%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO218+1 : 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 : n006.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 1.97s 6.30s
% Output : CNFRefutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 7 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 136 ( 58 ~; 58 |; 15 &)
% ( 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 74 ( 0 sgn 68 !; 6 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f15,axiom,
! [X0,X1] :
~ ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f16,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(f17,axiom,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X2)
& ~ unorthogonal_lines(X0,X1) )
=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(f18,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(f19,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X2)
& ~ convergent_lines(X0,X1) )
=> ~ unorthogonal_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f24]) ).
fof(f38,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,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,[],[f16]) ).
fof(f40,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,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f42,plain,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
& ~ convergent_lines(X0,X1)
& unorthogonal_lines(X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
? [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
& ~ convergent_lines(X0,X1)
& unorthogonal_lines(X1,X2) ),
inference(flattening,[],[f43]) ).
fof(f45,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)],[f44]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f60,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f63,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| convergent_lines(X0,X1)
| ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f65,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,plain,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f45]) ).
fof(f67,plain,
~ convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f45]) ).
fof(f68,plain,
unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f45]) ).
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,[],[f51]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
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,[],[f63]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X2,X1)
| unorthogonal_lines(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_69,negated_conjecture,
unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f68]) ).
tcf(c_70,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f67]) ).
tcf(c_71,negated_conjecture,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f66]) ).
tcf(c_253,plain,
( unorthogonal_lines(sK0,sK2)
| convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_259,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| convergent_lines(sK2,X0)
| ~ convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X1,sK2)
| unorthogonal_lines(X1,X0)
| ~ convergent_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_271,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_280,plain,
( unorthogonal_lines(sK0,sK2)
| ~ convergent_lines(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_269]) ).
tcf(c_314,plain,
! [X0: $i] :
( convergent_lines(sK2,sK2)
| convergent_lines(X0,sK2)
| ~ convergent_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_271]) ).
tcf(c_343,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_372,plain,
! [X0: $i] :
( unorthogonal_lines(X0,sK2)
| convergent_lines(X0,sK1)
| ~ unorthogonal_lines(sK1,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_343]) ).
tcf(c_373,plain,
( unorthogonal_lines(sK0,sK2)
| convergent_lines(sK0,sK1)
| ~ unorthogonal_lines(sK1,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_372]) ).
tcf(c_388,plain,
( convergent_lines(sK2,sK2)
| convergent_lines(sK1,sK2)
| ~ convergent_lines(sK2,sK1) ),
inference(instantiation,[status(thm)],[c_314]) ).
tcf(c_423,plain,
( convergent_lines(sK0,sK1)
| convergent_lines(sK2,sK1)
| ~ convergent_lines(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_259]) ).
tcf(c_424,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_423,c_388,c_373,c_280,c_253,c_70,c_71,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.38 % Computer : n006.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Wed Sep 23 11:32:03 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 1.97/6.30 % SZS status Started for theBenchmark.p
% 1.97/6.30 % SZS status Theorem for theBenchmark.p
% 1.97/6.30
% 1.97/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.97/6.30
% 1.97/6.30 % ------ iProver source info
% 1.97/6.30
% 1.97/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.97/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.97/6.30 % git: non_committed_changes: false
% 1.97/6.30
% 1.97/6.30 % ------ Parsing...
% 1.97/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.97/6.30
% 1.97/6.30 % ------ Preprocessing... sf_s rm: 9 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.97/6.30
% 1.97/6.30 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.97/6.30 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.97/6.30 % ------ Proving...
% 1.97/6.30 % ------ Problem Properties
% 1.97/6.30
% 1.97/6.30 %
% 1.97/6.30 % clauses 13
% 1.97/6.30 % conjectures 3
% 1.97/6.30 % EPR 13
% 1.97/6.30 % Horn 5
% 1.97/6.30 % unary 5
% 1.97/6.30 % binary 1
% 1.97/6.30 % lits 31
% 1.97/6.30 % lits eq 0
% 1.97/6.30 % fd_pure 0
% 1.97/6.30 % fd_pseudo 0
% 1.97/6.30 % fd_cond 0
% 1.97/6.30 % fd_pseudo_cond 0
% 1.97/6.30 % AC symbols 0
% 1.97/6.30
% 1.97/6.30 % ------ Schedule EPR non Horn non eq is on
% 1.97/6.30
% 1.97/6.30 % ------ no equalities: superposition off
% 1.97/6.30
% 1.97/6.30 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.97/6.30
% 1.97/6.30
% 1.97/6.30 % ------
% 1.97/6.30 % Current options:
% 1.97/6.30 % ------
% 1.97/6.30
% 1.97/6.30
% 1.97/6.30 %
% 1.97/6.30
% 1.97/6.30 % ------ Proving...
% 1.97/6.30 %
% 1.97/6.30
% 1.97/6.30 % SZS status Theorem for theBenchmark.p
% 1.97/6.30
% 1.97/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.97/6.30
% 1.97/6.30
%------------------------------------------------------------------------------