%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO224+3 : TPTP v9.3.1. Released v4.0.0.
% 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 01:20:27 PM UTC 2026
% Result : Theorem 2.49s 1.16s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 12 unt; 0 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 158 ( 73 ~; 61 |; 15 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 103 !; 6 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
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(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(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f24,axiom,
! [X0,X1] :
~ ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f28,axiom,
! [X0,X1] :
( ( convergent_lines(X0,X1)
& line(X1)
& line(X0) )
=> point(intersection_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',int1) ).
fof(f29,axiom,
! [X0,X1] :
( ( point(X1)
& line(X0) )
=> line(parallel_through_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',par1) ).
fof(f30,axiom,
! [X0,X1] :
( ( point(X1)
& line(X0) )
=> line(orthogonal_through_point(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',orth1) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(f36,conjecture,
! [X0,X1] :
( ( line(X1)
& point(X0) )
=> ? [X2] :
( incident_point_and_line(X2,X1)
& point(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( line(X1)
& point(X0) )
=> ? [X2] :
( incident_point_and_line(X2,X1)
& point(X2) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
=> incident_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f43]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f64,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f71,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ~ point(X1)
| ~ line(X0)
| line(parallel_through_point(X0,X1)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f74,plain,
! [X0,X1] :
( ~ point(X1)
| ~ line(X0)
| line(parallel_through_point(X0,X1)) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ~ point(X1)
| ~ line(X0)
| line(orthogonal_through_point(X0,X1)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f76,plain,
! [X0,X1] :
( ~ point(X1)
| ~ line(X0)
| line(orthogonal_through_point(X0,X1)) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1] :
( line(X1)
& point(X0)
& ! [X2] :
( ~ incident_point_and_line(X2,X1)
| ~ point(X2) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1] :
( line(X1)
& point(X0)
& ! [X2] :
( ~ incident_point_and_line(X2,X1)
| ~ point(X2) ) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
( line(sK1)
& point(sK0)
& ! [X2] :
( ~ incident_point_and_line(X2,sK1)
| ~ point(X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f79]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f90,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f104,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f107,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f114,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f115,plain,
! [X0,X1] :
( ~ point(X1)
| ~ line(X0)
| line(parallel_through_point(X0,X1)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f116,plain,
! [X0,X1] :
( ~ point(X1)
| ~ line(X0)
| line(orthogonal_through_point(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f117,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f118,plain,
line(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f119,plain,
point(sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X2] :
( ~ incident_point_and_line(X2,sK1)
| ~ point(X2) ),
inference(cnf_transformation,[],[f80]) ).
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,[],[f86]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f104]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( point(intersection_point(X0,X1))
| ~ line(X1)
| ~ line(X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( line(parallel_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( line(orthogonal_through_point(X0,X1))
| ~ point(X1)
| ~ line(X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_86,negated_conjecture,
! [X0: $i] :
( ~ point(X0)
| ~ incident_point_and_line(X0,sK1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_87,negated_conjecture,
point(sK0),
inference(cnf_transformation,[],[f119]) ).
tcf(c_88,negated_conjecture,
line(sK1),
inference(cnf_transformation,[],[f118]) ).
tcf(c_297,plain,
! [X0: $i] :
( apart_point_and_line(X0,sK1)
| ~ point(X0) ),
inference(resolution,[status(thm)],[c_85,c_86]) ).
tcf(c_493,plain,
! [X0: $i] :
( apart_point_and_line(X0,sK1)
| ~ point(X0) ),
inference(demodulation,[status(thm)],[c_297]) ).
tcf(c_494,negated_conjecture,
line(sK1),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_495,negated_conjecture,
point(sK0),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_956,plain,
! [X0: $i,X1: $i] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(superposition,[status(thm)],[c_75,c_72]) ).
tcf(c_1005,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X0,X2)
| convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_956,c_54]) ).
tcf(c_1112,plain,
! [X0: $i] :
( ~ convergent_lines(X0,sK1)
| ~ point(intersection_point(X0,sK1)) ),
inference(superposition,[status(thm)],[c_493,c_58]) ).
tcf(c_1171,plain,
! [X0: $i] :
( ~ line(sK1)
| ~ line(X0)
| ~ convergent_lines(X0,sK1) ),
inference(superposition,[status(thm)],[c_82,c_1112]) ).
tcf(c_1172,plain,
! [X0: $i] :
( ~ line(X0)
| ~ convergent_lines(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1171,c_494]) ).
tcf(c_1594,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,sK1)
| ~ line(orthogonal_through_point(X0,X1)) ),
inference(superposition,[status(thm)],[c_1005,c_1172]) ).
tcf(c_3237,plain,
! [X0: $i,X1: $i] :
( ~ line(X0)
| ~ point(X1) ),
inference(global_subsumption_just,[status(thm)],[c_83,c_84,c_1172,c_1594]) ).
tcf(c_3238,plain,
! [X0: $i,X1: $i] :
( ~ point(X1)
| ~ line(X0) ),
inference(renaming,[status(thm)],[c_3237]) ).
tcf(c_3252,plain,
! [X0: $i] : ~ line(X0),
inference(superposition,[status(thm)],[c_495,c_3238]) ).
tcf(c_3253,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_494,c_3252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO224+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 11:29:32 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.49/1.16 % SZS status Started for theBenchmark.p
% 2.49/1.16 % SZS status Theorem for theBenchmark.p
% 2.49/1.16
% 2.49/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.49/1.16
% 2.49/1.16 % ------ iProver source info
% 2.49/1.16
% 2.49/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 2.49/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.49/1.16 % git: non_committed_changes: false
% 2.49/1.16
% 2.49/1.16 % ------ Parsing...
% 2.49/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.49/1.16
% 2.49/1.16 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.49/1.16
% 2.49/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.49/1.16 % ------ Proving...
% 2.49/1.16 % ------ Problem Properties
% 2.49/1.16
% 2.49/1.16 %
% 2.49/1.16 % clauses 35
% 2.49/1.16 % conjectures 2
% 2.49/1.16 % EPR 23
% 2.49/1.16 % Horn 19
% 2.49/1.16 % unary 9
% 2.49/1.16 % binary 7
% 2.49/1.16 % lits 93
% 2.49/1.16 % lits eq 0
% 2.49/1.16 % fd_pure 0
% 2.49/1.16 % fd_pseudo 0
% 2.49/1.16 % fd_cond 0
% 2.49/1.16 % fd_pseudo_cond 0
% 2.49/1.16 % AC symbols 0
% 2.49/1.16
% 2.49/1.16 % ------ Schedule dynamic 5 is on
% 2.49/1.16
% 2.49/1.16 % ------ no equalities: superposition off
% 2.49/1.16
% 2.49/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.49/1.16
% 2.49/1.16
% 2.49/1.16 % ------
% 2.49/1.16 % Current options:
% 2.49/1.16 % ------
% 2.49/1.16
% 2.49/1.16
% 2.49/1.16 %
% 2.49/1.16
% 2.49/1.16 % ------ Proving...
% 2.49/1.16 %
% 2.49/1.16
% 2.49/1.16 % SZS status Theorem for theBenchmark.p
% 2.49/1.16
% 2.49/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.49/1.17
% 2.49/1.17
%------------------------------------------------------------------------------