%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO225+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 01:20:27 PM UTC 2026
% Result : Theorem 0.99s 6.89s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 3 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 35 ~; 21 |; 18 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 37 !; 6 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(f36,conjecture,
! [X0,X1] :
( ( distinct_points(X0,X1)
& point(X1)
& point(X0) )
=> ? [X2] :
( line(X2)
=> ( incident_point_and_line(X1,X2)
& incident_point_and_line(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( distinct_points(X0,X1)
& point(X1)
& point(X0) )
=> ? [X2] :
( line(X2)
=> ( incident_point_and_line(X1,X2)
& incident_point_and_line(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
=> incident_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f45,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f77,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1] :
( distinct_points(X0,X1)
& point(X1)
& point(X0)
& ! [X2] :
( line(X2)
& ( ~ incident_point_and_line(X1,X2)
| ~ incident_point_and_line(X0,X2) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1] :
( distinct_points(X0,X1)
& point(X1)
& point(X0)
& ! [X2] :
( line(X2)
& ( ~ incident_point_and_line(X1,X2)
| ~ incident_point_and_line(X0,X2) ) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
( distinct_points(sK0,sK1)
& point(sK1)
& point(sK0)
& ! [X2] :
( line(X2)
& ( ~ incident_point_and_line(sK1,X2)
| ~ incident_point_and_line(sK0,X2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f79]) ).
fof(f87,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f88,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f117,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f118,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
! [X2] :
( ~ incident_point_and_line(sK1,X2)
| ~ incident_point_and_line(sK0,X2) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_86,negated_conjecture,
! [X0: $i] :
( ~ incident_point_and_line(sK1,X0)
| ~ incident_point_and_line(sK0,X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_90,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f118]) ).
tcf(c_450,negated_conjecture,
! [X0: $i] :
( ~ incident_point_and_line(sK1,X0)
| ~ incident_point_and_line(sK0,X0) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_451,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_452,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_486,plain,
! [X0: $i] :
( incident_point_and_line(sK1,X0)
| apart_point_and_line(sK1,X0) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_761,plain,
( incident_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_486]) ).
tcf(c_1237,plain,
( ~ incident_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_450]) ).
tcf(c_1395,plain,
( incident_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_1396,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1395,c_1237,c_761,c_452,c_451,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO225+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.98 % Computer : n010.cluster.edu
% 0.10/5.98 % Model : x86_64 x86_64
% 0.10/5.98 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.98 % Memory : 8046.5625MB
% 0.10/5.98 % OS : Linux 6.8.0-71-generic
% 0.10/5.98 % CPULimit : 300
% 0.10/5.98 % WCLimit : 300
% 0.10/5.98 % DateTime : Wed Sep 23 11:34:59 UTC 2026
% 0.10/5.99 % CPUTime :
% 0.10/5.99 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/6.02 Running first-order theorem proving
% 0.10/6.02 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
% 0.14/6.04
% 0.14/6.04 % ======== iProver multi-core TPTP/SMT =========
% 0.14/6.04
% 0.14/6.04 % Detected problem language: tptp
% 0.14/6.05 % Proving...
% 0.99/6.89 % SZS status Started for theBenchmark.p
% 0.99/6.89 % SZS status Theorem for theBenchmark.p
% 0.99/6.89
% 0.99/6.89 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.99/6.89
% 0.99/6.89 % ------ iProver source info
% 0.99/6.89
% 0.99/6.89 % git: date: 2026-07-19 20:42:38 +0200
% 0.99/6.89 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.99/6.89 % git: non_committed_changes: false
% 0.99/6.89
% 0.99/6.89 % ------ Parsing...
% 0.99/6.89 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.99/6.89
% 0.99/6.89 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.99/6.89
% 0.99/6.89 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.99/6.89 % ------ Proving...
% 0.99/6.89 % ------ Problem Properties
% 0.99/6.89
% 0.99/6.89 %
% 0.99/6.89 % clauses 31
% 0.99/6.89 % conjectures 2
% 0.99/6.89 % EPR 23
% 0.99/6.89 % Horn 14
% 0.99/6.89 % unary 8
% 0.99/6.89 % binary 8
% 0.99/6.89 % lits 80
% 0.99/6.89 % lits eq 0
% 0.99/6.89 % fd_pure 0
% 0.99/6.89 % fd_pseudo 0
% 0.99/6.89 % fd_cond 0
% 0.99/6.89 % fd_pseudo_cond 0
% 0.99/6.89 % AC symbols 0
% 0.99/6.89
% 0.99/6.89 % ------ Schedule dynamic 5 is on
% 0.99/6.89
% 0.99/6.89 % ------ no equalities: superposition off
% 0.99/6.89
% 0.99/6.89 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.99/6.89
% 0.99/6.89
% 0.99/6.89 % ------
% 0.99/6.89 % Current options:
% 0.99/6.89 % ------
% 0.99/6.89
% 0.99/6.89
% 0.99/6.89 %
% 0.99/6.89
% 0.99/6.89 % ------ Proving...
% 0.99/6.89 %
% 0.99/6.89
% 0.99/6.89 % SZS status Theorem for theBenchmark.p
% 0.99/6.89
% 0.99/6.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.99/6.89
% 0.99/6.89
%------------------------------------------------------------------------------