%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO205+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 : n016.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 2.10s 1.16s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 20 unt; 2 def)
% Number of atoms : 217 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 181 ( 68 ~; 94 |; 11 &)
% ( 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 : 112 ( 0 sgn 106 !; 6 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
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(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,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/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,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)],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f21]) ).
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(f31,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f31]) ).
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] :
( ~ 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,[],[f16]) ).
fof(f36,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,[],[f35]) ).
fof(f37,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)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
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(f50,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
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,
~ distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f40]) ).
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,[],[f43]) ).
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_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,[],[f50]) ).
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,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_64,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f53]) ).
tcf(c_65,negated_conjecture,
~ distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f52]) ).
tcf(c_147,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_148,definition,
iPr_def_11 = intersection_point(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_149,negated_conjecture,
~ distinct_lines(sK1,sK2),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_150,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_151,negated_conjecture,
( distinct_points(iPr_def_10,iPr_def_11)
| ~ convergent_lines(sK0,sK2) ),
inference(demodulation,[status(thm)],[c_63,c_148,c_147]) ).
tcf(c_441,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_150,c_54]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] :
( convergent_lines(sK1,X1)
| convergent_lines(sK0,X0)
| convergent_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_441,c_54]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(sK1,X1)
| convergent_lines(sK0,X2)
| convergent_lines(X0,X2)
| convergent_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_458,c_54]) ).
tcf(c_479,plain,
( convergent_lines(sK1,sK0)
| convergent_lines(sK0,sK0) ),
inference(equality_factoring,[status(thm)],[c_458]) ).
tcf(c_480,plain,
convergent_lines(sK1,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_479,c_51]) ).
tcf(c_700,plain,
( ~ apart_point_and_line(iPr_def_10,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_147,c_57]) ).
tcf(c_701,plain,
( ~ apart_point_and_line(iPr_def_11,sK0)
| ~ convergent_lines(sK0,sK2) ),
inference(superposition,[status(thm)],[c_148,c_57]) ).
tcf(c_704,plain,
~ apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_700,c_150]) ).
tcf(c_712,plain,
( ~ apart_point_and_line(iPr_def_10,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_147,c_58]) ).
tcf(c_713,plain,
( ~ apart_point_and_line(iPr_def_11,sK2)
| ~ convergent_lines(sK0,sK2) ),
inference(superposition,[status(thm)],[c_148,c_58]) ).
tcf(c_716,plain,
~ apart_point_and_line(iPr_def_10,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_712,c_150]) ).
tcf(c_730,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i] :
( distinct_points(iPr_def_10,iPr_def_11)
| convergent_lines(sK1,X1)
| convergent_lines(X0,sK2)
| convergent_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_471,c_151]) ).
tcf(c_871,plain,
( convergent_lines(sK0,sK2)
| distinct_lines(sK1,sK2)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_730]) ).
tcf(c_872,plain,
distinct_points(iPr_def_10,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_815,c_64,c_65,c_151,c_871]) ).
tcf(c_998,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0) ),
inference(superposition,[status(thm)],[c_150,c_62]) ).
tcf(c_1004,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| distinct_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_480,c_62]) ).
tcf(c_1151,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_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_872,c_59]) ).
tcf(c_1241,plain,
convergent_lines(sK0,sK2),
inference(superposition,[status(thm)],[c_998,c_149]) ).
tcf(c_1245,plain,
~ apart_point_and_line(iPr_def_11,sK0),
inference(backward_subsumption_resolution,[status(thm)],[c_701,c_1241]) ).
tcf(c_1402,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_11,sK0)
| apart_point_and_line(iPr_def_10,sK0)
| apart_point_and_line(iPr_def_11,X0)
| apart_point_and_line(iPr_def_10,X0)
| convergent_lines(sK1,X0) ),
inference(superposition,[status(thm)],[c_1004,c_1151]) ).
tcf(c_1410,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_11,X0)
| apart_point_and_line(iPr_def_10,X0)
| convergent_lines(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1402,c_1245,c_704]) ).
tcf(c_1454,plain,
( apart_point_and_line(iPr_def_11,sK1)
| apart_point_and_line(iPr_def_10,sK1) ),
inference(superposition,[status(thm)],[c_1410,c_51]) ).
tcf(c_1457,plain,
apart_point_and_line(iPr_def_11,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_1454,c_716]) ).
tcf(c_1466,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_11,X0)
| distinct_lines(sK1,X0) ),
inference(superposition,[status(thm)],[c_1457,c_61]) ).
tcf(c_1638,plain,
apart_point_and_line(iPr_def_11,sK2),
inference(superposition,[status(thm)],[c_1466,c_149]) ).
tcf(c_1642,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1638,c_871,c_713,c_65,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO205+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 11:33:26 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 2.10/1.16 % SZS status Started for theBenchmark.p
% 2.10/1.16 % SZS status Theorem for theBenchmark.p
% 2.10/1.16
% 2.10/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.10/1.16
% 2.10/1.16 % ------ iProver source info
% 2.10/1.16
% 2.10/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 2.10/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.10/1.16 % git: non_committed_changes: false
% 2.10/1.16
% 2.10/1.16 % ------ Parsing...
% 2.10/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.10/1.16
% 2.10/1.16 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.10/1.16
% 2.10/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.10/1.16
% 2.10/1.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.10/1.16 % ------ Proving...
% 2.10/1.16 % ------ Problem Properties
% 2.10/1.16
% 2.10/1.16 %
% 2.10/1.16 % clauses 19
% 2.10/1.16 % conjectures 3
% 2.10/1.16 % EPR 13
% 2.10/1.16 % Horn 12
% 2.10/1.16 % unary 7
% 2.10/1.16 % binary 5
% 2.10/1.16 % lits 41
% 2.10/1.16 % lits eq 2
% 2.10/1.16 % fd_pure 0
% 2.10/1.16 % fd_pseudo 0
% 2.10/1.16 % fd_cond 0
% 2.10/1.16 % fd_pseudo_cond 0
% 2.10/1.16 % AC symbols 0
% 2.10/1.16
% 2.10/1.16 % ------ Schedule dynamic 5 is on
% 2.10/1.16
% 2.10/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.10/1.16
% 2.10/1.16
% 2.10/1.16 % ------
% 2.10/1.16 % Current options:
% 2.10/1.16 % ------
% 2.10/1.16
% 2.10/1.16
% 2.10/1.16 %
% 2.10/1.16
% 2.10/1.16 % ------ Proving...
% 2.10/1.16 %
% 2.10/1.16
% 2.10/1.16 % SZS status Theorem for theBenchmark.p
% 2.10/1.16
% 2.10/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.10/1.17
% 2.10/1.17
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