%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO189+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 01:20:12 PM UTC 2026
% Result : Theorem 2.90s 1.27s
% Output : CNFRefutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 22 unt; 2 def)
% Number of atoms : 207 ( 2 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 169 ( 58 ~; 82 |; 22 &)
% ( 0 <=>; 7 =>; 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 : 100 ( 0 sgn 94 !; 6 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
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/sandbox/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/sandbox/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(f10,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/GEO008+0.ax',ceq1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq2) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X1,X2)
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ~ apart_point_and_line(X1,line_connecting(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X1,X2)
& distinct_points(X0,X2)
& distinct_points(X0,X1) )
=> ~ apart_point_and_line(X1,line_connecting(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
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(f27,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f29]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X1,X2)
& distinct_points(X0,X2)
& distinct_points(X0,X1)
& apart_point_and_line(X1,line_connecting(X0,X2)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X1,X2)
& distinct_points(X0,X2)
& distinct_points(X0,X1)
& apart_point_and_line(X1,line_connecting(X0,X2)) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK1,sK2)
& distinct_points(sK0,sK2)
& distinct_points(sK0,sK1)
& apart_point_and_line(sK1,line_connecting(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,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(f42,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(f45,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(f46,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
apart_point_and_line(sK1,line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f35]) ).
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,[],[f42]) ).
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,[],[f41]) ).
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,[],[f45]) ).
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,[],[f46]) ).
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,[],[f47]) ).
tcf(c_63,negated_conjecture,
apart_point_and_line(sK1,line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_64,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f52]) ).
tcf(c_65,negated_conjecture,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f51]) ).
tcf(c_67,negated_conjecture,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f49]) ).
tcf(c_70,plain,
~ distinct_points(sK0,sK0),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_219,definition,
iPr_def_10 = line_connecting(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_220,definition,
iPr_def_11 = line_connecting(sK0,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_221,negated_conjecture,
~ apart_point_and_line(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_67,c_219]) ).
tcf(c_223,negated_conjecture,
distinct_points(sK0,sK2),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_224,negated_conjecture,
distinct_points(sK0,sK1),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_225,negated_conjecture,
apart_point_and_line(sK1,iPr_def_11),
inference(demodulation,[status(thm)],[c_63,c_220]) ).
tcf(c_456,plain,
! [X0: $i] :
( apart_point_and_line(X0,iPr_def_11)
| distinct_points(sK1,X0) ),
inference(superposition,[status(thm)],[c_225,c_60]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i] :
( distinct_lines(iPr_def_11,X1)
| distinct_points(sK1,X0)
| apart_point_and_line(X0,X1) ),
inference(superposition,[status(thm)],[c_456,c_61]) ).
tcf(c_720,plain,
! [X0: $i] :
( distinct_points(X0,sK0)
| ~ distinct_points(sK0,sK2)
| ~ apart_point_and_line(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_220,c_55]) ).
tcf(c_721,plain,
! [X0: $i] :
( distinct_points(X0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_219,c_55]) ).
tcf(c_722,plain,
! [X0: $i] :
( distinct_points(X0,sK0)
| ~ apart_point_and_line(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_721,c_224]) ).
tcf(c_725,plain,
! [X0: $i] :
( distinct_points(X0,sK0)
| ~ apart_point_and_line(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_720,c_223]) ).
tcf(c_732,plain,
( distinct_points(sK0,sK0)
| ~ apart_point_and_line(sK0,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_725]) ).
tcf(c_733,plain,
( distinct_points(sK0,sK0)
| ~ apart_point_and_line(sK0,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_722]) ).
tcf(c_741,plain,
! [X0: $i] :
( distinct_points(X0,sK2)
| ~ distinct_points(sK0,sK2)
| ~ apart_point_and_line(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_220,c_56]) ).
tcf(c_742,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_219,c_56]) ).
tcf(c_743,plain,
! [X0: $i] :
( distinct_points(X0,sK1)
| ~ apart_point_and_line(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_742,c_224]) ).
tcf(c_746,plain,
! [X0: $i] :
( distinct_points(X0,sK2)
| ~ apart_point_and_line(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_741,c_223]) ).
tcf(c_772,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_223,c_59]) ).
tcf(c_1033,plain,
! [X0: $i] :
( distinct_lines(iPr_def_11,iPr_def_10)
| distinct_points(sK1,X0)
| distinct_points(X0,sK1) ),
inference(superposition,[status(thm)],[c_502,c_743]) ).
tcf(c_1184,plain,
( distinct_lines(iPr_def_11,iPr_def_10)
| distinct_points(sK1,sK1) ),
inference(equality_factoring,[status(thm)],[c_1033]) ).
tcf(c_1186,plain,
distinct_lines(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1184,c_49]) ).
tcf(c_1517,plain,
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK2,iPr_def_10)
| apart_point_and_line(sK0,iPr_def_11)
| apart_point_and_line(sK0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1186,c_772]) ).
tcf(c_1521,plain,
( apart_point_and_line(sK2,iPr_def_11)
| apart_point_and_line(sK0,iPr_def_11)
| apart_point_and_line(sK0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1517,c_221]) ).
tcf(c_1622,plain,
apart_point_and_line(sK2,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_1521,c_70,c_732,c_733,c_1521]) ).
tcf(c_1626,plain,
distinct_points(sK2,sK2),
inference(superposition,[status(thm)],[c_1622,c_746]) ).
tcf(c_1628,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1626,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO189+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 11:18:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.90/1.27 % SZS status Started for theBenchmark.p
% 2.90/1.27 % SZS status Theorem for theBenchmark.p
% 2.90/1.27
% 2.90/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.90/1.27
% 2.90/1.27 % ------ iProver source info
% 2.90/1.27
% 2.90/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.90/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.90/1.27 % git: non_committed_changes: false
% 2.90/1.27
% 2.90/1.27 % ------ Parsing...
% 2.90/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.90/1.27
% 2.90/1.27 % ------ Preprocessing... sf_s rm: 5 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.90/1.27
% 2.90/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.90/1.27
% 2.90/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.90/1.27 % ------ Proving...
% 2.90/1.27 % ------ Problem Properties
% 2.90/1.27
% 2.90/1.27 %
% 2.90/1.27 % clauses 16
% 2.90/1.27 % conjectures 5
% 2.90/1.27 % EPR 12
% 2.90/1.27 % Horn 11
% 2.90/1.27 % unary 9
% 2.90/1.27 % binary 0
% 2.90/1.27 % lits 33
% 2.90/1.27 % lits eq 2
% 2.90/1.27 % fd_pure 0
% 2.90/1.27 % fd_pseudo 0
% 2.90/1.27 % fd_cond 0
% 2.90/1.27 % fd_pseudo_cond 0
% 2.90/1.27 % AC symbols 0
% 2.90/1.27
% 2.90/1.27 % ------ Schedule dynamic 5 is on
% 2.90/1.27
% 2.90/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.90/1.27
% 2.90/1.27
% 2.90/1.27 % ------
% 2.90/1.27 % Current options:
% 2.90/1.27 % ------
% 2.90/1.27
% 2.90/1.27
% 2.90/1.27 %
% 2.90/1.27
% 2.90/1.27 % ------ Proving...
% 2.90/1.27 %
% 2.90/1.27
% 2.90/1.27 % SZS status Theorem for theBenchmark.p
% 2.90/1.27
% 2.90/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.90/1.27
% 2.90/1.27
%------------------------------------------------------------------------------