%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU235+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:56:17 PM UTC 2026
% Result : Theorem 17.78s 3.34s
% Output : CNFRefutation 17.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 172 ( 24 unt; 0 def)
% Number of atoms : 523 ( 24 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 622 ( 271 ~; 275 |; 51 &)
% ( 6 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-1 aty)
% Number of variables : 259 ( 1 sgn 249 !; 10 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f8,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f9,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f13,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f17,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f30,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f32,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f34,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f35,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f37,conjecture,
! [X0,X1] :
( ordinal(X1)
=> ~ ( ! [X2] :
( ordinal(X2)
=> ~ ( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) )
& in(X2,X0) ) )
& X0 != empty_set
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_ordinal1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( ordinal(X1)
=> ~ ( ! [X2] :
( ordinal(X2)
=> ~ ( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) )
& in(X2,X0) ) )
& X0 != empty_set
& subset(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f41,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f44,axiom,
! [X0,X1] :
~ ( ! [X2] :
~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& in(X2,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
fof(f45,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f46,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f32]) ).
fof(f57,plain,
! [X0] :
( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f63,plain,
! [X0] :
( ~ empty(X0)
| ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f64,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f67,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f68,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f67]) ).
fof(f72,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f73,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f75,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f77,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
? [X0,X1] :
( ordinal(X1)
& ! [X2] :
( ~ ordinal(X2)
| ? [X3] :
( ordinal(X3)
& in(X3,X0)
& ~ ordinal_subset(X2,X3) )
| ~ in(X2,X0) )
& X0 != empty_set
& subset(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f79,plain,
? [X0,X1] :
( ordinal(X1)
& ! [X2] :
( ~ ordinal(X2)
| ? [X3] :
( ordinal(X3)
& in(X3,X0)
& ~ ordinal_subset(X2,X3) )
| ~ in(X2,X0) )
& X0 != empty_set
& subset(X0,X1) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f84,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f85,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f87,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f88,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK0(X0),X0)
& ~ subset(sK0(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f88]) ).
fof(f90,plain,
! [X0] : element(sK1(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f13]) ).
fof(f103,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f104,plain,
( ordinal(sK15)
& ! [X2] :
( ~ ordinal(X2)
| ( ordinal(sK16(X2))
& in(sK16(X2),sK14)
& ~ ordinal_subset(X2,sK16(X2)) )
| ~ in(X2,sK14) )
& empty_set != sK14
& subset(sK14,sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X3,sK16(X2))],[f79]) ).
fof(f105,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f106,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK17(X1))
| ~ in(X3,X1) )
& in(sK17(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X2,sK17(X1))],[f85]) ).
fof(f110,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f115,plain,
! [X0] :
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f118,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f119,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f120,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f122,plain,
! [X0] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f90]) ).
fof(f133,plain,
empty(empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f163,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f164,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f166,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f168,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f170,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f171,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f172,plain,
! [X2] :
( ~ ordinal(X2)
| ordinal(sK16(X2))
| ~ in(X2,sK14) ),
inference(cnf_transformation,[],[f104]) ).
fof(f173,plain,
! [X2] :
( ~ ordinal(X2)
| in(sK16(X2),sK14)
| ~ in(X2,sK14) ),
inference(cnf_transformation,[],[f104]) ).
fof(f174,plain,
! [X2] :
( ~ ordinal(X2)
| ~ ordinal_subset(X2,sK16(X2))
| ~ in(X2,sK14) ),
inference(cnf_transformation,[],[f104]) ).
fof(f175,plain,
empty_set != sK14,
inference(cnf_transformation,[],[f104]) ).
fof(f176,plain,
subset(sK14,sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f178,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f182,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f183,plain,
! [X3,X0,X1] :
( ~ in(X3,sK17(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f184,plain,
! [X0,X1] :
( in(sK17(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f185,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_51,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_57,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_60,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_62,plain,
! [X0: $i] : element(sK1(X0),X0),
inference(cnf_transformation,[],[f122]) ).
tcf(c_72,plain,
empty(empty_set),
inference(cnf_transformation,[],[f133]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_106,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f166]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_111,negated_conjecture,
subset(sK14,sK15),
inference(cnf_transformation,[],[f176]) ).
tcf(c_112,negated_conjecture,
empty_set != sK14,
inference(cnf_transformation,[],[f175]) ).
tcf(c_113,negated_conjecture,
! [X0: $i] :
( ~ ordinal(X0)
| ~ in(X0,sK14)
| ~ ordinal_subset(X0,sK16(X0)) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_114,negated_conjecture,
! [X0: $i] :
( in(sK16(X0),sK14)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_115,negated_conjecture,
! [X0: $i] :
( ordinal(sK16(X0))
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_116,negated_conjecture,
ordinal(sK15),
inference(cnf_transformation,[],[f171]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( in(sK17(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X0,X1)
| ~ in(X0,sK17(X1)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_117]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_119,c_142]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_120,c_142]) ).
tcf(c_996,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(X0,X2)
| ~ ordinal(X2)
| ~ ordinal(X0)
| ( X1 != X2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_103,c_106]) ).
tcf(c_997,plain,
! [X0: $i] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ),
inference(unflattening,[status(thm)],[c_996]) ).
tcf(c_1188,plain,
! [X0: $i] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_997]) ).
tcf(c_2029,negated_conjecture,
ordinal(sK15),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_2030,negated_conjecture,
! [X0: $i] :
( ordinal(sK16(X0))
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_2031,negated_conjecture,
! [X0: $i] :
( in(sK16(X0),sK14)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_2032,negated_conjecture,
! [X0: $i] :
( ~ ordinal(X0)
| ~ in(X0,sK14)
| ~ ordinal_subset(X0,sK16(X0)) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_2034,negated_conjecture,
subset(sK14,sK15),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_2042,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(X2,X0)
| ~ ordinal_subset(X2,X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2974,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK17(X0),X0) ),
inference(superposition,[status(thm)],[c_60,c_123]) ).
tcf(c_3013,plain,
! [X0: $i] :
( empty(X0)
| in(sK1(X0),X0) ),
inference(superposition,[status(thm)],[c_62,c_110]) ).
tcf(c_3032,plain,
! [X0: $i] :
( subset(sK16(X0),sK14)
| ~ epsilon_transitive(sK14)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_2031,c_61]) ).
tcf(c_3076,plain,
! [X0: $i] :
( empty(X0)
| in(sK17(X0),X0) ),
inference(superposition,[status(thm)],[c_3013,c_123]) ).
tcf(c_3117,plain,
( empty(sK14)
| ordinal(sK16(sK17(sK14)))
| ~ ordinal(sK17(sK14)) ),
inference(superposition,[status(thm)],[c_3076,c_2030]) ).
tcf(c_3161,plain,
( empty(sK14)
| epsilon_transitive(sK16(sK17(sK14)))
| ~ ordinal(sK17(sK14)) ),
inference(superposition,[status(thm)],[c_3117,c_51]) ).
tcf(c_3199,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| element(sK0(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_60,c_282]) ).
tcf(c_3229,plain,
! [X0: $i] :
( ordinal_subset(sK16(X0),X0)
| ~ ordinal(X0)
| ~ ordinal(sK16(X0))
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_58,c_2032]) ).
tcf(c_3373,plain,
( ( empty_set = sK14 )
| ~ empty(sK14)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_3437,plain,
! [X0: $i] :
( ordinal_subset(sK16(X0),X0)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_3229,c_115,c_3229]) ).
tcf(c_3446,plain,
! [X0: $i] :
( subset(sK16(X0),X0)
| ~ ordinal(X0)
| ~ ordinal(sK16(X0))
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_3437,c_104]) ).
tcf(c_3543,plain,
! [X0: $i] :
( empty(sK14)
| in(X0,sK14)
| ~ element(X0,sK14) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_3560,plain,
! [X0: $i] :
( subset(sK16(X0),X0)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_3446,c_115,c_3446]) ).
tcf(c_4058,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| empty(X1)
| in(sK0(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3199,c_110]) ).
tcf(c_4075,plain,
( empty(sK14)
| in(sK1(sK14),sK14)
| ~ element(sK1(sK14),sK14) ),
inference(instantiation,[status(thm)],[c_3543]) ).
tcf(c_4076,plain,
element(sK1(sK14),sK14),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_4270,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_2974,c_283]) ).
tcf(c_4542,plain,
! [X0: $i] :
( epsilon_transitive(sK16(X0))
| ~ ordinal(X0)
| ~ empty(X0)
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_3560,c_4270]) ).
tcf(c_4801,plain,
! [X0: $i] :
( epsilon_transitive(sK16(X0))
| ~ in(X0,sK14)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_4542,c_57,c_4542]) ).
tcf(c_4802,plain,
! [X0: $i] :
( epsilon_transitive(sK16(X0))
| ~ empty(X0)
| ~ in(X0,sK14) ),
inference(renaming,[status(thm)],[c_4801]) ).
tcf(c_5122,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ subset(X0,X1)
| in(sK0(X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_4058,c_4058,c_4270]) ).
tcf(c_5123,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X1)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_5122]) ).
tcf(c_5135,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| in(sK17(X1),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5123,c_123]) ).
tcf(c_5356,plain,
! [X0: $i] :
( epsilon_transitive(sK16(X0))
| in(sK17(sK14),sK14)
| ~ epsilon_transitive(sK14)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_3032,c_5135]) ).
tcf(c_5758,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ subset(sK14,X0)
| ~ in(sK1(sK14),sK14) ),
inference(instantiation,[status(thm)],[c_283]) ).
tcf(c_5759,plain,
( in(sK17(sK14),sK14)
| ~ in(sK1(sK14),sK14) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_5942,plain,
in(sK17(sK14),sK14),
inference(global_subsumption_just,[status(thm)],[c_5356,c_72,c_112,c_3373,c_4075,c_4076,c_5759]) ).
tcf(c_5946,plain,
! [X0: $i] :
( element(sK17(sK14),X0)
| ~ subset(sK14,X0) ),
inference(superposition,[status(thm)],[c_5942,c_282]) ).
tcf(c_6195,plain,
! [X0: $i] :
( empty(X0)
| in(sK17(sK14),X0)
| ~ subset(sK14,X0) ),
inference(superposition,[status(thm)],[c_5946,c_110]) ).
tcf(c_6840,plain,
! [X0: $i] :
( ~ subset(sK14,X0)
| in(sK17(sK14),X0) ),
inference(global_subsumption_just,[status(thm)],[c_6195,c_72,c_112,c_3373,c_4075,c_4076,c_5758,c_6195]) ).
tcf(c_6841,plain,
! [X0: $i] :
( in(sK17(sK14),X0)
| ~ subset(sK14,X0) ),
inference(renaming,[status(thm)],[c_6840]) ).
tcf(c_6851,plain,
! [X0: $i] :
( ordinal(sK17(sK14))
| ~ ordinal(X0)
| ~ subset(sK14,X0) ),
inference(superposition,[status(thm)],[c_6841,c_108]) ).
tcf(c_8003,plain,
( ordinal(sK17(sK14))
| ~ ordinal(sK15) ),
inference(superposition,[status(thm)],[c_2034,c_6851]) ).
tcf(c_8006,plain,
ordinal(sK17(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_8003,c_2029]) ).
tcf(c_8325,plain,
( ~ ordinal(sK17(sK14))
| ~ in(sK17(sK14),sK14)
| ~ ordinal_subset(sK17(sK14),sK16(sK17(sK14))) ),
inference(instantiation,[status(thm)],[c_2032]) ).
tcf(c_8326,plain,
( in(sK16(sK17(sK14)),sK14)
| ~ ordinal(sK17(sK14))
| ~ in(sK17(sK14),sK14) ),
inference(instantiation,[status(thm)],[c_2031]) ).
tcf(c_11365,plain,
( ordinal_subset(sK17(sK14),sK16(sK17(sK14)))
| ~ ordinal(sK17(sK14))
| ~ ordinal(sK16(sK17(sK14)))
| ~ subset(sK17(sK14),sK16(sK17(sK14))) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_11367,plain,
! [X0: $i] :
( ordinal_subset(sK17(sK14),sK16(sK17(sK14)))
| ~ ordinal_subset(sK17(sK14),X0)
| ( sK16(sK17(sK14)) != X0 ) ),
inference(instantiation,[status(thm)],[c_2042]) ).
tcf(c_11392,plain,
! [X0: $i] :
( ~ in(X0,sK14)
| ~ in(sK16(sK17(sK14)),sK14)
| ~ in(sK16(sK17(sK14)),sK17(sK14)) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_18769,plain,
( subset(sK17(sK14),sK16(sK17(sK14)))
| ~ epsilon_transitive(sK16(sK17(sK14)))
| ~ in(sK17(sK14),sK16(sK17(sK14))) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_19080,plain,
( ordinal_subset(sK17(sK14),sK16(sK17(sK14)))
| ~ ordinal_subset(sK17(sK14),sK17(sK14))
| ( sK16(sK17(sK14)) != sK17(sK14) ) ),
inference(instantiation,[status(thm)],[c_11367]) ).
tcf(c_19081,plain,
( ordinal_subset(sK17(sK14),sK17(sK14))
| ~ ordinal(sK17(sK14)) ),
inference(instantiation,[status(thm)],[c_1188]) ).
tcf(c_20219,plain,
! [X0: $i] :
( in(X0,sK17(sK14))
| in(sK17(sK14),X0)
| ( X0 = sK17(sK14) )
| ~ ordinal(X0)
| ~ ordinal(sK17(sK14)) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_35128,plain,
! [X0: $i] :
( in(sK17(sK14),sK14)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_2031,c_123]) ).
tcf(c_35134,plain,
in(sK17(sK14),sK14),
inference(global_subsumption_just,[status(thm)],[c_35128,c_72,c_112,c_3373,c_4075,c_4076,c_5759]) ).
tcf(c_35300,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_58,c_104]) ).
tcf(c_35343,plain,
! [X0: $i] :
( subset(sK16(X0),X0)
| ~ ordinal(X0)
| ~ ordinal(sK16(X0))
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_35300,c_2032]) ).
tcf(c_35378,plain,
! [X0: $i] :
( subset(sK16(X0),X0)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_35343,c_3560]) ).
tcf(c_37976,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| element(sK0(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_60,c_282]) ).
tcf(c_38098,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| empty(X1)
| in(sK0(X0),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_37976,c_110]) ).
tcf(c_38246,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ subset(X0,X1)
| in(sK0(X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_38098,c_5123]) ).
tcf(c_38247,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X1)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_38246]) ).
tcf(c_38260,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| in(sK17(X1),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_38247,c_123]) ).
tcf(c_38574,plain,
! [X0: $i] :
( epsilon_transitive(sK16(X0))
| in(sK17(X0),X0)
| ~ ordinal(X0)
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_35378,c_38260]) ).
tcf(c_38786,plain,
! [X0: $i] :
( epsilon_transitive(sK16(X0))
| in(sK17(X0),X0)
| ~ in(X0,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_38574,c_3076,c_4802]) ).
tcf(c_38803,plain,
! [X0: $i] :
( epsilon_transitive(sK16(X0))
| ~ empty(X0)
| ~ in(X0,sK14) ),
inference(superposition,[status(thm)],[c_38786,c_122]) ).
tcf(c_42439,plain,
( in(sK17(sK14),sK16(sK17(sK14)))
| in(sK16(sK17(sK14)),sK17(sK14))
| ( sK16(sK17(sK14)) = sK17(sK14) )
| ~ ordinal(sK17(sK14))
| ~ ordinal(sK16(sK17(sK14))) ),
inference(instantiation,[status(thm)],[c_20219]) ).
tcf(c_44007,plain,
! [X0: $i] : ~ in(X0,sK14),
inference(global_subsumption_just,[status(thm)],[c_38803,c_72,c_112,c_3117,c_3161,c_3373,c_4075,c_4076,c_5759,c_8006,c_8326,c_8325,c_11365,c_11392,c_18769,c_19080,c_19081,c_42439]) ).
tcf(c_44010,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_35134,c_44007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU235+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 13:25:54 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 17.78/3.34 % SZS status Started for theBenchmark.p
% 17.78/3.34 % SZS status Theorem for theBenchmark.p
% 17.78/3.34
% 17.78/3.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.78/3.34
% 17.78/3.34 % ------ iProver source info
% 17.78/3.34
% 17.78/3.34 % git: date: 2026-07-19 20:42:38 +0200
% 17.78/3.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.78/3.34 % git: non_committed_changes: false
% 17.78/3.34
% 17.78/3.34 % ------ Parsing...
% 17.78/3.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.78/3.34
% 17.78/3.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 20 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 17.78/3.34
% 17.78/3.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.78/3.34
% 17.78/3.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.78/3.34 % ------ Proving...
% 17.78/3.34 % ------ Problem Properties
% 17.78/3.34
% 17.78/3.34 %
% 17.78/3.34 % clauses 48
% 17.78/3.34 % conjectures 6
% 17.78/3.34 % EPR 38
% 17.78/3.34 % Horn 44
% 17.78/3.34 % unary 21
% 17.78/3.34 % binary 13
% 17.78/3.34 % lits 94
% 17.78/3.34 % lits eq 4
% 17.78/3.34 % fd_pure 0
% 17.78/3.34 % fd_pseudo 0
% 17.78/3.34 % fd_cond 1
% 17.78/3.34 % fd_pseudo_cond 2
% 17.78/3.34 % AC symbols 0
% 17.78/3.34
% 17.78/3.34 % ------ Schedule dynamic 5 is on
% 17.78/3.34
% 17.78/3.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.78/3.34
% 17.78/3.34
% 17.78/3.34 % ------
% 17.78/3.34 % Current options:
% 17.78/3.34 % ------
% 17.78/3.34
% 17.78/3.34
% 17.78/3.34 %
% 17.78/3.34
% 17.78/3.34 % ------ Proving...
% 17.78/3.34 %
% 17.78/3.34
% 17.78/3.34 % SZS status Theorem for theBenchmark.p
% 17.78/3.34
% 17.78/3.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.78/3.34
% 17.78/3.34
%------------------------------------------------------------------------------