%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO192+1 : 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 : n004.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 01:20:14 PM UTC 2026
% Result : Theorem 2.66s 16.52s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 18 unt; 1 def)
% Number of atoms : 169 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 152 ( 64 ~; 70 |; 8 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 98 !; 6 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
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/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> ( distinct_lines(X1,X2)
& distinct_lines(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> ( distinct_lines(X1,X2)
& distinct_lines(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
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(f21,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
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(f33,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& ( ~ distinct_lines(X1,X2)
| ~ distinct_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( convergent_lines(X0,X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& ( ~ distinct_lines(X1,X2)
| ~ distinct_lines(X0,X2) ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( convergent_lines(sK0,sK1)
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& ( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f39,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
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(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_50,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f39]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f40]) ).
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_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
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_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_63,negated_conjecture,
( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_64,negated_conjecture,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f53]) ).
tcf(c_65,negated_conjecture,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f52]) ).
tcf(c_147,definition,
iPr_def_10 = intersection_point(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_148,negated_conjecture,
convergent_lines(sK0,sK1),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_149,negated_conjecture,
apart_point_and_line(iPr_def_10,sK2),
inference(demodulation,[status(thm)],[c_64,c_147]) ).
tcf(c_150,negated_conjecture,
( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_423,plain,
! [X0: $i] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(superposition,[status(thm)],[c_148,c_54]) ).
tcf(c_435,plain,
( ~ apart_point_and_line(iPr_def_10,sK0)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_147,c_57]) ).
tcf(c_436,plain,
~ apart_point_and_line(iPr_def_10,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_435,c_148]) ).
tcf(c_689,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_10,X0)
| distinct_lines(sK2,X0)
| ~ apart_point_and_line(iPr_def_10,sK2) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_690,plain,
( apart_point_and_line(iPr_def_10,sK0)
| distinct_lines(sK2,sK0)
| ~ apart_point_and_line(iPr_def_10,sK2) ),
inference(instantiation,[status(thm)],[c_689]) ).
tcf(c_842,plain,
( ~ apart_point_and_line(iPr_def_10,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(superposition,[status(thm)],[c_147,c_58]) ).
tcf(c_843,plain,
~ apart_point_and_line(iPr_def_10,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_842,c_148]) ).
tcf(c_867,plain,
! [X0: $i] :
( apart_point_and_line(iPr_def_10,X0)
| distinct_lines(sK2,X0) ),
inference(superposition,[status(thm)],[c_149,c_61]) ).
tcf(c_898,plain,
! [X0: $i,X1: $i] :
( convergent_lines(sK1,X1)
| convergent_lines(sK0,X0)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_423,c_62]) ).
tcf(c_1079,plain,
! [X0: $i,X1: $i] :
( distinct_lines(sK2,X1)
| distinct_lines(X0,X1)
| ~ distinct_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1205,plain,
! [X0: $i] :
( distinct_lines(sK2,sK2)
| distinct_lines(X0,sK2)
| ~ distinct_lines(sK2,X0) ),
inference(instantiation,[status(thm)],[c_1079]) ).
tcf(c_1206,plain,
~ distinct_lines(sK2,sK2),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1207,plain,
( distinct_lines(sK2,sK2)
| distinct_lines(sK0,sK2)
| ~ distinct_lines(sK2,sK0) ),
inference(instantiation,[status(thm)],[c_1205]) ).
tcf(c_1255,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(iPr_def_10,X0)
| distinct_lines(sK2,X1)
| distinct_lines(X0,X1) ),
inference(superposition,[status(thm)],[c_867,c_53]) ).
tcf(c_1358,plain,
( convergent_lines(sK1,sK2)
| convergent_lines(sK0,sK0)
| ~ distinct_lines(sK1,sK2) ),
inference(superposition,[status(thm)],[c_898,c_150]) ).
tcf(c_1361,plain,
( convergent_lines(sK1,sK2)
| ~ distinct_lines(sK1,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1358,c_51]) ).
tcf(c_1388,plain,
~ distinct_lines(sK1,sK2),
inference(global_subsumption_just,[status(thm)],[c_1361,c_63,c_149,c_436,c_690,c_1207,c_1206]) ).
tcf(c_1428,plain,
( apart_point_and_line(iPr_def_10,sK1)
| distinct_lines(sK2,sK2) ),
inference(superposition,[status(thm)],[c_1255,c_1388]) ).
tcf(c_1431,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1428,c_843,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO192+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/15.60 % Computer : n004.cluster.edu
% 0.11/15.60 % Model : x86_64 x86_64
% 0.11/15.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.60 % Memory : 8046.5625MB
% 0.11/15.60 % OS : Linux 6.8.0-71-generic
% 0.11/15.60 % CPULimit : 300
% 0.11/15.60 % WCLimit : 300
% 0.11/15.60 % DateTime : Wed Sep 23 11:23:23 UTC 2026
% 0.11/15.61 % CPUTime :
% 0.11/15.61 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/15.64 Running first-order theorem proving
% 0.11/15.65 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
% 0.11/15.66
% 0.11/15.66 % ======== iProver multi-core TPTP/SMT =========
% 0.11/15.66
% 0.11/15.66 % Detected problem language: tptp
% 0.11/15.67 % Proving...
% 2.66/16.52 % SZS status Started for theBenchmark.p
% 2.66/16.52 % SZS status Theorem for theBenchmark.p
% 2.66/16.52
% 2.66/16.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.66/16.52
% 2.66/16.52 % ------ iProver source info
% 2.66/16.52
% 2.66/16.52 % git: date: 2026-07-19 20:42:38 +0200
% 2.66/16.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.66/16.52 % git: non_committed_changes: false
% 2.66/16.52
% 2.66/16.52 % ------ Parsing...
% 2.66/16.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.66/16.52
% 2.66/16.52 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.66/16.52
% 2.66/16.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.66/16.52
% 2.66/16.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.66/16.52 % ------ Proving...
% 2.66/16.52 % ------ Problem Properties
% 2.66/16.52
% 2.66/16.52 %
% 2.66/16.52 % clauses 18
% 2.66/16.52 % conjectures 3
% 2.66/16.52 % EPR 13
% 2.66/16.52 % Horn 11
% 2.66/16.52 % unary 6
% 2.66/16.52 % binary 5
% 2.66/16.52 % lits 40
% 2.66/16.52 % lits eq 1
% 2.66/16.52 % fd_pure 0
% 2.66/16.52 % fd_pseudo 0
% 2.66/16.52 % fd_cond 0
% 2.66/16.52 % fd_pseudo_cond 0
% 2.66/16.52 % AC symbols 0
% 2.66/16.52
% 2.66/16.52 % ------ Schedule dynamic 5 is on
% 2.66/16.52
% 2.66/16.52 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.66/16.52
% 2.66/16.52
% 2.66/16.52 % ------
% 2.66/16.52 % Current options:
% 2.66/16.52 % ------
% 2.66/16.52
% 2.66/16.52
% 2.66/16.52 %
% 2.66/16.52
% 2.66/16.52 % ------ Proving...
% 2.66/16.52 %
% 2.66/16.52
% 2.66/16.52 % SZS status Theorem for theBenchmark.p
% 2.66/16.52
% 2.66/16.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.66/16.52
% 2.66/16.52
%------------------------------------------------------------------------------