%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO215+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 : n009.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 01:20:23 PM UTC 2026
% Result : Theorem 1.40s 1.49s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 120 ( 48 ~; 58 |; 8 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 63 !; 6 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con2) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f21,conjecture,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(flattening,[],[f31]) ).
fof(f39,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X1)
& ~ unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X1)
& ~ unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( convergent_lines(sK0,sK1)
& ~ unorthogonal_lines(sK1,sK2)
& ~ unorthogonal_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f47]) ).
fof(f49,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f62,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f74,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f48]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f49]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_74,negated_conjecture,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f76]) ).
tcf(c_75,negated_conjecture,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f75]) ).
tcf(c_76,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f74]) ).
tcf(c_362,plain,
( distinct_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_369,plain,
! [X0: $i] :
( distinct_points(X0,intersection_point(sK0,sK1))
| ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(X0,sK0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_371,plain,
! [X0: $i] :
( distinct_points(X0,intersection_point(sK0,sK1))
| ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(X0,sK1) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(sK0,sK2)
| unorthogonal_lines(X0,sK2)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X1,X0)
| ~ distinct_lines(sK0,X0) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_416,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK1))
| ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_369]) ).
tcf(c_417,plain,
~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK1)),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_473,plain,
! [X0: $i] :
( unorthogonal_lines(sK1,sK2)
| unorthogonal_lines(sK0,sK2)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0)
| ~ distinct_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_388]) ).
tcf(c_554,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK1))
| ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_371]) ).
tcf(c_1043,plain,
( unorthogonal_lines(sK1,sK2)
| unorthogonal_lines(sK0,sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_473]) ).
tcf(c_1044,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1043,c_554,c_417,c_416,c_362,c_74,c_75,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO215+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n009.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Wed Sep 23 11:32:00 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 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
% 0.10/0.63
% 0.10/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.63
% 0.10/0.63 % Detected problem language: tptp
% 0.13/0.64 % Proving...
% 1.40/1.49 % SZS status Started for theBenchmark.p
% 1.40/1.49 % SZS status Theorem for theBenchmark.p
% 1.40/1.49
% 1.40/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.40/1.49
% 1.40/1.49 % ------ iProver source info
% 1.40/1.49
% 1.40/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 1.40/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.40/1.49 % git: non_committed_changes: false
% 1.40/1.49
% 1.40/1.49 % ------ Parsing...
% 1.40/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.40/1.49
% 1.40/1.49 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.40/1.49
% 1.40/1.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.40/1.49 % ------ Proving...
% 1.40/1.49 % ------ Problem Properties
% 1.40/1.49
% 1.40/1.49 %
% 1.40/1.49 % clauses 27
% 1.40/1.49 % conjectures 3
% 1.40/1.49 % EPR 19
% 1.40/1.49 % Horn 15
% 1.40/1.49 % unary 10
% 1.40/1.49 % binary 2
% 1.40/1.49 % lits 68
% 1.40/1.49 % lits eq 0
% 1.40/1.49 % fd_pure 0
% 1.40/1.49 % fd_pseudo 0
% 1.40/1.49 % fd_cond 0
% 1.40/1.49 % fd_pseudo_cond 0
% 1.40/1.49 % AC symbols 0
% 1.40/1.49
% 1.40/1.49 % ------ Schedule dynamic 5 is on
% 1.40/1.49
% 1.40/1.49 % ------ no equalities: superposition off
% 1.40/1.49
% 1.40/1.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.40/1.49
% 1.40/1.49
% 1.40/1.49 % ------
% 1.40/1.49 % Current options:
% 1.40/1.49 % ------
% 1.40/1.49
% 1.40/1.49
% 1.40/1.49 %
% 1.40/1.49
% 1.40/1.49 % ------ Proving...
% 1.40/1.49 %
% 1.40/1.49
% 1.40/1.49 % SZS status Theorem for theBenchmark.p
% 1.40/1.49
% 1.40/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.40/1.49
% 1.40/1.49
%------------------------------------------------------------------------------