%------------------------------------------------------------------------------
% 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 : n007.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 : Unsatisfiable 91.34s 21.00s
% Output : CNFRefutation 91.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 109 ( 14 unt; 0 def)
% Number of atoms : 305 ( 42 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 325 ( 129 ~; 196 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 159 ( 0 sgn 159 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',part_of_defn_1) ).
fof(f2,axiom,
! [X0,X1] :
( part_of(X0,X1)
| incident_c(ax0_sk1(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',part_of_defn_2) ).
fof(f3,axiom,
! [X0,X1] :
( part_of(X0,X1)
| ~ incident_c(ax0_sk1(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',part_of_defn_3) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| X0 != sum(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',sum_defn_5) ).
fof(f7,plain,
! [X2,X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| sum(X1,X2) != X0 ),
inference(reorient_equations,[],[f6]) ).
fof(f10,axiom,
! [X2,X0,X1] :
( X2 = sum(X1,X0)
| incident_c(ax0_sk2(X0,X1,X2),X0)
| incident_c(ax0_sk2(X0,X1,X2),X1)
| incident_c(ax0_sk2(X0,X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',sum_defn_7) ).
fof(f11,plain,
! [X2,X0,X1] :
( sum(X1,X0) = X2
| incident_c(ax0_sk2(X0,X1,X2),X0)
| incident_c(ax0_sk2(X0,X1,X2),X1)
| incident_c(ax0_sk2(X0,X1,X2),X2) ),
inference(reorient_equations,[],[f10]) ).
fof(f20,axiom,
! [X2,X0,X1] :
( X2 = sum(X1,X0)
| ~ incident_c(ax0_sk2(X0,X1,X2),X2)
| ~ incident_c(ax0_sk2(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',sum_defn_12) ).
fof(f21,plain,
! [X2,X0,X1] :
( sum(X1,X0) = X2
| ~ incident_c(ax0_sk2(X0,X1,X2),X2)
| ~ incident_c(ax0_sk2(X0,X1,X2),X0) ),
inference(reorient_equations,[],[f20]) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( part_of(X3,X2)
| part_of(X2,X3)
| ~ incident_c(X0,X3)
| ~ incident_c(X0,X2)
| ~ part_of(X3,X1)
| ~ part_of(X2,X1)
| ~ end_point(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',end_point_defn_14) ).
fof(f24,axiom,
! [X0,X1] :
( end_point(X0,X1)
| part_of(ax0_sk3(X1,X0),X1)
| ~ incident_c(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',end_point_defn_15) ).
fof(f25,axiom,
! [X0,X1] :
( end_point(X0,X1)
| part_of(ax0_sk4(X1,X0),X1)
| ~ incident_c(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',end_point_defn_16) ).
fof(f26,axiom,
! [X0,X1] :
( end_point(X0,X1)
| incident_c(X0,ax0_sk3(X1,X0))
| ~ incident_c(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',end_point_defn_17) ).
fof(f27,axiom,
! [X0,X1] :
( end_point(X0,X1)
| incident_c(X0,ax0_sk4(X1,X0))
| ~ incident_c(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',end_point_defn_18) ).
fof(f28,axiom,
! [X0,X1] :
( end_point(X0,X1)
| ~ part_of(ax0_sk3(X1,X0),ax0_sk4(X1,X0))
| ~ incident_c(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',end_point_defn_19) ).
fof(f29,axiom,
! [X0,X1] :
( end_point(X0,X1)
| ~ part_of(ax0_sk4(X1,X0),ax0_sk3(X1,X0))
| ~ incident_c(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',end_point_defn_20) ).
fof(f30,axiom,
! [X0,X1] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',inner_point_defn_21) ).
fof(f31,axiom,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',inner_point_defn_22) ).
fof(f32,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_23) ).
fof(f66,negated_conjecture,
part_of(sk16,sk14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_11_67) ).
fof(f67,negated_conjecture,
inner_point(sk15,sk16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_11_68) ).
fof(f68,negated_conjecture,
~ inner_point(sk15,sk14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_11_69) ).
fof(f70,plain,
! [X2,X3,X1] :
( incident_c(X3,sum(X1,X2))
| ~ incident_c(X3,X1) ),
inference(equality_resolution,[],[f7]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( part_of(X0,X1)
| incident_c(ax0_sk1(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( part_of(X0,X1)
| ~ incident_c(ax0_sk1(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X0,sum(X1,X2))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(ax0_sk2(X1,X0,X2),X2)
| incident_c(ax0_sk2(X1,X0,X2),X1)
| incident_c(ax0_sk2(X1,X0,X2),X0)
| ( sum(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sum(X1,X0) = X2 )
| ~ incident_c(ax0_sk2(X0,X1,X2),X2)
| ~ incident_c(ax0_sk2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_110,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,[],[f23]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| part_of(ax0_sk3(X1,X0),X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| part_of(ax0_sk4(X1,X0),X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| incident_c(X0,ax0_sk3(X1,X0))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| incident_c(X0,ax0_sk4(X1,X0))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( end_point(X1,X0)
| ~ incident_c(X1,X0)
| ~ part_of(ax0_sk3(X0,X1),ax0_sk4(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( end_point(X1,X0)
| ~ incident_c(X1,X0)
| ~ part_of(ax0_sk4(X0,X1),ax0_sk3(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| inner_point(X0,X1)
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_143,negated_conjecture,
part_of(sk16,sk14),
inference(cnf_transformation,[],[f66]) ).
tcf(c_144,negated_conjecture,
inner_point(sk15,sk16),
inference(cnf_transformation,[],[f67]) ).
tcf(c_145,negated_conjecture,
~ inner_point(sk15,sk14),
inference(cnf_transformation,[],[f68]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_118]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(renaming,[status(thm)],[c_188]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_117]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,X1)
| ~ inner_point(X0,X1) ),
inference(renaming,[status(thm)],[c_206]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i] :
( ~ end_point(X1,X0)
| ( X1 != sk15 )
| ( X0 != sk16 ) ),
inference(resolution_lifted,[status(thm)],[c_144,c_189]) ).
tcf(c_635,plain,
~ end_point(sk15,sk16),
inference(unflattening,[status(thm)],[c_634]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i] :
( incident_c(X1,X0)
| ( X1 != sk15 )
| ( X0 != sk16 ) ),
inference(resolution_lifted,[status(thm)],[c_144,c_207]) ).
tcf(c_640,plain,
incident_c(sk15,sk16),
inference(unflattening,[status(thm)],[c_639]) ).
tcf(c_644,plain,
! [X0: $i,X1: $i] :
( end_point(X1,X0)
| ~ incident_c(X1,X0)
| ( X1 != sk15 )
| ( X0 != sk14 ) ),
inference(resolution_lifted,[status(thm)],[c_145,c_119]) ).
tcf(c_645,plain,
( end_point(sk15,sk14)
| ~ incident_c(sk15,sk14) ),
inference(unflattening,[status(thm)],[c_644]) ).
tcf(c_1575,plain,
! [X0: $i] :
( incident_c(sk15,X0)
| ~ incident_c(sk15,sk16)
| ~ part_of(sk16,X0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_1576,plain,
( incident_c(sk15,sk14)
| ~ incident_c(sk15,sk16)
| ~ part_of(sk16,sk14) ),
inference(instantiation,[status(thm)],[c_1575]) ).
tcf(c_1584,plain,
( end_point(sk15,sk16)
| incident_c(sk15,ax0_sk4(sk16,sk15))
| ~ incident_c(sk15,sk16) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_1585,plain,
( end_point(sk15,sk16)
| incident_c(sk15,ax0_sk3(sk16,sk15))
| ~ incident_c(sk15,sk16) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_1593,plain,
( end_point(sk15,sk16)
| ~ incident_c(sk15,sk16)
| ~ part_of(ax0_sk4(sk16,sk15),ax0_sk3(sk16,sk15)) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_1594,plain,
( end_point(sk15,sk16)
| ~ incident_c(sk15,sk16)
| ~ part_of(ax0_sk3(sk16,sk15),ax0_sk4(sk16,sk15)) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_1744,plain,
! [X0: $i,X1: $i,X2: $i] :
( end_point(X2,X1)
| incident_c(X0,X1)
| ~ incident_c(X2,X1)
| ~ incident_c(X0,ax0_sk3(X1,X2)) ),
inference(superposition,[status(thm)],[c_111,c_100]) ).
tcf(c_1747,plain,
! [X0: $i,X1: $i,X2: $i] :
( end_point(X2,X1)
| incident_c(X0,X1)
| ~ incident_c(X2,X1)
| ~ incident_c(X0,ax0_sk4(X1,X2)) ),
inference(superposition,[status(thm)],[c_112,c_100]) ).
tcf(c_1775,plain,
! [X0: $i,X1: $i] :
( incident_c(ax0_sk2(X1,X0,sk16),sk16)
| incident_c(ax0_sk2(X1,X0,sk16),X1)
| incident_c(ax0_sk2(X1,X0,sk16),X0)
| ( sum(X0,X1) = sk16 ) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_1884,plain,
! [X0: $i,X1: $i] :
( part_of(ax0_sk4(sk16,sk15),ax0_sk3(sk16,sk15))
| part_of(ax0_sk3(sk16,sk15),ax0_sk4(sk16,sk15))
| ~ end_point(X1,X0)
| ~ incident_c(X1,ax0_sk4(sk16,sk15))
| ~ incident_c(X1,ax0_sk3(sk16,sk15))
| ~ part_of(ax0_sk4(sk16,sk15),X0)
| ~ part_of(ax0_sk3(sk16,sk15),X0) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_2186,plain,
! [X0: $i,X1: $i] :
( ( sum(X1,X0) = sk16 )
| ~ incident_c(ax0_sk2(X0,X1,sk16),sk16)
| ~ incident_c(ax0_sk2(X0,X1,sk16),X0) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_3742,plain,
! [X0: $i] :
( part_of(ax0_sk4(sk16,sk15),X0)
| ~ incident_c(ax0_sk1(ax0_sk4(sk16,sk15),X0),X0) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_3745,plain,
( part_of(ax0_sk4(sk16,sk15),sk14)
| ~ incident_c(ax0_sk1(ax0_sk4(sk16,sk15),sk14),sk14) ),
inference(instantiation,[status(thm)],[c_3742]) ).
tcf(c_6012,plain,
! [X0: $i] :
( incident_c(ax0_sk2(sk16,X0,sk16),sk16)
| incident_c(ax0_sk2(sk16,X0,sk16),X0)
| ( sum(X0,sk16) = sk16 ) ),
inference(instantiation,[status(thm)],[c_1775]) ).
tcf(c_6014,plain,
! [X0: $i] :
( ( sum(X0,sk16) = sk16 )
| ~ incident_c(ax0_sk2(sk16,X0,sk16),sk16) ),
inference(instantiation,[status(thm)],[c_2186]) ).
tcf(c_8289,plain,
! [X0: $i] :
( incident_c(X0,sk14)
| ~ incident_c(X0,sk16) ),
inference(superposition,[status(thm)],[c_143,c_100]) ).
tcf(c_8813,plain,
! [X0: $i,X1: $i] :
( incident_c(ax0_sk2(X1,X0,sk16),sk14)
| incident_c(ax0_sk2(X1,X0,sk16),X1)
| incident_c(ax0_sk2(X1,X0,sk16),X0)
| ( sum(X0,X1) = sk16 ) ),
inference(superposition,[status(thm)],[c_106,c_8289]) ).
tcf(c_8896,plain,
! [X0: $i] :
( incident_c(ax0_sk2(sk16,X0,sk16),sk14)
| incident_c(ax0_sk2(sk16,X0,sk16),X0)
| ( sum(X0,sk16) = sk16 ) ),
inference(superposition,[status(thm)],[c_8813,c_8289]) ).
tcf(c_8937,plain,
! [X0: $i] :
( ( sum(X0,sk16) = sk16 )
| incident_c(ax0_sk2(sk16,X0,sk16),X0) ),
inference(global_subsumption_just,[status(thm)],[c_8896,c_6012,c_6014]) ).
tcf(c_8938,plain,
! [X0: $i] :
( incident_c(ax0_sk2(sk16,X0,sk16),X0)
| ( sum(X0,sk16) = sk16 ) ),
inference(renaming,[status(thm)],[c_8937]) ).
tcf(c_25403,plain,
! [X0: $i] :
( part_of(ax0_sk4(sk16,sk15),ax0_sk3(sk16,sk15))
| part_of(ax0_sk3(sk16,sk15),ax0_sk4(sk16,sk15))
| ~ end_point(sk15,X0)
| ~ incident_c(sk15,ax0_sk4(sk16,sk15))
| ~ incident_c(sk15,ax0_sk3(sk16,sk15))
| ~ part_of(ax0_sk4(sk16,sk15),X0)
| ~ part_of(ax0_sk3(sk16,sk15),X0) ),
inference(instantiation,[status(thm)],[c_1884]) ).
tcf(c_25404,plain,
( part_of(ax0_sk4(sk16,sk15),ax0_sk3(sk16,sk15))
| part_of(ax0_sk3(sk16,sk15),ax0_sk4(sk16,sk15))
| ~ end_point(sk15,sk14)
| ~ incident_c(sk15,ax0_sk4(sk16,sk15))
| ~ incident_c(sk15,ax0_sk3(sk16,sk15))
| ~ part_of(ax0_sk4(sk16,sk15),sk14)
| ~ part_of(ax0_sk3(sk16,sk15),sk14) ),
inference(instantiation,[status(thm)],[c_25403]) ).
tcf(c_60474,plain,
incident_c(sk15,sk16),
inference(superposition,[status(thm)],[c_144,c_117]) ).
tcf(c_60593,plain,
! [X0: $i] :
( incident_c(X0,sk14)
| ~ incident_c(X0,sk16) ),
inference(superposition,[status(thm)],[c_143,c_100]) ).
tcf(c_60758,plain,
! [X0: $i,X1: $i] :
( incident_c(ax0_sk2(X1,X0,sk16),sk14)
| incident_c(ax0_sk2(X1,X0,sk16),X1)
| incident_c(ax0_sk2(X1,X0,sk16),X0)
| ( sum(X0,X1) = sk16 ) ),
inference(superposition,[status(thm)],[c_106,c_60593]) ).
tcf(c_60826,plain,
! [X0: $i] :
( incident_c(ax0_sk2(sk16,X0,sk16),sk14)
| incident_c(ax0_sk2(sk16,X0,sk16),X0)
| ( sum(X0,sk16) = sk16 ) ),
inference(superposition,[status(thm)],[c_60758,c_60593]) ).
tcf(c_60860,plain,
! [X0: $i] :
( ( sum(X0,sk16) = sk16 )
| incident_c(ax0_sk2(sk16,X0,sk16),X0) ),
inference(global_subsumption_just,[status(thm)],[c_60826,c_6012,c_6014]) ).
tcf(c_60861,plain,
! [X0: $i] :
( incident_c(ax0_sk2(sk16,X0,sk16),X0)
| ( sum(X0,sk16) = sk16 ) ),
inference(renaming,[status(thm)],[c_60860]) ).
tcf(c_61035,plain,
! [X0: $i,X1: $i] :
( part_of(sk16,X1)
| part_of(X1,sk16)
| ~ end_point(X0,sk14)
| ~ incident_c(X0,sk16)
| ~ part_of(X1,sk14)
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_143,c_110]) ).
tcf(c_61122,plain,
! [X0: $i] :
( part_of(sk16,X0)
| part_of(X0,sk16)
| ( sum(X0,sk16) = sk16 )
| ~ part_of(X0,sk14)
| ~ end_point(ax0_sk2(sk16,X0,sk16),sk14)
| ~ incident_c(ax0_sk2(sk16,X0,sk16),sk16) ),
inference(superposition,[status(thm)],[c_60861,c_61035]) ).
tcf(c_61664,plain,
! [X0: $i] :
( ( sum(X0,sk16) = sk16 )
| ~ incident_c(ax0_sk2(sk16,X0,sk16),sk16) ),
inference(global_subsumption_just,[status(thm)],[c_61122,c_6014]) ).
tcf(c_70187,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| incident_c(ax0_sk2(sk16,ax0_sk3(X1,X0),sk16),X1)
| ( sum(ax0_sk3(X1,X0),sk16) = sk16 )
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_60861,c_1744]) ).
tcf(c_78455,plain,
! [X0: $i] :
( end_point(X0,sk16)
| ( sum(ax0_sk3(sk16,X0),sk16) = sk16 )
| ~ incident_c(X0,sk16) ),
inference(superposition,[status(thm)],[c_70187,c_61664]) ).
tcf(c_78897,plain,
( end_point(sk15,sk16)
| ( sum(ax0_sk3(sk16,sk15),sk16) = sk16 ) ),
inference(superposition,[status(thm)],[c_60474,c_78455]) ).
tcf(c_79390,plain,
sum(ax0_sk3(sk16,sk15),sk16) = sk16,
inference(global_subsumption_just,[status(thm)],[c_78897,c_635,c_78897]) ).
tcf(c_79396,plain,
! [X0: $i] :
( incident_c(X0,sk16)
| ~ incident_c(X0,ax0_sk3(sk16,sk15)) ),
inference(superposition,[status(thm)],[c_79390,c_104]) ).
tcf(c_79457,plain,
! [X0: $i] :
( part_of(ax0_sk3(sk16,sk15),X0)
| incident_c(ax0_sk1(ax0_sk3(sk16,sk15),X0),sk16) ),
inference(superposition,[status(thm)],[c_101,c_79396]) ).
tcf(c_79785,plain,
! [X0: $i] :
( part_of(ax0_sk3(sk16,sk15),X0)
| incident_c(ax0_sk1(ax0_sk3(sk16,sk15),X0),sk14) ),
inference(superposition,[status(thm)],[c_79457,c_60593]) ).
tcf(c_80488,plain,
part_of(ax0_sk3(sk16,sk15),sk14),
inference(superposition,[status(thm)],[c_79785,c_102]) ).
tcf(c_120299,plain,
incident_c(sk15,sk16),
inference(superposition,[status(thm)],[c_144,c_117]) ).
tcf(c_120345,plain,
! [X0: $i] :
( incident_c(X0,sk14)
| ~ incident_c(X0,sk16) ),
inference(superposition,[status(thm)],[c_143,c_100]) ).
tcf(c_120658,plain,
! [X0: $i,X1: $i] :
( incident_c(ax0_sk2(X1,X0,sk16),sk14)
| incident_c(ax0_sk2(X1,X0,sk16),X1)
| incident_c(ax0_sk2(X1,X0,sk16),X0)
| ( sum(X0,X1) = sk16 ) ),
inference(superposition,[status(thm)],[c_106,c_120345]) ).
tcf(c_120701,plain,
! [X0: $i] :
( incident_c(ax0_sk2(sk16,X0,sk16),sk14)
| incident_c(ax0_sk2(sk16,X0,sk16),X0)
| ( sum(X0,sk16) = sk16 ) ),
inference(superposition,[status(thm)],[c_120658,c_120345]) ).
tcf(c_121066,plain,
! [X0: $i] :
( ( sum(X0,sk16) = sk16 )
| incident_c(ax0_sk2(sk16,X0,sk16),X0) ),
inference(global_subsumption_just,[status(thm)],[c_120701,c_8938]) ).
tcf(c_121067,plain,
! [X0: $i] :
( incident_c(ax0_sk2(sk16,X0,sk16),X0)
| ( sum(X0,sk16) = sk16 ) ),
inference(renaming,[status(thm)],[c_121066]) ).
tcf(c_121126,plain,
! [X0: $i,X1: $i] :
( part_of(sk16,X1)
| part_of(X1,sk16)
| ~ end_point(X0,sk14)
| ~ incident_c(X0,sk16)
| ~ part_of(X1,sk14)
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_143,c_110]) ).
tcf(c_121199,plain,
! [X0: $i] :
( part_of(sk16,X0)
| part_of(X0,sk16)
| ( sum(X0,sk16) = sk16 )
| ~ part_of(X0,sk14)
| ~ end_point(ax0_sk2(sk16,X0,sk16),sk14)
| ~ incident_c(ax0_sk2(sk16,X0,sk16),sk16) ),
inference(superposition,[status(thm)],[c_121067,c_121126]) ).
tcf(c_121518,plain,
! [X0: $i] :
( ( sum(X0,sk16) = sk16 )
| ~ incident_c(ax0_sk2(sk16,X0,sk16),sk16) ),
inference(global_subsumption_just,[status(thm)],[c_121199,c_6014]) ).
tcf(c_132542,plain,
! [X0: $i,X1: $i] :
( end_point(X0,X1)
| incident_c(ax0_sk2(sk16,ax0_sk4(X1,X0),sk16),X1)
| ( sum(ax0_sk4(X1,X0),sk16) = sk16 )
| ~ incident_c(X0,X1) ),
inference(superposition,[status(thm)],[c_121067,c_1747]) ).
tcf(c_165221,plain,
! [X0: $i] :
( end_point(X0,sk16)
| ( sum(ax0_sk4(sk16,X0),sk16) = sk16 )
| ~ incident_c(X0,sk16) ),
inference(superposition,[status(thm)],[c_132542,c_121518]) ).
tcf(c_166426,plain,
( end_point(sk15,sk16)
| ( sum(ax0_sk4(sk16,sk15),sk16) = sk16 ) ),
inference(superposition,[status(thm)],[c_120299,c_165221]) ).
tcf(c_167186,plain,
sum(ax0_sk4(sk16,sk15),sk16) = sk16,
inference(global_subsumption_just,[status(thm)],[c_166426,c_635,c_166426]) ).
tcf(c_167194,plain,
! [X0: $i] :
( incident_c(X0,sk16)
| ~ incident_c(X0,ax0_sk4(sk16,sk15)) ),
inference(superposition,[status(thm)],[c_167186,c_104]) ).
tcf(c_167507,plain,
! [X0: $i] :
( part_of(ax0_sk4(sk16,sk15),X0)
| incident_c(ax0_sk1(ax0_sk4(sk16,sk15),X0),sk16) ),
inference(superposition,[status(thm)],[c_101,c_167194]) ).
tcf(c_167825,plain,
! [X0: $i] :
( part_of(ax0_sk4(sk16,sk15),X0)
| incident_c(ax0_sk1(ax0_sk4(sk16,sk15),X0),sk14) ),
inference(superposition,[status(thm)],[c_167507,c_120345]) ).
tcf(c_167840,plain,
( part_of(ax0_sk4(sk16,sk15),sk14)
| incident_c(ax0_sk1(ax0_sk4(sk16,sk15),sk14),sk14) ),
inference(instantiation,[status(thm)],[c_167825]) ).
tcf(c_167841,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_167840,c_80488,c_25404,c_3745,c_1593,c_1594,c_1584,c_1585,c_1576,c_645,c_640,c_635,c_143]) ).
%------------------------------------------------------------------------------
%----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
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 10:46:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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...
% 91.34/21.00 % SZS status Started for theBenchmark.p
% 91.34/21.00 % SZS status Unsatisfiable for theBenchmark.p
% 91.34/21.00
% 91.34/21.00 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 91.34/21.00
% 91.34/21.00 % ------ iProver source info
% 91.34/21.00
% 91.34/21.00 % git: date: 2026-07-19 20:42:38 +0200
% 91.34/21.00 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 91.34/21.00 % git: non_committed_changes: false
% 91.34/21.00
% 91.34/21.00 % ------ Parsing...% successful
% 91.34/21.00
% 91.34/21.00
% 91.34/21.00 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 91.34/21.00
% 91.34/21.00 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 91.34/21.00
% 91.34/21.00 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 91.34/21.00
% 91.34/21.00 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 91.34/21.00 % ------ Proving...
% 91.34/21.00 % ------ Problem Properties
% 91.34/21.00
% 91.34/21.00 %
% 91.34/21.00 % clauses 46
% 91.34/21.00 % conjectures 3
% 91.34/21.00 % EPR 18
% 91.34/21.00 % Horn 30
% 91.34/21.00 % unary 4
% 91.34/21.00 % binary 18
% 91.34/21.00 % lits 136
% 91.34/21.00 % lits eq 12
% 91.34/21.00 % fd_pure 0
% 91.34/21.00 % fd_pseudo 0
% 91.34/21.00 % fd_cond 0
% 91.34/21.00 % fd_pseudo_cond 7
% 91.34/21.00 % AC symbols 0
% 91.34/21.00
% 91.34/21.00 % ------ Input Options Time Limit: Unbounded
% 91.34/21.00
% 91.34/21.00
% 91.34/21.00 % ------
% 91.34/21.00 % Current options:
% 91.34/21.00 % ------
% 91.34/21.00
% 91.34/21.00
% 91.34/21.00 %
% 91.34/21.00
% 91.34/21.00 % ------ Proving...
% 91.34/21.00 %
% 91.34/21.00
% 91.34/21.00 % SZS status Unsatisfiable for theBenchmark.p
% 91.34/21.00
% 91.34/21.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 91.34/21.01
% 91.34/21.01
%------------------------------------------------------------------------------