%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO203+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 : n013.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 0.74s 1.05s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 20 unt; 3 def)
% Number of atoms : 153 ( 3 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 114 ( 48 ~; 46 |; 14 &)
% ( 0 <=>; 6 =>; 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 : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 52 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
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(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(f15,conjecture,
! [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) )
=> ~ distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) )
=> ~ distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f25,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
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(f35,plain,
? [X0,X1,X2] :
( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1)
& distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1)
& distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
& convergent_lines(sK0,sK2)
& convergent_lines(sK0,sK1)
& distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,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(f52,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
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,[],[f48]) ).
tcf(c_63,negated_conjecture,
distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f55]) ).
tcf(c_64,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f54]) ).
tcf(c_65,negated_conjecture,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f53]) ).
tcf(c_66,negated_conjecture,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_148,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_149,definition,
iPr_def_11 = intersection_point(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_150,definition,
iPr_def_12 = line_connecting(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_151,negated_conjecture,
distinct_points(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_66,c_149,c_148]) ).
tcf(c_152,negated_conjecture,
convergent_lines(sK0,sK2),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_153,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_154,negated_conjecture,
distinct_lines(iPr_def_12,sK0),
inference(demodulation,[status(thm)],[c_63,c_150]) ).
tcf(c_737,plain,
( ~ apart_point_and_line(iPr_def_10,iPr_def_12)
| ~ distinct_points(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_150,c_55]) ).
tcf(c_738,plain,
~ apart_point_and_line(iPr_def_10,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_737,c_151]) ).
tcf(c_743,plain,
( ~ apart_point_and_line(iPr_def_11,iPr_def_12)
| ~ distinct_points(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_150,c_56]) ).
tcf(c_744,plain,
~ apart_point_and_line(iPr_def_11,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_743,c_151]) ).
tcf(c_750,plain,
( ~ apart_point_and_line(iPr_def_10,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_148,c_57]) ).
tcf(c_751,plain,
( ~ apart_point_and_line(iPr_def_11,sK0)
| ~ convergent_lines(sK0,sK2) ),
inference(superposition,[status(thm)],[c_149,c_57]) ).
tcf(c_752,plain,
~ apart_point_and_line(iPr_def_11,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_751,c_152]) ).
tcf(c_753,plain,
~ apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_750,c_153]) ).
tcf(c_874,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_1511,plain,
( apart_point_and_line(iPr_def_11,iPr_def_12)
| apart_point_and_line(iPr_def_11,sK0)
| apart_point_and_line(iPr_def_10,iPr_def_12)
| apart_point_and_line(iPr_def_10,sK0)
| ~ distinct_lines(iPr_def_12,sK0)
| ~ distinct_points(iPr_def_10,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_874]) ).
tcf(c_1512,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1511,c_752,c_753,c_744,c_738,c_154,c_151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Wed Sep 23 11:26:51 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 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...
% 0.74/1.05 % SZS status Started for theBenchmark.p
% 0.74/1.05 % SZS status Theorem for theBenchmark.p
% 0.74/1.05
% 0.74/1.05 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.74/1.05
% 0.74/1.05 % ------ iProver source info
% 0.74/1.05
% 0.74/1.05 % git: date: 2026-07-19 20:42:38 +0200
% 0.74/1.05 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.74/1.05 % git: non_committed_changes: false
% 0.74/1.05
% 0.74/1.05 % ------ Parsing...
% 0.74/1.05 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.74/1.05
% 0.74/1.05 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.74/1.05
% 0.74/1.05 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.74/1.05
% 0.74/1.05 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.74/1.05 % ------ Proving...
% 0.74/1.05 % ------ Problem Properties
% 0.74/1.05
% 0.74/1.05 %
% 0.74/1.05 % clauses 21
% 0.74/1.05 % conjectures 4
% 0.74/1.05 % EPR 14
% 0.74/1.05 % Horn 14
% 0.74/1.05 % unary 10
% 0.74/1.05 % binary 4
% 0.74/1.05 % lits 42
% 0.74/1.05 % lits eq 3
% 0.74/1.05 % fd_pure 0
% 0.74/1.05 % fd_pseudo 0
% 0.74/1.05 % fd_cond 0
% 0.74/1.05 % fd_pseudo_cond 0
% 0.74/1.05 % AC symbols 0
% 0.74/1.05
% 0.74/1.05 % ------ Schedule dynamic 5 is on
% 0.74/1.05
% 0.74/1.05 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.74/1.05
% 0.74/1.05
% 0.74/1.05 % ------
% 0.74/1.05 % Current options:
% 0.74/1.05 % ------
% 0.74/1.05
% 0.74/1.05
% 0.74/1.05 %
% 0.74/1.05
% 0.74/1.05 % ------ Proving...
% 0.74/1.05 %
% 0.74/1.05
% 0.74/1.05 % SZS status Theorem for theBenchmark.p
% 0.74/1.05
% 0.74/1.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.74/1.05
% 0.74/1.05
%------------------------------------------------------------------------------