%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO194+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 : n014.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 01:20:15 PM UTC 2026
% Result : Theorem 3.77s 1.21s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 13 unt; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 165 ( 60 ~; 79 |; 17 &)
% ( 0 <=>; 9 =>; 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 : 5 ( 4 usr; 1 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/sandbox/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/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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> apart_point_and_line(intersection_point(X0,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> apart_point_and_line(intersection_point(X0,X2),X1) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f39,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(flattening,[],[f38]) ).
fof(f42,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f43,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f59]) ).
fof(f61,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(f62,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,[],[f61]) ).
fof(f67,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(f68,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f67]) ).
fof(f78,plain,
( convergent_lines(sK0,sK2)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK1)
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& ~ 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)],[f39]) ).
fof(f79,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f78]) ).
fof(f81,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f82,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f78]) ).
fof(f83,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f85,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f86,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f88,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f97,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,[],[f62]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_49,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f83]) ).
tcf(c_50,negated_conjecture,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f82]) ).
tcf(c_51,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f81]) ).
tcf(c_53,negated_conjecture,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f79]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_58,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f88]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_92,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_454,plain,
( ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_456,plain,
( ~ convergent_lines(sK0,sK2)
| ~ apart_point_and_line(intersection_point(sK0,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_457,plain,
( ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_459,plain,
( ~ convergent_lines(sK0,sK2)
| ~ apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_468,plain,
! [X0: $i] :
( distinct_lines(sK1,X0)
| convergent_lines(sK0,X0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_469,plain,
( distinct_lines(sK1,sK0)
| convergent_lines(sK0,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_468]) ).
tcf(c_474,plain,
! [X0: $i] :
( apart_point_and_line(X0,sK2)
| distinct_points(intersection_point(sK0,sK1),X0)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X1,sK1)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(sK1,X2)
| ~ distinct_points(X0,X1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1066,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),X1)
| ~ distinct_lines(sK1,X1)
| ~ distinct_points(intersection_point(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_519]) ).
tcf(c_1523,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK2)
| distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_474]) ).
tcf(c_4190,plain,
! [X0: $i] :
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK2),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK2),X0)
| ~ distinct_lines(sK1,X0)
| ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_1066]) ).
tcf(c_4191,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK1)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ distinct_lines(sK1,sK0)
| ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_4190]) ).
tcf(c_4192,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4191,c_1523,c_469,c_459,c_457,c_456,c_454,c_49,c_50,c_92,c_51,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO194+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 11:24:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 3.77/1.21 % SZS status Started for theBenchmark.p
% 3.77/1.21 % SZS status Theorem for theBenchmark.p
% 3.77/1.21
% 3.77/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.77/1.21
% 3.77/1.21 % ------ iProver source info
% 3.77/1.21
% 3.77/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 3.77/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.77/1.21 % git: non_committed_changes: false
% 3.77/1.21
% 3.77/1.21 % ------ Parsing...
% 3.77/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.77/1.21
% 3.77/1.21 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.77/1.21
% 3.77/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.77/1.21 % ------ Proving...
% 3.77/1.21 % ------ Problem Properties
% 3.77/1.21
% 3.77/1.21 %
% 3.77/1.21 % clauses 33
% 3.77/1.21 % conjectures 5
% 3.77/1.21 % EPR 23
% 3.77/1.21 % Horn 17
% 3.77/1.21 % unary 12
% 3.77/1.21 % binary 6
% 3.77/1.21 % lits 80
% 3.77/1.21 % lits eq 0
% 3.77/1.21 % fd_pure 0
% 3.77/1.21 % fd_pseudo 0
% 3.77/1.21 % fd_cond 0
% 3.77/1.21 % fd_pseudo_cond 0
% 3.77/1.21 % AC symbols 0
% 3.77/1.21
% 3.77/1.21 % ------ Schedule dynamic 5 is on
% 3.77/1.21
% 3.77/1.21 % ------ no equalities: superposition off
% 3.77/1.21
% 3.77/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.77/1.21
% 3.77/1.21
% 3.77/1.21 % ------
% 3.77/1.21 % Current options:
% 3.77/1.21 % ------
% 3.77/1.21
% 3.77/1.21
% 3.77/1.21 %
% 3.77/1.21
% 3.77/1.21 % ------ Proving...
% 3.77/1.21 %
% 3.77/1.21
% 3.77/1.21 % SZS status Theorem for theBenchmark.p
% 3.77/1.21
% 3.77/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.77/1.21
% 3.77/1.21
%------------------------------------------------------------------------------