%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU355+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 02:57:01 PM UTC 2026
% Result : Theorem 25.04s 10.31s
% Output : CNFRefutation 25.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 9 unt; 0 def)
% Number of atoms : 183 ( 14 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 242 ( 102 ~; 94 |; 27 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 90 ( 0 sgn 82 !; 8 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f89,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f145,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f153,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice3) ).
fof(f643,conjecture,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_element_smaller(X0,empty_set,X1)
& relstr_set_smaller(X0,empty_set,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f644,negated_conjecture,
~ ! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_element_smaller(X0,empty_set,X1)
& relstr_set_smaller(X0,empty_set,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f643]) ).
fof(f1011,plain,
? [X0] :
( rel_str(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ( ~ relstr_element_smaller(X0,empty_set,X1)
| ~ relstr_set_smaller(X0,empty_set,X1) ) ) ),
inference(ennf_transformation,[],[f644]) ).
fof(f1262,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X3,X2) ) ) ) ),
inference(ennf_transformation,[],[f153]) ).
fof(f1263,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X3,X2) ) ) ) ),
inference(flattening,[],[f1262]) ).
fof(f1264,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X2,X3) ) ) ) ),
inference(ennf_transformation,[],[f145]) ).
fof(f1265,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X2,X3) ) ) ) ),
inference(flattening,[],[f1264]) ).
fof(f1726,plain,
( rel_str(sK182)
& element(sK183,the_carrier(sK182))
& ( ~ relstr_element_smaller(sK182,empty_set,sK183)
| ~ relstr_set_smaller(sK182,empty_set,sK183) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182,sK183]),skolemize(X0,sK182),skolemize(X1,sK183)],[f1011]) ).
fof(f1762,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f1763,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f1762]) ).
fof(f1764,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK208(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(X1,sK208(X0))],[f1763]) ).
fof(f2013,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_set_smaller(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X3,X2) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& in(X3,X1)
& ~ related(X0,X3,X2) )
| relstr_set_smaller(X0,X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f1263]) ).
fof(f2014,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_set_smaller(X0,X1,X2)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ~ in(X4,X1)
| related(X0,X4,X2) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& in(X3,X1)
& ~ related(X0,X3,X2) )
| relstr_set_smaller(X0,X1,X2) ) ) ) ),
inference(rectify,[],[f2013]) ).
fof(f2015,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_set_smaller(X0,X1,X2)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ~ in(X4,X1)
| related(X0,X4,X2) ) )
& ( ( element(sK412(X0,X1,X2),the_carrier(X0))
& in(sK412(X0,X1,X2),X1)
& ~ related(X0,sK412(X0,X1,X2),X2) )
| relstr_set_smaller(X0,X1,X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(X3,sK412(X0,X1,X2))],[f2014]) ).
fof(f2016,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_element_smaller(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X2,X3) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& in(X3,X1)
& ~ related(X0,X2,X3) )
| relstr_element_smaller(X0,X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f1265]) ).
fof(f2017,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_element_smaller(X0,X1,X2)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ~ in(X4,X1)
| related(X0,X2,X4) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& in(X3,X1)
& ~ related(X0,X2,X3) )
| relstr_element_smaller(X0,X1,X2) ) ) ) ),
inference(rectify,[],[f2016]) ).
fof(f2018,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_element_smaller(X0,X1,X2)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ~ in(X4,X1)
| related(X0,X2,X4) ) )
& ( ( element(sK413(X0,X1,X2),the_carrier(X0))
& in(sK413(X0,X1,X2),X1)
& ~ related(X0,X2,sK413(X0,X1,X2)) )
| relstr_element_smaller(X0,X1,X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(X3,sK413(X0,X1,X2))],[f2017]) ).
fof(f2637,plain,
rel_str(sK182),
inference(cnf_transformation,[],[f1726]) ).
fof(f2638,plain,
element(sK183,the_carrier(sK182)),
inference(cnf_transformation,[],[f1726]) ).
fof(f2639,plain,
( ~ relstr_element_smaller(sK182,empty_set,sK183)
| ~ relstr_set_smaller(sK182,empty_set,sK183) ),
inference(cnf_transformation,[],[f1726]) ).
fof(f2728,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f1764]) ).
fof(f3392,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| in(sK412(X0,X1,X2),X1)
| relstr_set_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f2015]) ).
fof(f3396,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| in(sK413(X0,X1,X2),X1)
| relstr_element_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f2018]) ).
fof(f4222,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f2728]) ).
tcf(c_580,negated_conjecture,
( ~ relstr_set_smaller(sK182,empty_set,sK183)
| ~ relstr_element_smaller(sK182,empty_set,sK183) ),
inference(cnf_transformation,[],[f2639]) ).
tcf(c_581,negated_conjecture,
element(sK183,the_carrier(sK182)),
inference(cnf_transformation,[],[f2638]) ).
tcf(c_582,negated_conjecture,
rel_str(sK182),
inference(cnf_transformation,[],[f2637]) ).
tcf(c_670,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f4222]) ).
tcf(c_1330,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_set_smaller(X1,X2,X0)
| in(sK412(X1,X2,X0),X2)
| ~ rel_str(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f3392]) ).
tcf(c_1334,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_element_smaller(X1,X2,X0)
| in(sK413(X1,X2,X0),X2)
| ~ rel_str(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f3396]) ).
tcf(c_3481,plain,
( ~ relstr_element_smaller(sK182,empty_set,sK183)
| ~ relstr_set_smaller(sK182,empty_set,sK183) ),
inference(prop_impl_just,[status(thm)],[c_580]) ).
tcf(c_3482,plain,
( ~ relstr_set_smaller(sK182,empty_set,sK183)
| ~ relstr_element_smaller(sK182,empty_set,sK183) ),
inference(renaming,[status(thm)],[c_3481]) ).
tcf(c_45161,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK413(X1,X0,X2),X0)
| ~ rel_str(X1)
| ~ relstr_set_smaller(sK182,empty_set,sK183)
| ~ element(X2,the_carrier(X1))
| ( X2 != sK183 )
| ( X1 != sK182 )
| ( X0 != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_3482,c_1334]) ).
tcf(c_45162,plain,
( in(sK413(sK182,empty_set,sK183),empty_set)
| ~ rel_str(sK182)
| ~ relstr_set_smaller(sK182,empty_set,sK183)
| ~ element(sK183,the_carrier(sK182)) ),
inference(unflattening,[status(thm)],[c_45161]) ).
tcf(c_45163,plain,
( in(sK413(sK182,empty_set,sK183),empty_set)
| ~ relstr_set_smaller(sK182,empty_set,sK183) ),
inference(global_subsumption_just,[status(thm)],[c_45162,c_582,c_581,c_45162]) ).
tcf(c_45169,plain,
~ relstr_set_smaller(sK182,empty_set,sK183),
inference(forward_subsumption_resolution,[status(thm)],[c_45163,c_670]) ).
tcf(c_46213,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK412(X1,X0,X2),X0)
| ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ( X2 != sK183 )
| ( X1 != sK182 )
| ( X0 != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_45169,c_1330]) ).
tcf(c_46214,plain,
( in(sK412(sK182,empty_set,sK183),empty_set)
| ~ rel_str(sK182)
| ~ element(sK183,the_carrier(sK182)) ),
inference(unflattening,[status(thm)],[c_46213]) ).
tcf(c_46215,plain,
in(sK412(sK182,empty_set,sK183),empty_set),
inference(global_subsumption_just,[status(thm)],[c_46214,c_582,c_581,c_46214]) ).
tcf(c_46219,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_46215,c_670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU355+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n004.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 13:49:26 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 25.04/10.31 % SZS status Started for theBenchmark.p
% 25.04/10.31 % SZS status Theorem for theBenchmark.p
% 25.04/10.31
% 25.04/10.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.04/10.31
% 25.04/10.31 % ------ iProver source info
% 25.04/10.31
% 25.04/10.31 % git: date: 2026-07-19 20:42:38 +0200
% 25.04/10.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.04/10.31 % git: non_committed_changes: false
% 25.04/10.31
% 25.04/10.31 % ------ Parsing...
% 25.04/10.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.04/10.31
% 25.04/10.31 % ------ Preprocessing... sup_sim: 109 sf_s rm: 76 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s%
% 25.04/10.31
% 25.04/10.31 % SZS status Theorem for theBenchmark.p
% 25.04/10.31
% 25.04/10.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.04/10.31
% 25.04/10.31
%------------------------------------------------------------------------------