%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO215+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 : n011.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 01:20:23 PM UTC 2026
% Result : Theorem 0.91s 1.29s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 107 ( 45 ~; 50 |; 6 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 63 !; 6 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f23,conjecture,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f33,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X1)
& ~ unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X1)
& ~ unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( convergent_lines(sK0,sK1)
& ~ unorthogonal_lines(sK1,sK2)
& ~ unorthogonal_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f50]) ).
fof(f54,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f60,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f77,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f51]) ).
fof(f78,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f51]) ).
fof(f79,plain,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f51]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f54]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_74,negated_conjecture,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f79]) ).
tcf(c_75,negated_conjecture,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f78]) ).
tcf(c_76,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f77]) ).
tcf(c_77,plain,
~ convergent_lines(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_354,plain,
( ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_355,plain,
( ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_358,plain,
! [X0: $i] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_359,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK1,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_358]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(sK1,sK2)
| unorthogonal_lines(X0,sK2)
| apart_point_and_line(X1,sK1)
| apart_point_and_line(X1,X0)
| ~ distinct_lines(sK1,X0) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_449,plain,
( unorthogonal_lines(sK1,sK2)
| unorthogonal_lines(sK0,sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_376]) ).
tcf(c_450,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_449,c_359,c_355,c_354,c_77,c_74,c_75,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO215+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n011.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Wed Sep 23 11:31:27 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.43
% 0.13/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.43
% 0.13/0.43 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 0.91/1.29 % SZS status Started for theBenchmark.p
% 0.91/1.29 % SZS status Theorem for theBenchmark.p
% 0.91/1.29
% 0.91/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.91/1.29
% 0.91/1.29 % ------ iProver source info
% 0.91/1.29
% 0.91/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.91/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.91/1.29 % git: non_committed_changes: false
% 0.91/1.29
% 0.91/1.29 % ------ Parsing...
% 0.91/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.91/1.29
% 0.91/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.91/1.29
% 0.91/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.91/1.29 % ------ Proving...
% 0.91/1.29 % ------ Problem Properties
% 0.91/1.29
% 0.91/1.29 %
% 0.91/1.29 % clauses 27
% 0.91/1.29 % conjectures 3
% 0.91/1.29 % EPR 19
% 0.91/1.29 % Horn 14
% 0.91/1.29 % unary 10
% 0.91/1.29 % binary 5
% 0.91/1.29 % lits 65
% 0.91/1.29 % lits eq 0
% 0.91/1.29 % fd_pure 0
% 0.91/1.29 % fd_pseudo 0
% 0.91/1.29 % fd_cond 0
% 0.91/1.29 % fd_pseudo_cond 0
% 0.91/1.29 % AC symbols 0
% 0.91/1.29
% 0.91/1.29 % ------ Schedule dynamic 5 is on
% 0.91/1.29
% 0.91/1.29 % ------ no equalities: superposition off
% 0.91/1.29
% 0.91/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.91/1.29
% 0.91/1.29
% 0.91/1.29 % ------
% 0.91/1.29 % Current options:
% 0.91/1.29 % ------
% 0.91/1.29
% 0.91/1.29
% 0.91/1.29 %
% 0.91/1.29
% 0.91/1.29 % ------ Proving...
% 0.91/1.29 %
% 0.91/1.29
% 0.91/1.29 % SZS status Theorem for theBenchmark.p
% 0.91/1.29
% 0.91/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.91/1.29
% 0.91/1.29
%------------------------------------------------------------------------------