%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU350+2 : 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 : n028.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 05:11:34 PM UTC 2026
% Result : Theorem 8.03s 6.73s
% Output : CNFRefutation 8.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 136 ( 10 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 156 ( 55 ~; 51 |; 28 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).
fof(t31_lattice3,conjecture,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice3) ).
fof(dt_k5_lattice3,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).
fof(d3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(t30_lattice3,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice3) ).
fof(c_0_5,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_lattice3]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t31_lattice3])]) ).
fof(c_0_7,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(poset_of_lattice(X1))) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattice3]) ).
fof(c_0_8,plain,
! [X2164,X2165] :
( empty_carrier(X2164)
| ~ lattice(X2164)
| ~ latt_str(X2164)
| ~ element(X2165,the_carrier(poset_of_lattice(X2164)))
| cast_to_el_of_lattice(X2164,X2165) = X2165 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,negated_conjecture,
( ~ empty_carrier(esk417_0)
& lattice(esk417_0)
& latt_str(esk417_0)
& element(esk418_0,the_carrier(poset_of_lattice(esk417_0)))
& ( ~ relstr_set_smaller(poset_of_lattice(esk417_0),esk416_0,esk418_0)
| ~ latt_element_smaller(esk417_0,cast_to_el_of_lattice(esk417_0,esk418_0),esk416_0) )
& ( relstr_set_smaller(poset_of_lattice(esk417_0),esk416_0,esk418_0)
| latt_element_smaller(esk417_0,cast_to_el_of_lattice(esk417_0,esk418_0),esk416_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d3_lattice3]) ).
fof(c_0_11,plain,
! [X2389,X2390] :
( empty_carrier(X2389)
| ~ lattice(X2389)
| ~ latt_str(X2389)
| ~ element(X2390,the_carrier(poset_of_lattice(X2389)))
| element(cast_to_el_of_lattice(X2389,X2390),the_carrier(X2389)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,plain,
( empty_carrier(X1)
| cast_to_el_of_lattice(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
element(esk418_0,the_carrier(poset_of_lattice(esk417_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
lattice(esk417_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
latt_str(esk417_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
~ empty_carrier(esk417_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_17,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t30_lattice3]) ).
fof(c_0_18,plain,
! [X2121,X2122] :
( empty_carrier(X2121)
| ~ lattice(X2121)
| ~ latt_str(X2121)
| ~ element(X2122,the_carrier(X2121))
| cast_to_el_of_LattPOSet(X2121,X2122) = X2122 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_19,plain,
( empty_carrier(X1)
| element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(poset_of_lattice(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
cast_to_el_of_lattice(esk417_0,esk418_0) = esk418_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
fof(c_0_21,lemma,
! [X3514,X3515,X3516] :
( ( ~ latt_element_smaller(X3515,X3516,X3514)
| relstr_set_smaller(poset_of_lattice(X3515),X3514,cast_to_el_of_LattPOSet(X3515,X3516))
| ~ element(X3516,the_carrier(X3515))
| empty_carrier(X3515)
| ~ lattice(X3515)
| ~ latt_str(X3515) )
& ( ~ relstr_set_smaller(poset_of_lattice(X3515),X3514,cast_to_el_of_LattPOSet(X3515,X3516))
| latt_element_smaller(X3515,X3516,X3514)
| ~ element(X3516,the_carrier(X3515))
| empty_carrier(X3515)
| ~ lattice(X3515)
| ~ latt_str(X3515) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_22,plain,
( empty_carrier(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
element(esk418_0,the_carrier(esk417_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_19,c_0_13]),c_0_20]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_24,lemma,
( latt_element_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| ~ element(X3,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
cast_to_el_of_LattPOSet(esk417_0,esk418_0) = esk418_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk417_0),esk416_0,esk418_0)
| latt_element_smaller(esk417_0,cast_to_el_of_lattice(esk417_0,esk418_0),esk416_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(esk417_0),esk416_0,esk418_0)
| ~ latt_element_smaller(esk417_0,cast_to_el_of_lattice(esk417_0,esk418_0),esk416_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( latt_element_smaller(esk417_0,esk418_0,X1)
| ~ relstr_set_smaller(poset_of_lattice(esk417_0),X1,esk418_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_24,c_0_25]),c_0_14]),c_0_23]),c_0_15])]),c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(esk417_0),esk416_0,esk418_0)
| latt_element_smaller(esk417_0,esk418_0,esk416_0) ),
inference(rw,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(esk417_0),esk416_0,esk418_0)
| ~ latt_element_smaller(esk417_0,esk418_0,esk416_0) ),
inference(rw,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_31,negated_conjecture,
latt_element_smaller(esk417_0,esk418_0,esk416_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,lemma,
( relstr_set_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2))
| empty_carrier(X1)
| ~ latt_element_smaller(X1,X2,X3)
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,negated_conjecture,
~ relstr_set_smaller(poset_of_lattice(esk417_0),esk416_0,esk418_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[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(spm,[status(thm)],[c_0_32,c_0_31]),c_0_25]),c_0_14]),c_0_23]),c_0_15])]),c_0_33]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.18 % Problem : SEU350+2 : TPTP v9.2.1. Released v3.3.0.
% 0.02/0.18 % 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
% 0.11/0.43 % Computer : n028.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8042.1875MB
% 0.11/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Tue May 5 03:00:01 EDT 2026
% 0.11/0.45 % CPUTime :
% 0.14/0.48 % start to proof: theBenchmark
% 8.03/6.73 % Version : CSE_E---1.7
% 8.03/6.73 % Problem : theBenchmark.p
% 8.03/6.73 % SZS status Theorem for theBenchmark.p
% 8.03/6.73 % SZS output start CNFRefutation
% See solution above
% 8.03/6.75 % Total time : 5.571s
%------------------------------------------------------------------------------