%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO200+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 : n026.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 01:20:17 PM UTC 2026
% Result : Theorem 2.21s 1.50s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 11 unt; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 154 ( 58 ~; 84 |; 6 &)
% ( 0 <=>; 6 =>; 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 78 !; 2 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart4) ).
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(f9,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/GEO008+0.ax',cu1) ).
fof(f13,conjecture,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( distinct_points(X0,X1)
=> ~ distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(flattening,[],[f15]) ).
fof(f21,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(f22,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,[],[f21]) ).
fof(f25,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,[],[f9]) ).
fof(f26,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,[],[f25]) ).
fof(f32,plain,
? [X0,X1] :
( distinct_points(X0,X1)
& distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
( distinct_points(sK0,sK1)
& distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f32]) ).
fof(f34,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,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,[],[f26]) ).
fof(f48,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
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,[],[f41]) ).
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,[],[f40]) ).
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,[],[f44]) ).
tcf(c_63,negated_conjecture,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)),
inference(cnf_transformation,[],[f49]) ).
tcf(c_64,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f48]) ).
tcf(c_67,plain,
~ distinct_points(sK0,sK0),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_206,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_415,plain,
! [X0: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_206,c_52]) ).
tcf(c_418,plain,
( distinct_points(sK1,sK0)
| distinct_points(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_415]) ).
tcf(c_615,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_616,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_615]) ).
tcf(c_665,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_716,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_points(sK1,X2)
| ~ distinct_lines(X0,X1) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_718,plain,
! [X0: $i,X1: $i] :
( distinct_points(X0,X1)
| ~ distinct_points(sK1,X1)
| ~ apart_point_and_line(X0,line_connecting(sK1,X1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_719,plain,
! [X0: $i,X1: $i] :
( distinct_points(X0,sK1)
| ~ distinct_points(sK1,X1)
| ~ apart_point_and_line(X0,line_connecting(sK1,X1)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_720,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK1,sK0)
| ~ apart_point_and_line(sK0,line_connecting(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_718]) ).
tcf(c_886,plain,
( distinct_points(sK1,sK1)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_665]) ).
tcf(c_887,plain,
~ distinct_points(sK1,sK1),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1468,plain,
! [X0: $i] :
( distinct_points(sK1,sK1)
| ~ distinct_points(sK1,X0)
| ~ apart_point_and_line(sK1,line_connecting(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_719]) ).
tcf(c_1469,plain,
( distinct_points(sK1,sK1)
| ~ distinct_points(sK1,sK0)
| ~ apart_point_and_line(sK1,line_connecting(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_1468]) ).
tcf(c_1762,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(X1,X0)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| ~ distinct_points(sK1,X1)
| ~ distinct_lines(line_connecting(sK0,sK1),X0) ),
inference(instantiation,[status(thm)],[c_716]) ).
tcf(c_2108,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK1,X0))
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X1,line_connecting(sK1,X0))
| ~ distinct_points(sK1,X1)
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_1762]) ).
tcf(c_2119,plain,
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ distinct_points(sK1,sK0)
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_2108]) ).
tcf(c_2120,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2119,c_1469,c_887,c_886,c_720,c_616,c_418,c_63,c_67,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO200+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n026.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Wed Sep 23 11:29:24 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.63 Running first-order theorem proving
% 0.15/0.63 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
% 0.15/0.64
% 0.15/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.64
% 0.15/0.64 % Detected problem language: tptp
% 0.15/0.65 % Proving...
% 2.21/1.50 % SZS status Started for theBenchmark.p
% 2.21/1.50 % SZS status Theorem for theBenchmark.p
% 2.21/1.50
% 2.21/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.21/1.50
% 2.21/1.50 % ------ iProver source info
% 2.21/1.50
% 2.21/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 2.21/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.21/1.50 % git: non_committed_changes: false
% 2.21/1.50
% 2.21/1.50 % ------ Parsing...
% 2.21/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.21/1.50
% 2.21/1.50 % ------ Preprocessing... sf_s rm: 5 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.21/1.50
% 2.21/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.21/1.50
% 2.21/1.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.21/1.50 % ------ Proving...
% 2.21/1.50 % ------ Problem Properties
% 2.21/1.50
% 2.21/1.50 %
% 2.21/1.50 % clauses 13
% 2.21/1.50 % conjectures 2
% 2.21/1.50 % EPR 9
% 2.21/1.50 % Horn 8
% 2.21/1.50 % unary 6
% 2.21/1.50 % binary 0
% 2.21/1.50 % lits 30
% 2.21/1.50 % lits eq 2
% 2.21/1.50 % fd_pure 0
% 2.21/1.50 % fd_pseudo 0
% 2.21/1.50 % fd_cond 0
% 2.21/1.50 % fd_pseudo_cond 0
% 2.21/1.50 % AC symbols 0
% 2.21/1.50
% 2.21/1.50 % ------ Schedule dynamic 5 is on
% 2.21/1.50
% 2.21/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.21/1.50
% 2.21/1.50
% 2.21/1.50 % ------
% 2.21/1.50 % Current options:
% 2.21/1.50 % ------
% 2.21/1.50
% 2.21/1.50
% 2.21/1.50 %
% 2.21/1.50
% 2.21/1.50 % ------ Proving...
% 2.21/1.50 %
% 2.21/1.50
% 2.21/1.50 % SZS status Theorem for theBenchmark.p
% 2.21/1.50
% 2.21/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.21/1.50
% 2.21/1.50
%------------------------------------------------------------------------------