%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO174+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 : n007.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 01:20:06 PM UTC 2026
% Result : Theorem 2.45s 1.27s
% Output : CNFRefutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 12 unt; 1 def)
% Number of atoms : 93 ( 1 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 78 ( 31 ~; 29 |; 13 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 41 !; 8 ?; 9 :)
% 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(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( ( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) )
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> distinct_lines(X2,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) )
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> distinct_lines(X2,line_connecting(X0,X1)) ),
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(f52,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f52]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) )
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ~ distinct_lines(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2) )
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ~ distinct_lines(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( ( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK0,sK2) )
& convergent_lines(sK2,sK3)
& distinct_points(sK0,sK1)
& ~ distinct_lines(sK2,line_connecting(sK0,sK1)) ),
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(f91,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f115,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK0,sK2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f118,plain,
~ distinct_lines(sK2,line_connecting(sK0,sK1)),
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_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_85,negated_conjecture,
~ distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f118]) ).
tcf(c_86,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f117]) ).
tcf(c_88,negated_conjecture,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK0,sK2) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_453,definition,
iPr_def_10 = line_connecting(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_454,negated_conjecture,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK0,sK2) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_456,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_457,negated_conjecture,
~ distinct_lines(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_85,c_453]) ).
tcf(c_1284,plain,
( ~ apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_453,c_55]) ).
tcf(c_1285,plain,
~ apart_point_and_line(sK0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1284,c_456]) ).
tcf(c_1291,plain,
( ~ apart_point_and_line(sK1,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_453,c_56]) ).
tcf(c_1292,plain,
~ apart_point_and_line(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1291,c_456]) ).
tcf(c_1680,plain,
! [X0: $i] :
( apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK1,X0)
| distinct_lines(sK2,X0) ),
inference(superposition,[status(thm)],[c_454,c_61]) ).
tcf(c_1733,plain,
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK0,sK2) ),
inference(superposition,[status(thm)],[c_1680,c_457]) ).
tcf(c_1734,plain,
apart_point_and_line(sK0,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_1733,c_1292]) ).
tcf(c_1736,plain,
! [X0: $i] :
( apart_point_and_line(sK0,X0)
| distinct_lines(sK2,X0) ),
inference(superposition,[status(thm)],[c_1734,c_61]) ).
tcf(c_1752,plain,
apart_point_and_line(sK0,iPr_def_10),
inference(superposition,[status(thm)],[c_1736,c_457]) ).
tcf(c_1753,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1752,c_1285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO174+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 11:14:54 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 2.45/1.27 % SZS status Started for theBenchmark.p
% 2.45/1.27 % SZS status Theorem for theBenchmark.p
% 2.45/1.27
% 2.45/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.45/1.27
% 2.45/1.27 % ------ iProver source info
% 2.45/1.27
% 2.45/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.45/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.45/1.27 % git: non_committed_changes: false
% 2.45/1.27
% 2.45/1.27 % ------ Parsing...
% 2.45/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.45/1.27
% 2.45/1.27 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.45/1.27
% 2.45/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.45/1.27
% 2.45/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.45/1.27 % ------ Proving...
% 2.45/1.27 % ------ Problem Properties
% 2.45/1.27
% 2.45/1.27 %
% 2.45/1.27 % clauses 33
% 2.45/1.27 % conjectures 4
% 2.45/1.27 % EPR 24
% 2.45/1.27 % Horn 16
% 2.45/1.27 % unary 11
% 2.45/1.27 % binary 7
% 2.45/1.27 % lits 81
% 2.45/1.27 % lits eq 1
% 2.45/1.27 % fd_pure 0
% 2.45/1.27 % fd_pseudo 0
% 2.45/1.27 % fd_cond 0
% 2.45/1.27 % fd_pseudo_cond 0
% 2.45/1.27 % AC symbols 0
% 2.45/1.27
% 2.45/1.27 % ------ Schedule dynamic 5 is on
% 2.45/1.27
% 2.45/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.45/1.27
% 2.45/1.27
% 2.45/1.27 % ------
% 2.45/1.27 % Current options:
% 2.45/1.27 % ------
% 2.45/1.27
% 2.45/1.27
% 2.45/1.27 %
% 2.45/1.27
% 2.45/1.27 % ------ Proving...
% 2.45/1.27 %
% 2.45/1.27
% 2.45/1.27 % SZS status Theorem for theBenchmark.p
% 2.45/1.27
% 2.45/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.45/1.27
% 2.45/1.27
%------------------------------------------------------------------------------