%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO212+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 : n009.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 01:20:22 PM UTC 2026
% Result : Theorem 0.31s 6.10s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 40 ~; 50 |; 13 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 59 ( 0 sgn 53 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart3) ).
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(f16,axiom,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( unorthogonal_lines(X0,X1)
& convergent_lines(X0,X1) )
=> ( ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(f21,conjecture,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f27]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ),
inference(flattening,[],[f42]) ).
fof(f46,plain,
? [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X1,X2)
& ~ convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
? [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X1,X2)
& ~ convergent_lines(X0,X2) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( unorthogonal_lines(sK0,sK1)
& ~ unorthogonal_lines(sK1,sK2)
& ~ convergent_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f47]) ).
fof(f51,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f66,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f74,plain,
unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
~ convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f48]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f51]) ).
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,[],[f54]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_74,negated_conjecture,
~ convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f76]) ).
tcf(c_75,negated_conjecture,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f75]) ).
tcf(c_76,negated_conjecture,
unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f74]) ).
tcf(c_364,plain,
( unorthogonal_lines(sK1,sK2)
| convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_367,plain,
! [X0: $i] :
( unorthogonal_lines(sK1,sK2)
| convergent_lines(X0,sK2)
| ~ unorthogonal_lines(X0,sK1)
| ~ convergent_lines(X0,sK1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_368,plain,
( unorthogonal_lines(sK1,sK2)
| convergent_lines(sK0,sK2)
| ~ unorthogonal_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_367]) ).
tcf(c_381,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| convergent_lines(sK2,X0)
| ~ convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_383,plain,
( convergent_lines(sK1,sK0)
| convergent_lines(sK2,sK0)
| ~ convergent_lines(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_381]) ).
tcf(c_444,plain,
~ convergent_lines(sK1,sK1),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i] :
( convergent_lines(sK1,X1)
| convergent_lines(X0,X1)
| ~ convergent_lines(sK1,X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_513,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_792,plain,
! [X0: $i] :
( convergent_lines(sK1,sK1)
| convergent_lines(X0,sK1)
| ~ convergent_lines(sK1,X0) ),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_793,plain,
( convergent_lines(sK1,sK1)
| convergent_lines(sK0,sK1)
| ~ convergent_lines(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_1323,plain,
~ convergent_lines(sK2,sK2),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_2982,plain,
! [X0: $i] :
( convergent_lines(sK2,sK2)
| convergent_lines(X0,sK2)
| ~ convergent_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_513]) ).
tcf(c_2983,plain,
( convergent_lines(sK2,sK2)
| convergent_lines(sK0,sK2)
| ~ convergent_lines(sK2,sK0) ),
inference(instantiation,[status(thm)],[c_2982]) ).
tcf(c_2984,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2983,c_1323,c_793,c_444,c_383,c_368,c_364,c_74,c_75,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO212+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.39 % Computer : n009.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Wed Sep 23 11:31:04 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 0.31/6.10 % SZS status Started for theBenchmark.p
% 0.31/6.10 % SZS status Theorem for theBenchmark.p
% 0.31/6.10
% 0.31/6.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.31/6.10
% 0.31/6.10 % ------ iProver source info
% 0.31/6.10
% 0.31/6.10 % git: date: 2026-07-19 20:42:38 +0200
% 0.31/6.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.31/6.10 % git: non_committed_changes: false
% 0.31/6.10
% 0.31/6.10 % ------ Parsing...
% 0.31/6.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.31/6.10
% 0.31/6.10 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.31/6.10
% 0.31/6.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.31/6.10 % ------ Proving...
% 0.31/6.10 % ------ Problem Properties
% 0.31/6.10
% 0.31/6.10 %
% 0.31/6.10 % clauses 27
% 0.31/6.10 % conjectures 3
% 0.31/6.10 % EPR 19
% 0.31/6.10 % Horn 15
% 0.31/6.10 % unary 10
% 0.31/6.10 % binary 2
% 0.31/6.10 % lits 68
% 0.31/6.10 % lits eq 0
% 0.31/6.10 % fd_pure 0
% 0.31/6.10 % fd_pseudo 0
% 0.31/6.10 % fd_cond 0
% 0.31/6.10 % fd_pseudo_cond 0
% 0.31/6.10 % AC symbols 0
% 0.31/6.10
% 0.31/6.10 % ------ Schedule dynamic 5 is on
% 0.31/6.10
% 0.31/6.10 % ------ no equalities: superposition off
% 0.31/6.10
% 0.31/6.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.31/6.10
% 0.31/6.10
% 0.31/6.10 % ------
% 0.31/6.10 % Current options:
% 0.31/6.10 % ------
% 0.31/6.10
% 0.31/6.10
% 0.31/6.10 %
% 0.31/6.10
% 0.31/6.10 % ------ Proving...
% 0.31/6.10 %
% 0.31/6.10
% 0.31/6.10 % SZS status Theorem for theBenchmark.p
% 0.31/6.10
% 0.31/6.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.31/6.10
% 0.31/6.10
%------------------------------------------------------------------------------