%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO265+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 01:20:37 PM UTC 2026
% Result : Theorem 2.66s 1.30s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 14 unt; 1 def)
% Number of atoms : 118 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 119 ( 60 ~; 41 |; 8 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 83 !; 2 ?; 27 :)
% 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(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(f5,axiom,
! [X0,X1] :
( equally_directed_opposite_lines(X0,X1)
<=> ~ unequally_directed_opposite_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a5_defns) ).
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,X1] :
( equally_directed_lines(X0,reverse_line(X1))
=> equally_directed_opposite_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( equally_directed_lines(X0,reverse_line(X1))
=> equally_directed_opposite_lines(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( equally_directed_lines(X0,X1)
=> ~ unequally_directed_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f42,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
=> equally_directed_opposite_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f43,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
=> unequally_directed_lines(X0,reverse_line(X1)) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f44,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f47,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f57,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(f58,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,[],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f69,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(f70,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,[],[f69]) ).
fof(f82,plain,
? [X0,X1] :
( equally_directed_lines(X0,reverse_line(X1))
& ~ equally_directed_opposite_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f83,plain,
( equally_directed_lines(sK0,reverse_line(sK1))
& ~ equally_directed_opposite_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f87,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f100,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f101,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,[],[f58]) ).
fof(f104,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f60]) ).
fof(f105,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f60]) ).
fof(f112,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,[],[f70]) ).
fof(f123,plain,
equally_directed_lines(sK0,reverse_line(sK1)),
inference(cnf_transformation,[],[f83]) ).
fof(f124,plain,
~ equally_directed_opposite_lines(sK0,sK1),
inference(cnf_transformation,[],[f83]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( equally_directed_opposite_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_66,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,[],[f101]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f105]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f104]) ).
tcf(c_78,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,[],[f112]) ).
tcf(c_88,negated_conjecture,
~ equally_directed_opposite_lines(sK0,sK1),
inference(cnf_transformation,[],[f124]) ).
tcf(c_89,negated_conjecture,
equally_directed_lines(sK0,reverse_line(sK1)),
inference(cnf_transformation,[],[f123]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_78,c_69,c_70,c_66]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_49,c_118]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_141]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( equally_directed_opposite_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
tcf(c_149,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_337,plain,
unequally_directed_opposite_lines(sK0,sK1),
inference(resolution,[status(thm)],[c_143,c_88]) ).
tcf(c_342,plain,
~ unequally_directed_lines(sK0,sK1),
inference(resolution,[status(thm)],[c_142,c_337]) ).
tcf(c_357,plain,
~ unequally_directed_lines(sK0,reverse_line(sK1)),
inference(resolution,[status(thm)],[c_149,c_89]) ).
tcf(c_402,definition,
iPr_def_10 = reverse_line(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_403,plain,
~ unequally_directed_lines(sK0,iPr_def_10),
inference(demodulation,[status(thm)],[c_357,c_402]) ).
tcf(c_562,plain,
! [X0: $i] :
( unequally_directed_lines(X0,iPr_def_10)
| unequally_directed_lines(X0,sK1) ),
inference(superposition,[status(thm)],[c_402,c_65]) ).
tcf(c_569,plain,
( unequally_directed_lines(sK0,iPr_def_10)
| unequally_directed_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_562]) ).
tcf(c_570,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_569,c_403,c_342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO265+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % 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 11:46:34 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 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...
% 2.66/1.30 % SZS status Started for theBenchmark.p
% 2.66/1.30 % SZS status Theorem for theBenchmark.p
% 2.66/1.30
% 2.66/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.66/1.30
% 2.66/1.30 % ------ iProver source info
% 2.66/1.30
% 2.66/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.66/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.66/1.30 % git: non_committed_changes: false
% 2.66/1.30
% 2.66/1.30 % ------ Parsing...
% 2.66/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.66/1.30
% 2.66/1.30 % ------ Preprocessing... sf_s rm: 16 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.66/1.30
% 2.66/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.66/1.30
% 2.66/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.66/1.30 % ------ Proving...
% 2.66/1.30 % ------ Problem Properties
% 2.66/1.30
% 2.66/1.30 %
% 2.66/1.30 % clauses 8
% 2.66/1.30 % conjectures 0
% 2.66/1.30 % EPR 4
% 2.66/1.30 % Horn 6
% 2.66/1.30 % unary 5
% 2.66/1.30 % binary 2
% 2.66/1.30 % lits 12
% 2.66/1.30 % lits eq 1
% 2.66/1.30 % fd_pure 0
% 2.66/1.30 % fd_pseudo 0
% 2.66/1.30 % fd_cond 0
% 2.66/1.30 % fd_pseudo_cond 0
% 2.66/1.30 % AC symbols 0
% 2.66/1.30
% 2.66/1.30 % ------ Schedule dynamic 5 is on
% 2.66/1.30
% 2.66/1.30 % ------ no conjectures: strip conj schedule
% 2.66/1.30
% 2.66/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.66/1.30
% 2.66/1.30
% 2.66/1.30 % ------
% 2.66/1.30 % Current options:
% 2.66/1.30 % ------
% 2.66/1.30
% 2.66/1.30
% 2.66/1.30 %
% 2.66/1.30
% 2.66/1.30 % ------ Proving...
% 2.66/1.30 %
% 2.66/1.30
% 2.66/1.30 % SZS status Theorem for theBenchmark.p
% 2.66/1.30
% 2.66/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.66/1.30
% 2.66/1.30
%------------------------------------------------------------------------------