%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO180+1 : 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 01:20:08 PM UTC 2026
% Result : Theorem 2.83s 1.28s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 78 ( 24 unt; 2 def)
% Number of atoms : 221 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 182 ( 65 ~; 99 |; 7 &)
% ( 0 <=>; 11 =>; 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; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 128 !; 6 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart5) ).
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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq1) ).
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(f15,conjecture,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X0,line_connecting(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X0,line_connecting(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(flattening,[],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f29,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(f30,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f29]) ).
fof(f31,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(f32,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f31]) ).
fof(f35,plain,
? [X0,X1,X2] :
( distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1))
& ~ apart_point_and_line(X0,line_connecting(X2,X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( distinct_points(X0,X1)
& apart_point_and_line(X2,line_connecting(X0,X1))
& ~ apart_point_and_line(X0,line_connecting(X2,X1)) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( distinct_points(sK0,sK1)
& apart_point_and_line(sK2,line_connecting(sK0,sK1))
& ~ apart_point_and_line(sK0,line_connecting(sK2,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f38,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f44,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,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,[],[f28]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
~ apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f39]) ).
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,[],[f41]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(cnf_transformation,[],[f45]) ).
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,[],[f48]) ).
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,[],[f49]) ).
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,[],[f50]) ).
tcf(c_63,negated_conjecture,
~ apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_64,negated_conjecture,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_65,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f52]) ).
tcf(c_199,definition,
iPr_def_10 = line_connecting(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_200,definition,
iPr_def_11 = line_connecting(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_201,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_202,negated_conjecture,
apart_point_and_line(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_64,c_199]) ).
tcf(c_203,negated_conjecture,
~ apart_point_and_line(sK0,iPr_def_11),
inference(demodulation,[status(thm)],[c_63,c_200]) ).
tcf(c_394,plain,
! [X0: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_201,c_52]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK1,X1)
| distinct_points(sK0,X0)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_394,c_52]) ).
tcf(c_417,plain,
( ~ apart_point_and_line(sK2,iPr_def_11)
| ~ distinct_points(sK2,sK1) ),
inference(superposition,[status(thm)],[c_200,c_55]) ).
tcf(c_418,plain,
( ~ apart_point_and_line(sK0,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_199,c_55]) ).
tcf(c_419,plain,
~ apart_point_and_line(sK0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_418,c_201]) ).
tcf(c_426,plain,
( ~ apart_point_and_line(sK1,iPr_def_11)
| ~ distinct_points(sK2,sK1) ),
inference(superposition,[status(thm)],[c_200,c_56]) ).
tcf(c_427,plain,
( ~ apart_point_and_line(sK1,iPr_def_10)
| ~ distinct_points(sK0,sK1) ),
inference(superposition,[status(thm)],[c_199,c_56]) ).
tcf(c_428,plain,
~ apart_point_and_line(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_427,c_201]) ).
tcf(c_437,plain,
! [X0: $i] :
( apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK2,X0) ),
inference(superposition,[status(thm)],[c_202,c_60]) ).
tcf(c_743,plain,
! [X0: $i] :
( apart_point_and_line(sK2,X0)
| distinct_lines(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_202,c_61]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| distinct_points(sK1,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,X3)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_403,c_59]) ).
tcf(c_1014,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X0)
| distinct_lines(iPr_def_10,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_743,c_53]) ).
tcf(c_1032,plain,
( apart_point_and_line(sK1,iPr_def_10)
| ~ apart_point_and_line(sK1,iPr_def_11) ),
inference(superposition,[status(thm)],[c_437,c_426]) ).
tcf(c_1038,plain,
~ apart_point_and_line(sK1,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1032,c_428]) ).
tcf(c_1142,plain,
! [X0: $i] :
( apart_point_and_line(sK2,X0)
| distinct_lines(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1014,c_50]) ).
tcf(c_1881,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK0,iPr_def_10)
| apart_point_and_line(sK2,X2)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK1,X1)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_1142,c_773]) ).
tcf(c_1884,plain,
! [X0: $i,X1: $i,X2: $i] :
( apart_point_and_line(sK2,X2)
| apart_point_and_line(sK0,X2)
| apart_point_and_line(X0,iPr_def_10)
| distinct_points(sK1,X1)
| apart_point_and_line(X0,X2)
| distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1881,c_419]) ).
tcf(c_2001,plain,
! [X0: $i] :
( apart_point_and_line(sK1,iPr_def_10)
| apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK0,iPr_def_11)
| distinct_points(sK1,X0) ),
inference(superposition,[status(thm)],[c_1884,c_1038]) ).
tcf(c_2010,plain,
! [X0: $i] :
( apart_point_and_line(sK2,iPr_def_11)
| distinct_points(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2001,c_428,c_203]) ).
tcf(c_2190,plain,
apart_point_and_line(sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_2010,c_49]) ).
tcf(c_2193,plain,
~ distinct_points(sK2,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_417,c_2190]) ).
tcf(c_2727,plain,
apart_point_and_line(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_437,c_2193]) ).
tcf(c_2735,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2727,c_428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO180+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.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 11:21:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 2.83/1.28 % SZS status Started for theBenchmark.p
% 2.83/1.28 % SZS status Theorem for theBenchmark.p
% 2.83/1.28
% 2.83/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.83/1.28
% 2.83/1.28 % ------ iProver source info
% 2.83/1.28
% 2.83/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.83/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.83/1.28 % git: non_committed_changes: false
% 2.83/1.28
% 2.83/1.28 % ------ Parsing...
% 2.83/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... sf_s rm: 5 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.83/1.28
% 2.83/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.83/1.28 % ------ Proving...
% 2.83/1.28 % ------ Problem Properties
% 2.83/1.28
% 2.83/1.28 %
% 2.83/1.28 % clauses 14
% 2.83/1.28 % conjectures 3
% 2.83/1.28 % EPR 10
% 2.83/1.28 % Horn 9
% 2.83/1.28 % unary 7
% 2.83/1.28 % binary 2
% 2.83/1.28 % lits 29
% 2.83/1.28 % lits eq 2
% 2.83/1.28 % fd_pure 0
% 2.83/1.28 % fd_pseudo 0
% 2.83/1.28 % fd_cond 0
% 2.83/1.28 % fd_pseudo_cond 0
% 2.83/1.28 % AC symbols 0
% 2.83/1.28
% 2.83/1.28 % ------ Schedule dynamic 5 is on
% 2.83/1.28
% 2.83/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 % ------
% 2.83/1.28 % Current options:
% 2.83/1.28 % ------
% 2.83/1.28
% 2.83/1.28
% 2.83/1.28 %
% 2.83/1.28
% 2.83/1.28 % ------ Proving...
% 2.83/1.28 %
% 2.83/1.28
% 2.83/1.28 % SZS status Theorem for theBenchmark.p
% 2.83/1.28
% 2.83/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.83/1.28
% 2.83/1.28
%------------------------------------------------------------------------------