%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU355+1 : 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 : n015.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 2.28s 1.28s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 10 unt; 0 def)
% Number of atoms : 190 ( 2 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 232 ( 96 ~; 93 |; 25 &)
% ( 6 <=>; 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 : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 90 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f4,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(f13,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f20,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(f21,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)],[f20]) ).
fof(f22,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f29,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,[],[f3]) ).
fof(f30,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,[],[f29]) ).
fof(f31,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,[],[f4]) ).
fof(f32,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,[],[f31]) ).
fof(f37,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,[],[f21]) ).
fof(f38,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f40,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,[],[f30]) ).
fof(f41,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,[],[f40]) ).
fof(f42,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(sK0(X0,X1,X2),the_carrier(X0))
& in(sK0(X0,X1,X2),X1)
& ~ related(X0,X2,sK0(X0,X1,X2)) )
| relstr_element_smaller(X0,X1,X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f41]) ).
fof(f43,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,[],[f32]) ).
fof(f44,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,[],[f43]) ).
fof(f45,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(sK1(X0,X1,X2),the_carrier(X0))
& in(sK1(X0,X1,X2),X1)
& ~ related(X0,sK1(X0,X1,X2),X2) )
| relstr_set_smaller(X0,X1,X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f44]) ).
fof(f51,plain,
( rel_str(sK7)
& element(sK8,the_carrier(sK7))
& ( ~ relstr_element_smaller(sK7,empty_set,sK8)
| ~ relstr_set_smaller(sK7,empty_set,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f37]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| in(sK0(X0,X1,X2),X1)
| relstr_element_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| in(sK1(X0,X1,X2),X1)
| relstr_set_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f63,plain,
empty(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f70,plain,
rel_str(sK7),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
element(sK8,the_carrier(sK7)),
inference(cnf_transformation,[],[f51]) ).
fof(f72,plain,
( ~ relstr_element_smaller(sK7,empty_set,sK8)
| ~ relstr_set_smaller(sK7,empty_set,sK8) ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_element_smaller(X1,X2,X0)
| in(sK0(X1,X2,X0),X2)
| ~ rel_str(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_set_smaller(X1,X2,X0)
| in(sK1(X1,X2,X0),X2)
| ~ rel_str(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_60,plain,
empty(empty_set),
inference(cnf_transformation,[],[f63]) ).
tcf(c_67,negated_conjecture,
( ~ relstr_set_smaller(sK7,empty_set,sK8)
| ~ relstr_element_smaller(sK7,empty_set,sK8) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_68,negated_conjecture,
element(sK8,the_carrier(sK7)),
inference(cnf_transformation,[],[f71]) ).
tcf(c_69,negated_conjecture,
rel_str(sK7),
inference(cnf_transformation,[],[f70]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_704,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_set_smaller(X0,X2,X1)
| in(sK1(X0,X2,X1),X2)
| ~ element(X1,the_carrier(X0))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_69]) ).
tcf(c_705,plain,
! [X0: $i,X1: $i] :
( relstr_set_smaller(sK7,X1,X0)
| in(sK1(sK7,X1,X0),X1)
| ~ element(X0,the_carrier(sK7)) ),
inference(unflattening,[status(thm)],[c_704]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_element_smaller(X0,X2,X1)
| in(sK0(X0,X2,X1),X2)
| ~ element(X1,the_carrier(X0))
| ( X0 != sK7 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_69]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i] :
( relstr_element_smaller(sK7,X1,X0)
| in(sK0(sK7,X1,X0),X1)
| ~ element(X0,the_carrier(sK7)) ),
inference(unflattening,[status(thm)],[c_728]) ).
tcf(c_2133,plain,
! [X0: $i,X1: $i] :
( relstr_element_smaller(sK7,X1,X0)
| in(sK0(sK7,X1,X0),X1)
| ~ element(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_729]) ).
tcf(c_2135,plain,
! [X0: $i,X1: $i] :
( relstr_set_smaller(sK7,X1,X0)
| in(sK1(sK7,X1,X0),X1)
| ~ element(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_705]) ).
tcf(c_2137,negated_conjecture,
element(sK8,iPr_def_10),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_2138,negated_conjecture,
( ~ relstr_set_smaller(sK7,empty_set,sK8)
| ~ relstr_element_smaller(sK7,empty_set,sK8) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_2721,plain,
! [X0: $i,X1: $i] :
( relstr_set_smaller(sK7,X1,X0)
| ~ empty(X1)
| ~ element(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2135,c_70]) ).
tcf(c_2722,plain,
! [X0: $i,X1: $i] :
( relstr_element_smaller(sK7,X1,X0)
| ~ empty(X1)
| ~ element(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2133,c_70]) ).
tcf(c_2737,plain,
( ~ empty(empty_set)
| ~ element(sK8,iPr_def_10)
| ~ relstr_element_smaller(sK7,empty_set,sK8) ),
inference(superposition,[status(thm)],[c_2721,c_2138]) ).
tcf(c_2739,plain,
~ relstr_element_smaller(sK7,empty_set,sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_2737,c_60,c_2137]) ).
tcf(c_2842,plain,
( ~ empty(empty_set)
| ~ element(sK8,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2722,c_2739]) ).
tcf(c_2844,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2842,c_60,c_2137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:52:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.28/1.28 % SZS status Started for theBenchmark.p
% 2.28/1.28 % SZS status Theorem for theBenchmark.p
% 2.28/1.28
% 2.28/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.28/1.28
% 2.28/1.28 % ------ iProver source info
% 2.28/1.28
% 2.28/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.28/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.28/1.28 % git: non_committed_changes: false
% 2.28/1.28
% 2.28/1.28 % ------ Parsing...
% 2.28/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.28/1.28 % ------ Proving...
% 2.28/1.28 % ------ Problem Properties
% 2.28/1.28
% 2.28/1.28 %
% 2.28/1.28 % clauses 30
% 2.28/1.28 % conjectures 2
% 2.28/1.28 % EPR 14
% 2.28/1.28 % Horn 21
% 2.28/1.28 % unary 7
% 2.28/1.28 % binary 5
% 2.28/1.28 % lits 79
% 2.28/1.28 % lits eq 3
% 2.28/1.28 % fd_pure 0
% 2.28/1.28 % fd_pseudo 0
% 2.28/1.28 % fd_cond 1
% 2.28/1.28 % fd_pseudo_cond 1
% 2.28/1.28 % AC symbols 0
% 2.28/1.28
% 2.28/1.28 % ------ Schedule dynamic 5 is on
% 2.28/1.28
% 2.28/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.28/1.28
% 2.28/1.28
% 2.28/1.28 % ------
% 2.28/1.28 % Current options:
% 2.28/1.28 % ------
% 2.28/1.28
% 2.28/1.28
% 2.28/1.28 %
% 2.28/1.28
% 2.28/1.28 % ------ Proving...
% 2.28/1.28 %
% 2.28/1.28
% 2.28/1.28 % SZS status Theorem for theBenchmark.p
% 2.28/1.28
% 2.28/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.28/1.28
% 2.28/1.28
%------------------------------------------------------------------------------