%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO219+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 : n015.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 01:20:25 PM UTC 2026
% Result : Theorem 2.02s 1.27s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 10 unt; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 133 ( 57 ~; 54 |; 15 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 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; 3 con; 0-0 aty)
% Number of variables : 91 ( 0 sgn 85 !; 6 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f24,axiom,
! [X0,X1] :
~ ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( ( ~ unorthogonal_lines(X0,X2)
| ~ convergent_lines(X0,X2) )
& ( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ) )
=> ( ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',cotno1) ).
fof(f33,axiom,
! [X0,X1] :
( parallel_lines(X0,X1)
<=> ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a3) ).
fof(f35,axiom,
! [X0,X1] :
( orthogonal_lines(X0,X1)
<=> ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a5) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( parallel_lines(X0,X2)
& orthogonal_lines(X0,X1) )
=> orthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( parallel_lines(X0,X2)
& orthogonal_lines(X0,X1) )
=> orthogonal_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( parallel_lines(X0,X1)
=> ~ convergent_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f43]) ).
fof(f64,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) )
| ( unorthogonal_lines(X0,X1)
& convergent_lines(X0,X1) )
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) )
| ( unorthogonal_lines(X0,X1)
& convergent_lines(X0,X1) )
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f65]) ).
fof(f77,plain,
! [X0,X1] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1,X2] :
( parallel_lines(X0,X2)
& orthogonal_lines(X0,X1)
& ~ orthogonal_lines(X1,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1,X2] :
( parallel_lines(X0,X2)
& orthogonal_lines(X0,X1)
& ~ orthogonal_lines(X1,X2) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) )
& ( unorthogonal_lines(X0,X1)
| orthogonal_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f81,plain,
( parallel_lines(sK0,sK2)
& orthogonal_lines(sK0,sK1)
& ~ orthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f79]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f108,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f110,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f118,plain,
! [X0,X1] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f119,plain,
! [X0,X1] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
parallel_lines(sK0,sK2),
inference(cnf_transformation,[],[f81]) ).
fof(f122,plain,
orthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f81]) ).
fof(f123,plain,
~ orthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f81]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X2,X0)
| convergent_lines(X2,X1)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( orthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_88,negated_conjecture,
~ orthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f123]) ).
tcf(c_89,negated_conjecture,
orthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f122]) ).
tcf(c_90,negated_conjecture,
parallel_lines(sK0,sK2),
inference(cnf_transformation,[],[f121]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_109]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| orthogonal_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( orthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_111]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( ~ orthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_75,c_87]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(renaming,[status(thm)],[c_125]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( orthogonal_lines(X0,X1)
| unorthogonal_lines(X2,X0)
| convergent_lines(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_78,c_112]) ).
tcf(c_400,plain,
~ convergent_lines(sK0,sK2),
inference(resolution,[status(thm)],[c_121,c_90]) ).
tcf(c_497,plain,
! [X0: $i] :
( unorthogonal_lines(X0,sK1)
| convergent_lines(X0,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(resolution,[status(thm)],[c_202,c_88]) ).
tcf(c_498,plain,
( unorthogonal_lines(sK0,sK1)
| convergent_lines(sK0,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_497]) ).
tcf(c_567,plain,
convergent_lines(sK0,sK1),
inference(resolution,[status(thm)],[c_126,c_89]) ).
tcf(c_571,plain,
~ unorthogonal_lines(sK0,sK1),
inference(resolution,[status(thm)],[c_110,c_89]) ).
tcf(c_964,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| convergent_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_995,plain,
( convergent_lines(sK0,sK2)
| convergent_lines(sK1,sK2)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_964]) ).
tcf(c_996,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_995,c_571,c_567,c_498,c_400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO219+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 11:36:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.02/1.27 % SZS status Started for theBenchmark.p
% 2.02/1.27 % SZS status Theorem for theBenchmark.p
% 2.02/1.27
% 2.02/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.02/1.27
% 2.02/1.27 % ------ iProver source info
% 2.02/1.27
% 2.02/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.02/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.02/1.27 % git: non_committed_changes: false
% 2.02/1.27
% 2.02/1.27 % ------ Parsing...
% 2.02/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.02/1.27
% 2.02/1.27 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.02/1.27
% 2.02/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.02/1.27 % ------ Proving...
% 2.02/1.27 % ------ Problem Properties
% 2.02/1.27
% 2.02/1.27 %
% 2.02/1.27 % clauses 33
% 2.02/1.27 % conjectures 0
% 2.02/1.27 % EPR 25
% 2.02/1.27 % Horn 17
% 2.02/1.27 % unary 12
% 2.02/1.27 % binary 6
% 2.02/1.27 % lits 80
% 2.02/1.27 % lits eq 0
% 2.02/1.27 % fd_pure 0
% 2.02/1.27 % fd_pseudo 0
% 2.02/1.27 % fd_cond 0
% 2.02/1.27 % fd_pseudo_cond 0
% 2.02/1.27 % AC symbols 0
% 2.02/1.27
% 2.02/1.27 % ------ Schedule dynamic 5 is on
% 2.02/1.27
% 2.02/1.27 % ------ no conjectures: strip conj schedule
% 2.02/1.27
% 2.02/1.27 % ------ no equalities: superposition off
% 2.02/1.27
% 2.02/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.02/1.27
% 2.02/1.27
% 2.02/1.27 % ------
% 2.02/1.27 % Current options:
% 2.02/1.27 % ------
% 2.02/1.27
% 2.02/1.27
% 2.02/1.27 %
% 2.02/1.27
% 2.02/1.27 % ------ Proving...
% 2.02/1.27 %
% 2.02/1.27
% 2.02/1.27 % SZS status Theorem for theBenchmark.p
% 2.02/1.27
% 2.02/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.02/1.27
% 2.02/1.27
%------------------------------------------------------------------------------