%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO202+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 : n008.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 3.61s 1.25s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 25 unt; 3 def)
% Number of atoms : 198 ( 3 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 148 ( 63 ~; 62 |; 14 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 81 !; 6 ?; 19 :)
% 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(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax1) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
=> equal_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f45,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f47,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f55]) ).
fof(f77,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1,X2] :
( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1)
& ~ equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1,X2] :
( convergent_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2)
& distinct_points(X0,X1)
& ~ equal_points(intersection_point(line_connecting(X0,X1),line_connecting(X0,X2)),X0) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
( convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
& distinct_points(sK0,sK2)
& distinct_points(sK0,sK1)
& ~ equal_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)],[f79]) ).
fof(f83,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f87,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f90,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f91,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,[],[f50]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f117,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f118,plain,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f80]) ).
fof(f119,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
~ equal_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f80]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f83]) ).
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_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f90]) ).
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,[],[f91]) ).
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,[],[f94]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_86,negated_conjecture,
~ equal_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f121]) ).
tcf(c_87,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f120]) ).
tcf(c_88,negated_conjecture,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f119]) ).
tcf(c_89,negated_conjecture,
convergent_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f118]) ).
tcf(c_297,plain,
distinct_points(intersection_point(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),sK0),
inference(resolution,[status(thm)],[c_85,c_86]) ).
tcf(c_460,definition,
iPr_def_10 = line_connecting(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_461,definition,
iPr_def_11 = line_connecting(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_462,definition,
iPr_def_12 = intersection_point(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_463,plain,
distinct_points(iPr_def_12,sK0),
inference(demodulation,[status(thm)],[c_297,c_461,c_460,c_462]) ).
tcf(c_464,negated_conjecture,
convergent_lines(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_465,negated_conjecture,
distinct_points(sK0,sK2),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_466,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1118,plain,
( ~ apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_460,c_55]) ).
tcf(c_1119,plain,
( ~ apart_point_and_line(sK0,iPr_def_11)
| ~ distinct_points(sK0,sK2) ),
inference(superposition,[status(thm)],[c_461,c_55]) ).
tcf(c_1120,plain,
~ apart_point_and_line(sK0,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1119,c_465]) ).
tcf(c_1121,plain,
~ apart_point_and_line(sK0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1118,c_466]) ).
tcf(c_1354,plain,
( ~ apart_point_and_line(iPr_def_12,iPr_def_10)
| ~ convergent_lines(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_462,c_57]) ).
tcf(c_1355,plain,
~ apart_point_and_line(iPr_def_12,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1354,c_464]) ).
tcf(c_1361,plain,
( ~ apart_point_and_line(iPr_def_12,iPr_def_11)
| ~ convergent_lines(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_462,c_58]) ).
tcf(c_1362,plain,
~ apart_point_and_line(iPr_def_12,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1361,c_464]) ).
tcf(c_1369,plain,
! [X0: $i] :
( convergent_lines(iPr_def_10,X0)
| distinct_lines(iPr_def_11,X0)
| ~ convergent_lines(iPr_def_10,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1486,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_12,X1)
| apart_point_and_line(iPr_def_12,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| ~ distinct_points(iPr_def_12,sK0)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1778,plain,
~ convergent_lines(iPr_def_10,iPr_def_10),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_3086,plain,
( convergent_lines(iPr_def_10,iPr_def_10)
| distinct_lines(iPr_def_11,iPr_def_10)
| ~ convergent_lines(iPr_def_10,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_1369]) ).
tcf(c_5396,plain,
( apart_point_and_line(iPr_def_12,iPr_def_11)
| apart_point_and_line(iPr_def_12,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_11)
| apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_lines(iPr_def_11,iPr_def_10)
| ~ distinct_points(iPr_def_12,sK0) ),
inference(instantiation,[status(thm)],[c_1486]) ).
tcf(c_5402,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5396,c_3086,c_1778,c_1362,c_1355,c_1120,c_1121,c_464,c_463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n008.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 11:28:30 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 3.61/1.25 % SZS status Started for theBenchmark.p
% 3.61/1.25 % SZS status Theorem for theBenchmark.p
% 3.61/1.25
% 3.61/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.61/1.25
% 3.61/1.25 % ------ iProver source info
% 3.61/1.25
% 3.61/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 3.61/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.61/1.25 % git: non_committed_changes: false
% 3.61/1.25
% 3.61/1.25 % ------ Parsing...
% 3.61/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.61/1.25
% 3.61/1.25 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.61/1.25
% 3.61/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.61/1.25
% 3.61/1.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.61/1.25 % ------ Proving...
% 3.61/1.25 % ------ Problem Properties
% 3.61/1.25
% 3.61/1.25 %
% 3.61/1.25 % clauses 35
% 3.61/1.25 % conjectures 3
% 3.61/1.25 % EPR 24
% 3.61/1.25 % Horn 19
% 3.61/1.25 % unary 14
% 3.61/1.25 % binary 6
% 3.61/1.25 % lits 82
% 3.61/1.25 % lits eq 3
% 3.61/1.25 % fd_pure 0
% 3.61/1.25 % fd_pseudo 0
% 3.61/1.25 % fd_cond 0
% 3.61/1.25 % fd_pseudo_cond 0
% 3.61/1.25 % AC symbols 0
% 3.61/1.25
% 3.61/1.25 % ------ Schedule dynamic 5 is on
% 3.61/1.25
% 3.61/1.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.61/1.25
% 3.61/1.25
% 3.61/1.25 % ------
% 3.61/1.25 % Current options:
% 3.61/1.25 % ------
% 3.61/1.25
% 3.61/1.25
% 3.61/1.25 %
% 3.61/1.25
% 3.61/1.25 % ------ Proving...
% 3.61/1.25 %
% 3.61/1.25
% 3.61/1.25 % SZS status Theorem for theBenchmark.p
% 3.61/1.25
% 3.61/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.61/1.25
% 3.61/1.25
%------------------------------------------------------------------------------