lattices(X13029)
| ~ l3_lattices(X13029)
| ~ epred1_1(X13029) )
& ( v15_lattices(k1_lattice2(X13029))
| v3_struct_0(X13029)
| ~ v10_lattices(X13029)
| ~ v15_lattices(X13029)
| ~ v16_lattices(X13029)
| ~ l3_lattices(X13029)
| ~ epred1_1(X13029) )
& ( v16_lattices(k1_lattice2(X13029))
| v3_struct_0(X13029)
| ~ v10_lattices(X13029)
| ~ v15_lattices(X13029)
| ~ v16_lattices(X13029)
| ~ l3_lattices(X13029)
| ~ epred1_1(X13029) )
& ( l3_lattices(k1_lattice2(X13029))
| v3_struct_0(X13029)
| ~ v10_lattices(X13029)
| ~ v15_lattices(X13029)
| ~ v16_lattices(X13029)
| ~ l3_lattices(X13029)
| ~ epred1_1(X13029) )
& ( ~ v3_struct_0(X13029)
| v3_struct_0(k1_lattice2(X13029))
| ~ v10_lattices(k1_lattice2(X13029))
| ~ v15_lattices(k1_lattice2(X13029))
| ~ v16_lattices(k1_lattice2(X13029))
| ~ l3_lattices(k1_lattice2(X13029))
| ~ epred1_1(X13029) )
& ( v10_lattices(X13029)
| v3_struct_0(k1_lattice2(X13029))
| ~ v10_lattices(k1_lattice2(X13029))
| ~ v15_lattices(k1_lattice2(X13029))
| ~ v16_lattices(k1_lattice2(X13029))
| ~ l3_lattices(k1_lattice2(X13029))
| ~ epred1_1(X13029) )
& ( v15_lattices(X13029)
| v3_struct_0(k1_lattice2(X13029))
| ~ v10_lattices(k1_lattice2(X13029))
| ~ v15_lattices(k1_lattice2(X13029))
| ~ v16_lattices(k1_lattice2(X13029))
| ~ l3_lattices(k1_lattice2(X13029))
| ~ epred1_1(X13029) )
& ( v16_lattices(X13029)
| v3_struct_0(k1_lattice2(X13029))
| ~ v10_lattices(k1_lattice2(X13029))
| ~ v15_lattices(k1_lattice2(X13029))
| ~ v16_lattices(k1_lattice2(X13029))
| ~ l3_lattices(k1_lattice2(X13029))
| ~ epred1_1(X13029) )
& ( l3_lattices(X13029)
| v3_struct_0(k1_lattice2(X13029))
| ~ v10_lattices(k1_lattice2(X13029))
| ~ v15_lattices(k1_lattice2(X13029))
| ~ v16_lattices(k1_lattice2(X13029))
| ~ l3_lattices(k1_lattice2(X13029))
| ~ epred1_1(X13029) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])]) ).
cnf(c_0_65,plain,
( v3_struct_0(X1)
| epred1_1(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,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_56,c_0_20]),c_0_57]),c_0_34])]),c_0_22]) ).
cnf(c_0_67,negated_conjecture,
v13_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_58,c_0_20]),c_0_59]),c_0_34])]),c_0_22]) ).
cnf(c_0_68,plain,
( v16_lattices(X1)
| v3_struct_0(X1)
| ~ v17_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_69,plain,
( v17_lattices(X1)
| v3_struct_0(X1)
| ~ v11_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_70,negated_conjecture,
v15_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_61,c_0_20]),c_0_59]),c_0_57])]),c_0_22]) ).
cnf(c_0_71,negated_conjecture,
( v11_lattices(esk1_0)
| ~ v11_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_20]),c_0_34])]),c_0_22]) ).
cnf(c_0_72,negated_conjecture,
( v17_lattices(esk1_0)
| v11_lattices(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_36]) ).
cnf(c_0_73,negated_conjecture,
( v11_lattices(esk1_0)
| ~ v17_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_20]),c_0_22]) ).
cnf(c_0_74,plain,
( v11_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v11_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_75,plain,
( v16_lattices(X1)
| v3_struct_0(k1_lattice2(X1))
| ~ v10_lattices(k1_lattice2(X1))
| ~ v15_lattices(k1_lattice2(X1))
| ~ v16_lattices(k1_lattice2(X1))
| ~ l3_lattices(k1_lattice2(X1))
| ~ epred1_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_76,negated_conjecture,
epred1_1(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_20]),c_0_34])]),c_0_22]) ).
cnf(c_0_77,negated_conjecture,
v15_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_61,c_0_26]),c_0_66]),c_0_67])]),c_0_27]) ).
cnf(c_0_78,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_52,c_0_20]),c_0_34])]),c_0_22]) ).
cnf(c_0_79,negated_conjecture,
( v16_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_26]),c_0_27]) ).
cnf(c_0_80,negated_conjecture,
( v17_lattices(esk1_0)
| ~ v16_lattices(esk1_0)
| ~ v11_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_20]),c_0_70])]),c_0_22]) ).
cnf(c_0_81,negated_conjecture,
v11_lattices(esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_82,negated_conjecture,
( v3_struct_0(esk1_0)
| v3_struct_0(k1_lattice2(esk1_0))
| ~ v10_lattices(esk1_0)
| ~ v17_lattices(esk1_0)
| ~ l3_lattices(esk1_0)
| ~ v10_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_83,plain,
( v3_struct_0(X1)
| v11_lattices(k1_lattice2(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ v11_lattices(X1) ),
inference(cn,[status(thm)],[c_0_74]) ).
cnf(c_0_84,negated_conjecture,
( v16_lattices(esk1_0)
| ~ v16_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78]),c_0_26])]),c_0_27]) ).
cnf(c_0_85,negated_conjecture,
( v17_lattices(esk1_0)
| v16_lattices(k1_lattice2(esk1_0)) ),
inference(spm,[status(thm)],[c_0_79,c_0_36]) ).
cnf(c_0_86,negated_conjecture,
( v17_lattices(esk1_0)
| ~ v16_lattices(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
cnf(c_0_87,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ v17_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(esk1_0)
| ~ v10_lattices(k1_lattice2(esk1_0))
| ~ l3_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_20]),c_0_34])]),c_0_22]) ).
cnf(c_0_88,negated_conjecture,
( v11_lattices(k1_lattice2(esk1_0))
| ~ v11_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_20]),c_0_34])]),c_0_22]) ).
cnf(c_0_89,plain,
( v16_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ v15_lattices(X1)
| ~ v16_lattices(X1)
| ~ l3_lattices(X1)
| ~ epred1_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_90,negated_conjecture,
( v16_lattices(esk1_0)
| ~ v17_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_20]),c_0_22]) ).
cnf(c_0_91,negated_conjecture,
v17_lattices(esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_92,negated_conjecture,
( v3_struct_0(k1_lattice2(esk1_0))
| ~ v17_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(esk1_0)
| ~ v10_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_26])]) ).
cnf(c_0_93,negated_conjecture,
( v17_lattices(k1_lattice2(esk1_0))
| ~ v16_lattices(k1_lattice2(esk1_0))
| ~ v11_lattices(k1_lattice2(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_26]),c_0_77])]),c_0_27]) ).
cnf(c_0_94,negated_conjecture,
v11_lattices(k1_lattice2(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_81])]) ).
cnf(c_0_95,plain,
( v16_lattices(k1_lattice2(X1))
| v3_struct_0(X1)
| ~ v16_lattices(X1)
| ~ v15_lattices(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1) ),
inference(csr,[status(thm)],[c_0_89,c_0_65]) ).
cnf(c_0_96,negated_conjecture,
v16_lattices(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
cnf(c_0_97,negated_conjecture,
( ~ v17_lattices(k1_lattice2(esk1_0))
| ~ v17_lattices(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_78])]),c_0_27]) ).
cnf(c_0_98,negated_conjecture,
( v17_lattices(k1_lattice2(esk1_0))
| ~ v16_lattices(k1_lattice2(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_99,negated_conjecture,
v16_lattices(k1_lattice2(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_20]),c_0_96]),c_0_70]),c_0_34])]),c_0_22]) ).
cnf(c_0_100,negated_conjecture,
~ v17_lattices(k1_lattice2(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_91])]) ).
cnf(c_0_101,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]),c_0_100]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LAT319+2 : TPTP v9.2.1. Released v3.4.0.
% 0.11/0.13 % 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
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 21:13:43 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 32.79/20.20 % Version : CSE_E---1.7
% 32.79/20.20 % Problem : theBenchmark.p
% 32.79/20.20 % SZS status Theorem for theBenchmark.p
% 32.79/20.20 % SZS output start CNFRefutation
% See solution above
% 32.90/20.30 % Total time : 15.400s
%------------------------------------------------------------------------------