%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU408+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 : n001.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 05:12:12 PM UTC 2026
% Result : Theorem 1.31s 1.75s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 138 ( 24 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 167 ( 57 ~; 51 |; 45 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 56 ( 2 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t11_latsum_1,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_orders_2(X2)
& v3_orders_2(X2)
& v4_orders_2(X2)
& v1_lattice3(X2)
& l1_orders_2(X2) )
=> ! [X3] :
( r2_hidden(X3,u1_struct_0(X2))
=> m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_latsum_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(d2_latsum_1,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3] :
( ( v1_orders_2(X3)
& l1_orders_2(X3) )
=> ( X3 = k1_latsum_1(X1,X2)
<=> ( u1_struct_0(X3) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
& u1_orders_2(X3) = k2_xboole_0(k2_xboole_0(u1_orders_2(X1),u1_orders_2(X2)),k7_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X2),u1_struct_0(X2),u1_orders_2(X1),u1_orders_2(X2))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_latsum_1) ).
fof(dt_k1_latsum_1,axiom,
! [X1,X2] :
( ( l1_orders_2(X1)
& l1_orders_2(X2) )
=> ( v1_orders_2(k1_latsum_1(X1,X2))
& l1_orders_2(k1_latsum_1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
| r2_hidden(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_orders_2(X2)
& v3_orders_2(X2)
& v4_orders_2(X2)
& v1_lattice3(X2)
& l1_orders_2(X2) )
=> ! [X3] :
( r2_hidden(X3,u1_struct_0(X2))
=> m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2))) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t11_latsum_1])]) ).
fof(c_0_7,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v2_orders_2(esk1_0)
& v3_orders_2(esk1_0)
& v4_orders_2(esk1_0)
& v1_lattice3(esk1_0)
& l1_orders_2(esk1_0)
& ~ v3_struct_0(esk2_0)
& v2_orders_2(esk2_0)
& v3_orders_2(esk2_0)
& v4_orders_2(esk2_0)
& v1_lattice3(esk2_0)
& l1_orders_2(esk2_0)
& r2_hidden(esk3_0,u1_struct_0(esk2_0))
& ~ m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X181,X182] :
( ~ r2_hidden(X181,X182)
| m1_subset_1(X181,X182) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_9,plain,
! [X112,X113,X114] :
( ( u1_struct_0(X114) = k2_xboole_0(u1_struct_0(X112),u1_struct_0(X113))
| X114 != k1_latsum_1(X112,X113)
| ~ v1_orders_2(X114)
| ~ l1_orders_2(X114)
| ~ l1_orders_2(X113)
| ~ l1_orders_2(X112) )
& ( u1_orders_2(X114) = k2_xboole_0(k2_xboole_0(u1_orders_2(X112),u1_orders_2(X113)),k7_relset_1(u1_struct_0(X112),u1_struct_0(X112),u1_struct_0(X113),u1_struct_0(X113),u1_orders_2(X112),u1_orders_2(X113)))
| X114 != k1_latsum_1(X112,X113)
| ~ v1_orders_2(X114)
| ~ l1_orders_2(X114)
| ~ l1_orders_2(X113)
| ~ l1_orders_2(X112) )
& ( u1_struct_0(X114) != k2_xboole_0(u1_struct_0(X112),u1_struct_0(X113))
| u1_orders_2(X114) != k2_xboole_0(k2_xboole_0(u1_orders_2(X112),u1_orders_2(X113)),k7_relset_1(u1_struct_0(X112),u1_struct_0(X112),u1_struct_0(X113),u1_struct_0(X113),u1_orders_2(X112),u1_orders_2(X113)))
| X114 = k1_latsum_1(X112,X113)
| ~ v1_orders_2(X114)
| ~ l1_orders_2(X114)
| ~ l1_orders_2(X113)
| ~ l1_orders_2(X112) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_latsum_1])])])]) ).
fof(c_0_10,plain,
! [X126,X127] :
( ( v1_orders_2(k1_latsum_1(X126,X127))
| ~ l1_orders_2(X126)
| ~ l1_orders_2(X127) )
& ( l1_orders_2(k1_latsum_1(X126,X127))
| ~ l1_orders_2(X126)
| ~ l1_orders_2(X127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_latsum_1])])]) ).
cnf(c_0_11,negated_conjecture,
~ m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( u1_struct_0(X1) = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
| X1 != k1_latsum_1(X2,X3)
| ~ v1_orders_2(X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X3)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( l1_orders_2(k1_latsum_1(X1,X2))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( v1_orders_2(k1_latsum_1(X1,X2))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X110,X111] : k2_xboole_0(X110,X111) = k2_xboole_0(X111,X110),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_17,plain,
! [X115,X116,X117,X118,X119,X120,X121,X122] :
( ( ~ r2_hidden(X118,X117)
| r2_hidden(X118,X115)
| r2_hidden(X118,X116)
| X117 != k2_xboole_0(X115,X116) )
& ( ~ r2_hidden(X119,X115)
| r2_hidden(X119,X117)
| X117 != k2_xboole_0(X115,X116) )
& ( ~ r2_hidden(X119,X116)
| r2_hidden(X119,X117)
| X117 != k2_xboole_0(X115,X116) )
& ( ~ r2_hidden(esk4_3(X120,X121,X122),X120)
| ~ r2_hidden(esk4_3(X120,X121,X122),X122)
| X122 = k2_xboole_0(X120,X121) )
& ( ~ r2_hidden(esk4_3(X120,X121,X122),X121)
| ~ r2_hidden(esk4_3(X120,X121,X122),X122)
| X122 = k2_xboole_0(X120,X121) )
& ( r2_hidden(esk4_3(X120,X121,X122),X122)
| r2_hidden(esk4_3(X120,X121,X122),X120)
| r2_hidden(esk4_3(X120,X121,X122),X121)
| X122 = k2_xboole_0(X120,X121) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_18,negated_conjecture,
~ r2_hidden(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
( u1_struct_0(k1_latsum_1(X1,X2)) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
| ~ l1_orders_2(X2)
| ~ l1_orders_2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
l1_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
l1_orders_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( r2_hidden(X1,X3)
| ~ r2_hidden(X1,X2)
| X3 != k2_xboole_0(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
~ r2_hidden(esk3_0,k2_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_25,plain,
( r2_hidden(X1,k2_xboole_0(X2,X3))
| ~ r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
r2_hidden(esk3_0,u1_struct_0(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU408+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
% 0.18/0.35 % Computer : n001.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue May 5 03:12:33 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.20/0.36 % start to proof: theBenchmark
% 1.31/1.75 % Version : CSE_E---1.7
% 1.31/1.75 % Problem : theBenchmark.p
% 1.31/1.75 % SZS status Theorem for theBenchmark.p
% 1.31/1.75 % SZS output start CNFRefutation
% See solution above
% 1.31/1.75 % Total time : 1.378s
%------------------------------------------------------------------------------