%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO205+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 : n010.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 01:20:19 PM UTC 2026
% Result : Theorem 2.47s 1.20s
% Output : CNFRefutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 21 unt; 2 def)
% Number of atoms : 249 ( 14 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 216 ( 92 ~; 103 |; 13 &)
% ( 0 <=>; 8 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 109 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart6) ).
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(f9,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/GEO008+0.ax',cu1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq2) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1) )
=> ( ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1) )
=> ( ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f19]) ).
fof(f23,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(f24,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,[],[f23]) ).
fof(f25,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,[],[f9]) ).
fof(f26,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,[],[f25]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1)
& ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
| ~ convergent_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1)
& ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
| ~ convergent_lines(X0,X2) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ~ distinct_lines(sK1,sK2)
& convergent_lines(sK0,sK1)
& ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
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,[],[f26]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
~ distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f35]) ).
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,[],[f40]) ).
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,[],[f44]) ).
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,[],[f43]) ).
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,[],[f45]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_63,negated_conjecture,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_64,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f50]) ).
tcf(c_65,negated_conjecture,
~ distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f49]) ).
tcf(c_153,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_154,definition,
iPr_def_11 = intersection_point(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_155,negated_conjecture,
~ distinct_lines(sK1,sK2),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_156,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_157,negated_conjecture,
( distinct_points(iPr_def_10,iPr_def_11)
| ~ convergent_lines(sK0,sK2) ),
inference(demodulation,[status(thm)],[c_63,c_154,c_153]) ).
tcf(c_158,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_points(X0,X2)
| ~ distinct_points(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_447,plain,
distinct_lines(sK0,sK1),
inference(superposition,[status(thm)],[c_156,c_62]) ).
tcf(c_460,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_156,c_54]) ).
tcf(c_480,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0) ),
inference(superposition,[status(thm)],[c_460,c_62]) ).
tcf(c_507,plain,
convergent_lines(sK0,sK2),
inference(superposition,[status(thm)],[c_480,c_155]) ).
tcf(c_511,plain,
distinct_points(iPr_def_10,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_157,c_507]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_57,c_49]) ).
tcf(c_722,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_885,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_58,c_49]) ).
tcf(c_1147,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(sK0,sK1)
| ~ distinct_points(iPr_def_10,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_722]) ).
tcf(c_1668,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X0,X1)
| ~ distinct_points(iPr_def_11,X2)
| ( X1 != X2 )
| ( X0 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_2193,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_11,X0)
| distinct_lines(sK1,X0)
| ~ apart_point_and_line(iPr_def_11,sK1) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2256,plain,
~ distinct_points(iPr_def_11,iPr_def_11),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_2401,plain,
! [X0: $i,X1: $i] :
( distinct_points(iPr_def_11,X0)
| ~ distinct_points(iPr_def_11,X1)
| ( iPr_def_11 != iPr_def_11 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1668]) ).
tcf(c_2402,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_158]) ).
tcf(c_3772,plain,
! [X0: $i] :
( distinct_points(X0,intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2)
| ~ apart_point_and_line(X0,sK2) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_5395,plain,
( apart_point_and_line(iPr_def_11,sK2)
| distinct_lines(sK1,sK2)
| ~ apart_point_and_line(iPr_def_11,sK1) ),
inference(instantiation,[status(thm)],[c_2193]) ).
tcf(c_5797,plain,
! [X0: $i] :
( distinct_points(iPr_def_11,iPr_def_11)
| ~ distinct_points(iPr_def_11,X0)
| ( iPr_def_11 != iPr_def_11 )
| ( iPr_def_11 != X0 ) ),
inference(instantiation,[status(thm)],[c_2401]) ).
tcf(c_8493,plain,
( distinct_points(iPr_def_11,intersection_point(sK0,sK2))
| ~ apart_point_and_line(iPr_def_11,sK2)
| ~ convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_3772]) ).
tcf(c_10601,plain,
( ~ apart_point_and_line(iPr_def_10,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_153,c_667]) ).
tcf(c_10602,plain,
( ~ apart_point_and_line(iPr_def_11,sK0)
| ~ convergent_lines(sK0,sK2) ),
inference(superposition,[status(thm)],[c_154,c_667]) ).
tcf(c_10603,plain,
~ apart_point_and_line(iPr_def_11,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_10602,c_507]) ).
tcf(c_10604,plain,
~ apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_10601,c_156]) ).
tcf(c_11138,plain,
( distinct_points(iPr_def_11,iPr_def_11)
| ~ distinct_points(iPr_def_11,intersection_point(sK0,sK2))
| ( iPr_def_11 != iPr_def_11 )
| ( iPr_def_11 != intersection_point(sK0,sK2) ) ),
inference(instantiation,[status(thm)],[c_5797]) ).
tcf(c_11472,plain,
( ~ apart_point_and_line(iPr_def_10,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_153,c_885]) ).
tcf(c_11475,plain,
~ apart_point_and_line(iPr_def_10,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_11472,c_156]) ).
tcf(c_11476,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11475,c_11138,c_10603,c_10604,c_8493,c_5395,c_2402,c_2256,c_1147,c_507,c_511,c_447,c_154,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 11:28:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 2.47/1.20 % SZS status Started for theBenchmark.p
% 2.47/1.20 % SZS status Theorem for theBenchmark.p
% 2.47/1.20
% 2.47/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.47/1.20
% 2.47/1.20 % ------ iProver source info
% 2.47/1.20
% 2.47/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.47/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.47/1.20 % git: non_committed_changes: false
% 2.47/1.20
% 2.47/1.20 % ------ Parsing...
% 2.47/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.47/1.20
% 2.47/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.47/1.20
% 2.47/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.47/1.20
% 2.47/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.47/1.20 % ------ Proving...
% 2.47/1.20 % ------ Problem Properties
% 2.47/1.20
% 2.47/1.20 %
% 2.47/1.20 % clauses 19
% 2.47/1.20 % conjectures 3
% 2.47/1.20 % EPR 13
% 2.47/1.20 % Horn 13
% 2.47/1.20 % unary 7
% 2.47/1.20 % binary 2
% 2.47/1.20 % lits 44
% 2.47/1.20 % lits eq 2
% 2.47/1.20 % fd_pure 0
% 2.47/1.20 % fd_pseudo 0
% 2.47/1.20 % fd_cond 0
% 2.47/1.20 % fd_pseudo_cond 0
% 2.47/1.20 % AC symbols 0
% 2.47/1.20
% 2.47/1.20 % ------ Schedule dynamic 5 is on
% 2.47/1.20
% 2.47/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.47/1.20
% 2.47/1.20
% 2.47/1.20 % ------
% 2.47/1.20 % Current options:
% 2.47/1.20 % ------
% 2.47/1.20
% 2.47/1.20
% 2.47/1.20 %
% 2.47/1.20
% 2.47/1.20 % ------ Proving...
% 2.47/1.20 %
% 2.47/1.20
% 2.47/1.20 % SZS status Theorem for theBenchmark.p
% 2.47/1.20
% 2.47/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.47/1.21
% 2.47/1.21
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