%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO089+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:19:51 PM UTC 2026
% Result : Theorem 91.65s 14.89s
% Output : CNFRefutation 91.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 125 ( 16 unt; 0 def)
% Number of atoms : 473 ( 49 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 560 ( 212 ~; 265 |; 71 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 254 ( 0 sgn 238 !; 16 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( X0 = sum(X1,X2)
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X2)
| incident_c(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',sum_defn) ).
fof(f3,axiom,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( ( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1) )
=> ( part_of(X3,X2)
| part_of(X2,X3) ) )
& incident_c(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).
fof(f4,axiom,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).
fof(f17,conjecture,
! [X0,X1] :
( ? [X2] :
( inner_point(X1,X2)
& part_of(X2,X0) )
=> inner_point(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_11) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ? [X2] :
( inner_point(X1,X2)
& part_of(X2,X0) )
=> inner_point(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( ~ incident_c(X2,X1)
| incident_c(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f22,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| part_of(X3,X2)
| part_of(X2,X3) )
& incident_c(X0,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( ! [X2,X3] :
( ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| part_of(X3,X2)
| part_of(X2,X3) )
& incident_c(X0,X1) ) ),
inference(flattening,[],[f22]) ).
fof(f40,plain,
? [X0,X1] :
( ? [X2] :
( inner_point(X1,X2)
& part_of(X2,X0) )
& ~ inner_point(X1,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X2] :
( ~ incident_c(X2,X1)
| incident_c(X2,X0) ) )
& ( ? [X2] :
( incident_c(X2,X1)
& ~ incident_c(X2,X0) )
| part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f42,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0) ) )
& ( ? [X2] :
( incident_c(X2,X1)
& ~ incident_c(X2,X0) )
| part_of(X1,X0) ) ),
inference(rectify,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0) ) )
& ( ( incident_c(sK0(X0,X1),X1)
& ~ incident_c(sK0(X0,X1),X0) )
| part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X3] :
( ( ~ incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| incident_c(X3,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X3] :
( ( ~ incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| incident_c(X3,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X4] :
( ( ~ incident_c(X4,X0)
| incident_c(X4,X2)
| incident_c(X4,X1) )
& ( ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) )
| incident_c(X4,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X4] :
( ( ~ incident_c(X4,X0)
| incident_c(X4,X2)
| incident_c(X4,X1) )
& ( ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) )
| incident_c(X4,X0) ) ) )
& ( ( ( incident_c(sK1(X0,X1,X2),X0)
| incident_c(sK1(X0,X1,X2),X2)
| incident_c(sK1(X0,X1,X2),X1) )
& ( ~ incident_c(sK1(X0,X1,X2),X0)
| ( ~ incident_c(sK1(X0,X1,X2),X2)
& ~ incident_c(sK1(X0,X1,X2),X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ( ~ end_point(X0,X1)
| ( ! [X2,X3] :
( ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| part_of(X3,X2)
| part_of(X2,X3) )
& incident_c(X0,X1) ) )
& ( ? [X2,X3] :
( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1)
& ~ part_of(X3,X2)
& ~ part_of(X2,X3) )
| ~ incident_c(X0,X1)
| end_point(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f49,plain,
! [X0,X1] :
( ( ~ end_point(X0,X1)
| ( ! [X2,X3] :
( ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| part_of(X3,X2)
| part_of(X2,X3) )
& incident_c(X0,X1) ) )
& ( ? [X2,X3] :
( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1)
& ~ part_of(X3,X2)
& ~ part_of(X2,X3) )
| ~ incident_c(X0,X1)
| end_point(X0,X1) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ( ~ end_point(X0,X1)
| ( ! [X4,X5] :
( ~ incident_c(X0,X5)
| ~ incident_c(X0,X4)
| ~ part_of(X5,X1)
| ~ part_of(X4,X1)
| part_of(X5,X4)
| part_of(X4,X5) )
& incident_c(X0,X1) ) )
& ( ? [X2,X3] :
( incident_c(X0,X3)
& incident_c(X0,X2)
& part_of(X3,X1)
& part_of(X2,X1)
& ~ part_of(X3,X2)
& ~ part_of(X2,X3) )
| ~ incident_c(X0,X1)
| end_point(X0,X1) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ( ~ end_point(X0,X1)
| ( ! [X4,X5] :
( ~ incident_c(X0,X5)
| ~ incident_c(X0,X4)
| ~ part_of(X5,X1)
| ~ part_of(X4,X1)
| part_of(X5,X4)
| part_of(X4,X5) )
& incident_c(X0,X1) ) )
& ( ( incident_c(X0,sK3(X0,X1))
& incident_c(X0,sK2(X0,X1))
& part_of(sK3(X0,X1),X1)
& part_of(sK2(X0,X1),X1)
& ~ part_of(sK3(X0,X1),sK2(X0,X1))
& ~ part_of(sK2(X0,X1),sK3(X0,X1)) )
| ~ incident_c(X0,X1)
| end_point(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ( ~ inner_point(X0,X1)
| ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) )
& ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| inner_point(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f53,plain,
! [X0,X1] :
( ( ~ inner_point(X0,X1)
| ( ~ end_point(X0,X1)
& incident_c(X0,X1) ) )
& ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| inner_point(X0,X1) ) ),
inference(flattening,[],[f52]) ).
fof(f67,plain,
( inner_point(sK14,sK15)
& part_of(sK15,sK13)
& ~ inner_point(sK14,sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f40]) ).
fof(f68,plain,
! [X3,X0,X1] :
( ~ part_of(X1,X0)
| ~ incident_c(X3,X1)
| incident_c(X3,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f69,plain,
! [X0,X1] :
( incident_c(sK0(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0,X1] :
( ~ incident_c(sK0(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f72,plain,
! [X2,X0,X1,X4] :
( sum(X1,X2) != X0
| ~ incident_c(X4,X2)
| incident_c(X4,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
! [X2,X0,X1] :
( incident_c(sK1(X0,X1,X2),X0)
| incident_c(sK1(X0,X1,X2),X2)
| incident_c(sK1(X0,X1,X2),X1)
| sum(X1,X2) = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ incident_c(sK1(X0,X1,X2),X0)
| ~ incident_c(sK1(X0,X1,X2),X2)
| sum(X1,X2) = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ incident_c(sK1(X0,X1,X2),X0)
| ~ incident_c(sK1(X0,X1,X2),X1)
| sum(X1,X2) = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f77,plain,
! [X0,X1,X4,X5] :
( ~ end_point(X0,X1)
| ~ incident_c(X0,X5)
| ~ incident_c(X0,X4)
| ~ part_of(X5,X1)
| ~ part_of(X4,X1)
| part_of(X5,X4)
| part_of(X4,X5) ),
inference(cnf_transformation,[],[f51]) ).
fof(f79,plain,
! [X0,X1] :
( incident_c(X0,sK3(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f80,plain,
! [X0,X1] :
( incident_c(X0,sK2(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f81,plain,
! [X0,X1] :
( part_of(sK3(X0,X1),X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f82,plain,
! [X0,X1] :
( part_of(sK2(X0,X1),X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f83,plain,
! [X0,X1] :
( ~ part_of(sK3(X0,X1),sK2(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f84,plain,
! [X0,X1] :
( ~ part_of(sK2(X0,X1),sK3(X0,X1))
| ~ incident_c(X0,X1)
| end_point(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f85,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f86,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f87,plain,
! [X0,X1] :
( end_point(X0,X1)
| ~ incident_c(X0,X1)
| inner_point(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f109,plain,
inner_point(sK14,sK15),
inference(cnf_transformation,[],[f67]) ).
fof(f110,plain,
part_of(sK15,sK13),
inference(cnf_transformation,[],[f67]) ).
fof(f111,plain,
~ inner_point(sK14,sK13),
inference(cnf_transformation,[],[f67]) ).
fof(f113,plain,
! [X2,X1,X4] :
( ~ incident_c(X4,X2)
| incident_c(X4,sum(X1,X2)) ),
inference(equality_resolution,[],[f72]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| ~ incident_c(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| incident_c(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sum(X1,X2) = X0 )
| ~ incident_c(sK1(X0,X1,X2),X1)
| ~ incident_c(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sum(X1,X2) = X0 )
| ~ incident_c(sK1(X0,X1,X2),X2)
| ~ incident_c(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(sK1(X2,X0,X1),X2)
| incident_c(sK1(X2,X0,X1),X1)
| incident_c(sK1(X2,X0,X1),X0)
| ( sum(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X0,sum(X2,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ~ part_of(sK2(X0,X1),sK3(X0,X1)) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ~ part_of(sK3(X0,X1),sK2(X0,X1)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| part_of(sK2(X0,X1),X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| part_of(sK3(X0,X1),X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| incident_c(X0,sK2(X0,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| incident_c(X0,sK3(X0,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( part_of(X2,X0)
| part_of(X0,X2)
| ~ end_point(X3,X1)
| ~ incident_c(X3,X2)
| ~ incident_c(X3,X0)
| ~ part_of(X2,X1)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( inner_point(X0,X1)
| end_point(X0,X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_90,negated_conjecture,
~ inner_point(sK14,sK13),
inference(cnf_transformation,[],[f111]) ).
tcf(c_91,negated_conjecture,
part_of(sK15,sK13),
inference(cnf_transformation,[],[f110]) ).
tcf(c_92,negated_conjecture,
inner_point(sK14,sK15),
inference(cnf_transformation,[],[f109]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ( X1 != sK13 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_90]) ).
tcf(c_739,plain,
( end_point(sK14,sK13)
| ~ incident_c(sK14,sK13) ),
inference(unflattening,[status(thm)],[c_738]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i] :
( ~ end_point(X0,X1)
| ( X1 != sK15 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_92]) ).
tcf(c_757,plain,
~ end_point(sK14,sK15),
inference(unflattening,[status(thm)],[c_756]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,X1)
| ( X1 != sK15 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_92]) ).
tcf(c_762,plain,
incident_c(sK14,sK15),
inference(unflattening,[status(thm)],[c_761]) ).
tcf(c_1476,plain,
! [X0: $i] :
( incident_c(sK14,X0)
| ~ incident_c(sK14,sK15)
| ~ part_of(sK15,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1477,plain,
( incident_c(sK14,sK13)
| ~ incident_c(sK14,sK15)
| ~ part_of(sK15,sK13) ),
inference(instantiation,[status(thm)],[c_1476]) ).
tcf(c_1478,plain,
( end_point(sK14,sK15)
| incident_c(sK14,sK3(sK14,sK15))
| ~ incident_c(sK14,sK15) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1479,plain,
( end_point(sK14,sK15)
| incident_c(sK14,sK2(sK14,sK15))
| ~ incident_c(sK14,sK15) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1482,plain,
( end_point(sK14,sK15)
| ~ incident_c(sK14,sK15)
| ~ part_of(sK3(sK14,sK15),sK2(sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1483,plain,
( end_point(sK14,sK15)
| ~ incident_c(sK14,sK15)
| ~ part_of(sK2(sK14,sK15),sK3(sK14,sK15)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_2029,plain,
! [X0: $i,X1: $i] :
( part_of(sK3(sK14,sK15),sK2(sK14,sK15))
| part_of(sK2(sK14,sK15),sK3(sK14,sK15))
| ~ end_point(X1,X0)
| ~ incident_c(X1,sK3(sK14,sK15))
| ~ incident_c(X1,sK2(sK14,sK15))
| ~ part_of(sK3(sK14,sK15),X0)
| ~ part_of(sK2(sK14,sK15),X0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3908,plain,
! [X0: $i,X1: $i] :
( incident_c(sK1(X0,X0,X1),X1)
| incident_c(sK1(X0,X0,X1),X0)
| ( sum(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
tcf(c_5987,plain,
! [X0: $i] :
( part_of(sK3(sK14,sK15),X0)
| ~ incident_c(sK0(X0,sK3(sK14,sK15)),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_5988,plain,
( part_of(sK3(sK14,sK15),sK13)
| ~ incident_c(sK0(sK13,sK3(sK14,sK15)),sK13) ),
inference(instantiation,[status(thm)],[c_5987]) ).
tcf(c_9178,plain,
! [X0: $i] :
( part_of(sK3(sK14,sK15),sK2(sK14,sK15))
| part_of(sK2(sK14,sK15),sK3(sK14,sK15))
| ~ end_point(sK14,X0)
| ~ incident_c(sK14,sK3(sK14,sK15))
| ~ incident_c(sK14,sK2(sK14,sK15))
| ~ part_of(sK3(sK14,sK15),X0)
| ~ part_of(sK2(sK14,sK15),X0) ),
inference(instantiation,[status(thm)],[c_2029]) ).
tcf(c_9181,plain,
( part_of(sK3(sK14,sK15),sK2(sK14,sK15))
| part_of(sK2(sK14,sK15),sK3(sK14,sK15))
| ~ end_point(sK14,sK13)
| ~ incident_c(sK14,sK3(sK14,sK15))
| ~ incident_c(sK14,sK2(sK14,sK15))
| ~ part_of(sK3(sK14,sK15),sK13)
| ~ part_of(sK2(sK14,sK15),sK13) ),
inference(instantiation,[status(thm)],[c_9178]) ).
tcf(c_9923,plain,
! [X0: $i,X1: $i] :
( incident_c(sK1(X0,X0,X1),X1)
| incident_c(sK1(X0,X0,X1),X0)
| ( sum(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
tcf(c_9992,plain,
! [X0: $i,X1: $i] :
( part_of(sK15,X1)
| part_of(X1,sK15)
| ~ end_point(X0,sK13)
| ~ incident_c(X0,sK15)
| ~ part_of(X1,sK13)
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_91,c_65]) ).
tcf(c_10059,plain,
! [X0: $i,X1: $i] :
( incident_c(sK1(X0,X0,X1),X1)
| ( sum(X0,X1) = X0 )
| ~ incident_c(sK1(X0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_9923,c_52]) ).
tcf(c_10138,plain,
! [X0: $i,X1: $i] :
( part_of(sK15,X0)
| part_of(X0,sK15)
| incident_c(sK1(X0,X0,X1),X1)
| ( sum(X0,X1) = X0 )
| ~ part_of(X0,sK13)
| ~ end_point(sK1(X0,X0,X1),sK13)
| ~ incident_c(sK1(X0,X0,X1),sK15) ),
inference(superposition,[status(thm)],[c_9923,c_9992]) ).
tcf(c_11918,plain,
! [X0: $i,X1: $i] :
( incident_c(sK1(X0,X0,X1),X1)
| ( sum(X0,X1) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_10138,c_3908,c_10059]) ).
tcf(c_35989,plain,
incident_c(sK14,sK15),
inference(superposition,[status(thm)],[c_92,c_67]) ).
tcf(c_36470,plain,
! [X0: $i,X1: $i] :
( incident_c(sK1(X0,X0,X1),X1)
| incident_c(sK1(X0,X0,X1),X0)
| ( sum(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
tcf(c_36912,plain,
! [X0: $i,X1: $i] :
( incident_c(sK1(X0,X0,X1),X1)
| ( sum(X0,X1) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_36470,c_3908,c_10059]) ).
tcf(c_36916,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(sK1(X2,X2,X0),X1)
| ( sum(X2,X0) = X2 )
| ~ part_of(X0,X1) ),
inference(superposition,[status(thm)],[c_36912,c_51]) ).
tcf(c_37021,plain,
! [X0: $i,X1: $i] :
( ( sum(X0,X1) = X0 )
| ~ part_of(X1,X0)
| ~ incident_c(sK1(X0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_36916,c_52]) ).
tcf(c_37022,plain,
! [X0: $i,X1: $i] :
( ( sum(X0,X1) = X0 )
| ~ part_of(X1,X0)
| ~ incident_c(sK1(X0,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_36916,c_53]) ).
tcf(c_104800,plain,
! [X0: $i,X1: $i] :
( ( sum(X0,X1) = X0 )
| ~ part_of(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_37021,c_11918,c_37022]) ).
tcf(c_104801,plain,
! [X0: $i,X1: $i] :
( ( sum(X1,X0) = X1 )
| ~ part_of(X0,X1) ),
inference(renaming,[status(thm)],[c_104800]) ).
tcf(c_104804,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| ( sum(X1,sK2(X0,X1)) = X1 )
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_60,c_104801]) ).
tcf(c_108748,plain,
( end_point(sK14,sK15)
| ( sum(sK15,sK2(sK14,sK15)) = sK15 ) ),
inference(superposition,[status(thm)],[c_35989,c_104804]) ).
tcf(c_115195,plain,
incident_c(sK14,sK15),
inference(superposition,[status(thm)],[c_92,c_67]) ).
tcf(c_115230,plain,
! [X0: $i,X1: $i,X2: $i] :
( part_of(X2,sum(X0,X1))
| ~ incident_c(sK0(sum(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_56,c_49]) ).
tcf(c_115268,plain,
! [X0: $i,X1: $i,X2: $i] :
( part_of(X0,X2)
| incident_c(sK0(X2,X0),X1)
| ~ part_of(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_115365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( part_of(X0,X3)
| incident_c(sK0(X3,X0),X2)
| ~ part_of(X1,X2)
| ~ part_of(X0,X1) ),
inference(superposition,[status(thm)],[c_115268,c_51]) ).
tcf(c_115640,plain,
! [X0: $i,X1: $i] :
( incident_c(sK1(X0,X0,X1),X1)
| incident_c(sK1(X0,X0,X1),X0)
| ( sum(X0,X1) = X0 ) ),
inference(equality_factoring,[status(thm)],[c_54]) ).
tcf(c_115642,plain,
! [X0: $i,X1: $i] :
( incident_c(sK1(X0,X0,X1),X1)
| ( sum(X0,X1) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_115640,c_11918]) ).
tcf(c_115646,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(sK1(X2,X2,X0),X1)
| ( sum(X2,X0) = X2 )
| ~ part_of(X0,X1) ),
inference(superposition,[status(thm)],[c_115642,c_51]) ).
tcf(c_116215,plain,
! [X0: $i,X1: $i] : part_of(X0,sum(X1,X0)),
inference(superposition,[status(thm)],[c_50,c_115230]) ).
tcf(c_120768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( part_of(X1,X3)
| incident_c(sK0(X3,X1),X2)
| ~ part_of(sum(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_116215,c_115365]) ).
tcf(c_121033,plain,
! [X0: $i,X1: $i] :
( ( sum(X0,X1) = X0 )
| ~ part_of(X1,X0)
| ~ incident_c(sK1(X0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_115646,c_52]) ).
tcf(c_127621,plain,
! [X0: $i,X1: $i] :
( ( sum(X0,X1) = X0 )
| ~ part_of(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_121033,c_11918,c_37022]) ).
tcf(c_127622,plain,
! [X0: $i,X1: $i] :
( ( sum(X1,X0) = X1 )
| ~ part_of(X0,X1) ),
inference(renaming,[status(thm)],[c_127621]) ).
tcf(c_127625,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| ( sum(X1,sK2(X0,X1)) = X1 )
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_60,c_127622]) ).
tcf(c_127626,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| ( sum(X1,sK3(X0,X1)) = X1 )
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_61,c_127622]) ).
tcf(c_127627,plain,
sum(sK13,sK15) = sK13,
inference(superposition,[status(thm)],[c_91,c_127622]) ).
tcf(c_130001,plain,
! [X0: $i] :
( part_of(X0,sum(sK13,sK15))
| ~ incident_c(sK0(sK13,X0),sK15) ),
inference(superposition,[status(thm)],[c_127627,c_115230]) ).
tcf(c_130261,plain,
! [X0: $i] :
( part_of(X0,sK13)
| ~ incident_c(sK0(sK13,X0),sK15) ),
inference(light_normalisation,[status(thm)],[c_130001,c_127627]) ).
tcf(c_130961,plain,
( end_point(sK14,sK15)
| ( sum(sK15,sK2(sK14,sK15)) = sK15 ) ),
inference(superposition,[status(thm)],[c_115195,c_127625]) ).
tcf(c_131485,plain,
sum(sK15,sK2(sK14,sK15)) = sK15,
inference(global_subsumption_just,[status(thm)],[c_130961,c_757,c_108748]) ).
tcf(c_131603,plain,
! [X0: $i] :
( incident_c(X0,sK15)
| ~ incident_c(X0,sK2(sK14,sK15)) ),
inference(superposition,[status(thm)],[c_131485,c_56]) ).
tcf(c_131795,plain,
! [X0: $i] :
( part_of(sK2(sK14,sK15),X0)
| incident_c(sK0(X0,sK2(sK14,sK15)),sK15) ),
inference(superposition,[status(thm)],[c_50,c_131603]) ).
tcf(c_132041,plain,
part_of(sK2(sK14,sK15),sK13),
inference(superposition,[status(thm)],[c_131795,c_130261]) ).
tcf(c_142665,plain,
( end_point(sK14,sK15)
| ( sum(sK15,sK3(sK14,sK15)) = sK15 ) ),
inference(superposition,[status(thm)],[c_115195,c_127626]) ).
tcf(c_150158,plain,
sum(sK15,sK3(sK14,sK15)) = sK15,
inference(global_subsumption_just,[status(thm)],[c_142665,c_757,c_142665]) ).
tcf(c_150201,plain,
! [X0: $i,X1: $i] :
( part_of(sK3(sK14,sK15),X1)
| incident_c(sK0(X1,sK3(sK14,sK15)),X0)
| ~ part_of(sK15,X0) ),
inference(superposition,[status(thm)],[c_150158,c_120768]) ).
tcf(c_150418,plain,
( part_of(sK3(sK14,sK15),sK13)
| incident_c(sK0(sK13,sK3(sK14,sK15)),sK13)
| ~ part_of(sK15,sK13) ),
inference(instantiation,[status(thm)],[c_150201]) ).
tcf(c_150419,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_150418,c_132041,c_9181,c_5988,c_1478,c_1479,c_1482,c_1483,c_1477,c_762,c_757,c_739,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO089+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 10:49:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 91.65/14.89 % SZS status Started for theBenchmark.p
% 91.65/14.89 % SZS status Theorem for theBenchmark.p
% 91.65/14.89
% 91.65/14.89 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 91.65/14.89
% 91.65/14.89 % ------ iProver source info
% 91.65/14.89
% 91.65/14.89 % git: date: 2026-07-19 20:42:38 +0200
% 91.65/14.89 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 91.65/14.89 % git: non_committed_changes: false
% 91.65/14.89
% 91.65/14.89 % ------ Parsing...
% 91.65/14.89 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 91.65/14.89
% 91.65/14.89 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 91.65/14.89
% 91.65/14.89 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 91.65/14.89
% 91.65/14.89 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 91.65/14.89 % ------ Proving...
% 91.65/14.89 % ------ Problem Properties
% 91.65/14.89
% 91.65/14.89 %
% 91.65/14.89 % clauses 44
% 91.65/14.89 % conjectures 3
% 91.65/14.89 % EPR 16
% 91.65/14.89 % Horn 28
% 91.65/14.89 % unary 4
% 91.65/14.89 % binary 16
% 91.65/14.89 % lits 132
% 91.65/14.89 % lits eq 12
% 91.65/14.89 % fd_pure 0
% 91.65/14.89 % fd_pseudo 0
% 91.65/14.89 % fd_cond 0
% 91.65/14.89 % fd_pseudo_cond 7
% 91.65/14.89 % AC symbols 0
% 91.65/14.89
% 91.65/14.89 % ------ Input Options Time Limit: Unbounded
% 91.65/14.89
% 91.65/14.89
% 91.65/14.89 % ------
% 91.65/14.89 % Current options:
% 91.65/14.89 % ------
% 91.65/14.89
% 91.65/14.89
% 91.65/14.89 %
% 91.65/14.89
% 91.65/14.89 % ------ Proving...
% 91.65/14.89 %
% 91.65/14.89
% 91.65/14.89 % SZS status Theorem for theBenchmark.p
% 91.65/14.89
% 91.65/14.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 91.65/14.89
% 91.65/14.89
%------------------------------------------------------------------------------