%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO198+1 : 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 : n017.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 01:20:16 PM UTC 2026
% Result : Theorem 0.73s 6.08s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 18 unt; 1 def)
% Number of atoms : 185 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 171 ( 66 ~; 79 |; 19 &)
% ( 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 83 !; 6 ?; 23 :)
% 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(f15,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
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(f29,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(f30,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK2)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK1)
& apart_point_and_line(intersection_point(sK0,sK2),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
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(f49,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f37]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f40]) ).
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_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
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_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,[],[f49]) ).
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,[],[f51]) ).
tcf(c_63,negated_conjecture,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f56]) ).
tcf(c_64,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f55]) ).
tcf(c_66,negated_conjecture,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f53]) ).
tcf(c_67,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f52]) ).
tcf(c_68,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_152,definition,
iPr_def_11 = intersection_point(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_154,negated_conjecture,
convergent_lines(sK0,sK2),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_157,negated_conjecture,
apart_point_and_line(iPr_def_11,sK1),
inference(demodulation,[status(thm)],[c_63,c_152]) ).
tcf(c_626,plain,
( ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_629,plain,
( ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_727,plain,
! [X0: $i] :
( apart_point_and_line(X0,sK1)
| distinct_points(iPr_def_11,X0)
| ~ apart_point_and_line(iPr_def_11,sK1) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_735,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK2,X0)
| ~ convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_736,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK2,sK0)
| ~ convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_735]) ).
tcf(c_749,plain,
( ~ apart_point_and_line(iPr_def_11,sK0)
| ~ convergent_lines(sK0,sK2) ),
inference(superposition,[status(thm)],[c_152,c_57]) ).
tcf(c_752,plain,
~ apart_point_and_line(iPr_def_11,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_749,c_154]) ).
tcf(c_757,plain,
( ~ apart_point_and_line(iPr_def_11,sK2)
| ~ convergent_lines(sK0,sK2) ),
inference(superposition,[status(thm)],[c_152,c_58]) ).
tcf(c_760,plain,
~ apart_point_and_line(iPr_def_11,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_757,c_154]) ).
tcf(c_1104,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(iPr_def_11,X1)
| apart_point_and_line(iPr_def_11,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_points(iPr_def_11,X2)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1708,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_11,sK2)
| apart_point_and_line(iPr_def_11,X1)
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(sK2,X1)
| ~ distinct_points(iPr_def_11,X0) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_2019,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| distinct_points(iPr_def_11,intersection_point(sK0,sK1))
| ~ apart_point_and_line(iPr_def_11,sK1) ),
inference(instantiation,[status(thm)],[c_727]) ).
tcf(c_2477,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_11,sK2)
| apart_point_and_line(iPr_def_11,X0)
| apart_point_and_line(intersection_point(sK0,sK1),sK2)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| ~ distinct_lines(sK2,X0)
| ~ distinct_points(iPr_def_11,intersection_point(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1708]) ).
tcf(c_2481,plain,
( apart_point_and_line(iPr_def_11,sK2)
| apart_point_and_line(iPr_def_11,sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK2,sK0)
| ~ distinct_points(iPr_def_11,intersection_point(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_2477]) ).
tcf(c_2482,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2481,c_2019,c_760,c_752,c_736,c_629,c_626,c_157,c_67,c_68,c_64,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO198+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n017.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 11:20:51 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.42 Running first-order theorem proving
% 0.13/5.42 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
% 0.13/5.43
% 0.13/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.43
% 0.13/5.43 % Detected problem language: tptp
% 0.13/5.44 % Proving...
% 0.73/6.08 % SZS status Started for theBenchmark.p
% 0.73/6.08 % SZS status Theorem for theBenchmark.p
% 0.73/6.08
% 0.73/6.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.73/6.08
% 0.73/6.08 % ------ iProver source info
% 0.73/6.08
% 0.73/6.08 % git: date: 2026-07-19 20:42:38 +0200
% 0.73/6.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.73/6.08 % git: non_committed_changes: false
% 0.73/6.08
% 0.73/6.08 % ------ Parsing...
% 0.73/6.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.73/6.08
% 0.73/6.08 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.73/6.08
% 0.73/6.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.73/6.08
% 0.73/6.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.73/6.08 % ------ Proving...
% 0.73/6.08 % ------ Problem Properties
% 0.73/6.08
% 0.73/6.08 %
% 0.73/6.08 % clauses 21
% 0.73/6.08 % conjectures 5
% 0.73/6.08 % EPR 15
% 0.73/6.08 % Horn 14
% 0.73/6.08 % unary 10
% 0.73/6.08 % binary 4
% 0.73/6.08 % lits 42
% 0.73/6.08 % lits eq 2
% 0.73/6.08 % fd_pure 0
% 0.73/6.09 % fd_pseudo 0
% 0.73/6.09 % fd_cond 0
% 0.73/6.09 % fd_pseudo_cond 0
% 0.73/6.09 % AC symbols 0
% 0.73/6.09
% 0.73/6.09 % ------ Schedule dynamic 5 is on
% 0.73/6.09
% 0.73/6.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.73/6.09
% 0.73/6.09
% 0.73/6.09 % ------
% 0.73/6.09 % Current options:
% 0.73/6.09 % ------
% 0.73/6.09
% 0.73/6.09
% 0.73/6.09 %
% 0.73/6.09
% 0.73/6.09 % ------ Proving...
% 0.73/6.09 %
% 0.73/6.09
% 0.73/6.09 % SZS status Theorem for theBenchmark.p
% 0.73/6.09
% 0.73/6.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.73/6.09
% 0.73/6.09
%------------------------------------------------------------------------------