%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 01:20:11 PM UTC 2026
% Result : Theorem 1.45s 1.16s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 28 unt; 0 def)
% Number of atoms : 241 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 238 ( 94 ~; 113 |; 22 &)
% ( 1 <=>; 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 : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 175 ( 0 sgn 167 !; 8 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(f11,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/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
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/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( incident_point_and_line(X1,line_connecting(X2,X3))
& incident_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) )
=> ( incident_point_and_line(X3,line_connecting(X0,X1))
& incident_point_and_line(X2,line_connecting(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( incident_point_and_line(X1,line_connecting(X2,X3))
& incident_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) )
=> ( incident_point_and_line(X3,line_connecting(X0,X1))
& incident_point_and_line(X2,line_connecting(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f45,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f48,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,[],[f11]) ).
fof(f49,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,[],[f48]) ).
fof(f52,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(f53,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( incident_point_and_line(X1,line_connecting(X2,X3))
& incident_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1)
& ( ~ incident_point_and_line(X3,line_connecting(X0,X1))
| ~ incident_point_and_line(X2,line_connecting(X0,X1)) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( incident_point_and_line(X1,line_connecting(X2,X3))
& incident_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1)
& ( ~ incident_point_and_line(X3,line_connecting(X0,X1))
| ~ incident_point_and_line(X2,line_connecting(X0,X1)) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) )
& ( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f79,plain,
( incident_point_and_line(sK1,line_connecting(sK2,sK3))
& incident_point_and_line(sK0,line_connecting(sK2,sK3))
& distinct_points(sK2,sK3)
& distinct_points(sK0,sK1)
& ( ~ incident_point_and_line(sK3,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK2,line_connecting(sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f86,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f87,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f90,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,[],[f49]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f94,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f95,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f96,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f116,plain,
! [X0,X1] :
( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f118,plain,
incident_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f79]) ).
fof(f119,plain,
incident_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
distinct_points(sK2,sK3),
inference(cnf_transformation,[],[f79]) ).
fof(f121,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f79]) ).
fof(f122,plain,
( ~ incident_point_and_line(sK3,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f82]) ).
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,[],[f85]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(cnf_transformation,[],[f87]) ).
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,[],[f90]) ).
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,[],[f92]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f95]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f96]) ).
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,plain,
! [X0: $i,X1: $i] :
( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_87,negated_conjecture,
( ~ incident_point_and_line(sK3,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_88,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f121]) ).
tcf(c_89,negated_conjecture,
distinct_points(sK2,sK3),
inference(cnf_transformation,[],[f120]) ).
tcf(c_90,negated_conjecture,
incident_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f119]) ).
tcf(c_91,negated_conjecture,
incident_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f118]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(renaming,[status(thm)],[c_112]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_point_and_line(X2,X0)
| apart_point_and_line(X2,X1)
| distinct_lines(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_61,c_113]) ).
tcf(c_658,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| apart_point_and_line(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2)
| distinct_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_202]) ).
tcf(c_660,negated_conjecture,
incident_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(subtyping,[status(esa)],[c_91]) ).
tcf(c_661,negated_conjecture,
incident_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(subtyping,[status(esa)],[c_90]) ).
tcf(c_664,negated_conjecture,
( ~ incident_point_and_line(sK3,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(subtyping,[status(esa)],[c_87]) ).
tcf(c_665,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] :
( ~ incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| ~ apart_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_86]) ).
tcf(c_666,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| apart_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_85]) ).
tcf(c_678,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] : ~ apart_point_and_line(X0_iProver_incident_point_and_line_1,parallel_through_point(X0_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1)),
inference(subtyping,[status(esa)],[c_65]) ).
tcf(c_679,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] : ~ convergent_lines(parallel_through_point(X0_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1),X0_iProver_incident_point_and_line_2),
inference(subtyping,[status(esa)],[c_64]) ).
tcf(c_680,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( convergent_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2)
| ~ distinct_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_63]) ).
tcf(c_682,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] :
( apart_point_and_line(X1_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2)
| apart_point_and_line(X1_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| apart_point_and_line(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2)
| apart_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| ~ distinct_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2)
| ~ distinct_points(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_1) ),
inference(subtyping,[status(esa)],[c_59]) ).
tcf(c_685,plain,
! [X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] :
( ~ distinct_points(X1_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_1)
| ~ apart_point_and_line(X0_iProver_incident_point_and_line_1,line_connecting(X1_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_1)) ),
inference(subtyping,[status(esa)],[c_56]) ).
tcf(c_686,plain,
! [X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] :
( ~ distinct_points(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_1)
| ~ apart_point_and_line(X0_iProver_incident_point_and_line_1,line_connecting(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_1)) ),
inference(subtyping,[status(esa)],[c_55]) ).
tcf(c_687,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X2_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( convergent_lines(X1_iProver_incident_point_and_line_2,X2_iProver_incident_point_and_line_2)
| convergent_lines(X0_iProver_incident_point_and_line_2,X2_iProver_incident_point_and_line_2)
| ~ convergent_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_54]) ).
tcf(c_690,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] : ~ convergent_lines(X0_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_2),
inference(subtyping,[status(esa)],[c_51]) ).
tcf(c_717,plain,
~ apart_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(resolution,[status(thm)],[c_665,c_661]) ).
tcf(c_718,plain,
~ apart_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(resolution,[status(thm)],[c_665,c_660]) ).
tcf(c_734,plain,
( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(resolution,[status(thm)],[c_666,c_664]) ).
tcf(c_792,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_685]) ).
tcf(c_802,plain,
( ~ distinct_points(sK0,sK1)
| ~ apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_686]) ).
tcf(c_803,plain,
( ~ distinct_points(sK2,sK3)
| ~ apart_point_and_line(sK2,line_connecting(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_686]) ).
tcf(c_864,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK3,line_connecting(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_666,c_664]) ).
tcf(c_883,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] :
( apart_point_and_line(sK1,X0_iProver_incident_point_and_line_2)
| apart_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| apart_point_and_line(sK1,line_connecting(sK2,sK3))
| apart_point_and_line(X0_iProver_incident_point_and_line_1,line_connecting(sK2,sK3))
| ~ distinct_points(X0_iProver_incident_point_and_line_1,sK1)
| ~ distinct_lines(X0_iProver_incident_point_and_line_2,line_connecting(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_682]) ).
tcf(c_890,plain,
( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_666,c_864]) ).
tcf(c_921,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( convergent_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2)
| ~ convergent_lines(X0_iProver_incident_point_and_line_2,parallel_through_point(X1_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1)) ),
inference(resolution,[status(thm)],[c_687,c_679]) ).
tcf(c_942,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( apart_point_and_line(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2)
| distinct_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2)
| ~ apart_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2) ),
inference(superposition,[status(thm)],[c_658,c_665]) ).
tcf(c_944,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| distinct_lines(X0_iProver_incident_point_and_line_2,parallel_through_point(X1_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1)) ),
inference(superposition,[status(thm)],[c_658,c_678]) ).
tcf(c_947,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| apart_point_and_line(X0_iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2)
| convergent_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(superposition,[status(thm)],[c_658,c_680]) ).
tcf(c_1037,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( apart_point_and_line(sK2,X0_iProver_incident_point_and_line_2)
| incident_point_and_line(sK2,line_connecting(sK0,sK1))
| distinct_lines(line_connecting(sK0,sK1),X0_iProver_incident_point_and_line_2) ),
inference(instantiation,[status(thm)],[c_658]) ).
tcf(c_1080,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| convergent_lines(X0_iProver_incident_point_and_line_2,parallel_through_point(X1_iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1)) ),
inference(superposition,[status(thm)],[c_944,c_680]) ).
tcf(c_1262,plain,
( incident_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK2,sK3))
| distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_1263,plain,
! [X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] :
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK2,sK3))
| apart_point_and_line(X0_iProver_incident_point_and_line_1,line_connecting(sK0,sK1))
| apart_point_and_line(X0_iProver_incident_point_and_line_1,line_connecting(sK2,sK3))
| ~ distinct_points(X0_iProver_incident_point_and_line_1,sK1)
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_883]) ).
tcf(c_1265,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK2,sK3))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK2,sK3))
| ~ distinct_points(sK0,sK1)
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_1263]) ).
tcf(c_1268,plain,
apart_point_and_line(sK3,line_connecting(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_890,c_89,c_88,c_717,c_718,c_734,c_792,c_802,c_803,c_1262,c_1265]) ).
tcf(c_1311,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1,X1_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2] :
( incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2)
| convergent_lines(X0_iProver_incident_point_and_line_2,X1_iProver_incident_point_and_line_2) ),
inference(global_subsumption_just,[status(thm)],[c_947,c_921,c_1080]) ).
tcf(c_1315,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] : incident_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2),
inference(superposition,[status(thm)],[c_1311,c_690]) ).
tcf(c_1318,plain,
! [X0_iProver_incident_point_and_line_2: iProver_incident_point_and_line_2,X0_iProver_incident_point_and_line_1: iProver_incident_point_and_line_1] : ~ apart_point_and_line(X0_iProver_incident_point_and_line_1,X0_iProver_incident_point_and_line_2),
inference(global_subsumption_just,[status(thm)],[c_942,c_665,c_1315]) ).
tcf(c_1321,plain,
$false,
inference(superposition,[status(thm)],[c_1268,c_1318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8046.5625MB
% 0.11/0.33 % OS : Linux 6.8.0-71-generic
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Sep 23 11:21:11 UTC 2026
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 Running first-order theorem proving
% 0.11/0.36 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.38
% 0.15/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.38
% 0.15/0.38 % Detected problem language: tptp
% 0.15/0.39 % Proving...
% 1.45/1.16 % SZS status Started for theBenchmark.p
% 1.45/1.16 % SZS status Theorem for theBenchmark.p
% 1.45/1.16
% 1.45/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.45/1.16
% 1.45/1.16 % ------ iProver source info
% 1.45/1.16
% 1.45/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 1.45/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.45/1.16 % git: non_committed_changes: false
% 1.45/1.16
% 1.45/1.16 % ------ Parsing...
% 1.45/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.45/1.16
% 1.45/1.16 % ------ Preprocessing... sf_s rm: 4 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.45/1.16
% 1.45/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.45/1.16 % ------ Proving...
% 1.45/1.16 % ------ Problem Properties
% 1.45/1.16
% 1.45/1.16 %
% 1.45/1.16 % clauses 35
% 1.45/1.16 % conjectures 5
% 1.45/1.16 % EPR 24
% 1.45/1.16 % Horn 18
% 1.45/1.16 % unary 11
% 1.45/1.16 % binary 9
% 1.45/1.16 % lits 85
% 1.45/1.16 % lits eq 0
% 1.45/1.16 % fd_pure 0
% 1.45/1.16 % fd_pseudo 0
% 1.45/1.16 % fd_cond 0
% 1.45/1.16 % fd_pseudo_cond 0
% 1.45/1.16 % AC symbols 0
% 1.45/1.16
% 1.45/1.16 % ------ Input Options Time Limit: Unbounded
% 1.45/1.16
% 1.45/1.16
% 1.45/1.16 % ------
% 1.45/1.16 % Current options:
% 1.45/1.16 % ------
% 1.45/1.16
% 1.45/1.16
% 1.45/1.16 %
% 1.45/1.16
% 1.45/1.16 % ------ Proving...
% 1.45/1.16 %
% 1.45/1.16
% 1.45/1.16 % SZS status Theorem for theBenchmark.p
% 1.45/1.16
% 1.45/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.45/1.16
% 1.45/1.16
%------------------------------------------------------------------------------