%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU342+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n016.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 05:11:32 PM UTC 2026
% Result : Theorem 193.04s 156.68s
% Output : CNFRefutation 194.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 78 ( 16 unt; 0 def)
% Number of atoms : 269 ( 56 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 290 ( 99 ~; 130 |; 40 &)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 116 ( 8 sgn 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_k1_domain_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(d8_filter_1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_1) ).
fof(t32_filter_1,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(fraenkel_a_1_0_filter_1,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ( in(X1,a_1_0_filter_1(X2))
<=> ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
fof(t33_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(c_0_10,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_domain_1]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
inference(fof_simplification,[status(thm)],[d8_filter_1]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t32_filter_1])]) ).
fof(c_0_13,plain,
! [X108,X109,X110,X111] :
( empty(X108)
| empty(X109)
| ~ element(X110,X108)
| ~ element(X111,X109)
| ordered_pair_as_product_element(X108,X109,X110,X111) = ordered_pair(X110,X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
fof(c_0_14,plain,
! [X76,X77] : ordered_pair(X76,X77) = unordered_pair(unordered_pair(X76,X77),singleton(X76)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_15,plain,
! [X78] :
( empty_carrier(X78)
| ~ lattice(X78)
| ~ latt_str(X78)
| relation_of_lattice(X78) = a_1_0_filter_1(X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_16,negated_conjecture,
( ~ empty_carrier(esk12_0)
& lattice(esk12_0)
& latt_str(esk12_0)
& element(esk13_0,the_carrier(esk12_0))
& element(esk14_0,the_carrier(esk12_0))
& ( ~ in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),relation_of_lattice(esk12_0))
| ~ below_refl(esk12_0,esk13_0,esk14_0) )
& ( in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),relation_of_lattice(esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_17,plain,
( empty(X1)
| empty(X2)
| ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
| ~ element(X3,X1)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ( in(X1,a_1_0_filter_1(X2))
<=> ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_1_0_filter_1]) ).
cnf(c_0_20,plain,
( empty_carrier(X1)
| relation_of_lattice(X1) = a_1_0_filter_1(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
lattice(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
latt_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
~ empty_carrier(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_24,plain,
! [X128,X129,X130,X131] :
( ( X128 = X130
| ordered_pair(X128,X129) != ordered_pair(X130,X131) )
& ( X129 = X131
| ordered_pair(X128,X129) != ordered_pair(X130,X131) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
cnf(c_0_25,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_27,plain,
! [X99,X100,X103,X104] :
( ( element(esk6_2(X99,X100),the_carrier(X100))
| ~ in(X99,a_1_0_filter_1(X100))
| empty_carrier(X100)
| ~ lattice(X100)
| ~ latt_str(X100) )
& ( element(esk7_2(X99,X100),the_carrier(X100))
| ~ in(X99,a_1_0_filter_1(X100))
| empty_carrier(X100)
| ~ lattice(X100)
| ~ latt_str(X100) )
& ( X99 = ordered_pair_as_product_element(the_carrier(X100),the_carrier(X100),esk6_2(X99,X100),esk7_2(X99,X100))
| ~ in(X99,a_1_0_filter_1(X100))
| empty_carrier(X100)
| ~ lattice(X100)
| ~ latt_str(X100) )
& ( below_refl(X100,esk6_2(X99,X100),esk7_2(X99,X100))
| ~ in(X99,a_1_0_filter_1(X100))
| empty_carrier(X100)
| ~ lattice(X100)
| ~ latt_str(X100) )
& ( ~ element(X103,the_carrier(X100))
| ~ element(X104,the_carrier(X100))
| X99 != ordered_pair_as_product_element(the_carrier(X100),the_carrier(X100),X103,X104)
| ~ below_refl(X100,X103,X104)
| in(X99,a_1_0_filter_1(X100))
| empty_carrier(X100)
| ~ lattice(X100)
| ~ latt_str(X100) ) ),
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_19])])])])]) ).
cnf(c_0_28,negated_conjecture,
( in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),relation_of_lattice(esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,negated_conjecture,
relation_of_lattice(esk12_0) = a_1_0_filter_1(esk12_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_30,plain,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( ordered_pair_as_product_element(X1,the_carrier(esk12_0),X2,esk14_0) = unordered_pair(unordered_pair(X2,esk14_0),singleton(X2))
| empty(the_carrier(esk12_0))
| empty(X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
element(esk13_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_33,plain,
( element(esk7_2(X1,X2),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( below_refl(esk12_0,esk13_0,esk14_0)
| in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),a_1_0_filter_1(esk12_0)) ),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_35,plain,
! [X74,X75] : unordered_pair(X74,X75) = unordered_pair(X75,X74),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_36,plain,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,plain,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),singleton(X1)) != unordered_pair(unordered_pair(X2,X4),singleton(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_18]),c_0_18]) ).
cnf(c_0_38,negated_conjecture,
( unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( below_refl(esk12_0,esk13_0,esk14_0)
| element(esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_40,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
( element(esk6_2(X1,X2),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_42,plain,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),singleton(X3)) != unordered_pair(unordered_pair(X4,X2),singleton(X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_18]),c_0_18]) ).
cnf(c_0_43,negated_conjecture,
( esk13_0 = X1
| empty(the_carrier(esk12_0))
| unordered_pair(unordered_pair(X1,X2),singleton(X1)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( ordered_pair_as_product_element(X1,the_carrier(esk12_0),X2,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) = unordered_pair(singleton(X2),unordered_pair(X2,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)))
| below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0))
| empty(X1)
| ~ element(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_39]),c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( below_refl(esk12_0,esk13_0,esk14_0)
| element(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_34]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_46,plain,
( X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),esk6_2(X1,X2),esk7_2(X1,X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_47,negated_conjecture,
( X1 = esk14_0
| empty(the_carrier(esk12_0))
| unordered_pair(unordered_pair(X2,X1),singleton(X2)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( esk13_0 = X1
| empty(the_carrier(esk12_0))
| unordered_pair(singleton(X1),unordered_pair(X1,X2)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( unordered_pair(singleton(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)),unordered_pair(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0)
| below_refl(esk12_0,esk13_0,esk14_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_34]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_51,plain,
( below_refl(X1,esk6_2(X2,X1),esk7_2(X2,X1))
| empty_carrier(X1)
| ~ in(X2,a_1_0_filter_1(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_52,negated_conjecture,
( X1 = esk14_0
| empty(the_carrier(esk12_0))
| unordered_pair(singleton(X2),unordered_pair(X2,X1)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_40]) ).
cnf(c_0_53,negated_conjecture,
( unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_54,negated_conjecture,
( esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0) = esk13_0
| below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( below_refl(esk12_0,esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_56,negated_conjecture,
( esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0) = esk14_0
| below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0))
| ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0)
| below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_50,c_0_54]) ).
cnf(c_0_58,plain,
( in(X4,a_1_0_filter_1(X2))
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| X4 != ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X1,X3)
| ~ below_refl(X2,X1,X3)
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_59,negated_conjecture,
( ~ in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),relation_of_lattice(esk12_0))
| ~ below_refl(esk12_0,esk13_0,esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_60,negated_conjecture,
( below_refl(esk12_0,esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0) = esk14_0
| below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_62,plain,
! [X86] :
( ( meet_semilatt_str(X86)
| ~ latt_str(X86) )
& ( join_semilatt_str(X86)
| ~ latt_str(X86) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_63,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_64,plain,
( empty_carrier(X1)
| in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),a_1_0_filter_1(X1))
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( ~ below_refl(esk12_0,esk13_0,esk14_0)
| ~ in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),a_1_0_filter_1(esk12_0)) ),
inference(rw,[status(thm)],[c_0_59,c_0_29]) ).
cnf(c_0_66,negated_conjecture,
( below_refl(esk12_0,esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_67,plain,
! [X84] :
( ~ meet_semilatt_str(X84)
| one_sorted_str(X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
cnf(c_0_68,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_69,plain,
! [X93] :
( empty_carrier(X93)
| ~ one_sorted_str(X93)
| ~ empty(the_carrier(X93)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])]) ).
cnf(c_0_70,negated_conjecture,
( in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk14_0),a_1_0_filter_1(esk12_0))
| ~ below_refl(esk12_0,X1,esk14_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_26]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_71,negated_conjecture,
( empty(the_carrier(esk12_0))
| ~ in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),a_1_0_filter_1(esk12_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,negated_conjecture,
meet_semilatt_str(esk12_0),
inference(spm,[status(thm)],[c_0_68,c_0_22]) ).
cnf(c_0_74,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,negated_conjecture,
empty(the_carrier(esk12_0)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_66]),c_0_32])]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
one_sorted_str(esk12_0),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU342+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.09/0.25 % Computer : n016.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8042.1875MB
% 0.09/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue May 5 02:58:51 EDT 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.27 % start to proof: theBenchmark
% 193.04/156.68 % Version : CSE_E---1.7
% 193.04/156.68 % Problem : theBenchmark.p
% 193.04/156.68 % SZS status Theorem for theBenchmark.p
% 193.04/156.68 % SZS output start CNFRefutation
% See solution above
% 194.44/158.07 % Total time : 107.521s
%------------------------------------------------------------------------------