%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO221+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 : n016.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 2.99s 1.32s
% Output : CNFRefutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 22 unt; 2 def)
% Number of atoms : 141 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 96 ( 34 ~; 55 |; 2 &)
% ( 0 <=>; 5 =>; 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 78 !; 3 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
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(f17,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(f20,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f21,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).
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] :
( ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0))
=> ~ distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1,X2] :
( ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0))
=> ~ distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
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(f43,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(flattening,[],[f43]) ).
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] :
( ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0))
& distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
( ~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0))
& distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f49]) ).
fof(f53,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f73,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f20]) ).
fof(f74,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f75,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(f76,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f50]) ).
fof(f77,plain,
distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f53]) ).
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,[],[f64]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f73]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f74]) ).
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,[],[f75]) ).
tcf(c_74,negated_conjecture,
distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(cnf_transformation,[],[f77]) ).
tcf(c_75,negated_conjecture,
~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f76]) ).
tcf(c_342,definition,
iPr_def_10 = orthogonal_through_point(sK2,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_343,definition,
iPr_def_11 = orthogonal_through_point(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_344,negated_conjecture,
~ apart_point_and_line(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_75,c_342]) ).
tcf(c_345,negated_conjecture,
distinct_lines(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_74,c_343]) ).
tcf(c_710,plain,
~ unorthogonal_lines(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_342,c_71]) ).
tcf(c_713,plain,
~ unorthogonal_lines(iPr_def_11,sK2),
inference(superposition,[status(thm)],[c_343,c_71]) ).
tcf(c_714,plain,
~ apart_point_and_line(sK1,iPr_def_11),
inference(superposition,[status(thm)],[c_343,c_72]) ).
tcf(c_1841,plain,
! [X0: $i] :
( convergent_lines(iPr_def_10,iPr_def_11)
| apart_point_and_line(X0,iPr_def_11)
| apart_point_and_line(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_345,c_65]) ).
tcf(c_2913,plain,
( apart_point_and_line(sK1,iPr_def_10)
| convergent_lines(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1841,c_714]) ).
tcf(c_2914,plain,
convergent_lines(iPr_def_10,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_2913,c_344]) ).
tcf(c_2918,plain,
! [X0: $i] :
( convergent_lines(iPr_def_10,X0)
| distinct_lines(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_2914,c_62]) ).
tcf(c_3223,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(iPr_def_11,X2)
| apart_point_and_line(X0,iPr_def_11)
| convergent_lines(iPr_def_10,X1)
| unorthogonal_lines(X1,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_2918,c_73]) ).
tcf(c_7138,plain,
! [X0: $i] :
( apart_point_and_line(sK1,iPr_def_11)
| convergent_lines(iPr_def_10,iPr_def_10)
| unorthogonal_lines(iPr_def_11,X0)
| unorthogonal_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_3223,c_344]) ).
tcf(c_7149,plain,
! [X0: $i] :
( unorthogonal_lines(iPr_def_11,X0)
| unorthogonal_lines(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7138,c_714,c_51]) ).
tcf(c_7259,plain,
( unorthogonal_lines(iPr_def_11,sK2)
| unorthogonal_lines(iPr_def_10,sK2) ),
inference(instantiation,[status(thm)],[c_7149]) ).
tcf(c_7260,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7259,c_713,c_710]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO221+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 11:37:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 2.99/1.32 % SZS status Started for theBenchmark.p
% 2.99/1.32 % SZS status Theorem for theBenchmark.p
% 2.99/1.32
% 2.99/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.99/1.32
% 2.99/1.32 % ------ iProver source info
% 2.99/1.32
% 2.99/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 2.99/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.99/1.32 % git: non_committed_changes: false
% 2.99/1.32
% 2.99/1.32 % ------ Parsing...
% 2.99/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.99/1.32
% 2.99/1.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.99/1.32
% 2.99/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.99/1.32
% 2.99/1.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.99/1.32 % ------ Proving...
% 2.99/1.32 % ------ Problem Properties
% 2.99/1.32
% 2.99/1.32 %
% 2.99/1.32 % clauses 28
% 2.99/1.32 % conjectures 2
% 2.99/1.32 % EPR 18
% 2.99/1.32 % Horn 15
% 2.99/1.32 % unary 11
% 2.99/1.32 % binary 5
% 2.99/1.32 % lits 66
% 2.99/1.32 % lits eq 2
% 2.99/1.32 % fd_pure 0
% 2.99/1.32 % fd_pseudo 0
% 2.99/1.32 % fd_cond 0
% 2.99/1.32 % fd_pseudo_cond 0
% 2.99/1.32 % AC symbols 0
% 2.99/1.32
% 2.99/1.32 % ------ Schedule dynamic 5 is on
% 2.99/1.32
% 2.99/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.99/1.32
% 2.99/1.32
% 2.99/1.32 % ------
% 2.99/1.32 % Current options:
% 2.99/1.32 % ------
% 2.99/1.32
% 2.99/1.32
% 2.99/1.32 %
% 2.99/1.32
% 2.99/1.32 % ------ Proving...
% 2.99/1.32 %
% 2.99/1.32
% 2.99/1.32 % SZS status Theorem for theBenchmark.p
% 2.99/1.32
% 2.99/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.99/1.33
% 2.99/1.33
%------------------------------------------------------------------------------