%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO191+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 : n011.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 01:20:13 PM UTC 2026
% Result : Theorem 4.02s 1.33s
% Output : CNFRefutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 17 unt; 1 def)
% Number of atoms : 204 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 186 ( 69 ~; 93 |; 17 &)
% ( 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 86 !; 8 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq1) ).
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(f36,conjecture,
! [X0,X1,X2,X3] :
( ( ( apart_point_and_line(intersection_point(X0,X1),X3)
| apart_point_and_line(intersection_point(X0,X1),X2) )
& convergent_lines(X2,X3)
& convergent_lines(X0,X1) )
=> ( apart_point_and_line(intersection_point(X2,X3),X1)
| apart_point_and_line(intersection_point(X2,X3),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ( apart_point_and_line(intersection_point(X0,X1),X3)
| apart_point_and_line(intersection_point(X0,X1),X2) )
& convergent_lines(X2,X3)
& convergent_lines(X0,X1) )
=> ( apart_point_and_line(intersection_point(X2,X3),X1)
| apart_point_and_line(intersection_point(X2,X3),X0) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f47,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f48,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(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(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f54]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(intersection_point(X0,X1),X3)
| apart_point_and_line(intersection_point(X0,X1),X2) )
& convergent_lines(X2,X3)
& convergent_lines(X0,X1)
& ~ apart_point_and_line(intersection_point(X2,X3),X1)
& ~ apart_point_and_line(intersection_point(X2,X3),X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(intersection_point(X0,X1),X3)
| apart_point_and_line(intersection_point(X0,X1),X2) )
& convergent_lines(X2,X3)
& convergent_lines(X0,X1)
& ~ apart_point_and_line(intersection_point(X2,X3),X1)
& ~ apart_point_and_line(intersection_point(X2,X3),X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( ( apart_point_and_line(intersection_point(sK0,sK1),sK3)
| apart_point_and_line(intersection_point(sK0,sK1),sK2) )
& convergent_lines(sK2,sK3)
& convergent_lines(sK0,sK1)
& ~ apart_point_and_line(intersection_point(sK2,sK3),sK1)
& ~ apart_point_and_line(intersection_point(sK2,sK3),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f81,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f87,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f88,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f89,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,[],[f49]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f115,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK3)
| apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f116,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f118,plain,
~ apart_point_and_line(intersection_point(sK2,sK3),sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f119,plain,
~ apart_point_and_line(intersection_point(sK2,sK3),sK0),
inference(cnf_transformation,[],[f78]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f81]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f88]) ).
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,[],[f89]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
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,[],[f92]) ).
tcf(c_85,negated_conjecture,
~ apart_point_and_line(intersection_point(sK2,sK3),sK0),
inference(cnf_transformation,[],[f119]) ).
tcf(c_86,negated_conjecture,
~ apart_point_and_line(intersection_point(sK2,sK3),sK1),
inference(cnf_transformation,[],[f118]) ).
tcf(c_87,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f117]) ).
tcf(c_88,negated_conjecture,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f116]) ).
tcf(c_89,negated_conjecture,
( apart_point_and_line(intersection_point(sK0,sK1),sK3)
| apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_90,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_458,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_460,negated_conjecture,
( apart_point_and_line(iPr_def_10,sK3)
| apart_point_and_line(iPr_def_10,sK2) ),
inference(demodulation,[status(thm)],[c_89,c_458]) ).
tcf(c_462,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1046,plain,
( ~ apart_point_and_line(iPr_def_10,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_458,c_57]) ).
tcf(c_1047,plain,
~ apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_1046,c_462]) ).
tcf(c_1054,plain,
( ~ apart_point_and_line(iPr_def_10,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_458,c_58]) ).
tcf(c_1055,plain,
~ apart_point_and_line(iPr_def_10,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_1054,c_462]) ).
tcf(c_1146,plain,
( ~ convergent_lines(sK2,sK3)
| ~ apart_point_and_line(intersection_point(sK2,sK3),sK2) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_1201,plain,
( ~ convergent_lines(sK2,sK3)
| ~ apart_point_and_line(intersection_point(sK2,sK3),sK3) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1261,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1262,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_1261]) ).
tcf(c_1575,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(iPr_def_10,X1)
| apart_point_and_line(iPr_def_10,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_points(iPr_def_10,X2)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_3290,plain,
! [X0: $i] :
( apart_point_and_line(X0,sK3)
| distinct_points(iPr_def_10,X0)
| ~ apart_point_and_line(iPr_def_10,sK3) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_4889,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,X1)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(sK1,X1)
| ~ distinct_points(iPr_def_10,X0) ),
inference(instantiation,[status(thm)],[c_1575]) ).
tcf(c_7118,plain,
! [X0: $i] :
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| distinct_points(X0,intersection_point(sK2,sK3))
| ~ apart_point_and_line(X0,sK2) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_9435,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK3)
| distinct_points(iPr_def_10,intersection_point(sK2,sK3))
| ~ apart_point_and_line(iPr_def_10,sK3) ),
inference(instantiation,[status(thm)],[c_3290]) ).
tcf(c_10609,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,X0)
| apart_point_and_line(intersection_point(sK2,sK3),sK1)
| apart_point_and_line(intersection_point(sK2,sK3),X0)
| ~ distinct_lines(sK1,X0)
| ~ distinct_points(iPr_def_10,intersection_point(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_4889]) ).
tcf(c_10611,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| distinct_points(iPr_def_10,intersection_point(sK2,sK3))
| ~ apart_point_and_line(iPr_def_10,sK2) ),
inference(instantiation,[status(thm)],[c_7118]) ).
tcf(c_10612,plain,
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,sK0)
| apart_point_and_line(intersection_point(sK2,sK3),sK1)
| apart_point_and_line(intersection_point(sK2,sK3),sK0)
| ~ distinct_lines(sK1,sK0)
| ~ distinct_points(iPr_def_10,intersection_point(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_10609]) ).
tcf(c_10613,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10611,c_10612,c_9435,c_1262,c_1201,c_1146,c_1055,c_1047,c_460,c_85,c_86,c_90,c_87,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO191+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 % Computer : n011.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Wed Sep 23 11:23:13 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 0.11/0.45
% 0.11/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.45
% 0.11/0.46 % Detected problem language: tptp
% 0.11/0.47 % Proving...
% 4.02/1.33 % SZS status Started for theBenchmark.p
% 4.02/1.33 % SZS status Theorem for theBenchmark.p
% 4.02/1.33
% 4.02/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.02/1.33
% 4.02/1.33 % ------ iProver source info
% 4.02/1.33
% 4.02/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 4.02/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.02/1.33 % git: non_committed_changes: false
% 4.02/1.33
% 4.02/1.33 % ------ Parsing...
% 4.02/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.02/1.33
% 4.02/1.33 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.02/1.33
% 4.02/1.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.02/1.33
% 4.02/1.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.02/1.33 % ------ Proving...
% 4.02/1.33 % ------ Problem Properties
% 4.02/1.33
% 4.02/1.33 %
% 4.02/1.33 % clauses 35
% 4.02/1.33 % conjectures 5
% 4.02/1.33 % EPR 25
% 4.02/1.33 % Horn 18
% 4.02/1.33 % unary 13
% 4.02/1.33 % binary 7
% 4.02/1.33 % lits 83
% 4.02/1.33 % lits eq 2
% 4.02/1.33 % fd_pure 0
% 4.02/1.33 % fd_pseudo 0
% 4.02/1.33 % fd_cond 0
% 4.02/1.33 % fd_pseudo_cond 0
% 4.02/1.33 % AC symbols 0
% 4.02/1.33
% 4.02/1.33 % ------ Schedule dynamic 5 is on
% 4.02/1.33
% 4.02/1.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.02/1.33
% 4.02/1.33
% 4.02/1.33 % ------
% 4.02/1.33 % Current options:
% 4.02/1.33 % ------
% 4.02/1.33
% 4.02/1.33
% 4.02/1.33 %
% 4.02/1.33
% 4.02/1.33 % ------ Proving...
% 4.02/1.33 %
% 4.02/1.33
% 4.02/1.33 % SZS status Theorem for theBenchmark.p
% 4.02/1.33
% 4.02/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.02/1.33
% 4.02/1.33
%------------------------------------------------------------------------------