%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU371+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:57:15 PM UTC 2026
% Result : Theorem 4.13s 6.48s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 31 unt; 0 def)
% Number of atoms : 223 ( 43 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 222 ( 58 ~; 50 |; 111 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 63 !; 1 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(f22,axiom,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(f27,axiom,
! [X0] :
( latt_str(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(f36,axiom,
! [X0] :
( rel_str(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(f59,axiom,
! [X0] :
( complete_latt_str(boole_lattice(X0))
& boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& modular_lattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_knaster) ).
fof(f69,axiom,
! [X0] :
( boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& modular_lattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice3) ).
fof(f103,conjecture,
! [X0] : bottom_of_relstr(boole_POSet(X0)) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(f104,negated_conjecture,
~ ! [X0] : bottom_of_relstr(boole_POSet(X0)) = empty_set,
inference(negated_conjecture,[status(cth)],[f103]) ).
fof(f106,axiom,
! [X0] :
( ( latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1)
& join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_yellow_0) ).
fof(f109,axiom,
! [X0] :
( bottom_of_semilattstr(boole_lattice(X0)) = empty_set
& lower_bounded_semilattstr(boole_lattice(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice3) ).
fof(f112,axiom,
! [X0] :
( ( latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
& latt_str(X0)
& lower_bounded_semilattstr(X0)
& lattice(X0)
& ~ empty_carrier(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice3) ).
fof(f155,plain,
! [X0] :
( boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
inference(pure_predicate_removal,[],[f69]) ).
fof(f158,plain,
! [X0] :
( complete_latt_str(boole_lattice(X0))
& boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
inference(pure_predicate_removal,[],[f59]) ).
fof(f169,plain,
! [X0] :
( boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
inference(pure_predicate_removal,[],[f155]) ).
fof(f173,plain,
! [X0] :
( complete_latt_str(boole_lattice(X0))
& boolean_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lattice(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
inference(pure_predicate_removal,[],[f158]) ).
fof(f179,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(pure_predicate_removal,[],[f27]) ).
fof(f190,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(pure_predicate_removal,[],[f36]) ).
fof(f193,plain,
? [X0] : empty_set != bottom_of_relstr(boole_POSet(X0)),
inference(ennf_transformation,[],[f104]) ).
fof(f195,plain,
! [X0] :
( ~ rel_str(X0)
| bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
inference(ennf_transformation,[],[f19]) ).
fof(f197,plain,
! [X0] :
( ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ! [X1] :
( meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1)
& join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) ) ),
inference(ennf_transformation,[],[f106]) ).
fof(f198,plain,
! [X0] :
( ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ! [X1] :
( meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1)
& join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) ) ),
inference(flattening,[],[f197]) ).
fof(f227,plain,
! [X0] :
( ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ( bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
& latt_str(X0)
& lower_bounded_semilattstr(X0)
& lattice(X0)
& ~ empty_carrier(X0) ) ),
inference(ennf_transformation,[],[f112]) ).
fof(f228,plain,
! [X0] :
( ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ( bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
& latt_str(X0)
& lower_bounded_semilattstr(X0)
& lattice(X0)
& ~ empty_carrier(X0) ) ),
inference(flattening,[],[f227]) ).
fof(f245,plain,
empty_set != bottom_of_relstr(boole_POSet(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f193]) ).
fof(f263,plain,
empty_set != bottom_of_relstr(boole_POSet(sK1)),
inference(cnf_transformation,[],[f245]) ).
fof(f265,plain,
! [X0] :
( ~ rel_str(X0)
| bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
inference(cnf_transformation,[],[f195]) ).
fof(f276,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f190]) ).
fof(f277,plain,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f283,plain,
! [X0,X1] :
( ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) ),
inference(cnf_transformation,[],[f198]) ).
fof(f341,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f179]) ).
fof(f343,plain,
! [X0] : complete_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f173]) ).
fof(f371,plain,
! [X0] :
( ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set) ),
inference(cnf_transformation,[],[f228]) ).
fof(f435,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f169]) ).
fof(f442,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f169]) ).
fof(f484,plain,
! [X0] : empty_set = bottom_of_semilattstr(boole_lattice(X0)),
inference(cnf_transformation,[],[f109]) ).
fof(f486,plain,
empty_set != bottom_of_relstr(poset_of_lattice(boole_lattice(sK1))),
inference(definition_unfolding,[],[f263,f277]) ).
fof(f495,plain,
! [X0] : rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f276,f277]) ).
tcf(c_49,negated_conjecture,
bottom_of_relstr(poset_of_lattice(boole_lattice(sK1))) != empty_set,
inference(cnf_transformation,[],[f486]) ).
tcf(c_51,plain,
! [X0: $i] :
( ( join_on_relstr(X0,empty_set) = bottom_of_relstr(X0) )
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_62,plain,
! [X0: $i] : rel_str(poset_of_lattice(boole_lattice(X0))),
inference(cnf_transformation,[],[f495]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| ( join_on_relstr(poset_of_lattice(X0),X1) = join_of_latt_set(X0,X1) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_124,plain,
! [X0: $i] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f341]) ).
tcf(c_140,plain,
! [X0: $i] : complete_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f343]) ).
tcf(c_155,plain,
! [X0: $i] :
( empty_carrier(X0)
| ( join_of_latt_set(X0,empty_set) = bottom_of_semilattstr(X0) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0) ),
inference(cnf_transformation,[],[f371]) ).
tcf(c_205,plain,
! [X0: $i] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f442]) ).
tcf(c_212,plain,
! [X0: $i] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f435]) ).
tcf(c_257,plain,
! [X0: $i] : bottom_of_semilattstr(boole_lattice(X0)) = empty_set,
inference(cnf_transformation,[],[f484]) ).
tcf(c_1497,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| ( join_of_latt_set(X1,empty_set) = bottom_of_semilattstr(X1) )
| ~ latt_str(X1)
| ~ lattice(X1)
| ( boole_lattice(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_155,c_140]) ).
tcf(c_1498,plain,
! [X0: $i] :
( empty_carrier(boole_lattice(X0))
| ( join_of_latt_set(boole_lattice(X0),empty_set) = bottom_of_semilattstr(boole_lattice(X0)) )
| ~ latt_str(boole_lattice(X0))
| ~ lattice(boole_lattice(X0)) ),
inference(unflattening,[status(thm)],[c_1497]) ).
tcf(c_1500,plain,
! [X0: $i] : join_of_latt_set(boole_lattice(X0),empty_set) = bottom_of_semilattstr(boole_lattice(X0)),
inference(global_subsumption_just,[status(thm)],[c_1498,c_212,c_124,c_205,c_1498]) ).
tcf(c_1524,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| ( join_on_relstr(poset_of_lattice(X1),X2) = join_of_latt_set(X1,X2) )
| ~ latt_str(X1)
| ~ lattice(X1)
| ( boole_lattice(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_140]) ).
tcf(c_1525,plain,
! [X0: $i,X1: $i] :
( empty_carrier(boole_lattice(X0))
| ( join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1) = join_of_latt_set(boole_lattice(X0),X1) )
| ~ latt_str(boole_lattice(X0))
| ~ lattice(boole_lattice(X0)) ),
inference(unflattening,[status(thm)],[c_1524]) ).
tcf(c_1527,plain,
! [X0: $i,X1: $i] : join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1) = join_of_latt_set(boole_lattice(X0),X1),
inference(global_subsumption_just,[status(thm)],[c_1525,c_212,c_124,c_205,c_1525]) ).
tcf(c_1651,plain,
! [X0: $i,X1: $i] :
( ( join_on_relstr(X1,empty_set) = bottom_of_relstr(X1) )
| ( poset_of_lattice(boole_lattice(X0)) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_62]) ).
tcf(c_1652,plain,
! [X0: $i] : join_on_relstr(poset_of_lattice(boole_lattice(X0)),empty_set) = bottom_of_relstr(poset_of_lattice(boole_lattice(X0))),
inference(unflattening,[status(thm)],[c_1651]) ).
tcf(c_2091,plain,
! [X0: $i] : join_of_latt_set(boole_lattice(X0),empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_1500,c_257]) ).
tcf(c_2098,plain,
! [X0: $i] : bottom_of_relstr(poset_of_lattice(boole_lattice(X0))) = empty_set,
inference(demodulation,[status(thm)],[c_1652,c_1527,c_2091]) ).
tcf(c_2099,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[c_49,c_2098]) ).
tcf(c_2100,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2099]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU371+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n007.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 13:50:28 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.44 Running first-order theorem proving
% 0.15/5.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.46
% 0.15/5.46 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.46
% 0.15/5.46 % Detected problem language: tptp
% 0.15/5.48 % Proving...
% 4.13/6.48 % SZS status Started for theBenchmark.p
% 4.13/6.48 % SZS status Theorem for theBenchmark.p
% 4.13/6.48
% 4.13/6.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.13/6.48
% 4.13/6.48 % ------ iProver source info
% 4.13/6.48
% 4.13/6.48 % git: date: 2026-07-19 20:42:38 +0200
% 4.13/6.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.13/6.48 % git: non_committed_changes: false
% 4.13/6.48
% 4.13/6.48 % ------ Parsing...
% 4.13/6.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.13/6.48
% 4.13/6.48 % ------ Preprocessing... sup_sim: 0 sf_s rm: 60 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e %
% 4.13/6.48
% 4.13/6.48 % SZS status Theorem for theBenchmark.p
% 4.13/6.48
% 4.13/6.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.13/6.49
% 4.13/6.49
%------------------------------------------------------------------------------