%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO228+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 01:20:28 PM UTC 2026
% Result : Theorem 2.18s 6.55s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 11 unt; 1 def)
% Number of atoms : 136 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 160 ( 74 ~; 64 |; 16 &)
% ( 3 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 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 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 63 !; 6 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
<=> ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',con_def) ).
fof(f14,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/GEO007+0.ax',oag9) ).
fof(f16,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag11) ).
fof(f18,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1)
& line(X1)
& line(X0) )
=> point(intersection_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco2) ).
fof(f32,conjecture,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
<=> ( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( ~ convergent_lines(X0,X1)
<=> ( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f46,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,[],[f14]) ).
fof(f47,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,[],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f52,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(flattening,[],[f52]) ).
fof(f70,plain,
? [X0,X1] :
( ~ convergent_lines(X0,X1)
<~> ( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f71,plain,
! [X0,X1] :
( ( ~ convergent_lines(X0,X1)
| ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) ) )
& ( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| convergent_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f72,plain,
! [X0,X1] :
( ( ~ convergent_lines(X0,X1)
| ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) ) )
& ( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| convergent_lines(X0,X1) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0,X1] :
( ( ~ convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) )
& ( convergent_lines(X0,X1)
| ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f74,plain,
? [X0,X1] :
( ( ~ convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) )
& ( convergent_lines(X0,X1)
| ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) ) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
( ( ~ convergent_lines(sK0,sK1)
| ~ unequally_directed_lines(sK0,reverse_line(sK1))
| ~ unequally_directed_lines(sK0,sK1) )
& ( convergent_lines(sK0,sK1)
| ( unequally_directed_lines(sK0,reverse_line(sK1))
& unequally_directed_lines(sK0,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f74]) ).
fof(f78,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f79,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f80,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f92,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,[],[f47]) ).
fof(f95,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f96,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f49]) ).
fof(f98,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f115,plain,
( convergent_lines(sK0,sK1)
| unequally_directed_lines(sK0,reverse_line(sK1)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f116,plain,
( convergent_lines(sK0,sK1)
| unequally_directed_lines(sK0,sK1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
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,[],[f92]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f96]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f95]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( point(intersection_point(X0,X1))
| ~ line(X1)
| ~ line(X0)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_87,negated_conjecture,
( unequally_directed_lines(sK0,sK1)
| convergent_lines(sK0,sK1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_88,negated_conjecture,
( convergent_lines(sK0,sK1)
| unequally_directed_lines(sK0,reverse_line(sK1)) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_52,c_68,c_69,c_52,c_53,c_65]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_53,c_68,c_69,c_52,c_53,c_65]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_51,c_106]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(renaming,[status(thm)],[c_139]) ).
tcf(c_149,plain,
unequally_directed_lines(sK0,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_87,c_111]) ).
tcf(c_150,plain,
unequally_directed_lines(sK0,reverse_line(sK1)),
inference(backward_subsumption_resolution,[status(thm)],[c_88,c_111]) ).
tcf(c_260,definition,
iPr_def_10 = reverse_line(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_261,plain,
unequally_directed_lines(sK0,iPr_def_10),
inference(demodulation,[status(thm)],[c_150,c_260]) ).
tcf(c_359,plain,
! [X0: $i] :
( ~ unequally_directed_lines(X0,iPr_def_10)
| ~ unequally_directed_lines(X0,sK1) ),
inference(superposition,[status(thm)],[c_260,c_140]) ).
tcf(c_362,plain,
( ~ unequally_directed_lines(sK0,iPr_def_10)
| ~ unequally_directed_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_359]) ).
tcf(c_363,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_362,c_261,c_149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO228+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.57 % Computer : n001.cluster.edu
% 0.11/5.57 % Model : x86_64 x86_64
% 0.11/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.57 % Memory : 8046.5625MB
% 0.11/5.57 % OS : Linux 6.8.0-71-generic
% 0.11/5.57 % CPULimit : 300
% 0.11/5.57 % WCLimit : 300
% 0.11/5.57 % DateTime : Wed Sep 23 11:40:41 UTC 2026
% 0.11/5.57 % CPUTime :
% 0.11/5.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.63 Running first-order theorem proving
% 0.16/5.63 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
% 0.16/5.64
% 0.16/5.64 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.64
% 0.16/5.65 % Detected problem language: tptp
% 0.16/5.66 % Proving...
% 2.18/6.55 % SZS status Started for theBenchmark.p
% 2.18/6.55 % SZS status Theorem for theBenchmark.p
% 2.18/6.55
% 2.18/6.55 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.18/6.55
% 2.18/6.55 % ------ iProver source info
% 2.18/6.55
% 2.18/6.55 % git: date: 2026-07-19 20:42:38 +0200
% 2.18/6.55 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.18/6.55 % git: non_committed_changes: false
% 2.18/6.55
% 2.18/6.55 % ------ Parsing...
% 2.18/6.55 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.18/6.55
% 2.18/6.55 % ------ Preprocessing... sf_s rm: 16 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.18/6.55
% 2.18/6.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.18/6.55
% 2.18/6.55 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.18/6.55 % ------ Proving...
% 2.18/6.55 % ------ Problem Properties
% 2.18/6.55
% 2.18/6.55 %
% 2.18/6.55 % clauses 8
% 2.18/6.55 % conjectures 0
% 2.18/6.55 % EPR 4
% 2.18/6.55 % Horn 7
% 2.18/6.55 % unary 6
% 2.18/6.55 % binary 1
% 2.18/6.55 % lits 11
% 2.18/6.55 % lits eq 1
% 2.18/6.55 % fd_pure 0
% 2.18/6.55 % fd_pseudo 0
% 2.18/6.55 % fd_cond 0
% 2.18/6.55 % fd_pseudo_cond 0
% 2.18/6.55 % AC symbols 0
% 2.18/6.55
% 2.18/6.55 % ------ Schedule dynamic 5 is on
% 2.18/6.55
% 2.18/6.55 % ------ no conjectures: strip conj schedule
% 2.18/6.55
% 2.18/6.55 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.18/6.55
% 2.18/6.55
% 2.18/6.55 % ------
% 2.18/6.55 % Current options:
% 2.18/6.55 % ------
% 2.18/6.55
% 2.18/6.55
% 2.18/6.55 %
% 2.18/6.55
% 2.18/6.55 % ------ Proving...
% 2.18/6.55 %
% 2.18/6.55
% 2.18/6.55 % SZS status Theorem for theBenchmark.p
% 2.18/6.55
% 2.18/6.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.18/6.55
% 2.18/6.55
%------------------------------------------------------------------------------