%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU232+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 64.21s 11.20s
% Output : CNFRefutation 74.94s
% 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(f30,conjecture,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f34,axiom,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f41,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(f50,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f56,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f57,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f59,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(f60,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
? [X0,X1] :
( ordinal(X1)
& in(X0,X1)
& ~ ordinal(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f65,plain,
? [X0,X1] :
( ordinal(X1)
& in(X0,X1)
& ~ ordinal(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f67,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f69]) ).
fof(f73,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f76,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,[],[f58]) ).
fof(f77,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f76]) ).
fof(f78,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))],[f77]) ).
fof(f79,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,[],[f59]) ).
fof(f80,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,[],[f79]) ).
fof(f81,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))],[f80]) ).
fof(f82,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,[],[f60]) ).
fof(f83,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,[],[f82]) ).
fof(f84,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))],[f83]) ).
fof(f85,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f86,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(flattening,[],[f85]) ).
fof(f103,plain,
( ordinal(sK18)
& in(sK17,sK18)
& ~ ordinal(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f65]) ).
fof(f104,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f105,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK19(X1))
| ~ in(X3,X1) )
& in(sK19(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X2,sK19(X1))],[f74]) ).
fof(f106,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f113,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f114,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f115,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f116,plain,
! [X0] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f117,plain,
! [X3,X0,X4] :
( ~ epsilon_connected(X0)
| in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f118,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f119,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f120,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f121,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f122,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f123,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f124,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f125,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f126,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f127,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f165,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f103]) ).
fof(f166,plain,
in(sK17,sK18),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
~ ordinal(sK17),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f172,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f177,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f179,plain,
! [X0,X1] :
( in(sK19(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_54,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_55,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_56,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_58,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_59,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_60,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_61,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_62,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f118]) ).
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,[],[f117]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_68,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_69,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_106,negated_conjecture,
~ ordinal(sK17),
inference(cnf_transformation,[],[f167]) ).
tcf(c_107,negated_conjecture,
in(sK17,sK18),
inference(cnf_transformation,[],[f166]) ).
tcf(c_108,negated_conjecture,
ordinal(sK18),
inference(cnf_transformation,[],[f165]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( in(sK19(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_112]) ).
tcf(c_168,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_68]) ).
tcf(c_170,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_69]) ).
tcf(c_180,plain,
! [X0: $i] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_181,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(renaming,[status(thm)],[c_180]) ).
tcf(c_182,plain,
! [X0: $i] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
tcf(c_183,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(renaming,[status(thm)],[c_182]) ).
tcf(c_184,plain,
! [X0: $i] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_185,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(renaming,[status(thm)],[c_184]) ).
tcf(c_186,plain,
! [X0: $i] :
( ( sK1(X0) != sK2(X0) )
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_187,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(renaming,[status(thm)],[c_186]) ).
tcf(c_188,plain,
! [X0: $i] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_189,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(renaming,[status(thm)],[c_188]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_115,c_146]) ).
tcf(c_769,plain,
! [X0: $i] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_106]) ).
tcf(c_770,plain,
( ~ epsilon_connected(sK17)
| ~ epsilon_transitive(sK17) ),
inference(unflattening,[status(thm)],[c_769]) ).
tcf(c_777,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_170,c_108]) ).
tcf(c_778,plain,
epsilon_connected(sK18),
inference(unflattening,[status(thm)],[c_777]) ).
tcf(c_782,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_168,c_108]) ).
tcf(c_783,plain,
epsilon_transitive(sK18),
inference(unflattening,[status(thm)],[c_782]) ).
tcf(c_1083,plain,
! [X0: $i] :
( ~ epsilon_transitive(sK17)
| ~ in(sK2(X0),sK1(X0))
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_189,c_770]) ).
tcf(c_1084,plain,
( ~ epsilon_transitive(sK17)
| ~ in(sK2(sK17),sK1(sK17)) ),
inference(unflattening,[status(thm)],[c_1083]) ).
tcf(c_1091,plain,
! [X0: $i] :
( ~ epsilon_transitive(sK17)
| ( X0 != sK17 )
| ( sK1(X0) != sK2(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_187,c_770]) ).
tcf(c_1092,plain,
( ~ epsilon_transitive(sK17)
| ( sK1(sK17) != sK2(sK17) ) ),
inference(unflattening,[status(thm)],[c_1091]) ).
tcf(c_1099,plain,
! [X0: $i] :
( ~ epsilon_transitive(sK17)
| ~ in(sK1(X0),sK2(X0))
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_185,c_770]) ).
tcf(c_1100,plain,
( ~ epsilon_transitive(sK17)
| ~ in(sK1(sK17),sK2(sK17)) ),
inference(unflattening,[status(thm)],[c_1099]) ).
tcf(c_1107,plain,
! [X0: $i] :
( in(sK2(X0),X0)
| ~ epsilon_transitive(sK17)
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_183,c_770]) ).
tcf(c_1108,plain,
( in(sK2(sK17),sK17)
| ~ epsilon_transitive(sK17) ),
inference(unflattening,[status(thm)],[c_1107]) ).
tcf(c_1115,plain,
! [X0: $i] :
( in(sK1(X0),X0)
| ~ epsilon_transitive(sK17)
| ( X0 != sK17 ) ),
inference(resolution_lifted,[status(thm)],[c_181,c_770]) ).
tcf(c_1116,plain,
( in(sK1(sK17),sK17)
| ~ epsilon_transitive(sK17) ),
inference(unflattening,[status(thm)],[c_1115]) ).
tcf(c_2547,plain,
epsilon_transitive(sK18),
inference(demodulation,[status(thm)],[c_783]) ).
tcf(c_2548,plain,
epsilon_connected(sK18),
inference(demodulation,[status(thm)],[c_778]) ).
tcf(c_2549,negated_conjecture,
in(sK17,sK18),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_2550,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3442,plain,
~ empty(sK18),
inference(superposition,[status(thm)],[c_2549,c_118]) ).
tcf(c_3766,plain,
( epsilon_transitive(sK17)
| in(sK0(sK17),sK17) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_3911,plain,
( subset(sK17,sK18)
| ~ epsilon_transitive(sK18) ),
inference(superposition,[status(thm)],[c_2549,c_57]) ).
tcf(c_3919,plain,
subset(sK17,sK18),
inference(forward_subsumption_resolution,[status(thm)],[c_3911,c_2547]) ).
tcf(c_3967,plain,
( epsilon_transitive(sK17)
| ~ subset(sK0(sK17),sK17) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_4168,plain,
! [X0: $i] :
( empty(sK18)
| in(X0,sK18)
| ~ element(X0,sK18) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_4609,plain,
! [X0: $i,X1: $i] :
( in(sK17,X0)
| in(X0,sK17)
| ( X0 = sK17 )
| ~ epsilon_connected(X1)
| ~ in(sK17,X1)
| ~ in(X0,X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_4936,plain,
! [X0: $i] :
( in(sK0(sK17),X0)
| ~ subset(sK17,X0)
| ~ in(sK0(sK17),sK17) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_5191,plain,
( subset(sK0(sK17),sK17)
| in(sK3(sK0(sK17),sK17),sK0(sK17)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_5192,plain,
( subset(sK0(sK17),sK17)
| ~ in(sK3(sK0(sK17),sK17),sK17) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_6626,plain,
! [X0: $i] :
( in(sK17,X0)
| in(X0,sK17)
| ( X0 = sK17 )
| ~ epsilon_connected(sK18)
| ~ in(sK17,sK18)
| ~ in(X0,sK18) ),
inference(instantiation,[status(thm)],[c_4609]) ).
tcf(c_10081,plain,
! [X0: $i] :
( in(sK2(sK17),X0)
| ~ subset(sK17,X0)
| ~ in(sK2(sK17),sK17) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_10325,plain,
! [X0: $i] :
( in(sK1(sK17),X0)
| ~ subset(sK17,X0)
| ~ in(sK1(sK17),sK17) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_14134,plain,
( ~ in(sK0(sK17),sK3(sK0(sK17),sK17))
| ~ in(sK3(sK0(sK17),sK17),sK0(sK17)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_14969,plain,
( in(sK0(sK17),sK18)
| ~ subset(sK17,sK18)
| ~ in(sK0(sK17),sK17) ),
inference(instantiation,[status(thm)],[c_4936]) ).
tcf(c_22901,plain,
! [X0: $i] :
( in(sK2(sK17),sK1(sK17))
| in(sK1(sK17),sK2(sK17))
| ( sK1(sK17) = sK2(sK17) )
| ~ epsilon_connected(X0)
| ~ in(sK2(sK17),X0)
| ~ in(sK1(sK17),X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_29076,plain,
in(sK19(sK18),sK18),
inference(superposition,[status(thm)],[c_2549,c_119]) ).
tcf(c_29845,plain,
! [X0: $i] :
( in(sK17,X0)
| in(X0,sK17)
| ( X0 = sK17 )
| ~ epsilon_connected(sK18)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_2549,c_63]) ).
tcf(c_29854,plain,
! [X0: $i] :
( in(sK17,X0)
| in(X0,sK17)
| ( X0 = sK17 )
| ~ in(X0,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29845,c_2548]) ).
tcf(c_30123,plain,
( in(sK17,sK19(sK18))
| in(sK19(sK18),sK17)
| ( sK19(sK18) = sK17 ) ),
inference(superposition,[status(thm)],[c_29076,c_29854]) ).
tcf(c_30165,plain,
( subset(sK19(sK18),sK17)
| in(sK17,sK19(sK18))
| ( sK19(sK18) = sK17 )
| ~ epsilon_transitive(sK17) ),
inference(superposition,[status(thm)],[c_30123,c_57]) ).
tcf(c_37915,plain,
( in(sK2(sK17),sK18)
| ~ subset(sK17,sK18)
| ~ in(sK2(sK17),sK17) ),
inference(instantiation,[status(thm)],[c_10081]) ).
tcf(c_38101,plain,
( in(sK1(sK17),sK18)
| ~ subset(sK17,sK18)
| ~ in(sK1(sK17),sK17) ),
inference(instantiation,[status(thm)],[c_10325]) ).
tcf(c_42079,plain,
sK0(sK17) = sK0(sK17),
inference(instantiation,[status(thm)],[c_2550]) ).
tcf(c_65138,plain,
( in(sK2(sK17),sK1(sK17))
| in(sK1(sK17),sK2(sK17))
| ( sK1(sK17) = sK2(sK17) )
| ~ epsilon_connected(sK18)
| ~ in(sK2(sK17),sK18)
| ~ in(sK1(sK17),sK18) ),
inference(instantiation,[status(thm)],[c_22901]) ).
tcf(c_69415,plain,
~ epsilon_transitive(sK17),
inference(global_subsumption_just,[status(thm)],[c_30165,c_778,c_1084,c_1092,c_1100,c_1108,c_1116,c_3919,c_37915,c_38101,c_65138]) ).
tcf(c_105580,plain,
( in(sK17,sK3(sK0(sK17),sK17))
| in(sK3(sK0(sK17),sK17),sK17)
| ( sK3(sK0(sK17),sK17) = sK17 )
| ~ epsilon_connected(sK18)
| ~ in(sK17,sK18)
| ~ in(sK3(sK0(sK17),sK17),sK18) ),
inference(instantiation,[status(thm)],[c_6626]) ).
tcf(c_110351,plain,
( empty(sK18)
| in(sK3(sK0(sK17),sK17),sK18)
| ~ element(sK3(sK0(sK17),sK17),sK18) ),
inference(instantiation,[status(thm)],[c_4168]) ).
tcf(c_133676,plain,
! [X0: $i,X1: $i] :
( element(X0,sK18)
| ~ subset(X1,sK18)
| ~ in(X0,X1) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_133707,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(sK0(sK17),sK17)
| ( X1 != sK17 )
| ( X0 != sK0(sK17) ) ),
inference(instantiation,[status(thm)],[c_2553]) ).
tcf(c_134029,plain,
( element(sK3(sK0(sK17),sK17),sK18)
| ~ subset(sK0(sK17),sK18)
| ~ in(sK3(sK0(sK17),sK17),sK0(sK17)) ),
inference(instantiation,[status(thm)],[c_133676]) ).
tcf(c_134032,plain,
! [X0: $i] :
( ~ in(sK0(sK17),X0)
| ~ in(X0,sK3(sK0(sK17),sK17))
| ~ in(sK3(sK0(sK17),sK17),sK0(sK17)) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_135044,plain,
( subset(sK0(sK17),sK18)
| ~ epsilon_transitive(sK18)
| ~ in(sK0(sK17),sK18) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_135420,plain,
( ~ in(sK0(sK17),sK17)
| ~ in(sK17,sK3(sK0(sK17),sK17))
| ~ in(sK3(sK0(sK17),sK17),sK0(sK17)) ),
inference(instantiation,[status(thm)],[c_134032]) ).
tcf(c_136433,plain,
! [X0: $i] :
( in(X0,sK3(sK0(sK17),sK17))
| ~ in(sK0(sK17),sK17)
| ( X0 != sK0(sK17) )
| ( sK3(sK0(sK17),sK17) != sK17 ) ),
inference(instantiation,[status(thm)],[c_133707]) ).
tcf(c_141538,plain,
( in(sK0(sK17),sK3(sK0(sK17),sK17))
| ~ in(sK0(sK17),sK17)
| ( sK0(sK17) != sK0(sK17) )
| ( sK3(sK0(sK17),sK17) != sK17 ) ),
inference(instantiation,[status(thm)],[c_136433]) ).
tcf(c_141539,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_141538,c_135420,c_135044,c_134029,c_110351,c_105580,c_69415,c_42079,c_14969,c_14134,c_5191,c_5192,c_3967,c_3919,c_3766,c_3442,c_783,c_778,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU232+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/0.46 % Computer : n010.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Thu Sep 24 13:19:43 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.54
% 0.24/0.54 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.54
% 0.24/0.54 % Detected problem language: tptp
% 0.24/0.56 % Proving...
% 64.21/11.20 % SZS status Started for theBenchmark.p
% 64.21/11.20 % SZS status Theorem for theBenchmark.p
% 64.21/11.20
% 64.21/11.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 64.21/11.20
% 64.21/11.20 % ------ iProver source info
% 64.21/11.20
% 64.21/11.20 % git: date: 2026-07-19 20:42:38 +0200
% 64.21/11.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 64.21/11.20 % git: non_committed_changes: false
% 64.21/11.20
% 64.21/11.20 % ------ Parsing...
% 64.21/11.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 64.21/11.20
% 64.21/11.20 % ------ 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 %
% 64.21/11.20
% 64.21/11.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 64.21/11.20
% 64.21/11.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 64.21/11.20 % ------ Proving...
% 64.21/11.20 % ------ Problem Properties
% 64.21/11.20
% 64.21/11.20 %
% 64.21/11.20 % clauses 49
% 64.21/11.20 % conjectures 1
% 64.21/11.20 % EPR 27
% 64.21/11.20 % Horn 39
% 64.21/11.20 % unary 17
% 64.21/11.20 % binary 19
% 64.21/11.20 % lits 98
% 64.21/11.20 % lits eq 11
% 64.21/11.20 % fd_pure 0
% 64.21/11.20 % fd_pseudo 0
% 64.21/11.20 % fd_cond 1
% 64.21/11.20 % fd_pseudo_cond 5
% 64.21/11.20 % AC symbols 0
% 64.21/11.20
% 64.21/11.20 % ------ Schedule dynamic 5 is on
% 64.21/11.20
% 64.21/11.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 64.21/11.20
% 64.21/11.20
% 64.21/11.20 % ------
% 64.21/11.20 % Current options:
% 64.21/11.20 % ------
% 64.21/11.20
% 64.21/11.20
% 64.21/11.20 %
% 64.21/11.20
% 64.21/11.20 % ------ Proving...
% 64.21/11.20 %
% 64.21/11.20
% 64.21/11.20 % SZS status Theorem for theBenchmark.p
% 64.21/11.20
% 64.21/11.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 74.94/11.20
% 74.94/11.20
%------------------------------------------------------------------------------