%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU348+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 : n006.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 05:11:33 PM UTC 2026
% Result : Theorem 8.80s 6.60s
% Output : CNFRefutation 8.80s
% 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(t29_lattice3,conjecture,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_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(t28_lattice3,lemma,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_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_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t29_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,
! [X2144,X2145] :
( empty_carrier(X2144)
| ~ lattice(X2144)
| ~ latt_str(X2144)
| ~ element(X2145,the_carrier(poset_of_lattice(X2144)))
| cast_to_el_of_lattice(X2144,X2145) = X2145 ),
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(esk414_0)
& lattice(esk414_0)
& latt_str(esk414_0)
& element(esk415_0,the_carrier(poset_of_lattice(esk414_0)))
& ( ~ relstr_element_smaller(poset_of_lattice(esk414_0),esk413_0,esk415_0)
| ~ latt_set_smaller(esk414_0,cast_to_el_of_lattice(esk414_0,esk415_0),esk413_0) )
& ( relstr_element_smaller(poset_of_lattice(esk414_0),esk413_0,esk415_0)
| latt_set_smaller(esk414_0,cast_to_el_of_lattice(esk414_0,esk415_0),esk413_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,
! [X2364,X2365] :
( empty_carrier(X2364)
| ~ lattice(X2364)
| ~ latt_str(X2364)
| ~ element(X2365,the_carrier(poset_of_lattice(X2364)))
| element(cast_to_el_of_lattice(X2364,X2365),the_carrier(X2364)) ),
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(esk415_0,the_carrier(poset_of_lattice(esk414_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
lattice(esk414_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
latt_str(esk414_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
~ empty_carrier(esk414_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_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t28_lattice3]) ).
fof(c_0_18,plain,
! [X2101,X2102] :
( empty_carrier(X2101)
| ~ lattice(X2101)
| ~ latt_str(X2101)
| ~ element(X2102,the_carrier(X2101))
| cast_to_el_of_LattPOSet(X2101,X2102) = X2102 ),
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(esk414_0,esk415_0) = esk415_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,
! [X3464,X3465,X3466] :
( ( ~ latt_set_smaller(X3465,X3466,X3464)
| relstr_element_smaller(poset_of_lattice(X3465),X3464,cast_to_el_of_LattPOSet(X3465,X3466))
| ~ element(X3466,the_carrier(X3465))
| empty_carrier(X3465)
| ~ lattice(X3465)
| ~ latt_str(X3465) )
& ( ~ relstr_element_smaller(poset_of_lattice(X3465),X3464,cast_to_el_of_LattPOSet(X3465,X3466))
| latt_set_smaller(X3465,X3466,X3464)
| ~ element(X3466,the_carrier(X3465))
| empty_carrier(X3465)
| ~ lattice(X3465)
| ~ latt_str(X3465) ) ),
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(esk415_0,the_carrier(esk414_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_set_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ relstr_element_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(esk414_0,esk415_0) = esk415_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_element_smaller(poset_of_lattice(esk414_0),esk413_0,esk415_0)
| latt_set_smaller(esk414_0,cast_to_el_of_lattice(esk414_0,esk415_0),esk413_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( ~ relstr_element_smaller(poset_of_lattice(esk414_0),esk413_0,esk415_0)
| ~ latt_set_smaller(esk414_0,cast_to_el_of_lattice(esk414_0,esk415_0),esk413_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( latt_set_smaller(esk414_0,esk415_0,X1)
| ~ relstr_element_smaller(poset_of_lattice(esk414_0),X1,esk415_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_element_smaller(poset_of_lattice(esk414_0),esk413_0,esk415_0)
| latt_set_smaller(esk414_0,esk415_0,esk413_0) ),
inference(rw,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( ~ relstr_element_smaller(poset_of_lattice(esk414_0),esk413_0,esk415_0)
| ~ latt_set_smaller(esk414_0,esk415_0,esk413_0) ),
inference(rw,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_31,negated_conjecture,
latt_set_smaller(esk414_0,esk415_0,esk413_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,lemma,
( relstr_element_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2))
| empty_carrier(X1)
| ~ latt_set_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_element_smaller(poset_of_lattice(esk414_0),esk413_0,esk415_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
% 0.00/0.12 % Problem : SEU348+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n006.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:58:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 8.80/6.60 % Version : CSE_E---1.7
% 8.80/6.60 % Problem : theBenchmark.p
% 8.80/6.60 % SZS status Theorem for theBenchmark.p
% 8.80/6.60 % SZS output start CNFRefutation
% See solution above
% 8.80/6.62 % Total time : 5.592s
%------------------------------------------------------------------------------