%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 2.13s 1.29s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 18 unt; 2 def)
% Number of atoms : 182 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 150 ( 60 ~; 78 |; 3 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 90 !; 2 ?; 24 :)
% 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(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(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax1) ).
fof(f36,conjecture,
! [X0,X1] :
( convergent_lines(X0,X1)
=> equal_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( convergent_lines(X0,X1)
=> equal_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
=> equal_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
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(ennf_transformation,[],[f11]) ).
fof(f50,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,[],[f49]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f55]) ).
fof(f77,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1] :
( convergent_lines(X0,X1)
& ~ equal_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
( convergent_lines(sK0,sK1)
& ~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f78]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f88,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f89,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f90,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,[],[f50]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f116,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| equal_points(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f117,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f79]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f82]) ).
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,[],[f85]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
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,[],[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,[],[f93]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_86,negated_conjecture,
~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f118]) ).
tcf(c_87,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f117]) ).
tcf(c_88,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_291,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(resolution,[status(thm)],[c_85,c_86]) ).
tcf(c_450,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_451,definition,
iPr_def_11 = intersection_point(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_452,plain,
distinct_points(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_291,c_451,c_450]) ).
tcf(c_453,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1182,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_453,c_54]) ).
tcf(c_1188,plain,
( convergent_lines(sK1,sK0)
| convergent_lines(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_1182]) ).
tcf(c_1197,plain,
( ~ apart_point_and_line(iPr_def_10,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_450,c_57]) ).
tcf(c_1198,plain,
( ~ apart_point_and_line(iPr_def_11,sK1)
| ~ convergent_lines(sK1,sK0) ),
inference(superposition,[status(thm)],[c_451,c_57]) ).
tcf(c_1201,plain,
~ apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_1197,c_453]) ).
tcf(c_1222,plain,
! [X0: $i,X1: $i] :
( convergent_lines(sK1,X1)
| convergent_lines(sK0,X0)
| convergent_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1182,c_54]) ).
tcf(c_1242,plain,
( convergent_lines(sK1,sK0)
| convergent_lines(sK0,sK0) ),
inference(equality_factoring,[status(thm)],[c_1222]) ).
tcf(c_1243,plain,
convergent_lines(sK1,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_1242,c_51]) ).
tcf(c_1262,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1263,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_1262]) ).
tcf(c_1468,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_1498,plain,
( ~ apart_point_and_line(iPr_def_10,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_450,c_58]) ).
tcf(c_1499,plain,
( ~ apart_point_and_line(iPr_def_11,sK0)
| ~ convergent_lines(sK1,sK0) ),
inference(superposition,[status(thm)],[c_451,c_58]) ).
tcf(c_1500,plain,
~ apart_point_and_line(iPr_def_11,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_1499,c_1243]) ).
tcf(c_1501,plain,
~ apart_point_and_line(iPr_def_10,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_1498,c_453]) ).
tcf(c_1858,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_11,sK1)
| apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_11,X0)
| apart_point_and_line(iPr_def_10,X0)
| ~ distinct_points(iPr_def_10,iPr_def_11)
| ~ distinct_lines(sK1,X0) ),
inference(instantiation,[status(thm)],[c_1468]) ).
tcf(c_1859,plain,
( apart_point_and_line(iPr_def_11,sK1)
| apart_point_and_line(iPr_def_11,sK0)
| apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,sK0)
| ~ distinct_lines(sK1,sK0)
| ~ distinct_points(iPr_def_10,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_1858]) ).
tcf(c_1860,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1859,c_1500,c_1501,c_1263,c_1198,c_1201,c_1188,c_452,c_88,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 11:28:02 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 2.13/1.29 % SZS status Started for theBenchmark.p
% 2.13/1.29 % SZS status Theorem for theBenchmark.p
% 2.13/1.29
% 2.13/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.13/1.29
% 2.13/1.29 % ------ iProver source info
% 2.13/1.29
% 2.13/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.13/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.13/1.29 % git: non_committed_changes: false
% 2.13/1.29
% 2.13/1.29 % ------ Parsing...
% 2.13/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.13/1.29
% 2.13/1.29 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.13/1.29
% 2.13/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.13/1.29
% 2.13/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.13/1.29 % ------ Proving...
% 2.13/1.29 % ------ Problem Properties
% 2.13/1.29
% 2.13/1.29 %
% 2.13/1.29 % clauses 32
% 2.13/1.29 % conjectures 1
% 2.13/1.29 % EPR 22
% 2.13/1.29 % Horn 16
% 2.13/1.29 % unary 11
% 2.13/1.29 % binary 6
% 2.13/1.29 % lits 79
% 2.13/1.29 % lits eq 2
% 2.13/1.29 % fd_pure 0
% 2.13/1.29 % fd_pseudo 0
% 2.13/1.29 % fd_cond 0
% 2.13/1.29 % fd_pseudo_cond 0
% 2.13/1.29 % AC symbols 0
% 2.13/1.29
% 2.13/1.29 % ------ Schedule dynamic 5 is on
% 2.13/1.29
% 2.13/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.13/1.29
% 2.13/1.29
% 2.13/1.29 % ------
% 2.13/1.29 % Current options:
% 2.13/1.29 % ------
% 2.13/1.29
% 2.13/1.29
% 2.13/1.29 %
% 2.13/1.29
% 2.13/1.29 % ------ Proving...
% 2.13/1.29 %
% 2.13/1.29
% 2.13/1.29 % SZS status Theorem for theBenchmark.p
% 2.13/1.29
% 2.13/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.13/1.29
% 2.13/1.29
%------------------------------------------------------------------------------