%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO223+2 : 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 : n020.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 3.52s 1.40s
% Output : CNFRefutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 99 ( 34 unt; 0 def)
% Number of atoms : 268 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 270 ( 101 ~; 156 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 194 ( 0 sgn 192 !; 2 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart5) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f14,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f15,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(f16,axiom,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f17,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(f18,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f19,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(f20,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(f21,conjecture,
! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1] : distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(flattening,[],[f33]) ).
fof(f39,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,[],[f20]) ).
fof(f40,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,[],[f39]) ).
fof(f41,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,[],[f17]) ).
fof(f42,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,[],[f41]) ).
fof(f43,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).
fof(f44,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f43]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X1,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f51,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f52,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f54,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f18]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f56,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f60,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,[],[f40]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f65,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_49,negated_conjecture,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f44]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X0,X1)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_55,plain,
! [X0: $i] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f50]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : ~ convergent_lines(parallel_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f52]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(cnf_transformation,[],[f54]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_61,plain,
! [X0: $i] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f56]) ).
tcf(c_65,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,[],[f60]) ).
tcf(c_67,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,[],[f63]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_299,plain,
! [X0: $i] :
( apart_point_and_line(X0,parallel_through_point(sK1,sK0))
| apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_300,plain,
( apart_point_and_line(sK0,parallel_through_point(sK1,sK0))
| apart_point_and_line(sK0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_299]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( unorthogonal_lines(X2,X0)
| apart_point_and_line(X3,X2)
| unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
| apart_point_and_line(X3,orthogonal_through_point(X0,X1))
| ~ distinct_lines(orthogonal_through_point(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i] :
( unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
| convergent_lines(orthogonal_through_point(X0,X1),X0) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X0,X1)
| unorthogonal_lines(orthogonal_through_point(X1,X2),X1)
| ~ unorthogonal_lines(X0,orthogonal_through_point(X1,X2))
| ~ convergent_lines(X0,orthogonal_through_point(X1,X2)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i,X2: $i] :
( convergent_lines(X2,X0)
| unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
| ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X2)
| ~ convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(X2,X0)
| unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
| ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X2)
| ~ convergent_lines(orthogonal_through_point(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_316,plain,
! [X0: $i] :
( convergent_lines(parallel_through_point(sK1,sK0),X0)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_323,plain,
~ apart_point_and_line(sK0,parallel_through_point(sK1,sK0)),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] :
( distinct_lines(orthogonal_through_point(X0,X1),X0)
| ~ convergent_lines(orthogonal_through_point(X0,X1),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i,X2: $i] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1)) ),
inference(instantiation,[status(thm)],[c_304]) ).
tcf(c_340,plain,
~ apart_point_and_line(sK0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( unorthogonal_lines(orthogonal_through_point(X2,X3),X0)
| unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
| apart_point_and_line(X4,orthogonal_through_point(X2,X3))
| apart_point_and_line(X4,orthogonal_through_point(X0,X1))
| ~ distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X2,X3)) ),
inference(instantiation,[status(thm)],[c_301]) ).
tcf(c_372,plain,
( convergent_lines(parallel_through_point(sK1,sK0),sK1)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
| ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_373,plain,
~ convergent_lines(parallel_through_point(sK1,sK0),sK1),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X0,X2)
| distinct_lines(orthogonal_through_point(X0,X1),X2)
| ~ distinct_lines(orthogonal_through_point(X0,X1),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_499,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1))
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1)) ),
inference(instantiation,[status(thm)],[c_325]) ).
tcf(c_652,plain,
~ distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_775,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_lines(X0,orthogonal_through_point(X0,X2))
| distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X0,X2))
| ~ distinct_lines(orthogonal_through_point(X0,X1),X0) ),
inference(instantiation,[status(thm)],[c_416]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i,X2: $i] : ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1)),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_858,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_499]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( unorthogonal_lines(X3,orthogonal_through_point(X0,X1))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1))
| ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),X3)
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),X3) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_1149,plain,
! [X0: $i] :
( convergent_lines(X0,orthogonal_through_point(sK1,sK0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
| ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
inference(instantiation,[status(thm)],[c_308]) ).
tcf(c_1816,plain,
~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0)),
inference(instantiation,[status(thm)],[c_803]) ).
tcf(c_2080,plain,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_328]) ).
tcf(c_2105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
| apart_point_and_line(X3,orthogonal_through_point(X0,X1))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),X0)
| apart_point_and_line(X3,orthogonal_through_point(orthogonal_through_point(X0,X1),X2))
| ~ distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(orthogonal_through_point(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_346]) ).
tcf(c_2123,plain,
! [X0: $i] :
( distinct_lines(orthogonal_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),X0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),X0),orthogonal_through_point(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_775]) ).
tcf(c_2125,plain,
( distinct_lines(orthogonal_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| distinct_lines(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),orthogonal_through_point(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_2123]) ).
tcf(c_2304,plain,
! [X0: $i] :
( unorthogonal_lines(X0,orthogonal_through_point(sK1,sK0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
| ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
inference(instantiation,[status(thm)],[c_870]) ).
tcf(c_2846,plain,
( convergent_lines(sK1,orthogonal_through_point(sK1,sK0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
| ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1) ),
inference(instantiation,[status(thm)],[c_1149]) ).
tcf(c_2986,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))
| ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
| ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1) ),
inference(instantiation,[status(thm)],[c_2304]) ).
tcf(c_3279,plain,
! [X0: $i] :
( convergent_lines(X0,sK1)
| unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1)
| ~ unorthogonal_lines(X0,orthogonal_through_point(sK1,sK0))
| ~ convergent_lines(X0,orthogonal_through_point(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_306]) ).
tcf(c_7243,plain,
! [X0: $i] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1)
| apart_point_and_line(X0,orthogonal_through_point(sK1,sK0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
| apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ distinct_lines(orthogonal_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_2105]) ).
tcf(c_7244,plain,
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1)
| apart_point_and_line(sK0,orthogonal_through_point(sK1,sK0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
| apart_point_and_line(sK0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ distinct_lines(orthogonal_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_7243]) ).
tcf(c_7678,plain,
~ unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_7683,plain,
~ apart_point_and_line(sK0,orthogonal_through_point(sK1,sK0)),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_9363,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_3279]) ).
tcf(c_9364,plain,
~ convergent_lines(sK1,sK1),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_9365,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9364,c_9363,c_7683,c_7678,c_7244,c_2986,c_2846,c_2125,c_2080,c_1816,c_858,c_652,c_373,c_372,c_340,c_323,c_300,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.40 % Computer : n020.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.41 % DateTime : Wed Sep 23 11:34:33 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 0.15/0.47
% 0.15/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.47
% 0.15/0.48 % Detected problem language: tptp
% 0.15/0.50 % Proving...
% 3.52/1.40 % SZS status Started for theBenchmark.p
% 3.52/1.40 % SZS status Theorem for theBenchmark.p
% 3.52/1.40
% 3.52/1.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.52/1.40
% 3.52/1.40 % ------ iProver source info
% 3.52/1.40
% 3.52/1.40 % git: date: 2026-07-19 20:42:38 +0200
% 3.52/1.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.52/1.40 % git: non_committed_changes: false
% 3.52/1.40
% 3.52/1.40 % ------ Parsing...
% 3.52/1.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.52/1.40
% 3.52/1.40 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.52/1.40
% 3.52/1.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.52/1.40 % ------ Proving...
% 3.52/1.40 % ------ Problem Properties
% 3.52/1.40
% 3.52/1.40 %
% 3.52/1.40 % clauses 21
% 3.52/1.40 % conjectures 1
% 3.52/1.40 % EPR 16
% 3.52/1.40 % Horn 9
% 3.52/1.40 % unary 8
% 3.52/1.40 % binary 2
% 3.52/1.40 % lits 54
% 3.52/1.40 % lits eq 0
% 3.52/1.40 % fd_pure 0
% 3.52/1.40 % fd_pseudo 0
% 3.52/1.40 % fd_cond 0
% 3.52/1.40 % fd_pseudo_cond 0
% 3.52/1.40 % AC symbols 0
% 3.52/1.40
% 3.52/1.40 % ------ Schedule dynamic 5 is on
% 3.52/1.40
% 3.52/1.40 % ------ no equalities: superposition off
% 3.52/1.40
% 3.52/1.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.52/1.40
% 3.52/1.40
% 3.52/1.40 % ------
% 3.52/1.40 % Current options:
% 3.52/1.40 % ------
% 3.52/1.40
% 3.52/1.40
% 3.52/1.40 %
% 3.52/1.40
% 3.52/1.40 % ------ Proving...
% 3.52/1.40 %
% 3.52/1.40
% 3.52/1.40 % SZS status Theorem for theBenchmark.p
% 3.52/1.40
% 3.52/1.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.73/1.40
% 4.73/1.40
%------------------------------------------------------------------------------