%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO201+1 : 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 : n004.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 01:20:17 PM UTC 2026
% Result : Theorem 2.52s 11.31s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 15 unt; 2 def)
% Number of atoms : 163 ( 2 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 137 ( 55 ~; 72 |; 3 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 78 !; 2 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,conjecture,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0,X1] :
( convergent_lines(X0,X1)
& distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
( convergent_lines(sK0,sK1)
& distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f35]) ).
fof(f39,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,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,[],[f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f39]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_59,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,[],[f47]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_63,negated_conjecture,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_64,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f51]) ).
tcf(c_65,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_142,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_143,definition,
iPr_def_11 = intersection_point(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_144,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_145,negated_conjecture,
distinct_points(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_63,c_143,c_142]) ).
tcf(c_418,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_144,c_54]) ).
tcf(c_421,plain,
( convergent_lines(sK1,sK0)
| convergent_lines(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_418]) ).
tcf(c_723,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_724,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_723]) ).
tcf(c_777,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_11,X1)
| apart_point_and_line(iPr_def_11,X0)
| apart_point_and_line(iPr_def_10,X1)
| apart_point_and_line(iPr_def_10,X0)
| ~ distinct_points(iPr_def_10,iPr_def_11)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_878,plain,
( ~ apart_point_and_line(iPr_def_10,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_142,c_57]) ).
tcf(c_879,plain,
( ~ apart_point_and_line(iPr_def_11,sK1)
| ~ convergent_lines(sK1,sK0) ),
inference(superposition,[status(thm)],[c_143,c_57]) ).
tcf(c_882,plain,
~ apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_878,c_144]) ).
tcf(c_887,plain,
( ~ apart_point_and_line(iPr_def_10,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_142,c_58]) ).
tcf(c_888,plain,
( ~ apart_point_and_line(iPr_def_11,sK0)
| ~ convergent_lines(sK1,sK0) ),
inference(superposition,[status(thm)],[c_143,c_58]) ).
tcf(c_891,plain,
~ apart_point_and_line(iPr_def_10,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_887,c_144]) ).
tcf(c_1190,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_11,sK1)
| apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_11,X0)
| apart_point_and_line(iPr_def_10,X0)
| ~ distinct_points(iPr_def_10,iPr_def_11)
| ~ distinct_lines(sK1,X0) ),
inference(instantiation,[status(thm)],[c_777]) ).
tcf(c_1191,plain,
( apart_point_and_line(iPr_def_11,sK1)
| apart_point_and_line(iPr_def_11,sK0)
| apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,sK0)
| ~ distinct_lines(sK1,sK0)
| ~ distinct_points(iPr_def_10,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_1190]) ).
tcf(c_1192,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1191,c_888,c_891,c_879,c_882,c_724,c_421,c_145,c_65,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.38 % Computer : n004.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.38 % DateTime : Wed Sep 23 11:27:03 UTC 2026
% 0.12/10.38 % CPUTime :
% 0.12/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/10.42 Running first-order theorem proving
% 0.16/10.42 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
% 0.16/10.44
% 0.16/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.44
% 0.16/10.44 % Detected problem language: tptp
% 0.16/10.45 % Proving...
% 2.52/11.31 % SZS status Started for theBenchmark.p
% 2.52/11.31 % SZS status Theorem for theBenchmark.p
% 2.52/11.31
% 2.52/11.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.52/11.31
% 2.52/11.31 % ------ iProver source info
% 2.52/11.31
% 2.52/11.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.52/11.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.52/11.31 % git: non_committed_changes: false
% 2.52/11.31
% 2.52/11.31 % ------ Parsing...
% 2.52/11.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.52/11.31
% 2.52/11.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.52/11.31
% 2.52/11.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.52/11.31
% 2.52/11.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.52/11.31 % ------ Proving...
% 2.52/11.31 % ------ Problem Properties
% 2.52/11.31
% 2.52/11.31 %
% 2.52/11.31 % clauses 18
% 2.52/11.31 % conjectures 2
% 2.52/11.31 % EPR 12
% 2.52/11.31 % Horn 11
% 2.52/11.31 % unary 7
% 2.52/11.31 % binary 4
% 2.52/11.31 % lits 39
% 2.52/11.31 % lits eq 2
% 2.52/11.31 % fd_pure 0
% 2.52/11.31 % fd_pseudo 0
% 2.52/11.31 % fd_cond 0
% 2.52/11.31 % fd_pseudo_cond 0
% 2.52/11.31 % AC symbols 0
% 2.52/11.31
% 2.52/11.31 % ------ Schedule dynamic 5 is on
% 2.52/11.31
% 2.52/11.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.52/11.31
% 2.52/11.31
% 2.52/11.31 % ------
% 2.52/11.31 % Current options:
% 2.52/11.31 % ------
% 2.52/11.31
% 2.52/11.31
% 2.52/11.31 %
% 2.52/11.31
% 2.52/11.31 % ------ Proving...
% 2.52/11.31 %
% 2.52/11.31
% 2.52/11.31 % SZS status Theorem for theBenchmark.p
% 2.52/11.31
% 2.52/11.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.52/11.31
% 2.52/11.31
%------------------------------------------------------------------------------