%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO202+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 : n026.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 01:20:18 PM UTC 2026
% Result : Theorem 2.83s 1.28s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 54 ~; 59 |; 14 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 71 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
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(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ~ distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ~ distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
? [X0,X1,X2] :
( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1)
& distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f18,plain,
? [X0,X1,X2] :
( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1)
& distinct_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(flattening,[],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(flattening,[],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f29]) ).
fof(f37,plain,
( convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
& distinct_points(sK0,sK2)
& distinct_points(sK0,sK1)
& distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
fof(f38,plain,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f37]) ).
fof(f39,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f40,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f41,plain,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f43,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_49,negated_conjecture,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_50,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f40]) ).
tcf(c_51,negated_conjecture,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f39]) ).
tcf(c_52,negated_conjecture,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_63,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f52]) ).
tcf(c_152,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_153,plain,
( ~ distinct_points(sK0,sK2)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_154,plain,
( ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_155,plain,
( ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_161,plain,
! [X0: $i] :
( distinct_lines(line_connecting(sK0,sK2),X0)
| convergent_lines(line_connecting(sK0,sK1),X0)
| ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),X1)
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),X0)
| ~ distinct_lines(X0,X1)
| ~ distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_194,plain,
( distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1))
| convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK1))
| ~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_195,plain,
~ convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK1)),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_209,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK2))
| apart_point_and_line(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),line_connecting(sK0,sK1))
| ~ distinct_lines(line_connecting(sK0,sK2),line_connecting(sK0,sK1))
| ~ distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0) ),
inference(instantiation,[status(thm)],[c_165]) ).
tcf(c_212,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_209,c_195,c_194,c_155,c_154,c_153,c_152,c_49,c_52,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO202+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 11:30:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.83/1.28 % SZS status Started for theBenchmark.p
% 2.83/1.28 % SZS status Theorem for theBenchmark.p
% 2.83/1.28
% 2.83/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.83/1.28
% 2.83/1.28 % ------ iProver source info
% 2.83/1.28
% 2.83/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.83/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.83/1.28 % git: non_committed_changes: false
% 2.83/1.28
% 2.83/1.28 % ------ Parsing...
% 2.83/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.83/1.28 % ------ Proving...
% 2.83/1.28 % ------ Problem Properties
% 2.83/1.28
% 2.83/1.28 %
% 2.83/1.28 % clauses 18
% 2.83/1.28 % conjectures 4
% 2.83/1.28 % EPR 12
% 2.83/1.28 % Horn 11
% 2.83/1.28 % unary 7
% 2.83/1.28 % binary 4
% 2.83/1.28 % lits 39
% 2.83/1.28 % lits eq 0
% 2.83/1.28 % fd_pure 0
% 2.83/1.28 % fd_pseudo 0
% 2.83/1.28 % fd_cond 0
% 2.83/1.28 % fd_pseudo_cond 0
% 2.83/1.28 % AC symbols 0
% 2.83/1.28
% 2.83/1.28 % ------ Schedule dynamic 5 is on
% 2.83/1.28
% 2.83/1.28 % ------ no equalities: superposition off
% 2.83/1.28
% 2.83/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 % ------
% 2.83/1.28 % Current options:
% 2.83/1.28 % ------
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 %
% 2.83/1.28
% 2.83/1.28 % ------ Proving...
% 2.83/1.28 %
% 2.83/1.28
% 2.83/1.28 % SZS status Theorem for theBenchmark.p
% 2.83/1.28
% 2.83/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.83/1.28
% 2.83/1.28
%------------------------------------------------------------------------------