%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO175+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 : n001.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 01:20:06 PM UTC 2026
% Result : Theorem 2.35s 11.49s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 25 unt; 1 def)
% Number of atoms : 194 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 165 ( 59 ~; 79 |; 19 &)
% ( 0 <=>; 8 =>; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 103 !; 8 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).
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(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
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(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,X3] :
( ( distinct_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
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(f19,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f19]) ).
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(f31,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,plain,
? [X0,X1,X2,X3] :
( distinct_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ~ apart_point_and_line(X0,X3)
& ~ apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( distinct_points(X0,intersection_point(X2,X3))
& convergent_lines(X2,X3)
& distinct_points(X0,X1)
& ~ apart_point_and_line(X0,X3)
& ~ apart_point_and_line(X0,X2) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( distinct_points(sK0,intersection_point(sK2,sK3))
& convergent_lines(sK2,sK3)
& distinct_points(sK0,sK1)
& ~ apart_point_and_line(sK0,sK3)
& ~ apart_point_and_line(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f38,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] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
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(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
tcf(c_49,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f37]) ).
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_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
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_62,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_63,negated_conjecture,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f53]) ).
tcf(c_64,negated_conjecture,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f52]) ).
tcf(c_66,negated_conjecture,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f50]) ).
tcf(c_67,negated_conjecture,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f49]) ).
tcf(c_157,definition,
iPr_def_10 = intersection_point(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_158,negated_conjecture,
distinct_points(sK0,iPr_def_10),
inference(demodulation,[status(thm)],[c_67,c_157]) ).
tcf(c_159,negated_conjecture,
convergent_lines(sK2,sK3),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_161,negated_conjecture,
~ apart_point_and_line(sK0,sK3),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_162,negated_conjecture,
~ apart_point_and_line(sK0,sK2),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_437,plain,
! [X0: $i] :
( distinct_points(iPr_def_10,X0)
| distinct_points(sK0,X0) ),
inference(superposition,[status(thm)],[c_158,c_52]) ).
tcf(c_456,plain,
! [X0: $i] :
( convergent_lines(sK3,X0)
| convergent_lines(sK2,X0) ),
inference(superposition,[status(thm)],[c_159,c_54]) ).
tcf(c_477,plain,
distinct_points(iPr_def_10,sK0),
inference(superposition,[status(thm)],[c_437,c_49]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i] :
( convergent_lines(sK3,X1)
| convergent_lines(sK2,X0)
| convergent_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_456,c_54]) ).
tcf(c_593,plain,
( convergent_lines(sK3,sK2)
| convergent_lines(sK2,sK2) ),
inference(equality_factoring,[status(thm)],[c_488]) ).
tcf(c_594,plain,
convergent_lines(sK3,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_593,c_51]) ).
tcf(c_728,plain,
distinct_lines(sK3,sK2),
inference(superposition,[status(thm)],[c_594,c_62]) ).
tcf(c_1154,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ convergent_lines(sK2,sK3)
| ~ apart_point_and_line(X0,sK2) ),
inference(superposition,[status(thm)],[c_157,c_57]) ).
tcf(c_1159,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ apart_point_and_line(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1154,c_159]) ).
tcf(c_1181,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ convergent_lines(sK2,sK3)
| ~ apart_point_and_line(X0,sK3) ),
inference(superposition,[status(thm)],[c_157,c_58]) ).
tcf(c_1186,plain,
! [X0: $i] :
( distinct_points(X0,iPr_def_10)
| ~ apart_point_and_line(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1181,c_159]) ).
tcf(c_1239,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(sK0,X1)
| apart_point_and_line(sK0,X0)
| ~ distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_477,c_59]) ).
tcf(c_2047,plain,
( apart_point_and_line(iPr_def_10,sK3)
| apart_point_and_line(iPr_def_10,sK2)
| apart_point_and_line(sK0,sK3)
| apart_point_and_line(sK0,sK2) ),
inference(superposition,[status(thm)],[c_728,c_1239]) ).
tcf(c_2050,plain,
( apart_point_and_line(iPr_def_10,sK3)
| apart_point_and_line(iPr_def_10,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2047,c_161,c_162]) ).
tcf(c_2200,plain,
( apart_point_and_line(iPr_def_10,sK2)
| distinct_points(iPr_def_10,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2050,c_1186]) ).
tcf(c_2201,plain,
apart_point_and_line(iPr_def_10,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_2200,c_49]) ).
tcf(c_2406,plain,
distinct_points(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_2201,c_1159]) ).
tcf(c_2407,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2406,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO175+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/10.58 % Computer : n001.cluster.edu
% 0.09/10.58 % Model : x86_64 x86_64
% 0.09/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.58 % Memory : 8046.5625MB
% 0.09/10.58 % OS : Linux 6.8.0-71-generic
% 0.09/10.58 % CPULimit : 300
% 0.09/10.58 % WCLimit : 300
% 0.09/10.58 % DateTime : Wed Sep 23 11:23:00 UTC 2026
% 0.09/10.58 % CPUTime :
% 0.09/10.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.62 Running first-order theorem proving
% 0.13/10.62 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
% 0.13/10.63
% 0.13/10.63 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.63
% 0.13/10.63 % Detected problem language: tptp
% 0.13/10.65 % Proving...
% 2.35/11.49 % SZS status Started for theBenchmark.p
% 2.35/11.49 % SZS status Theorem for theBenchmark.p
% 2.35/11.49
% 2.35/11.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.35/11.49
% 2.35/11.49 % ------ iProver source info
% 2.35/11.49
% 2.35/11.49 % git: date: 2026-07-19 20:42:38 +0200
% 2.35/11.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.35/11.49 % git: non_committed_changes: false
% 2.35/11.49
% 2.35/11.49 % ------ Parsing...
% 2.35/11.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.35/11.49
% 2.35/11.49 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.35/11.49
% 2.35/11.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.35/11.49
% 2.35/11.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.35/11.49 % ------ Proving...
% 2.35/11.49 % ------ Problem Properties
% 2.35/11.49
% 2.35/11.49 %
% 2.35/11.49 % clauses 20
% 2.35/11.49 % conjectures 5
% 2.35/11.49 % EPR 15
% 2.35/11.49 % Horn 14
% 2.35/11.49 % unary 9
% 2.35/11.49 % binary 1
% 2.35/11.49 % lits 44
% 2.35/11.49 % lits eq 1
% 2.35/11.49 % fd_pure 0
% 2.35/11.49 % fd_pseudo 0
% 2.35/11.49 % fd_cond 0
% 2.35/11.49 % fd_pseudo_cond 0
% 2.35/11.49 % AC symbols 0
% 2.35/11.49
% 2.35/11.49 % ------ Schedule dynamic 5 is on
% 2.35/11.49
% 2.35/11.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.35/11.49
% 2.35/11.49
% 2.35/11.49 % ------
% 2.35/11.49 % Current options:
% 2.35/11.49 % ------
% 2.35/11.49
% 2.35/11.49
% 2.35/11.49 %
% 2.35/11.49
% 2.35/11.49 % ------ Proving...
% 2.35/11.49 %
% 2.35/11.49
% 2.35/11.49 % SZS status Theorem for theBenchmark.p
% 2.35/11.49
% 2.35/11.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.35/11.50
% 2.35/11.50
%------------------------------------------------------------------------------