%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO225+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 : n002.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 01:20:27 PM UTC 2026
% Result : Theorem 2.24s 1.29s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 30 ~; 27 |; 21 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 36 !; 6 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con1) ).
fof(f17,conjecture,
! [X0,X1] :
( ( distinct_points(X0,X1)
& point(X1)
& point(X0) )
=> ? [X2] :
( line(X2)
=> ( ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( distinct_points(X0,X1)
& point(X1)
& point(X0) )
=> ? [X2] :
( line(X2)
=> ( ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ),
inference(flattening,[],[f25]) ).
fof(f44,plain,
? [X0,X1] :
( distinct_points(X0,X1)
& point(X1)
& point(X0)
& ! [X2] :
( line(X2)
& ( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f45,plain,
? [X0,X1] :
( distinct_points(X0,X1)
& point(X1)
& point(X0)
& ! [X2] :
( line(X2)
& ( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) ) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( distinct_points(sK0,sK1)
& point(sK1)
& point(sK0)
& ! [X2] :
( line(X2)
& ( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK0,X2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f45]) ).
fof(f47,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f65,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
! [X2] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK0,X2) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f47]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X0,X1)
| ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X0,line_connecting(X1,X2)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X0,X2)
| ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X0,line_connecting(X1,X2)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_71,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f65]) ).
tcf(c_75,plain,
~ distinct_points(sK0,sK0),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_239,negated_conjecture,
! [X0: $i] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_242,plain,
! [X0: $i] :
( distinct_points(X0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_243,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_242]) ).
tcf(c_244,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(X0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_255,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_239]) ).
tcf(c_256,plain,
( distinct_points(sK1,sK1)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_244]) ).
tcf(c_257,plain,
~ distinct_points(sK1,sK1),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_258,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_257,c_256,c_255,c_243,c_75,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Wed Sep 23 11:37:20 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 2.24/1.29 % SZS status Started for theBenchmark.p
% 2.24/1.29 % SZS status Theorem for theBenchmark.p
% 2.24/1.29
% 2.24/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.24/1.29
% 2.24/1.29 % ------ iProver source info
% 2.24/1.29
% 2.24/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.24/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.24/1.29 % git: non_committed_changes: false
% 2.24/1.29
% 2.24/1.29 % ------ Parsing...
% 2.24/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.24/1.29
% 2.24/1.29 % ------ Preprocessing... sf_s rm: 9 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.24/1.29
% 2.24/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.24/1.29 % ------ Proving...
% 2.24/1.29 % ------ Problem Properties
% 2.24/1.29
% 2.24/1.29 %
% 2.24/1.29 % clauses 11
% 2.24/1.29 % conjectures 2
% 2.24/1.29 % EPR 9
% 2.24/1.29 % Horn 5
% 2.24/1.29 % unary 3
% 2.24/1.29 % binary 1
% 2.24/1.29 % lits 29
% 2.24/1.29 % lits eq 0
% 2.24/1.29 % fd_pure 0
% 2.24/1.29 % fd_pseudo 0
% 2.24/1.29 % fd_cond 0
% 2.24/1.29 % fd_pseudo_cond 0
% 2.24/1.29 % AC symbols 0
% 2.24/1.29
% 2.24/1.29 % ------ Schedule dynamic 5 is on
% 2.24/1.29
% 2.24/1.29 % ------ no equalities: superposition off
% 2.24/1.29
% 2.24/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.24/1.29
% 2.24/1.29
% 2.24/1.29 % ------
% 2.24/1.29 % Current options:
% 2.24/1.29 % ------
% 2.24/1.29
% 2.24/1.29
% 2.24/1.29 %
% 2.24/1.29
% 2.24/1.29 % ------ Proving...
% 2.24/1.29 %
% 2.24/1.29
% 2.24/1.29 % SZS status Theorem for theBenchmark.p
% 2.24/1.29
% 2.24/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.24/1.29
% 2.24/1.29
%------------------------------------------------------------------------------