%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO209+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 : n005.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 01:20:21 PM UTC 2026
% Result : Theorem 2.51s 1.30s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 28 ~; 23 |; 23 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 60 ( 0 sgn 52 !; 8 ?; 10 :)
% 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(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(f33,axiom,
! [X0,X1] :
( parallel_lines(X0,X1)
<=> ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a3) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( parallel_lines(X3,X1)
& parallel_lines(X2,X1)
& incident_point_and_line(X0,X3)
& incident_point_and_line(X0,X2)
& apart_point_and_line(X0,X1) )
=> equal_lines(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( parallel_lines(X3,X1)
& parallel_lines(X2,X1)
& incident_point_and_line(X0,X3)
& incident_point_and_line(X0,X2)
& apart_point_and_line(X0,X1) )
=> equal_lines(X2,X3) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( parallel_lines(X0,X1)
=> ~ convergent_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f40,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f45]) ).
fof(f59,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f79,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f80,plain,
! [X0,X1] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f82,plain,
? [X0,X1,X2,X3] :
( parallel_lines(X3,X1)
& parallel_lines(X2,X1)
& incident_point_and_line(X0,X3)
& incident_point_and_line(X0,X2)
& apart_point_and_line(X0,X1)
& ~ equal_lines(X2,X3) ),
inference(ennf_transformation,[],[f37]) ).
fof(f83,plain,
? [X0,X1,X2,X3] :
( parallel_lines(X3,X1)
& parallel_lines(X2,X1)
& incident_point_and_line(X0,X3)
& incident_point_and_line(X0,X2)
& apart_point_and_line(X0,X1)
& ~ equal_lines(X2,X3) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
( parallel_lines(sK3,sK1)
& parallel_lines(sK2,sK1)
& incident_point_and_line(sK0,sK3)
& incident_point_and_line(sK0,sK2)
& apart_point_and_line(sK0,sK1)
& ~ equal_lines(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f83]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f99,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f121,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| equal_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f122,plain,
! [X0,X1] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
parallel_lines(sK3,sK1),
inference(cnf_transformation,[],[f84]) ).
fof(f125,plain,
parallel_lines(sK2,sK1),
inference(cnf_transformation,[],[f84]) ).
fof(f129,plain,
~ equal_lines(sK2,sK3),
inference(cnf_transformation,[],[f84]) ).
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,[],[f90]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ~ parallel_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_88,negated_conjecture,
~ equal_lines(sK2,sK3),
inference(cnf_transformation,[],[f129]) ).
tcf(c_92,negated_conjecture,
parallel_lines(sK2,sK1),
inference(cnf_transformation,[],[f125]) ).
tcf(c_93,negated_conjecture,
parallel_lines(sK3,sK1),
inference(cnf_transformation,[],[f124]) ).
tcf(c_314,plain,
distinct_lines(sK2,sK3),
inference(resolution,[status(thm)],[c_85,c_88]) ).
tcf(c_319,plain,
~ convergent_lines(sK2,sK1),
inference(resolution,[status(thm)],[c_86,c_92]) ).
tcf(c_323,plain,
~ convergent_lines(sK3,sK1),
inference(resolution,[status(thm)],[c_86,c_93]) ).
tcf(c_512,plain,
( convergent_lines(sK2,sK3)
| ~ distinct_lines(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_532,plain,
! [X0: $i] :
( convergent_lines(sK3,X0)
| convergent_lines(sK2,X0)
| ~ convergent_lines(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_671,plain,
( convergent_lines(sK3,sK1)
| convergent_lines(sK2,sK1)
| ~ convergent_lines(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_672,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_671,c_512,c_323,c_319,c_314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 11:29:48 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.51/1.30 % SZS status Started for theBenchmark.p
% 2.51/1.30 % SZS status Theorem for theBenchmark.p
% 2.51/1.30
% 2.51/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.51/1.30
% 2.51/1.30 % ------ iProver source info
% 2.51/1.30
% 2.51/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.51/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.51/1.30 % git: non_committed_changes: false
% 2.51/1.30
% 2.51/1.30 % ------ Parsing...
% 2.51/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.51/1.30
% 2.51/1.30 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.51/1.30
% 2.51/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.51/1.30 % ------ Proving...
% 2.51/1.30 % ------ Problem Properties
% 2.51/1.30
% 2.51/1.30 %
% 2.51/1.30 % clauses 34
% 2.51/1.30 % conjectures 1
% 2.51/1.30 % EPR 26
% 2.51/1.30 % Horn 18
% 2.51/1.30 % unary 13
% 2.51/1.30 % binary 6
% 2.51/1.30 % lits 81
% 2.51/1.30 % lits eq 0
% 2.51/1.30 % fd_pure 0
% 2.51/1.30 % fd_pseudo 0
% 2.51/1.30 % fd_cond 0
% 2.51/1.30 % fd_pseudo_cond 0
% 2.51/1.30 % AC symbols 0
% 2.51/1.30
% 2.51/1.30 % ------ Schedule dynamic 5 is on
% 2.51/1.30
% 2.51/1.30 % ------ no equalities: superposition off
% 2.51/1.30
% 2.51/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.51/1.30
% 2.51/1.30
% 2.51/1.30 % ------
% 2.51/1.30 % Current options:
% 2.51/1.30 % ------
% 2.51/1.30
% 2.51/1.30
% 2.51/1.30 %
% 2.51/1.30
% 2.51/1.30 % ------ Proving...
% 2.51/1.30 %
% 2.51/1.30
% 2.51/1.30 % SZS status Theorem for theBenchmark.p
% 2.51/1.30
% 2.51/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.51/1.31
% 2.51/1.31
%------------------------------------------------------------------------------