%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO233+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 : n013.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 01:20:29 PM UTC 2026
% Result : Theorem 0.71s 1.28s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 104 ( 56 ~; 38 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 72 !; 1 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( equally_directed_lines(X0,X1)
<=> ~ unequally_directed_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a4_defns) ).
fof(f15,axiom,
! [X0] : equally_directed_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax5_basics) ).
fof(f18,axiom,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax8_basics) ).
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(f27,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) )
=> ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax6_cons_objs) ).
fof(f37,conjecture,
! [X0] : equally_directed_lines(reverse_line(reverse_line(X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0] : equally_directed_lines(reverse_line(reverse_line(X0)),X0),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f51,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(f52,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,[],[f51]) ).
fof(f54,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f63,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f64,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
inference(flattening,[],[f63]) ).
fof(f76,plain,
? [X0] : ~ equally_directed_lines(reverse_line(reverse_line(X0)),X0),
inference(ennf_transformation,[],[f38]) ).
fof(f77,plain,
! [X0,X1] :
( ( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) )
& ( unequally_directed_lines(X0,X1)
| equally_directed_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f78,plain,
~ equally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f76]) ).
fof(f80,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f81,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f88,plain,
! [X0] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f94,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f95,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,[],[f52]) ).
fof(f98,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f99,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f54]) ).
fof(f106,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f117,plain,
~ equally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(cnf_transformation,[],[f78]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_58,plain,
! [X0: $i] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f88]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_65,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,[],[f95]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f99]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f98]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_87,negated_conjecture,
~ equally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(cnf_transformation,[],[f117]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_77,c_68,c_69,c_65]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_135]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( equally_directed_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| equally_directed_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_137]) ).
tcf(c_317,plain,
! [X0: $i] : ~ unequally_directed_lines(X0,X0),
inference(resolution,[status(thm)],[c_136,c_58]) ).
tcf(c_327,plain,
unequally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(resolution,[status(thm)],[c_138,c_87]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_116]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(renaming,[status(thm)],[c_334]) ).
tcf(c_531,plain,
! [X0: $i] : unequally_directed_lines(reverse_line(X0),X0),
inference(superposition,[status(thm)],[c_64,c_317]) ).
tcf(c_548,plain,
! [X0: $i] : ~ unequally_directed_lines(reverse_line(reverse_line(X0)),X0),
inference(superposition,[status(thm)],[c_531,c_335]) ).
tcf(c_555,plain,
~ unequally_directed_lines(reverse_line(reverse_line(sK0)),sK0),
inference(instantiation,[status(thm)],[c_548]) ).
tcf(c_556,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_555,c_327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO233+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n013.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Wed Sep 23 11:35:23 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 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
% 0.14/0.63
% 0.14/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.63
% 0.14/0.63 % Detected problem language: tptp
% 0.14/0.64 % Proving...
% 0.71/1.28 % SZS status Started for theBenchmark.p
% 0.71/1.28 % SZS status Theorem for theBenchmark.p
% 0.71/1.28
% 0.71/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.71/1.28
% 0.71/1.28 % ------ iProver source info
% 0.71/1.28
% 0.71/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.71/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.71/1.28 % git: non_committed_changes: false
% 0.71/1.28
% 0.71/1.28 % ------ Parsing...
% 0.71/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.71/1.28
% 0.71/1.28 % ------ Preprocessing... sf_s rm: 16 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.71/1.28
% 0.71/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.71/1.28
% 0.71/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.71/1.28 % ------ Proving...
% 0.71/1.28 % ------ Problem Properties
% 0.71/1.28
% 0.71/1.28 %
% 0.71/1.28 % clauses 8
% 0.71/1.28 % conjectures 0
% 0.71/1.28 % EPR 3
% 0.71/1.28 % Horn 6
% 0.71/1.28 % unary 5
% 0.71/1.28 % binary 2
% 0.71/1.28 % lits 12
% 0.71/1.28 % lits eq 2
% 0.71/1.28 % fd_pure 0
% 0.71/1.28 % fd_pseudo 0
% 0.71/1.28 % fd_cond 0
% 0.71/1.28 % fd_pseudo_cond 0
% 0.71/1.28 % AC symbols 0
% 0.71/1.28
% 0.71/1.28 % ------ Schedule dynamic 5 is on
% 0.71/1.28
% 0.71/1.28 % ------ no conjectures: strip conj schedule
% 0.71/1.28
% 0.71/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.71/1.28
% 0.71/1.28
% 0.71/1.28 % ------
% 0.71/1.28 % Current options:
% 0.71/1.28 % ------
% 0.71/1.28
% 0.71/1.28
% 0.71/1.28 %
% 0.71/1.28
% 0.71/1.28 % ------ Proving...
% 0.71/1.28 %
% 0.71/1.28
% 0.71/1.28 % SZS status Theorem for theBenchmark.p
% 0.71/1.28
% 0.71/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.71/1.28
% 0.71/1.28
%------------------------------------------------------------------------------