%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU232+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 02:56:16 PM UTC 2026
% Result : Theorem 47.19s 8.35s
% Output : CNFRefutation 47.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 165 ( 18 unt; 0 def)
% Number of atoms : 487 ( 43 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 568 ( 246 ~; 251 |; 53 &)
% ( 8 <=>; 10 =>; 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 228 ( 0 sgn 215 !; 13 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f6,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f7,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f8,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f10,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f33,conjecture,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f37,axiom,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
fof(f52,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f58,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f61,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
? [X0,X1] :
( ordinal(X1)
& in(X0,X1)
& ~ ordinal(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f67,plain,
? [X0,X1] :
( ordinal(X1)
& in(X0,X1)
& ~ ordinal(X0) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f69,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f76,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f78,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,[],[f60]) ).
fof(f79,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f80,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))],[f79]) ).
fof(f81,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f82,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ( ~ in(sK2(X0),sK1(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK1(X0),sK2(X0))
& in(sK2(X0),X0)
& in(sK1(X0),X0) )
| epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f85,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK3(X0,X1),X0)
& ~ in(sK3(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f85]) ).
fof(f87,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f88,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(flattening,[],[f87]) ).
fof(f104,plain,
( ordinal(sK17)
& in(sK16,sK17)
& ~ ordinal(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f67]) ).
fof(f105,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f106,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK18(X1))
| ~ in(X3,X1) )
& in(sK18(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X2,sK18(X1))],[f76]) ).
fof(f107,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f114,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f115,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f117,plain,
! [X0] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f118,plain,
! [X3,X0,X4] :
( ~ epsilon_connected(X0)
| in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f119,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f120,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f121,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f122,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f123,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f124,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f125,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f126,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f127,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f128,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f164,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f104]) ).
fof(f165,plain,
in(sK16,sK17),
inference(cnf_transformation,[],[f104]) ).
fof(f166,plain,
~ ordinal(sK16),
inference(cnf_transformation,[],[f104]) ).
fof(f167,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f171,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f176,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f178,plain,
! [X0,X1] :
( in(sK18(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_54,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_55,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_56,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_58,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_59,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_60,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_61,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_62,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| ( X0 = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_68,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_69,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_104,negated_conjecture,
~ ordinal(sK16),
inference(cnf_transformation,[],[f166]) ).
tcf(c_105,negated_conjecture,
in(sK16,sK17),
inference(cnf_transformation,[],[f165]) ).
tcf(c_106,negated_conjecture,
ordinal(sK17),
inference(cnf_transformation,[],[f164]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( in(sK18(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_110]) ).
tcf(c_166,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_68]) ).
tcf(c_168,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_69]) ).
tcf(c_178,plain,
! [X0: $i] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_179,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(renaming,[status(thm)],[c_178]) ).
tcf(c_180,plain,
! [X0: $i] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
tcf(c_181,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(renaming,[status(thm)],[c_180]) ).
tcf(c_182,plain,
! [X0: $i] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_183,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(renaming,[status(thm)],[c_182]) ).
tcf(c_184,plain,
! [X0: $i] :
( ( sK1(X0) != sK2(X0) )
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_185,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(renaming,[status(thm)],[c_184]) ).
tcf(c_186,plain,
! [X0: $i] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_187,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(renaming,[status(thm)],[c_186]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_113,c_144]) ).
tcf(c_761,plain,
! [X0: $i] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_104]) ).
tcf(c_762,plain,
( ~ epsilon_connected(sK16)
| ~ epsilon_transitive(sK16) ),
inference(unflattening,[status(thm)],[c_761]) ).
tcf(c_769,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_168,c_106]) ).
tcf(c_770,plain,
epsilon_connected(sK17),
inference(unflattening,[status(thm)],[c_769]) ).
tcf(c_774,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_166,c_106]) ).
tcf(c_775,plain,
epsilon_transitive(sK17),
inference(unflattening,[status(thm)],[c_774]) ).
tcf(c_1075,plain,
! [X0: $i] :
( ~ epsilon_transitive(sK16)
| ~ in(sK2(X0),sK1(X0))
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_187,c_762]) ).
tcf(c_1076,plain,
( ~ epsilon_transitive(sK16)
| ~ in(sK2(sK16),sK1(sK16)) ),
inference(unflattening,[status(thm)],[c_1075]) ).
tcf(c_1083,plain,
! [X0: $i] :
( ~ epsilon_transitive(sK16)
| ( X0 != sK16 )
| ( sK1(X0) != sK2(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_185,c_762]) ).
tcf(c_1084,plain,
( ~ epsilon_transitive(sK16)
| ( sK1(sK16) != sK2(sK16) ) ),
inference(unflattening,[status(thm)],[c_1083]) ).
tcf(c_1091,plain,
! [X0: $i] :
( ~ epsilon_transitive(sK16)
| ~ in(sK1(X0),sK2(X0))
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_183,c_762]) ).
tcf(c_1092,plain,
( ~ epsilon_transitive(sK16)
| ~ in(sK1(sK16),sK2(sK16)) ),
inference(unflattening,[status(thm)],[c_1091]) ).
tcf(c_1099,plain,
! [X0: $i] :
( in(sK2(X0),X0)
| ~ epsilon_transitive(sK16)
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_181,c_762]) ).
tcf(c_1100,plain,
( in(sK2(sK16),sK16)
| ~ epsilon_transitive(sK16) ),
inference(unflattening,[status(thm)],[c_1099]) ).
tcf(c_1107,plain,
! [X0: $i] :
( in(sK1(X0),X0)
| ~ epsilon_transitive(sK16)
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_179,c_762]) ).
tcf(c_1108,plain,
( in(sK1(sK16),sK16)
| ~ epsilon_transitive(sK16) ),
inference(unflattening,[status(thm)],[c_1107]) ).
tcf(c_2539,plain,
epsilon_transitive(sK17),
inference(demodulation,[status(thm)],[c_775]) ).
tcf(c_2540,plain,
epsilon_connected(sK17),
inference(demodulation,[status(thm)],[c_770]) ).
tcf(c_2541,negated_conjecture,
in(sK16,sK17),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_2542,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3434,plain,
~ empty(sK17),
inference(superposition,[status(thm)],[c_2541,c_116]) ).
tcf(c_3758,plain,
( epsilon_transitive(sK16)
| in(sK0(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_3903,plain,
( subset(sK16,sK17)
| ~ epsilon_transitive(sK17) ),
inference(superposition,[status(thm)],[c_2541,c_57]) ).
tcf(c_3911,plain,
subset(sK16,sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_3903,c_2539]) ).
tcf(c_3959,plain,
( epsilon_transitive(sK16)
| ~ subset(sK0(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_4160,plain,
! [X0: $i] :
( empty(sK17)
| in(X0,sK17)
| ~ element(X0,sK17) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_4601,plain,
! [X0: $i,X1: $i] :
( in(sK16,X0)
| in(X0,sK16)
| ( X0 = sK16 )
| ~ epsilon_connected(X1)
| ~ in(sK16,X1)
| ~ in(X0,X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_4928,plain,
! [X0: $i] :
( in(sK0(sK16),X0)
| ~ subset(sK16,X0)
| ~ in(sK0(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_5183,plain,
( subset(sK0(sK16),sK16)
| in(sK3(sK0(sK16),sK16),sK0(sK16)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_5184,plain,
( subset(sK0(sK16),sK16)
| ~ in(sK3(sK0(sK16),sK16),sK16) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_6618,plain,
! [X0: $i] :
( in(sK16,X0)
| in(X0,sK16)
| ( X0 = sK16 )
| ~ epsilon_connected(sK17)
| ~ in(sK16,sK17)
| ~ in(X0,sK17) ),
inference(instantiation,[status(thm)],[c_4601]) ).
tcf(c_10073,plain,
! [X0: $i] :
( in(sK2(sK16),X0)
| ~ subset(sK16,X0)
| ~ in(sK2(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_10317,plain,
! [X0: $i] :
( in(sK1(sK16),X0)
| ~ subset(sK16,X0)
| ~ in(sK1(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_14126,plain,
( ~ in(sK0(sK16),sK3(sK0(sK16),sK16))
| ~ in(sK3(sK0(sK16),sK16),sK0(sK16)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_14961,plain,
( in(sK0(sK16),sK17)
| ~ subset(sK16,sK17)
| ~ in(sK0(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_4928]) ).
tcf(c_22893,plain,
! [X0: $i] :
( in(sK2(sK16),sK1(sK16))
| in(sK1(sK16),sK2(sK16))
| ( sK1(sK16) = sK2(sK16) )
| ~ epsilon_connected(X0)
| ~ in(sK2(sK16),X0)
| ~ in(sK1(sK16),X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_29068,plain,
in(sK18(sK17),sK17),
inference(superposition,[status(thm)],[c_2541,c_117]) ).
tcf(c_29837,plain,
! [X0: $i] :
( in(sK16,X0)
| in(X0,sK16)
| ( X0 = sK16 )
| ~ epsilon_connected(sK17)
| ~ in(X0,sK17) ),
inference(superposition,[status(thm)],[c_2541,c_63]) ).
tcf(c_29846,plain,
! [X0: $i] :
( in(sK16,X0)
| in(X0,sK16)
| ( X0 = sK16 )
| ~ in(X0,sK17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29837,c_2540]) ).
tcf(c_30115,plain,
( in(sK16,sK18(sK17))
| in(sK18(sK17),sK16)
| ( sK18(sK17) = sK16 ) ),
inference(superposition,[status(thm)],[c_29068,c_29846]) ).
tcf(c_30157,plain,
( subset(sK18(sK17),sK16)
| in(sK16,sK18(sK17))
| ( sK18(sK17) = sK16 )
| ~ epsilon_transitive(sK16) ),
inference(superposition,[status(thm)],[c_30115,c_57]) ).
tcf(c_37907,plain,
( in(sK2(sK16),sK17)
| ~ subset(sK16,sK17)
| ~ in(sK2(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_10073]) ).
tcf(c_38093,plain,
( in(sK1(sK16),sK17)
| ~ subset(sK16,sK17)
| ~ in(sK1(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_10317]) ).
tcf(c_42071,plain,
sK0(sK16) = sK0(sK16),
inference(instantiation,[status(thm)],[c_2542]) ).
tcf(c_65130,plain,
( in(sK2(sK16),sK1(sK16))
| in(sK1(sK16),sK2(sK16))
| ( sK1(sK16) = sK2(sK16) )
| ~ epsilon_connected(sK17)
| ~ in(sK2(sK16),sK17)
| ~ in(sK1(sK16),sK17) ),
inference(instantiation,[status(thm)],[c_22893]) ).
tcf(c_69407,plain,
~ epsilon_transitive(sK16),
inference(global_subsumption_just,[status(thm)],[c_30157,c_770,c_1076,c_1084,c_1092,c_1100,c_1108,c_3911,c_37907,c_38093,c_65130]) ).
tcf(c_105428,plain,
( in(sK16,sK3(sK0(sK16),sK16))
| in(sK3(sK0(sK16),sK16),sK16)
| ( sK3(sK0(sK16),sK16) = sK16 )
| ~ epsilon_connected(sK17)
| ~ in(sK16,sK17)
| ~ in(sK3(sK0(sK16),sK16),sK17) ),
inference(instantiation,[status(thm)],[c_6618]) ).
tcf(c_110097,plain,
( empty(sK17)
| in(sK3(sK0(sK16),sK16),sK17)
| ~ element(sK3(sK0(sK16),sK16),sK17) ),
inference(instantiation,[status(thm)],[c_4160]) ).
tcf(c_132995,plain,
! [X0: $i,X1: $i] :
( element(X0,sK17)
| ~ subset(X1,sK17)
| ~ in(X0,X1) ),
inference(instantiation,[status(thm)],[c_312]) ).
tcf(c_133027,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(sK0(sK16),sK16)
| ( X1 != sK16 )
| ( X0 != sK0(sK16) ) ),
inference(instantiation,[status(thm)],[c_2545]) ).
tcf(c_133368,plain,
( element(sK3(sK0(sK16),sK16),sK17)
| ~ subset(sK0(sK16),sK17)
| ~ in(sK3(sK0(sK16),sK16),sK0(sK16)) ),
inference(instantiation,[status(thm)],[c_132995]) ).
tcf(c_133371,plain,
! [X0: $i] :
( ~ in(sK0(sK16),X0)
| ~ in(X0,sK3(sK0(sK16),sK16))
| ~ in(sK3(sK0(sK16),sK16),sK0(sK16)) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_134388,plain,
( subset(sK0(sK16),sK17)
| ~ epsilon_transitive(sK17)
| ~ in(sK0(sK16),sK17) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_134729,plain,
( ~ in(sK0(sK16),sK16)
| ~ in(sK16,sK3(sK0(sK16),sK16))
| ~ in(sK3(sK0(sK16),sK16),sK0(sK16)) ),
inference(instantiation,[status(thm)],[c_133371]) ).
tcf(c_135878,plain,
! [X0: $i] :
( in(X0,sK3(sK0(sK16),sK16))
| ~ in(sK0(sK16),sK16)
| ( X0 != sK0(sK16) )
| ( sK3(sK0(sK16),sK16) != sK16 ) ),
inference(instantiation,[status(thm)],[c_133027]) ).
tcf(c_141147,plain,
( in(sK0(sK16),sK3(sK0(sK16),sK16))
| ~ in(sK0(sK16),sK16)
| ( sK0(sK16) != sK0(sK16) )
| ( sK3(sK0(sK16),sK16) != sK16 ) ),
inference(instantiation,[status(thm)],[c_135878]) ).
tcf(c_141148,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_141147,c_134729,c_134388,c_133368,c_110097,c_105428,c_69407,c_42071,c_14961,c_14126,c_5183,c_5184,c_3959,c_3911,c_3758,c_3434,c_775,c_770,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU232+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 13:19:11 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 47.19/8.35 % SZS status Started for theBenchmark.p
% 47.19/8.35 % SZS status Theorem for theBenchmark.p
% 47.19/8.35
% 47.19/8.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 47.19/8.35
% 47.19/8.35 % ------ iProver source info
% 47.19/8.35
% 47.19/8.35 % git: date: 2026-07-19 20:42:38 +0200
% 47.19/8.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 47.19/8.35 % git: non_committed_changes: false
% 47.19/8.35
% 47.19/8.35 % ------ Parsing...
% 47.19/8.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 47.19/8.35
% 47.19/8.35 % ------ Preprocessing... sup_sim: 0 sf_s rm: 18 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 47.19/8.35
% 47.19/8.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 47.19/8.35
% 47.19/8.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 47.19/8.35 % ------ Proving...
% 47.19/8.35 % ------ Problem Properties
% 47.19/8.35
% 47.19/8.35 %
% 47.19/8.35 % clauses 49
% 47.19/8.35 % conjectures 1
% 47.19/8.35 % EPR 27
% 47.19/8.35 % Horn 39
% 47.19/8.35 % unary 17
% 47.19/8.35 % binary 19
% 47.19/8.35 % lits 98
% 47.19/8.35 % lits eq 11
% 47.19/8.35 % fd_pure 0
% 47.19/8.35 % fd_pseudo 0
% 47.19/8.35 % fd_cond 1
% 47.19/8.35 % fd_pseudo_cond 5
% 47.19/8.35 % AC symbols 0
% 47.19/8.35
% 47.19/8.35 % ------ Schedule dynamic 5 is on
% 47.19/8.35
% 47.19/8.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 47.19/8.35
% 47.19/8.35
% 47.19/8.35 % ------
% 47.19/8.35 % Current options:
% 47.19/8.35 % ------
% 47.19/8.35
% 47.19/8.35
% 47.19/8.35 %
% 47.19/8.35
% 47.19/8.35 % ------ Proving...
% 47.19/8.35 %
% 47.19/8.35
% 47.19/8.35 % SZS status Theorem for theBenchmark.p
% 47.19/8.35
% 47.19/8.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 47.19/8.35
% 47.19/8.35
%------------------------------------------------------------------------------