%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO225+1 : 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 : n008.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 2.37s 6.65s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 3 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 23 ~; 15 |; 18 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 32 ( 0 sgn 26 !; 6 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(f19,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/sandbox/benchmark/theBenchmark.p',con) ).
fof(f20,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)],[f19]) ).
fof(f27,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f28,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,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,[],[f20]) ).
fof(f48,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,[],[f47]) ).
fof(f49,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)],[f48]) ).
fof(f56,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f57,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f68,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X2] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK0,X2) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_71,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f68]) ).
tcf(c_229,negated_conjecture,
! [X0: $i] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_230,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_231,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_238,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_229]) ).
tcf(c_239,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_238,c_231,c_230,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO225+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.74 % Computer : n008.cluster.edu
% 0.09/5.74 % Model : x86_64 x86_64
% 0.09/5.74 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.74 % Memory : 8046.5625MB
% 0.09/5.74 % OS : Linux 6.8.0-71-generic
% 0.09/5.74 % CPULimit : 300
% 0.09/5.74 % WCLimit : 300
% 0.09/5.74 % DateTime : Wed Sep 23 11:35:19 UTC 2026
% 0.09/5.75 % CPUTime :
% 0.09/5.75 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.78 Running first-order theorem proving
% 0.09/5.78 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
% 0.09/5.79
% 0.09/5.79 % ======== iProver multi-core TPTP/SMT =========
% 0.09/5.79
% 0.09/5.79 % Detected problem language: tptp
% 0.13/5.81 % Proving...
% 2.37/6.65 % SZS status Started for theBenchmark.p
% 2.37/6.65 % SZS status Theorem for theBenchmark.p
% 2.37/6.65
% 2.37/6.65 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.37/6.65
% 2.37/6.65 % ------ iProver source info
% 2.37/6.65
% 2.37/6.65 % git: date: 2026-07-19 20:42:38 +0200
% 2.37/6.65 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.37/6.65 % git: non_committed_changes: false
% 2.37/6.65
% 2.37/6.65 % ------ Parsing...
% 2.37/6.65 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.37/6.65
% 2.37/6.65 % ------ Preprocessing... sf_s rm: 9 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.37/6.65
% 2.37/6.65 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.37/6.65 % ------ Proving...
% 2.37/6.65 % ------ Problem Properties
% 2.37/6.65
% 2.37/6.65 %
% 2.37/6.65 % clauses 11
% 2.37/6.65 % conjectures 2
% 2.37/6.65 % EPR 9
% 2.37/6.65 % Horn 5
% 2.37/6.65 % unary 3
% 2.37/6.65 % binary 3
% 2.37/6.65 % lits 27
% 2.37/6.65 % lits eq 0
% 2.37/6.65 % fd_pure 0
% 2.37/6.65 % fd_pseudo 0
% 2.37/6.65 % fd_cond 0
% 2.37/6.65 % fd_pseudo_cond 0
% 2.37/6.65 % AC symbols 0
% 2.37/6.65
% 2.37/6.65 % ------ Schedule dynamic 5 is on
% 2.37/6.65
% 2.37/6.65 % ------ no equalities: superposition off
% 2.37/6.65
% 2.37/6.65 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.37/6.65
% 2.37/6.65
% 2.37/6.65 % ------
% 2.37/6.65 % Current options:
% 2.37/6.65 % ------
% 2.37/6.65
% 2.37/6.65
% 2.37/6.65 %
% 2.37/6.65
% 2.37/6.65 % ------ Proving...
% 2.37/6.65 %
% 2.37/6.65
% 2.37/6.65 % SZS status Theorem for theBenchmark.p
% 2.37/6.65
% 2.37/6.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.37/6.65
% 2.37/6.65
%------------------------------------------------------------------------------