%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO172+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 : n008.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 01:20:05 PM UTC 2026
% Result : Theorem 2.27s 6.16s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 80 ( 26 unt; 1 def)
% Number of atoms : 236 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 197 ( 73 ~; 99 |; 16 &)
% ( 0 <=>; 9 =>; 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; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 128 !; 6 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).
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(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0)
& convergent_lines(X0,X1) )
=> ~ distinct_points(X2,intersection_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0)
& convergent_lines(X0,X1) )
=> ~ distinct_points(X2,intersection_point(X0,X1)) ),
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(f17,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(flattening,[],[f17]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(flattening,[],[f23]) ).
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(f31,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0)
& convergent_lines(X0,X1)
& distinct_points(X2,intersection_point(X0,X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0)
& convergent_lines(X0,X1)
& distinct_points(X2,intersection_point(X0,X1)) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ~ apart_point_and_line(sK2,sK1)
& ~ apart_point_and_line(sK2,sK0)
& convergent_lines(sK0,sK1)
& distinct_points(sK2,intersection_point(sK0,sK1)) ),
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(f36,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f24]) ).
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(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
~ apart_point_and_line(sK2,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
~ apart_point_and_line(sK2,sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
distinct_points(sK2,intersection_point(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f36]) ).
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,[],[f38]) ).
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,[],[f39]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
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_62,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_63,negated_conjecture,
distinct_points(sK2,intersection_point(sK0,sK1)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_64,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f51]) ).
tcf(c_65,negated_conjecture,
~ apart_point_and_line(sK2,sK0),
inference(cnf_transformation,[],[f50]) ).
tcf(c_66,negated_conjecture,
~ apart_point_and_line(sK2,sK1),
inference(cnf_transformation,[],[f49]) ).
tcf(c_154,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_155,negated_conjecture,
~ apart_point_and_line(sK2,sK1),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_156,negated_conjecture,
~ apart_point_and_line(sK2,sK0),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_157,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_158,negated_conjecture,
distinct_points(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_63,c_154]) ).
tcf(c_422,plain,
! [X0: $i] :
( distinct_points(iPr_def_10,X0)
| distinct_points(sK2,X0) ),
inference(superposition,[status(thm)],[c_158,c_52]) ).
tcf(c_430,plain,
distinct_lines(sK0,sK1),
inference(superposition,[status(thm)],[c_157,c_62]) ).
tcf(c_453,plain,
! [X0: $i] :
( distinct_lines(sK1,X0)
| distinct_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_430,c_53]) ).
tcf(c_461,plain,
distinct_points(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_422,c_49]) ).
tcf(c_462,plain,
! [X0: $i,X1: $i] :
( distinct_points(iPr_def_10,X0)
| distinct_points(sK2,X1)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_422,c_52]) ).
tcf(c_485,plain,
! [X0: $i,X1: $i] :
( distinct_lines(sK1,X1)
| distinct_lines(sK0,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_453,c_53]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(iPr_def_10,X2)
| distinct_points(sK2,X1)
| distinct_points(X0,X2)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_462,c_52]) ).
tcf(c_617,plain,
( distinct_lines(sK1,sK0)
| distinct_lines(sK0,sK0) ),
inference(equality_factoring,[status(thm)],[c_485]) ).
tcf(c_618,plain,
distinct_lines(sK1,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_617,c_50]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i] :
( distinct_points(sK2,X1)
| distinct_points(X0,iPr_def_10)
| distinct_points(X0,X1) ),
inference(superposition,[status(thm)],[c_505,c_49]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i] :
( distinct_points(iPr_def_10,X1)
| distinct_points(X0,X1)
| ~ distinct_points(iPr_def_10,X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_763,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(X0,sK0) ),
inference(superposition,[status(thm)],[c_154,c_57]) ).
tcf(c_768,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ apart_point_and_line(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_763,c_157]) ).
tcf(c_1219,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ convergent_lines(sK0,sK1)
| ~ apart_point_and_line(X0,sK1) ),
inference(superposition,[status(thm)],[c_154,c_58]) ).
tcf(c_1224,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ apart_point_and_line(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1219,c_157]) ).
tcf(c_1272,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_10,X1)
| apart_point_and_line(iPr_def_10,X0)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK2,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_461,c_59]) ).
tcf(c_1459,plain,
! [X0: $i] :
( distinct_points(iPr_def_10,iPr_def_10)
| distinct_points(X0,iPr_def_10)
| ~ distinct_points(iPr_def_10,X0) ),
inference(instantiation,[status(thm)],[c_732]) ).
tcf(c_1460,plain,
~ distinct_points(iPr_def_10,iPr_def_10),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1669,plain,
! [X0: $i] :
( apart_point_and_line(X0,sK0)
| distinct_points(iPr_def_10,X0)
| ~ apart_point_and_line(iPr_def_10,sK0) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1772,plain,
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,sK0)
| apart_point_and_line(sK2,sK1)
| apart_point_and_line(sK2,sK0) ),
inference(superposition,[status(thm)],[c_618,c_1272]) ).
tcf(c_1778,plain,
( apart_point_and_line(iPr_def_10,sK1)
| apart_point_and_line(iPr_def_10,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1772,c_155,c_156]) ).
tcf(c_1871,plain,
( apart_point_and_line(iPr_def_10,sK0)
| distinct_points(iPr_def_10,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1778,c_1224]) ).
tcf(c_1872,plain,
apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_1871,c_49]) ).
tcf(c_1927,plain,
! [X0: $i] : distinct_points(X0,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_670,c_768,c_1459,c_1460,c_1669,c_1872]) ).
tcf(c_1930,plain,
$false,
inference(superposition,[status(thm)],[c_1927,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO172+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n008.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 11:16:46 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 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
% 0.13/5.41
% 0.13/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.41
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.42 % Proving...
% 2.27/6.16 % SZS status Started for theBenchmark.p
% 2.27/6.16 % SZS status Theorem for theBenchmark.p
% 2.27/6.16
% 2.27/6.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.27/6.16
% 2.27/6.16 % ------ iProver source info
% 2.27/6.16
% 2.27/6.16 % git: date: 2026-07-19 20:42:38 +0200
% 2.27/6.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.27/6.16 % git: non_committed_changes: false
% 2.27/6.16
% 2.27/6.16 % ------ Parsing...
% 2.27/6.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.27/6.16
% 2.27/6.16 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.27/6.16
% 2.27/6.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.27/6.16
% 2.27/6.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.27/6.16 % ------ Proving...
% 2.27/6.16 % ------ Problem Properties
% 2.27/6.16
% 2.27/6.16 %
% 2.27/6.16 % clauses 19
% 2.27/6.16 % conjectures 4
% 2.27/6.16 % EPR 14
% 2.27/6.16 % Horn 13
% 2.27/6.16 % unary 8
% 2.27/6.16 % binary 1
% 2.27/6.16 % lits 43
% 2.27/6.16 % lits eq 1
% 2.27/6.16 % fd_pure 0
% 2.27/6.16 % fd_pseudo 0
% 2.27/6.16 % fd_cond 0
% 2.27/6.16 % fd_pseudo_cond 0
% 2.27/6.16 % AC symbols 0
% 2.27/6.16
% 2.27/6.16 % ------ Schedule dynamic 5 is on
% 2.27/6.16
% 2.27/6.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.27/6.16
% 2.27/6.16
% 2.27/6.16 % ------
% 2.27/6.16 % Current options:
% 2.27/6.16 % ------
% 2.27/6.16
% 2.27/6.16
% 2.27/6.16 %
% 2.27/6.16
% 2.27/6.16 % ------ Proving...
% 2.27/6.16 %
% 2.27/6.16
% 2.27/6.16 % SZS status Theorem for theBenchmark.p
% 2.27/6.16
% 2.27/6.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.27/6.16
% 2.27/6.16
%------------------------------------------------------------------------------