%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO254+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 01:20:35 PM UTC 2026
% Result : Theorem 2.38s 1.35s
% Output : CNFRefutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 99 ( 19 unt; 0 def)
% Number of atoms : 302 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 356 ( 153 ~; 161 |; 32 &)
% ( 1 <=>; 9 =>; 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 : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 175 ( 0 sgn 169 !; 6 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
<=> ( ~ unequally_directed_lines(X0,line_connecting(X1,X2))
& ~ ( left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0) )
& ~ ( left_apart_point(X1,reverse_line(X0))
| left_apart_point(X1,X0) )
& distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',bf_def) ).
fof(f6,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag2) ).
fof(f11,axiom,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X1)
=> ( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag6) ).
fof(f14,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) )
=> ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag9) ).
fof(f15,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,reverse_line(X1))
| left_apart_point(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag10) ).
fof(f16,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag11) ).
fof(f18,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1)
& line(X1)
& line(X0) )
=> point(intersection_point(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco2) ).
fof(f22,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,reverse_line(X1))
& unequally_directed_lines(X0,X1) )
=> ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco6) ).
fof(f25,axiom,
! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco9) ).
fof(f28,axiom,
! [X0,X1,X2] :
( ( left_apart_point(X0,X2)
& distinct_points(X0,X1) )
=> ( left_convergent_lines(line_connecting(X0,X1),X2)
| left_apart_point(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oaguc2) ).
fof(f32,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X0,X2)
& distinct_points(X0,X1) )
=> ( before_on_line(X2,X1,X0)
& before_on_line(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X0,X2)
& distinct_points(X0,X1) )
=> ( before_on_line(X2,X1,X0)
& before_on_line(X2,X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( ~ unequally_directed_lines(X0,line_connecting(X1,X2))
& ~ ( left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0) )
& ~ ( left_apart_point(X1,reverse_line(X0))
| left_apart_point(X1,X0) )
& distinct_points(X1,X2) )
=> before_on_line(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f37,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,line_connecting(X1,X2))
| left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0)
| left_apart_point(X1,reverse_line(X0))
| left_apart_point(X1,X0)
| ~ distinct_points(X1,X2)
| before_on_line(X0,X1,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f38,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,line_connecting(X1,X2))
| left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0)
| left_apart_point(X1,reverse_line(X0))
| left_apart_point(X1,X0)
| ~ distinct_points(X1,X2)
| before_on_line(X0,X1,X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(flattening,[],[f43]) ).
fof(f49,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f50,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ left_apart_point(X0,reverse_line(X1))
& ~ left_apart_point(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f52,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,reverse_line(X1))
& ~ left_convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f55,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f56,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(flattening,[],[f55]) ).
fof(f61,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f62,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X0) ) ),
inference(flattening,[],[f61]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ left_apart_point(X0,X2)
| ~ distinct_points(X0,X1)
| left_convergent_lines(line_connecting(X0,X1),X2)
| left_apart_point(X1,X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ left_apart_point(X0,X2)
| ~ distinct_points(X0,X1)
| left_convergent_lines(line_connecting(X0,X1),X2)
| left_apart_point(X1,X2) ),
inference(flattening,[],[f65]) ).
fof(f73,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X0,X2)
& distinct_points(X0,X1)
& ( ~ before_on_line(X2,X1,X0)
| ~ before_on_line(X2,X0,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f74,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X0,X2)
& distinct_points(X0,X1)
& ( ~ before_on_line(X2,X1,X0)
| ~ before_on_line(X2,X0,X1) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
( ~ apart_point_and_line(sK1,sK2)
& ~ apart_point_and_line(sK0,sK2)
& distinct_points(sK0,sK1)
& ( ~ before_on_line(sK2,sK1,sK0)
| ~ before_on_line(sK2,sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f74]) ).
fof(f78,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,line_connecting(X1,X2))
| left_apart_point(X2,reverse_line(X0))
| left_apart_point(X2,X0)
| left_apart_point(X1,reverse_line(X0))
| left_apart_point(X1,X0)
| ~ distinct_points(X1,X2)
| before_on_line(X0,X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f79,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f90,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| left_convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f92,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f51]) ).
fof(f93,plain,
! [X0,X1] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f52]) ).
fof(f94,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f52]) ).
fof(f96,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ line(X1)
| ~ line(X0)
| point(intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f101,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f105,plain,
! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
inference(cnf_transformation,[],[f25]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ left_apart_point(X0,X2)
| ~ distinct_points(X0,X1)
| left_convergent_lines(line_connecting(X0,X1),X2)
| left_apart_point(X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f114,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f115,plain,
( ~ before_on_line(sK2,sK1,sK0)
| ~ before_on_line(sK2,sK0,sK1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( left_apart_point(X1,X2)
| left_apart_point(X0,X2)
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X0,reverse_line(X2))
| before_on_line(X2,X0,X1)
| unequally_directed_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_52,plain,
! [X0: $i] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f79]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f92]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f94]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : ~ left_convergent_lines(X0,reverse_line(X1)),
inference(cnf_transformation,[],[f93]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( point(intersection_point(X0,X1))
| ~ line(X1)
| ~ line(X0)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
inference(cnf_transformation,[],[f105]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( left_apart_point(X2,X1)
| left_convergent_lines(line_connecting(X0,X2),X1)
| ~ distinct_points(X0,X2)
| ~ left_apart_point(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_85,negated_conjecture,
( ~ before_on_line(sK2,sK1,sK0)
| ~ before_on_line(sK2,sK0,sK1) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_86,negated_conjecture,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f114]) ).
tcf(c_93,plain,
~ distinct_points(sK0,sK0),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_75,c_66,c_67,c_63]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] : ~ left_apart_point(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_81,c_64]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_113]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(renaming,[status(thm)],[c_129]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] :
( left_apart_point(X1,X2)
| left_apart_point(X0,X2)
| left_apart_point(X1,reverse_line(X2))
| before_on_line(X2,X0,X1)
| unequally_directed_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_119]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i] :
( before_on_line(X2,X0,X1)
| unequally_directed_lines(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147,c_119,c_119,c_119]) ).
tcf(c_287,plain,
! [X0: $i] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0)
| ~ distinct_points(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_288,plain,
( distinct_points(sK1,sK0)
| distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_287]) ).
tcf(c_289,plain,
! [X0: $i] :
( before_on_line(X0,sK0,sK1)
| unequally_directed_lines(X0,line_connecting(sK0,sK1))
| ~ distinct_points(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_223]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] :
( before_on_line(X1,sK1,X0)
| unequally_directed_lines(X1,line_connecting(sK1,X0))
| ~ distinct_points(sK1,X0) ),
inference(instantiation,[status(thm)],[c_223]) ).
tcf(c_295,plain,
( before_on_line(sK2,sK0,sK1)
| unequally_directed_lines(sK2,line_connecting(sK0,sK1))
| ~ distinct_points(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_289]) ).
tcf(c_296,plain,
! [X0: $i] :
( unequally_directed_lines(sK2,X0)
| unequally_directed_lines(line_connecting(sK0,sK1),X0)
| ~ unequally_directed_lines(sK2,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i,X2: $i] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(line_connecting(sK1,X1),X2)
| ~ unequally_directed_lines(X0,line_connecting(sK1,X1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,line_connecting(sK1,X1))
| ~ unequally_directed_lines(X0,reverse_line(line_connecting(sK1,X1))) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_321,plain,
( before_on_line(sK2,sK1,sK0)
| unequally_directed_lines(sK2,line_connecting(sK1,sK0))
| ~ distinct_points(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_291]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i,X2: $i] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(line_connecting(X1,sK1),X2)
| ~ unequally_directed_lines(X0,line_connecting(X1,sK1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(X0,line_connecting(X1,sK1))
| ~ unequally_directed_lines(X0,reverse_line(line_connecting(X1,sK1))) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_344,plain,
! [X0: $i] :
( unequally_directed_lines(sK2,X0)
| unequally_directed_lines(line_connecting(sK1,sK0),X0)
| ~ unequally_directed_lines(sK2,line_connecting(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_307]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i] :
( unequally_directed_lines(X0,reverse_line(line_connecting(sK1,X1)))
| unequally_directed_lines(line_connecting(X1,sK1),reverse_line(line_connecting(sK1,X1)))
| ~ unequally_directed_lines(X0,line_connecting(X1,sK1)) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_354,plain,
! [X0: $i] : ~ unequally_directed_lines(line_connecting(X0,sK1),reverse_line(line_connecting(sK1,X0))),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( ~ unequally_directed_lines(line_connecting(X0,sK1),line_connecting(X1,sK1))
| ~ unequally_directed_lines(line_connecting(X0,sK1),reverse_line(line_connecting(X1,sK1))) ),
inference(instantiation,[status(thm)],[c_331]) ).
tcf(c_391,plain,
! [X0: $i] :
( unequally_directed_lines(sK2,line_connecting(sK1,X0))
| unequally_directed_lines(line_connecting(sK0,sK1),line_connecting(sK1,X0))
| ~ unequally_directed_lines(sK2,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_296]) ).
tcf(c_462,plain,
! [X0: $i] :
( ~ unequally_directed_lines(sK2,line_connecting(sK1,X0))
| ~ unequally_directed_lines(sK2,reverse_line(line_connecting(sK1,X0))) ),
inference(instantiation,[status(thm)],[c_308]) ).
tcf(c_463,plain,
! [X0: $i] :
( unequally_directed_lines(sK2,line_connecting(X0,sK1))
| unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(X0,sK1))
| ~ unequally_directed_lines(sK2,line_connecting(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_344]) ).
tcf(c_687,plain,
( unequally_directed_lines(sK2,line_connecting(sK1,sK1))
| unequally_directed_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK1))
| ~ unequally_directed_lines(sK2,line_connecting(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_391]) ).
tcf(c_689,plain,
( unequally_directed_lines(sK2,reverse_line(line_connecting(sK1,sK1)))
| unequally_directed_lines(line_connecting(sK1,sK1),reverse_line(line_connecting(sK1,sK1)))
| ~ unequally_directed_lines(sK2,line_connecting(sK1,sK1)) ),
inference(instantiation,[status(thm)],[c_353]) ).
tcf(c_755,plain,
( unequally_directed_lines(sK2,line_connecting(sK1,sK1))
| unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(sK1,sK1))
| ~ unequally_directed_lines(sK2,line_connecting(sK1,sK0)) ),
inference(instantiation,[status(thm)],[c_463]) ).
tcf(c_757,plain,
( ~ unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(sK1,sK1))
| ~ unequally_directed_lines(line_connecting(sK1,sK0),reverse_line(line_connecting(sK1,sK1))) ),
inference(instantiation,[status(thm)],[c_308]) ).
tcf(c_836,plain,
( ~ unequally_directed_lines(sK2,line_connecting(sK1,sK1))
| ~ unequally_directed_lines(sK2,reverse_line(line_connecting(sK1,sK1))) ),
inference(instantiation,[status(thm)],[c_462]) ).
tcf(c_881,plain,
! [X0: $i] :
( unequally_directed_lines(line_connecting(sK1,sK1),reverse_line(line_connecting(sK1,sK1)))
| unequally_directed_lines(line_connecting(sK1,X0),reverse_line(line_connecting(sK1,sK1)))
| ~ unequally_directed_lines(line_connecting(sK1,X0),line_connecting(sK1,sK1)) ),
inference(instantiation,[status(thm)],[c_353]) ).
tcf(c_884,plain,
( unequally_directed_lines(line_connecting(sK1,sK1),reverse_line(line_connecting(sK1,sK1)))
| unequally_directed_lines(line_connecting(sK1,sK0),reverse_line(line_connecting(sK1,sK1)))
| ~ unequally_directed_lines(line_connecting(sK1,sK0),line_connecting(sK1,sK1)) ),
inference(instantiation,[status(thm)],[c_881]) ).
tcf(c_974,plain,
! [X0: $i] :
( unequally_directed_lines(line_connecting(sK1,sK1),reverse_line(line_connecting(sK1,sK1)))
| unequally_directed_lines(line_connecting(X0,sK1),reverse_line(line_connecting(sK1,sK1)))
| ~ unequally_directed_lines(line_connecting(X0,sK1),line_connecting(sK1,sK1)) ),
inference(instantiation,[status(thm)],[c_353]) ).
tcf(c_976,plain,
( unequally_directed_lines(line_connecting(sK1,sK1),reverse_line(line_connecting(sK1,sK1)))
| unequally_directed_lines(line_connecting(sK0,sK1),reverse_line(line_connecting(sK1,sK1)))
| ~ unequally_directed_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK1)) ),
inference(instantiation,[status(thm)],[c_974]) ).
tcf(c_1266,plain,
! [X0: $i] :
( ~ unequally_directed_lines(line_connecting(X0,sK1),line_connecting(sK1,sK1))
| ~ unequally_directed_lines(line_connecting(X0,sK1),reverse_line(line_connecting(sK1,sK1))) ),
inference(instantiation,[status(thm)],[c_365]) ).
tcf(c_1268,plain,
( ~ unequally_directed_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK1))
| ~ unequally_directed_lines(line_connecting(sK0,sK1),reverse_line(line_connecting(sK1,sK1))) ),
inference(instantiation,[status(thm)],[c_1266]) ).
tcf(c_2067,plain,
~ unequally_directed_lines(line_connecting(sK1,sK1),reverse_line(line_connecting(sK1,sK1))),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_2069,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2067,c_1268,c_976,c_884,c_836,c_757,c_755,c_689,c_687,c_321,c_295,c_288,c_85,c_93,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO254+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n001.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 11:48:06 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.44
% 0.14/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.44
% 0.14/0.44 % Detected problem language: tptp
% 0.14/0.46 % Proving...
% 2.38/1.35 % SZS status Started for theBenchmark.p
% 2.38/1.35 % SZS status Theorem for theBenchmark.p
% 2.38/1.35
% 2.38/1.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.38/1.35
% 2.38/1.35 % ------ iProver source info
% 2.38/1.35
% 2.38/1.35 % git: date: 2026-07-19 20:42:38 +0200
% 2.38/1.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.38/1.35 % git: non_committed_changes: false
% 2.38/1.35
% 2.38/1.35 % ------ Parsing...
% 2.38/1.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.38/1.35
% 2.38/1.35 % ------ Preprocessing... sf_s rm: 15 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.38/1.35
% 2.38/1.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.38/1.35 % ------ Proving...
% 2.38/1.35 % ------ Problem Properties
% 2.38/1.35
% 2.38/1.35 %
% 2.38/1.35 % clauses 10
% 2.38/1.35 % conjectures 2
% 2.38/1.35 % EPR 6
% 2.38/1.35 % Horn 7
% 2.38/1.35 % unary 5
% 2.38/1.35 % binary 2
% 2.38/1.35 % lits 18
% 2.38/1.35 % lits eq 0
% 2.38/1.35 % fd_pure 0
% 2.38/1.35 % fd_pseudo 0
% 2.38/1.35 % fd_cond 0
% 2.38/1.35 % fd_pseudo_cond 0
% 2.38/1.35 % AC symbols 0
% 2.38/1.35
% 2.38/1.35 % ------ Schedule dynamic 5 is on
% 2.38/1.35
% 2.38/1.35 % ------ no equalities: superposition off
% 2.38/1.35
% 2.38/1.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.38/1.35
% 2.38/1.35
% 2.38/1.35 % ------
% 2.38/1.35 % Current options:
% 2.38/1.35 % ------
% 2.38/1.35
% 2.38/1.35
% 2.38/1.35 %
% 2.38/1.35
% 2.38/1.35 % ------ Proving...
% 2.38/1.35 %
% 2.38/1.35
% 2.38/1.35 % SZS status Theorem for theBenchmark.p
% 2.38/1.35
% 2.38/1.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.38/1.35
% 2.38/1.35
%------------------------------------------------------------------------------