%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO222+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 01:20:26 PM UTC 2026
% Result : Theorem 3.94s 1.31s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 22 unt; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 199 ( 78 ~; 108 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 146 !; 2 ?; 68 :)
% 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(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f18,axiom,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( unorthogonal_lines(X0,X1)
& convergent_lines(X0,X1) )
=> ( ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(f20,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f23,conjecture,
! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
? [X0,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f49]) ).
fof(f53,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f59,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f68,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f73,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f20]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_51,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f53]) ).
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,[],[f56]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f60]) ).
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,[],[f64]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f73]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( unorthogonal_lines(X1,X3)
| unorthogonal_lines(X0,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_74,negated_conjecture,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f76]) ).
tcf(c_338,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( unorthogonal_lines(X1_iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2)
| unorthogonal_lines(X0_iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2)
| apart_point_and_line(X0_iProver_orthogonal_through_point_2,X1_iProver_apart_point_and_line_2)
| apart_point_and_line(X0_iProver_orthogonal_through_point_2,X0_iProver_apart_point_and_line_2)
| ~ distinct_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_73]) ).
tcf(c_340,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2] : ~ unorthogonal_lines(orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2),X0_iProver_apart_point_and_line_2),
inference(subtyping,[status(esa)],[c_71]) ).
tcf(c_343,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( unorthogonal_lines(X1_iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2)
| convergent_lines(X0_iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2)
| ~ unorthogonal_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2)
| ~ convergent_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_68]) ).
tcf(c_344,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( unorthogonal_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2)
| convergent_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_66]) ).
tcf(c_348,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( convergent_lines(X0_iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2)
| distinct_lines(X1_iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2)
| ~ convergent_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_62]) ).
tcf(c_352,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( ~ convergent_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2)
| ~ apart_point_and_line(intersection_point(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2),X1_iProver_apart_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_353,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( ~ convergent_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2)
| ~ apart_point_and_line(intersection_point(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2),X0_iProver_apart_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_356,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( convergent_lines(X1_iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2)
| convergent_lines(X0_iProver_apart_point_and_line_2,X2_iProver_apart_point_and_line_2)
| ~ convergent_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2) ),
inference(subtyping,[status(esa)],[c_54]) ).
tcf(c_359,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] : ~ convergent_lines(X0_iProver_apart_point_and_line_2,X0_iProver_apart_point_and_line_2),
inference(subtyping,[status(esa)],[c_51]) ).
tcf(c_362,plain,
~ convergent_lines(sK1,sK1),
inference(instantiation,[status(thm)],[c_359]) ).
tcf(c_365,plain,
~ unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1),
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_379,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2] : convergent_lines(orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2),X0_iProver_apart_point_and_line_2),
inference(resolution,[status(thm)],[c_344,c_340]) ).
tcf(c_380,plain,
convergent_lines(orthogonal_through_point(sK1,sK0),sK1),
inference(instantiation,[status(thm)],[c_379]) ).
tcf(c_435,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( convergent_lines(sK1,X0_iProver_apart_point_and_line_2)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0_iProver_apart_point_and_line_2)
| ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_348]) ).
tcf(c_436,plain,
( convergent_lines(sK1,sK1)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
| ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_435]) ).
tcf(c_450,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( convergent_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2)
| unorthogonal_lines(orthogonal_through_point(X1_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2),X1_iProver_apart_point_and_line_2)
| ~ unorthogonal_lines(X0_iProver_apart_point_and_line_2,orthogonal_through_point(X1_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2))
| ~ convergent_lines(X0_iProver_apart_point_and_line_2,orthogonal_through_point(X1_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2)) ),
inference(instantiation,[status(thm)],[c_343]) ).
tcf(c_451,plain,
( convergent_lines(sK1,sK1)
| unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1)
| ~ unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
| ~ convergent_lines(sK1,orthogonal_through_point(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_450]) ).
tcf(c_456,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( convergent_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2)
| convergent_lines(orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2),X1_iProver_apart_point_and_line_2)
| ~ convergent_lines(orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2),X0_iProver_apart_point_and_line_2) ),
inference(instantiation,[status(thm)],[c_356]) ).
tcf(c_463,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( unorthogonal_lines(X0_iProver_apart_point_and_line_2,X1_iProver_apart_point_and_line_2)
| apart_point_and_line(X0_iProver_orthogonal_through_point_2,X0_iProver_apart_point_and_line_2)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1_iProver_apart_point_and_line_2)
| apart_point_and_line(X0_iProver_orthogonal_through_point_2,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0_iProver_apart_point_and_line_2) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_558,plain,
~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0)),
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_635,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2] : ~ convergent_lines(orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2),orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2)),
inference(instantiation,[status(thm)],[c_359]) ).
tcf(c_637,plain,
~ convergent_lines(orthogonal_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)),
inference(instantiation,[status(thm)],[c_635]) ).
tcf(c_702,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X1_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2] :
( apart_point_and_line(X1_iProver_orthogonal_through_point_2,X0_iProver_apart_point_and_line_2)
| unorthogonal_lines(X0_iProver_apart_point_and_line_2,orthogonal_through_point(X1_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2))
| apart_point_and_line(X1_iProver_orthogonal_through_point_2,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(X1_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2))
| ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0_iProver_apart_point_and_line_2) ),
inference(instantiation,[status(thm)],[c_463]) ).
tcf(c_780,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2] :
( convergent_lines(X0_iProver_apart_point_and_line_2,orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2))
| convergent_lines(orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2),orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2))
| ~ convergent_lines(orthogonal_through_point(X0_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2),X0_iProver_apart_point_and_line_2) ),
inference(instantiation,[status(thm)],[c_456]) ).
tcf(c_782,plain,
( convergent_lines(sK1,orthogonal_through_point(sK1,sK0))
| convergent_lines(orthogonal_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| ~ convergent_lines(orthogonal_through_point(sK1,sK0),sK1) ),
inference(instantiation,[status(thm)],[c_780]) ).
tcf(c_841,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( ~ convergent_lines(sK1,X0_iProver_apart_point_and_line_2)
| ~ apart_point_and_line(intersection_point(sK1,X0_iProver_apart_point_and_line_2),sK1) ),
inference(instantiation,[status(thm)],[c_353]) ).
tcf(c_1386,plain,
( ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_352]) ).
tcf(c_1847,plain,
( ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_841]) ).
tcf(c_2273,plain,
! [X0_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2: iProver_orthogonal_through_point_2,X1_iProver_apart_point_and_line_2: iProver_apart_point_and_line_2] :
( unorthogonal_lines(X0_iProver_apart_point_and_line_2,orthogonal_through_point(X1_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2))
| apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),X0_iProver_apart_point_and_line_2)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(X1_iProver_apart_point_and_line_2,X0_iProver_orthogonal_through_point_2))
| apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0_iProver_apart_point_and_line_2) ),
inference(instantiation,[status(thm)],[c_702]) ).
tcf(c_2274,plain,
( unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
| apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),sK1)
| apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1) ),
inference(instantiation,[status(thm)],[c_2273]) ).
tcf(c_2275,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2274,c_1847,c_1386,c_782,c_637,c_558,c_451,c_436,c_380,c_365,c_362,c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO222+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 11:38:12 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.46 % Proving...
% 3.94/1.31 % SZS status Started for theBenchmark.p
% 3.94/1.31 % SZS status Theorem for theBenchmark.p
% 3.94/1.31
% 3.94/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.94/1.31
% 3.94/1.31 % ------ iProver source info
% 3.94/1.31
% 3.94/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.94/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.94/1.31 % git: non_committed_changes: false
% 3.94/1.31
% 3.94/1.31 % ------ Parsing...
% 3.94/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.94/1.31
% 3.94/1.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.94/1.31
% 3.94/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.94/1.31 % ------ Proving...
% 3.94/1.31 % ------ Problem Properties
% 3.94/1.31
% 3.94/1.31 %
% 3.94/1.31 % clauses 25
% 3.94/1.31 % conjectures 1
% 3.94/1.31 % EPR 16
% 3.94/1.31 % Horn 12
% 3.94/1.31 % unary 8
% 3.94/1.31 % binary 5
% 3.94/1.31 % lits 63
% 3.94/1.31 % lits eq 0
% 3.94/1.31 % fd_pure 0
% 3.94/1.31 % fd_pseudo 0
% 3.94/1.31 % fd_cond 0
% 3.94/1.31 % fd_pseudo_cond 0
% 3.94/1.31 % AC symbols 0
% 3.94/1.31
% 3.94/1.31 % ------ Input Options Time Limit: Unbounded
% 3.94/1.31
% 3.94/1.31
% 3.94/1.31 % ------
% 3.94/1.31 % Current options:
% 3.94/1.31 % ------
% 3.94/1.31
% 3.94/1.31
% 3.94/1.31 %
% 3.94/1.31
% 3.94/1.31 % ------ Proving...
% 3.94/1.31 %
% 3.94/1.31
% 3.94/1.31 % SZS status Theorem for theBenchmark.p
% 3.94/1.31
% 3.94/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.94/1.32
% 3.94/1.32
%------------------------------------------------------------------------------