%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO261+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 01:20:36 PM UTC 2026
% Result : Theorem 1.17s 1.48s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 22 |; 16 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 75 ( 0 sgn 65 !; 10 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a1_defns) ).
fof(f7,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
<=> ( unequally_directed_opposite_lines(X0,X1)
& unequally_directed_lines(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a7_defns) ).
fof(f19,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) )
=> ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax9_basics) ).
fof(f21,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(f37,conjecture,
! [X0,X1,X2,X3,X4] :
( ( incident_point_and_line(X3,X1)
& convergent_lines(X0,X1)
& between_on_line(X0,X2,X3,X4) )
=> divides_points(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( incident_point_and_line(X3,X1)
& convergent_lines(X0,X1)
& between_on_line(X0,X2,X3,X4) )
=> divides_points(X1,X2,X4) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f43,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ( unequally_directed_opposite_lines(X0,X1)
& unequally_directed_lines(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f46,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
=> unequally_directed_lines(X0,reverse_line(X1)) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f47,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( convergent_lines(X0,X1)
& between_on_line(X0,X2,X3,X4) )
=> divides_points(X1,X2,X4) ),
inference(pure_predicate_removal,[],[f38]) ).
fof(f49,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f53,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ( unequally_directed_opposite_lines(X0,X1)
& unequally_directed_lines(X0,X1) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f66,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f67,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f69,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f91,plain,
? [X0,X1,X2,X3,X4] :
( convergent_lines(X0,X1)
& between_on_line(X0,X2,X3,X4)
& ~ divides_points(X1,X2,X4) ),
inference(ennf_transformation,[],[f47]) ).
fof(f92,plain,
? [X0,X1,X2,X3,X4] :
( convergent_lines(X0,X1)
& between_on_line(X0,X2,X3,X4)
& ~ divides_points(X1,X2,X4) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
( convergent_lines(sK0,sK1)
& between_on_line(sK0,sK2,sK3,sK4)
& ~ divides_points(sK1,sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f99,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f100,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f120,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f123,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f69]) ).
fof(f124,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f69]) ).
fof(f142,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f93]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( unequally_directed_opposite_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f124]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f123]) ).
tcf(c_99,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f142]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_78,c_79,c_55,c_54,c_49,c_75]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_54,c_124]) ).
tcf(c_264,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_99,c_127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO261+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.57 % Computer : n014.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Wed Sep 23 11:44:50 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.61 Running first-order theorem proving
% 0.12/0.61 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
% 0.12/0.62
% 0.12/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.62
% 0.12/0.62 % Detected problem language: tptp
% 0.14/0.64 % Proving...
% 1.17/1.48 % SZS status Started for theBenchmark.p
% 1.17/1.48 % SZS status Theorem for theBenchmark.p
% 1.17/1.48
% 1.17/1.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.17/1.48
% 1.17/1.48 % ------ iProver source info
% 1.17/1.48
% 1.17/1.48 % git: date: 2026-07-19 20:42:38 +0200
% 1.17/1.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.17/1.48 % git: non_committed_changes: false
% 1.17/1.48
% 1.17/1.48 % ------ Parsing...
% 1.17/1.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.17/1.48
% 1.17/1.48 % ------ Preprocessing...%
% 1.17/1.48
% 1.17/1.48 % SZS status Theorem for theBenchmark.p
% 1.17/1.48
% 1.17/1.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.17/1.49
% 1.17/1.49
%------------------------------------------------------------------------------