%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO263+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 01:20:37 PM UTC 2026
% Result : Theorem 1.17s 1.08s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 81 ( 29 ~; 22 |; 23 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 62 !; 12 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(f37,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( convergent_lines(X1,X2)
& convergent_lines(X0,X2)
& convergent_lines(X0,X1)
& between_on_line(X0,X3,X4,X5) )
=> between_on_line(X1,intersection_point(X1,parallel_through_point(X2,X3)),intersection_point(X1,parallel_through_point(X2,X4)),intersection_point(X1,parallel_through_point(X2,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( convergent_lines(X1,X2)
& convergent_lines(X0,X2)
& convergent_lines(X0,X1)
& between_on_line(X0,X3,X4,X5) )
=> between_on_line(X1,intersection_point(X1,parallel_through_point(X2,X3)),intersection_point(X1,parallel_through_point(X2,X4)),intersection_point(X1,parallel_through_point(X2,X5))) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,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(f42,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
=> unequally_directed_lines(X0,reverse_line(X1)) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f43,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ( unequally_directed_opposite_lines(X0,X1)
& unequally_directed_lines(X0,X1) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f55,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(f56,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,[],[f55]) ).
fof(f58,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f80,plain,
? [X0,X1,X2,X3,X4,X5] :
( convergent_lines(X1,X2)
& convergent_lines(X0,X2)
& convergent_lines(X0,X1)
& between_on_line(X0,X3,X4,X5)
& ~ between_on_line(X1,intersection_point(X1,parallel_through_point(X2,X3)),intersection_point(X1,parallel_through_point(X2,X4)),intersection_point(X1,parallel_through_point(X2,X5))) ),
inference(ennf_transformation,[],[f38]) ).
fof(f81,plain,
? [X0,X1,X2,X3,X4,X5] :
( convergent_lines(X1,X2)
& convergent_lines(X0,X2)
& convergent_lines(X0,X1)
& between_on_line(X0,X3,X4,X5)
& ~ between_on_line(X1,intersection_point(X1,parallel_through_point(X2,X3)),intersection_point(X1,parallel_through_point(X2,X4)),intersection_point(X1,parallel_through_point(X2,X5))) ),
inference(flattening,[],[f80]) ).
fof(f87,plain,
( convergent_lines(sK1,sK2)
& convergent_lines(sK0,sK2)
& convergent_lines(sK0,sK1)
& between_on_line(sK0,sK3,sK4,sK5)
& ~ between_on_line(sK1,intersection_point(sK1,parallel_through_point(sK2,sK3)),intersection_point(sK1,parallel_through_point(sK2,sK4)),intersection_point(sK1,parallel_through_point(sK2,sK5))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f81]) ).
fof(f88,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f94,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f95,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f118,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,[],[f56]) ).
fof(f121,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f58]) ).
fof(f122,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f58]) ).
fof(f142,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f87]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( unequally_directed_opposite_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_79,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,[],[f118]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f122]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_103,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f142]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_82,c_83,c_56,c_55,c_49,c_79]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_132]) ).
tcf(c_294,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_103,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO263+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 % Computer : n012.cluster.edu
% 0.03/0.32 % Model : x86_64 x86_64
% 0.03/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.32 % Memory : 8046.5625MB
% 0.03/0.32 % OS : Linux 6.8.0-71-generic
% 0.03/0.32 % CPULimit : 300
% 0.03/0.32 % WCLimit : 300
% 0.03/0.32 % DateTime : Wed Sep 23 11:45:27 UTC 2026
% 0.03/0.32 % CPUTime :
% 0.03/0.32 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.34 Running first-order theorem proving
% 0.07/0.34 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
% 0.07/0.35
% 0.07/0.35 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.35
% 0.07/0.35 % Detected problem language: tptp
% 0.07/0.35 % Proving...
% 1.17/1.08 % SZS status Started for theBenchmark.p
% 1.17/1.08 % SZS status Theorem for theBenchmark.p
% 1.17/1.08
% 1.17/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.17/1.08
% 1.17/1.08 % ------ iProver source info
% 1.17/1.08
% 1.17/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 1.17/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.17/1.08 % git: non_committed_changes: false
% 1.17/1.08
% 1.17/1.08 % ------ Parsing...
% 1.17/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.17/1.08
% 1.17/1.08 % ------ Preprocessing...%
% 1.17/1.08
% 1.17/1.08 % SZS status Theorem for theBenchmark.p
% 1.17/1.08
% 1.17/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.17/1.08
% 1.17/1.08
%------------------------------------------------------------------------------