%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO218+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 01:20:24 PM UTC 2026
% Result : Theorem 2.08s 1.30s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 58 ~; 52 |; 14 &)
% ( 0 <=>; 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 69 ( 0 sgn 63 !; 6 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,axiom,
! [X0,X1] :
~ ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f14,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/sandbox2/benchmark/Axioms/GEO006+4.ax',cotno1) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X2)
& ~ convergent_lines(X0,X1) )
=> ~ unorthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X2)
& ~ convergent_lines(X0,X1) )
=> ~ unorthogonal_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f35,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f36,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,[],[f14]) ).
fof(f37,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,[],[f36]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
& ~ convergent_lines(X0,X1)
& unorthogonal_lines(X1,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f41,plain,
? [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
& ~ convergent_lines(X0,X1)
& unorthogonal_lines(X1,X2) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
( ~ unorthogonal_lines(sK0,sK2)
& ~ convergent_lines(sK0,sK1)
& unorthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f41]) ).
fof(f44,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f56,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| convergent_lines(X0,X1)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f63,plain,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f64,plain,
~ convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f42]) ).
fof(f65,plain,
unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f42]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f44]) ).
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,[],[f48]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X2,X1)
| convergent_lines(X2,X0)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_69,negated_conjecture,
unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f65]) ).
tcf(c_70,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f64]) ).
tcf(c_71,negated_conjecture,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f63]) ).
tcf(c_257,plain,
( unorthogonal_lines(sK0,sK2)
| convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_262,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| convergent_lines(sK2,X0)
| ~ convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] :
( convergent_lines(sK2,X1)
| convergent_lines(X0,X1)
| ~ convergent_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_274,plain,
! [X0: $i] :
( distinct_lines(sK2,X0)
| ~ convergent_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_282,plain,
( distinct_lines(sK2,sK2)
| ~ convergent_lines(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_283,plain,
~ distinct_lines(sK2,sK2),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_286,plain,
! [X0: $i] :
( convergent_lines(sK2,sK2)
| convergent_lines(X0,sK2)
| ~ convergent_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_273]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X1,sK2)
| convergent_lines(X1,X0)
| ~ unorthogonal_lines(X0,sK2)
| ~ convergent_lines(X0,sK2) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_365,plain,
! [X0: $i] :
( unorthogonal_lines(X0,sK2)
| convergent_lines(X0,sK1)
| ~ unorthogonal_lines(sK1,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_320]) ).
tcf(c_366,plain,
( unorthogonal_lines(sK0,sK2)
| convergent_lines(sK0,sK1)
| ~ unorthogonal_lines(sK1,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_365]) ).
tcf(c_381,plain,
( convergent_lines(sK2,sK2)
| convergent_lines(sK1,sK2)
| ~ convergent_lines(sK2,sK1) ),
inference(instantiation,[status(thm)],[c_286]) ).
tcf(c_419,plain,
( convergent_lines(sK0,sK1)
| convergent_lines(sK2,sK1)
| ~ convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_262]) ).
tcf(c_420,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_419,c_381,c_366,c_283,c_282,c_257,c_70,c_71,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 11:32:17 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.08/1.30 % SZS status Started for theBenchmark.p
% 2.08/1.30 % SZS status Theorem for theBenchmark.p
% 2.08/1.30
% 2.08/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.08/1.30
% 2.08/1.30 % ------ iProver source info
% 2.08/1.30
% 2.08/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.08/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.08/1.30 % git: non_committed_changes: false
% 2.08/1.30
% 2.08/1.30 % ------ Parsing...
% 2.08/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.08/1.30
% 2.08/1.30 % ------ Preprocessing... sf_s rm: 9 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.08/1.30
% 2.08/1.30 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.08/1.30 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.08/1.30 % ------ Proving...
% 2.08/1.30 % ------ Problem Properties
% 2.08/1.30
% 2.08/1.30 %
% 2.08/1.30 % clauses 13
% 2.08/1.30 % conjectures 3
% 2.08/1.30 % EPR 13
% 2.08/1.30 % Horn 6
% 2.08/1.30 % unary 5
% 2.08/1.30 % binary 2
% 2.08/1.30 % lits 30
% 2.08/1.30 % lits eq 0
% 2.08/1.30 % fd_pure 0
% 2.08/1.30 % fd_pseudo 0
% 2.08/1.30 % fd_cond 0
% 2.08/1.30 % fd_pseudo_cond 0
% 2.08/1.30 % AC symbols 0
% 2.08/1.30
% 2.08/1.30 % ------ Schedule EPR non Horn non eq is on
% 2.08/1.30
% 2.08/1.30 % ------ no equalities: superposition off
% 2.08/1.30
% 2.08/1.30 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.08/1.30
% 2.08/1.30
% 2.08/1.30 % ------
% 2.08/1.30 % Current options:
% 2.08/1.30 % ------
% 2.08/1.30
% 2.08/1.30
% 2.08/1.30 %
% 2.08/1.30
% 2.08/1.30 % ------ Proving...
% 2.08/1.30 %
% 2.08/1.30
% 2.08/1.30 % SZS status Theorem for theBenchmark.p
% 2.08/1.30
% 2.08/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.30
% 2.08/1.30
%------------------------------------------------------------------------------