%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO226+2 : 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 : n014.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 2.12s 1.16s
% Output : CNFRefutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 85 ( 31 ~; 28 |; 20 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 36 !; 6 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).
fof(f17,conjecture,
! [X0,X1] :
( ( convergent_lines(X0,X1)
& line(X1)
& line(X0) )
=> ? [X2] :
( point(X2)
=> ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( convergent_lines(X0,X1)
& line(X1)
& line(X0) )
=> ? [X2] :
( point(X2)
=> ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f44,plain,
? [X0,X1] :
( convergent_lines(X0,X1)
& line(X1)
& line(X0)
& ! [X2] :
( point(X2)
& ( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f45,plain,
? [X0,X1] :
( convergent_lines(X0,X1)
& line(X1)
& line(X0)
& ! [X2] :
( point(X2)
& ( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) ) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( convergent_lines(sK0,sK1)
& line(sK1)
& line(sK0)
& ! [X2] :
( point(X2)
& ( apart_point_and_line(X2,sK1)
| apart_point_and_line(X2,sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f45]) ).
fof(f47,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f65,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
! [X2] :
( apart_point_and_line(X2,sK1)
| apart_point_and_line(X2,sK0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f47]) ).
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,[],[f56]) ).
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,[],[f55]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_71,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f65]) ).
tcf(c_269,negated_conjecture,
! [X0: $i] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_273,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_275,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_287,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_273]) ).
tcf(c_288,plain,
~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK1)),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_303,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_275]) ).
tcf(c_309,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_269]) ).
tcf(c_310,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_309,c_303,c_288,c_287,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO226+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 11:34:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 2.12/1.16 % SZS status Started for theBenchmark.p
% 2.12/1.16 % SZS status Theorem for theBenchmark.p
% 2.12/1.16
% 2.12/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.12/1.16
% 2.12/1.16 % ------ iProver source info
% 2.12/1.16
% 2.12/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 2.12/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.12/1.16 % git: non_committed_changes: false
% 2.12/1.16
% 2.12/1.16 % ------ Parsing...
% 2.12/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.12/1.16
% 2.12/1.16 % ------ Preprocessing... sf_s rm: 6 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.12/1.16
% 2.12/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.12/1.16 % ------ Proving...
% 2.12/1.16 % ------ Problem Properties
% 2.12/1.16
% 2.12/1.16 %
% 2.12/1.16 % clauses 16
% 2.12/1.16 % conjectures 2
% 2.12/1.16 % EPR 12
% 2.12/1.16 % Horn 9
% 2.12/1.16 % unary 4
% 2.12/1.16 % binary 2
% 2.12/1.16 % lits 41
% 2.12/1.16 % lits eq 0
% 2.12/1.16 % fd_pure 0
% 2.12/1.16 % fd_pseudo 0
% 2.12/1.16 % fd_cond 0
% 2.12/1.16 % fd_pseudo_cond 0
% 2.12/1.16 % AC symbols 0
% 2.12/1.16
% 2.12/1.16 % ------ Schedule dynamic 5 is on
% 2.12/1.16
% 2.12/1.16 % ------ no equalities: superposition off
% 2.12/1.16
% 2.12/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.12/1.16
% 2.12/1.16
% 2.12/1.16 % ------
% 2.12/1.16 % Current options:
% 2.12/1.16 % ------
% 2.12/1.16
% 2.12/1.16
% 2.12/1.16 %
% 2.12/1.16
% 2.12/1.16 % ------ Proving...
% 2.12/1.16 %
% 2.12/1.16
% 2.12/1.16 % SZS status Theorem for theBenchmark.p
% 2.12/1.16
% 2.12/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.12/1.16
% 2.12/1.16
%------------------------------------------------------------------------------