%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO221+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 0.77s 1.07s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 21 unt; 2 def)
% Number of atoms : 116 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 81 ( 30 ~; 45 |; 2 &)
% ( 0 <=>; 4 =>; 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 : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 67 !; 3 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).
fof(f18,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f19,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(f20,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/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f21,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/sandbox/benchmark/theBenchmark.p',con) ).
fof(f22,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)],[f21]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(flattening,[],[f25]) ).
fof(f44,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,[],[f20]) ).
fof(f45,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,[],[f44]) ).
fof(f46,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,[],[f22]) ).
fof(f47,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)],[f46]) ).
fof(f49,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f70,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f18]) ).
fof(f71,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f72,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,[],[f45]) ).
fof(f73,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f49]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f70]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f71]) ).
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,[],[f72]) ).
tcf(c_74,negated_conjecture,
distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(cnf_transformation,[],[f74]) ).
tcf(c_75,negated_conjecture,
~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f73]) ).
tcf(c_354,definition,
iPr_def_10 = orthogonal_through_point(sK2,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_355,definition,
iPr_def_11 = orthogonal_through_point(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_356,negated_conjecture,
~ apart_point_and_line(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_75,c_354]) ).
tcf(c_357,negated_conjecture,
distinct_lines(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_74,c_355]) ).
tcf(c_747,plain,
~ unorthogonal_lines(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_354,c_71]) ).
tcf(c_750,plain,
~ unorthogonal_lines(iPr_def_11,sK2),
inference(superposition,[status(thm)],[c_355,c_71]) ).
tcf(c_751,plain,
~ apart_point_and_line(sK1,iPr_def_11),
inference(superposition,[status(thm)],[c_355,c_72]) ).
tcf(c_778,plain,
! [X0: $i] :
( distinct_lines(iPr_def_11,X0)
| distinct_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_357,c_53]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_lines(iPr_def_10,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_778,c_53]) ).
tcf(c_1992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( distinct_lines(iPr_def_11,X2)
| distinct_lines(iPr_def_10,X1)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_795,c_73]) ).
tcf(c_3766,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_10,iPr_def_10)
| unorthogonal_lines(iPr_def_10,X1)
| apart_point_and_line(sK1,X0)
| distinct_lines(iPr_def_11,X0)
| unorthogonal_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_1992,c_356]) ).
tcf(c_3782,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(iPr_def_10,X1)
| apart_point_and_line(sK1,X0)
| distinct_lines(iPr_def_11,X0)
| unorthogonal_lines(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3766,c_50]) ).
tcf(c_4223,plain,
( unorthogonal_lines(iPr_def_10,sK2)
| apart_point_and_line(sK1,iPr_def_11)
| distinct_lines(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3782,c_750]) ).
tcf(c_4232,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4223,c_747,c_751,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO221+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n015.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 11:36:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.77/1.07 % SZS status Started for theBenchmark.p
% 0.77/1.07 % SZS status Theorem for theBenchmark.p
% 0.77/1.07
% 0.77/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.77/1.07
% 0.77/1.07 % ------ iProver source info
% 0.77/1.07
% 0.77/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.77/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.77/1.07 % git: non_committed_changes: false
% 0.77/1.07
% 0.77/1.07 % ------ Parsing...
% 0.77/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.77/1.07
% 0.77/1.07 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.77/1.07
% 0.77/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.77/1.07
% 0.77/1.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.77/1.07 % ------ Proving...
% 0.77/1.07 % ------ Problem Properties
% 0.77/1.07
% 0.77/1.07 %
% 0.77/1.07 % clauses 28
% 0.77/1.07 % conjectures 2
% 0.77/1.07 % EPR 18
% 0.77/1.07 % Horn 16
% 0.77/1.07 % unary 11
% 0.77/1.07 % binary 2
% 0.77/1.07 % lits 69
% 0.77/1.07 % lits eq 2
% 0.77/1.07 % fd_pure 0
% 0.77/1.07 % fd_pseudo 0
% 0.77/1.07 % fd_cond 0
% 0.77/1.07 % fd_pseudo_cond 0
% 0.77/1.07 % AC symbols 0
% 0.77/1.07
% 0.77/1.07 % ------ Schedule dynamic 5 is on
% 0.77/1.07
% 0.77/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.77/1.07
% 0.77/1.07
% 0.77/1.07 % ------
% 0.77/1.07 % Current options:
% 0.77/1.07 % ------
% 0.77/1.07
% 0.77/1.07
% 0.77/1.07 %
% 0.77/1.07
% 0.77/1.07 % ------ Proving...
% 0.77/1.07 %
% 0.77/1.07
% 0.77/1.07 % SZS status Theorem for theBenchmark.p
% 0.77/1.07
% 0.77/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.77/1.07
% 0.77/1.07
%------------------------------------------------------------------------------