%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO192+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 : n006.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 01:20:14 PM UTC 2026
% Result : Theorem 1.20s 11.92s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 16 unt; 1 def)
% Number of atoms : 143 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 120 ( 49 ~; 53 |; 10 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 70 !; 6 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart5) ).
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(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(f13,conjecture,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> ( distinct_lines(X1,X2)
& distinct_lines(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> ( distinct_lines(X1,X2)
& distinct_lines(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(flattening,[],[f17]) ).
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(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(f32,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& ( ~ distinct_lines(X1,X2)
| ~ distinct_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& ( ~ distinct_lines(X1,X2)
| ~ distinct_lines(X0,X2) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( convergent_lines(sK0,sK1)
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& ( ~ distinct_lines(sK1,sK2)
| ~ distinct_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(f36,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
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(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(f49,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
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_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_63,negated_conjecture,
( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_64,negated_conjecture,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f50]) ).
tcf(c_65,negated_conjecture,
convergent_lines(sK0,sK1),
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,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_155,negated_conjecture,
apart_point_and_line(iPr_def_10,sK2),
inference(demodulation,[status(thm)],[c_64,c_153]) ).
tcf(c_156,negated_conjecture,
( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_712,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_10,X0)
| distinct_lines(sK2,X0) ),
inference(superposition,[status(thm)],[c_155,c_61]) ).
tcf(c_737,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(X0,sK0) ),
inference(superposition,[status(thm)],[c_153,c_57]) ).
tcf(c_742,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ apart_point_and_line(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_737,c_154]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_10,X0)
| distinct_lines(sK2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_712,c_53]) ).
tcf(c_828,plain,
( apart_point_and_line(iPr_def_10,sK0)
| distinct_lines(sK2,sK2)
| ~ distinct_lines(sK1,sK2) ),
inference(superposition,[status(thm)],[c_797,c_156]) ).
tcf(c_837,plain,
( apart_point_and_line(iPr_def_10,sK0)
| ~ distinct_lines(sK1,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_828,c_50]) ).
tcf(c_858,plain,
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,sK0)
| distinct_lines(sK2,sK2) ),
inference(superposition,[status(thm)],[c_797,c_837]) ).
tcf(c_867,plain,
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_858,c_50]) ).
tcf(c_964,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(X0,sK1) ),
inference(superposition,[status(thm)],[c_153,c_58]) ).
tcf(c_969,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ apart_point_and_line(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_964,c_154]) ).
tcf(c_1133,plain,
( apart_point_and_line(iPr_def_10,sK0)
| distinct_points(iPr_def_10,iPr_def_10) ),
inference(superposition,[status(thm)],[c_867,c_969]) ).
tcf(c_1134,plain,
apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_1133,c_49]) ).
tcf(c_1145,plain,
distinct_points(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_1134,c_742]) ).
tcf(c_1146,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1145,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO192+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/11.01 % Computer : n006.cluster.edu
% 0.12/11.01 % Model : x86_64 x86_64
% 0.12/11.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/11.01 % Memory : 8046.5625MB
% 0.12/11.01 % OS : Linux 6.8.0-71-generic
% 0.12/11.02 % CPULimit : 300
% 0.12/11.02 % WCLimit : 300
% 0.12/11.02 % DateTime : Wed Sep 23 11:23:43 UTC 2026
% 0.12/11.02 % CPUTime :
% 0.12/11.02 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/11.05 Running first-order theorem proving
% 0.15/11.05 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
% 0.15/11.07
% 0.15/11.07 % ======== iProver multi-core TPTP/SMT =========
% 0.15/11.07
% 0.15/11.07 % Detected problem language: tptp
% 0.15/11.08 % Proving...
% 1.20/11.92 % SZS status Started for theBenchmark.p
% 1.20/11.92 % SZS status Theorem for theBenchmark.p
% 1.20/11.92
% 1.20/11.92 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.20/11.92
% 1.20/11.92 % ------ iProver source info
% 1.20/11.92
% 1.20/11.92 % git: date: 2026-07-19 20:42:38 +0200
% 1.20/11.92 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.20/11.92 % git: non_committed_changes: false
% 1.20/11.92
% 1.20/11.92 % ------ Parsing...
% 1.20/11.92 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.20/11.92
% 1.20/11.92 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.20/11.92
% 1.20/11.92 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.20/11.92
% 1.20/11.92 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.20/11.92 % ------ Proving...
% 1.20/11.92 % ------ Problem Properties
% 1.20/11.92
% 1.20/11.92 %
% 1.20/11.92 % clauses 18
% 1.20/11.92 % conjectures 3
% 1.20/11.92 % EPR 13
% 1.20/11.92 % Horn 12
% 1.20/11.92 % unary 6
% 1.20/11.92 % binary 2
% 1.20/11.92 % lits 43
% 1.20/11.92 % lits eq 1
% 1.20/11.92 % fd_pure 0
% 1.20/11.92 % fd_pseudo 0
% 1.20/11.92 % fd_cond 0
% 1.20/11.92 % fd_pseudo_cond 0
% 1.20/11.92 % AC symbols 0
% 1.20/11.92
% 1.20/11.92 % ------ Schedule dynamic 5 is on
% 1.20/11.92
% 1.20/11.92 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.20/11.92
% 1.20/11.92
% 1.20/11.92 % ------
% 1.20/11.92 % Current options:
% 1.20/11.92 % ------
% 1.20/11.92
% 1.20/11.92
% 1.20/11.92 %
% 1.20/11.92
% 1.20/11.92 % ------ Proving...
% 1.20/11.92 %
% 1.20/11.92
% 1.20/11.92 % SZS status Theorem for theBenchmark.p
% 1.20/11.92
% 1.20/11.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.20/11.93
% 1.20/11.93
%------------------------------------------------------------------------------