%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO173+3 : TPTP v9.3.1. Released v4.0.0.
% 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 01:20:05 PM UTC 2026
% Result : Theorem 2.67s 1.31s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 14 unt; 1 def)
% Number of atoms : 110 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 108 ( 43 ~; 43 |; 17 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 46 !; 8 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,line_connecting(X0,X1))
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_lines(X2,line_connecting(X0,X1))
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f45,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(flattening,[],[f48]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( distinct_lines(X2,line_connecting(X0,X1))
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( distinct_lines(X2,line_connecting(X0,X1))
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X0,X2) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( distinct_lines(sK2,line_connecting(sK0,sK1))
& convergent_lines(sK2,sK3)
& distinct_points(sK0,sK1)
& ~ apart_point_and_line(sK1,sK2)
& ~ apart_point_and_line(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f85,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f115,plain,
distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f118,plain,
~ apart_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f78]) ).
fof(f119,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f78]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_85,negated_conjecture,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f119]) ).
tcf(c_86,negated_conjecture,
~ apart_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f118]) ).
tcf(c_87,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f117]) ).
tcf(c_89,negated_conjecture,
distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f115]) ).
tcf(c_454,definition,
iPr_def_10 = line_connecting(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_455,negated_conjecture,
distinct_lines(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_89,c_454]) ).
tcf(c_457,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1181,plain,
( ~ apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_454,c_55]) ).
tcf(c_1182,plain,
~ apart_point_and_line(sK0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1181,c_457]) ).
tcf(c_1187,plain,
( ~ apart_point_and_line(sK1,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_454,c_56]) ).
tcf(c_1188,plain,
~ apart_point_and_line(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1187,c_457]) ).
tcf(c_1500,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| ~ distinct_points(sK0,sK1)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_2240,plain,
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK0,sK2)
| ~ distinct_lines(sK2,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_1500]) ).
tcf(c_2241,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2240,c_1188,c_1182,c_455,c_85,c_86,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO173+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n002.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 11:19:03 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
% 0.13/0.44
% 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...
% 2.67/1.31 % SZS status Started for theBenchmark.p
% 2.67/1.31 % SZS status Theorem for theBenchmark.p
% 2.67/1.31
% 2.67/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.67/1.31
% 2.67/1.31 % ------ iProver source info
% 2.67/1.31
% 2.67/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.67/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.67/1.31 % git: non_committed_changes: false
% 2.67/1.31
% 2.67/1.31 % ------ Parsing...
% 2.67/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.67/1.31
% 2.67/1.31 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.67/1.31
% 2.67/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.67/1.31
% 2.67/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.67/1.31 % ------ Proving...
% 2.67/1.31 % ------ Problem Properties
% 2.67/1.31
% 2.67/1.31 %
% 2.67/1.31 % clauses 34
% 2.67/1.31 % conjectures 5
% 2.67/1.31 % EPR 25
% 2.67/1.31 % Horn 18
% 2.67/1.31 % unary 13
% 2.67/1.31 % binary 6
% 2.67/1.31 % lits 81
% 2.67/1.31 % lits eq 1
% 2.67/1.31 % fd_pure 0
% 2.67/1.31 % fd_pseudo 0
% 2.67/1.31 % fd_cond 0
% 2.67/1.31 % fd_pseudo_cond 0
% 2.67/1.31 % AC symbols 0
% 2.67/1.31
% 2.67/1.31 % ------ Schedule dynamic 5 is on
% 2.67/1.31
% 2.67/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.67/1.31
% 2.67/1.31
% 2.67/1.31 % ------
% 2.67/1.31 % Current options:
% 2.67/1.31 % ------
% 2.67/1.31
% 2.67/1.31
% 2.67/1.31 %
% 2.67/1.31
% 2.67/1.31 % ------ Proving...
% 2.67/1.31 %
% 2.67/1.31
% 2.67/1.31 % SZS status Theorem for theBenchmark.p
% 2.67/1.31
% 2.67/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.67/1.31
% 2.67/1.31
%------------------------------------------------------------------------------