%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO241+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 : n003.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 01:20:31 PM UTC 2026
% Result : Theorem 1.20s 1.27s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 41 ( 15 ~; 10 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 34 !; 6 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(f36,axiom,
! [X0,X1,X2] :
( left_convergent_lines(X0,X1)
=> ( left_convergent_lines(X0,X2)
| unequally_directed_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax3_subs) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( ( left_convergent_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& incident_point_and_line(X0,X2) )
=> left_apart_point(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( ( left_convergent_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& incident_point_and_line(X0,X2) )
=> left_apart_point(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f42,plain,
~ ! [X0,X1,X2] :
( ( left_convergent_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) )
=> left_apart_point(X1,X2) ),
inference(pure_predicate_removal,[],[f38]) ).
fof(f57,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ left_convergent_lines(X0,X1)
| left_convergent_lines(X0,X2)
| unequally_directed_lines(X1,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ left_convergent_lines(X0,X1)
| left_convergent_lines(X0,X2)
| unequally_directed_lines(X1,X2) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
? [X0,X1,X2] :
( left_convergent_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& ~ left_apart_point(X1,X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f80,plain,
? [X0,X1,X2] :
( left_convergent_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& ~ left_apart_point(X1,X2) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
( left_convergent_lines(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1)
& ~ left_apart_point(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f80]) ).
fof(f101,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f57]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ left_convergent_lines(X0,X1)
| left_convergent_lines(X0,X2)
| unequally_directed_lines(X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f119,plain,
left_convergent_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f81]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f101]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( left_convergent_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ left_convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_88,negated_conjecture,
left_convergent_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f119]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_85,c_67]) ).
tcf(c_223,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_88,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO241+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 11:39:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.20/1.27 % SZS status Started for theBenchmark.p
% 1.20/1.27 % SZS status Theorem for theBenchmark.p
% 1.20/1.27
% 1.20/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.20/1.27
% 1.20/1.27 % ------ iProver source info
% 1.20/1.27
% 1.20/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.20/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.20/1.27 % git: non_committed_changes: false
% 1.20/1.27
% 1.20/1.27 % ------ Parsing...
% 1.20/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.20/1.27
% 1.20/1.27 % ------ Preprocessing...%
% 1.20/1.27
% 1.20/1.27 % SZS status Theorem for theBenchmark.p
% 1.20/1.27
% 1.20/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.20/1.27
% 1.20/1.27
%------------------------------------------------------------------------------