%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU371+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 05:12:05 PM UTC 2026
% Result : Theorem 1.31s 1.75s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 200 ( 27 equ)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 223 ( 61 ~; 60 |; 95 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 6 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t18_yellow_1,conjecture,
! [X1] : bottom_of_relstr(boole_POSet(X1)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(t29_yellow_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( join_of_latt_set(X1,X2) = join_on_relstr(poset_of_lattice(X1),X2)
& meet_of_latt_set(X1,X2) = meet_on_relstr(poset_of_lattice(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_yellow_0) ).
fof(dt_k3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(t50_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1)
& lower_bounded_semilattstr(X1)
& latt_str(X1)
& bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).
fof(fc1_knaster,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_knaster) ).
fof(d2_yellow_1,axiom,
! [X1] : boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(d11_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> bottom_of_relstr(X1) = join_on_relstr(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(t3_lattice3,axiom,
! [X1] :
( lower_bounded_semilattstr(boole_lattice(X1))
& bottom_of_semilattstr(boole_lattice(X1)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] : bottom_of_relstr(boole_POSet(X1)) = empty_set,
inference(assume_negation,[status(cth)],[t18_yellow_1]) ).
fof(c_0_10,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( join_of_latt_set(X1,X2) = join_on_relstr(poset_of_lattice(X1),X2)
& meet_of_latt_set(X1,X2) = meet_on_relstr(poset_of_lattice(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[t29_yellow_0]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_lattice3]) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1)
& lower_bounded_semilattstr(X1)
& latt_str(X1)
& bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ) ),
inference(fof_simplification,[status(thm)],[t50_lattice3]) ).
fof(c_0_13,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_knaster]) ).
fof(c_0_14,negated_conjecture,
bottom_of_relstr(boole_POSet(esk29_0)) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_15,plain,
! [X193] : boole_POSet(X193) = poset_of_lattice(boole_lattice(X193)),
inference(variable_rename,[status(thm)],[d2_yellow_1]) ).
fof(c_0_16,plain,
! [X189] :
( ~ rel_str(X189)
| bottom_of_relstr(X189) = join_on_relstr(X189,empty_set) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_yellow_0])]) ).
fof(c_0_17,plain,
! [X308,X309] :
( ( join_of_latt_set(X308,X309) = join_on_relstr(poset_of_lattice(X308),X309)
| empty_carrier(X308)
| ~ lattice(X308)
| ~ complete_latt_str(X308)
| ~ latt_str(X308) )
& ( meet_of_latt_set(X308,X309) = meet_on_relstr(poset_of_lattice(X308),X309)
| empty_carrier(X308)
| ~ lattice(X308)
| ~ complete_latt_str(X308)
| ~ latt_str(X308) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_18,plain,
! [X209] :
( ( strict_rel_str(poset_of_lattice(X209))
| empty_carrier(X209)
| ~ lattice(X209)
| ~ latt_str(X209) )
& ( reflexive_relstr(poset_of_lattice(X209))
| empty_carrier(X209)
| ~ lattice(X209)
| ~ latt_str(X209) )
& ( transitive_relstr(poset_of_lattice(X209))
| empty_carrier(X209)
| ~ lattice(X209)
| ~ latt_str(X209) )
& ( antisymmetric_relstr(poset_of_lattice(X209))
| empty_carrier(X209)
| ~ lattice(X209)
| ~ latt_str(X209) )
& ( rel_str(poset_of_lattice(X209))
| empty_carrier(X209)
| ~ lattice(X209)
| ~ latt_str(X209) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_19,plain,
! [X315] :
( lower_bounded_semilattstr(boole_lattice(X315))
& bottom_of_semilattstr(boole_lattice(X315)) = empty_set ),
inference(variable_rename,[status(thm)],[t3_lattice3]) ).
fof(c_0_20,plain,
! [X321] :
( ( ~ empty_carrier(X321)
| empty_carrier(X321)
| ~ lattice(X321)
| ~ complete_latt_str(X321)
| ~ latt_str(X321) )
& ( lattice(X321)
| empty_carrier(X321)
| ~ lattice(X321)
| ~ complete_latt_str(X321)
| ~ latt_str(X321) )
& ( lower_bounded_semilattstr(X321)
| empty_carrier(X321)
| ~ lattice(X321)
| ~ complete_latt_str(X321)
| ~ latt_str(X321) )
& ( latt_str(X321)
| empty_carrier(X321)
| ~ lattice(X321)
| ~ complete_latt_str(X321)
| ~ latt_str(X321) )
& ( bottom_of_semilattstr(X321) = join_of_latt_set(X321,empty_set)
| empty_carrier(X321)
| ~ lattice(X321)
| ~ complete_latt_str(X321)
| ~ latt_str(X321) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_21,plain,
! [X237] :
( ~ empty_carrier(boole_lattice(X237))
& strict_latt_str(boole_lattice(X237))
& join_commutative(boole_lattice(X237))
& join_associative(boole_lattice(X237))
& meet_commutative(boole_lattice(X237))
& meet_associative(boole_lattice(X237))
& meet_absorbing(boole_lattice(X237))
& join_absorbing(boole_lattice(X237))
& lattice(boole_lattice(X237))
& distributive_lattstr(boole_lattice(X237))
& modular_lattstr(boole_lattice(X237))
& lower_bounded_semilattstr(boole_lattice(X237))
& upper_bounded_semilattstr(boole_lattice(X237))
& bounded_lattstr(boole_lattice(X237))
& complemented_lattstr(boole_lattice(X237))
& boolean_lattstr(boole_lattice(X237))
& complete_latt_str(boole_lattice(X237)) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
fof(c_0_22,plain,
! [X203] :
( strict_latt_str(boole_lattice(X203))
& latt_str(boole_lattice(X203)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
cnf(c_0_23,negated_conjecture,
bottom_of_relstr(boole_POSet(esk29_0)) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( bottom_of_relstr(X1) = join_on_relstr(X1,empty_set)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( join_of_latt_set(X1,X2) = join_on_relstr(poset_of_lattice(X1),X2)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
bottom_of_semilattstr(boole_lattice(X1)) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
complete_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,negated_conjecture,
bottom_of_relstr(poset_of_lattice(boole_lattice(esk29_0))) != empty_set,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_35,plain,
( bottom_of_relstr(poset_of_lattice(X1)) = join_of_latt_set(X1,empty_set)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_36,plain,
join_of_latt_set(boole_lattice(X1),empty_set) = empty_set,
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_28,c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_37,negated_conjecture,
$false,
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_34,c_0_35]),c_0_36]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU371+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.31 % Computer : n020.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue May 5 03:00:49 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % 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 : 1.375s
%------------------------------------------------------------------------------