%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO178+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 01:20:08 PM UTC 2026
% Result : Theorem 1.78s 1.28s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 12 unt; 1 def)
% Number of atoms : 86 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 39 ~; 25 |; 10 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 38 !; 6 ?; 8 :)
% 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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) )
=> ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) )
=> ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ),
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(f50,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f50]) ).
fof(f76,plain,
? [X0,X1,X2] :
( apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& ( ~ distinct_points(X2,X1)
| ~ distinct_points(X2,X0) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2] :
( apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& ( ~ distinct_points(X2,X1)
| ~ distinct_points(X2,X0) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1)
& ( ~ distinct_points(sK2,sK1)
| ~ distinct_points(sK2,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[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(f90,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f115,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f78]) ).
fof(f116,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
( ~ distinct_points(sK2,sK1)
| ~ distinct_points(sK2,sK0) ),
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_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_85,negated_conjecture,
( ~ distinct_points(sK2,sK1)
| ~ distinct_points(sK2,sK0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_86,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f116]) ).
tcf(c_87,negated_conjecture,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f115]) ).
tcf(c_448,definition,
iPr_def_10 = line_connecting(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_449,negated_conjecture,
apart_point_and_line(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_87,c_448]) ).
tcf(c_450,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_451,negated_conjecture,
( ~ distinct_points(sK2,sK1)
| ~ distinct_points(sK2,sK0) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_1144,plain,
( ~ apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_448,c_55]) ).
tcf(c_1145,plain,
~ apart_point_and_line(sK0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1144,c_450]) ).
tcf(c_1150,plain,
( ~ apart_point_and_line(sK1,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_448,c_56]) ).
tcf(c_1151,plain,
~ apart_point_and_line(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1150,c_450]) ).
tcf(c_1451,plain,
! [X0: $i] :
( apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK2,X0) ),
inference(superposition,[status(thm)],[c_449,c_60]) ).
tcf(c_1481,plain,
( apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_points(sK2,sK1) ),
inference(superposition,[status(thm)],[c_1451,c_451]) ).
tcf(c_1484,plain,
~ distinct_points(sK2,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_1481,c_1145]) ).
tcf(c_1523,plain,
apart_point_and_line(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_1451,c_1484]) ).
tcf(c_1524,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1523,c_1151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO178+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 11:20:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.78/1.28 % SZS status Started for theBenchmark.p
% 1.78/1.28 % SZS status Theorem for theBenchmark.p
% 1.78/1.28
% 1.78/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.78/1.28
% 1.78/1.28 % ------ iProver source info
% 1.78/1.28
% 1.78/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.78/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.78/1.28 % git: non_committed_changes: false
% 1.78/1.28
% 1.78/1.28 % ------ Parsing...
% 1.78/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.78/1.28
% 1.78/1.28 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.78/1.28
% 1.78/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.78/1.28
% 1.78/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.78/1.28 % ------ Proving...
% 1.78/1.28 % ------ Problem Properties
% 1.78/1.28
% 1.78/1.28 %
% 1.78/1.28 % clauses 32
% 1.78/1.28 % conjectures 3
% 1.78/1.28 % EPR 23
% 1.78/1.28 % Horn 16
% 1.78/1.28 % unary 10
% 1.78/1.28 % binary 7
% 1.78/1.28 % lits 80
% 1.78/1.28 % lits eq 1
% 1.78/1.28 % fd_pure 0
% 1.78/1.28 % fd_pseudo 0
% 1.78/1.28 % fd_cond 0
% 1.78/1.28 % fd_pseudo_cond 0
% 1.78/1.28 % AC symbols 0
% 1.78/1.28
% 1.78/1.28 % ------ Schedule dynamic 5 is on
% 1.78/1.28
% 1.78/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.78/1.28
% 1.78/1.28
% 1.78/1.28 % ------
% 1.78/1.28 % Current options:
% 1.78/1.28 % ------
% 1.78/1.28
% 1.78/1.28
% 1.78/1.28 %
% 1.78/1.28
% 1.78/1.28 % ------ Proving...
% 1.78/1.28 %
% 1.78/1.28
% 1.78/1.28 % SZS status Theorem for theBenchmark.p
% 1.78/1.28
% 1.78/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.78/1.28
% 1.78/1.28
%------------------------------------------------------------------------------