%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU007+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 02:55:01 PM UTC 2026
% Result : Theorem 27.05s 4.48s
% Output : CNFRefutation 27.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 135 ( 47 unt; 5 def)
% Number of atoms : 652 ( 96 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 569 ( 242 ~; 253 |; 57 &)
% ( 9 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 193 ( 0 sgn 181 !; 12 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f15,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f34,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f35,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f36,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> relation_dom(relation_composition(identity_relation(X0),X1)) = set_intersection2(relation_dom(X1),X0) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f67,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f68,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(flattening,[],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f34]) ).
fof(f72,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f73,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& relation_dom(relation_composition(identity_relation(X0),X1)) != set_intersection2(relation_dom(X1),X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f75,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& relation_dom(relation_composition(identity_relation(X0),X1)) != set_intersection2(relation_dom(X1),X0) ),
inference(flattening,[],[f74]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f85]) ).
fof(f96,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f97,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f71]) ).
fof(f99,plain,
! [X0,X1] :
( ( ( in(sK10(X0,X1),X0)
| in(sK10(X0,X1),X1) )
& ( ~ in(sK10(X0,X1),X0)
| ~ in(sK10(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f101,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK11(X0,X1),X0)
& sK11(X0,X1) != apply(X1,sK11(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f102]) ).
fof(f104,plain,
( function(sK13)
& relation(sK13)
& relation_dom(relation_composition(identity_relation(sK12),sK13)) != set_intersection2(relation_dom(sK13),sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f75]) ).
fof(f108,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f116,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f127,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f128,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(apply(X2,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f154,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f157,plain,
! [X0,X1] :
( in(sK10(X0,X1),X0)
| in(sK10(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f158,plain,
! [X0,X1] :
( ~ in(sK10(X0,X1),X0)
| ~ in(sK10(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f159,plain,
! [X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X3,X0)
| apply(X1,X3) = X3 ),
inference(cnf_transformation,[],[f103]) ).
fof(f160,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| relation_dom(X1) = X0 ),
inference(cnf_transformation,[],[f103]) ).
fof(f163,plain,
function(sK13),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
relation(sK13),
inference(cnf_transformation,[],[f104]) ).
fof(f165,plain,
relation_dom(relation_composition(identity_relation(sK12),sK13)) != set_intersection2(relation_dom(sK13),sK12),
inference(cnf_transformation,[],[f104]) ).
fof(f172,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f111]) ).
fof(f173,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f174,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f109]) ).
fof(f177,plain,
! [X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(equality_resolution,[],[f160]) ).
fof(f178,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3 ),
inference(equality_resolution,[],[f159]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f108]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_60,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f116]) ).
tcf(c_71,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f128]) ).
tcf(c_72,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f127]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_dom(relation_composition(X0,X2)))
| ~ relation(X2)
| ~ relation(X0)
| ~ function(X2)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),relation_dom(X2)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK10(X0,X1),X1)
| ~ in(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( in(sK10(X0,X1),X1)
| in(sK10(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_105,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = X0 )
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_107,negated_conjecture,
relation_dom(relation_composition(identity_relation(sK12),sK13)) != set_intersection2(relation_dom(sK13),sK12),
inference(cnf_transformation,[],[f165]) ).
tcf(c_108,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f164]) ).
tcf(c_109,negated_conjecture,
function(sK13),
inference(cnf_transformation,[],[f163]) ).
tcf(c_148,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_105,c_72,c_71,c_105]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_106,c_60]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_177,c_72]) ).
tcf(c_549,plain,
relation_dom(relation_composition(identity_relation(sK12),sK13)) != set_intersection2(sK12,relation_dom(sK13)),
inference(demodulation,[status(thm)],[c_107,c_52]) ).
tcf(c_1175,definition,
iPr_def_10 = identity_relation(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1176,definition,
iPr_def_11 = relation_composition(iPr_def_10,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1177,definition,
iPr_def_12 = relation_dom(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1178,definition,
iPr_def_13 = relation_dom(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1179,definition,
iPr_def_14 = set_intersection2(sK12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1180,plain,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_549,c_1178,c_1179,c_1175,c_1176,c_1177]) ).
tcf(c_1181,negated_conjecture,
function(sK13),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_1182,negated_conjecture,
relation(sK13),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_1917,plain,
function(iPr_def_10),
inference(superposition,[status(thm)],[c_1175,c_72]) ).
tcf(c_1918,plain,
relation(iPr_def_10),
inference(superposition,[status(thm)],[c_1175,c_71]) ).
tcf(c_1919,plain,
relation_dom(iPr_def_10) = sK12,
inference(superposition,[status(thm)],[c_1175,c_148]) ).
tcf(c_1986,plain,
set_intersection2(iPr_def_13,sK12) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1179,c_52]) ).
tcf(c_2089,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_1986,c_57]) ).
tcf(c_2129,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_1986,c_58]) ).
tcf(c_2472,plain,
( ( iPr_def_12 = iPr_def_14 )
| ~ in(sK10(iPr_def_12,iPr_def_14),iPr_def_14)
| ~ in(sK10(iPr_def_12,iPr_def_14),iPr_def_12) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_2636,plain,
! [X0: $i] :
( in(X0,iPr_def_14)
| ~ in(X0,iPr_def_13)
| ~ in(X0,sK12) ),
inference(superposition,[status(thm)],[c_1986,c_56]) ).
tcf(c_3422,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ~ relation(iPr_def_10)
| ~ relation(sK13)
| ~ function(iPr_def_10)
| ~ function(sK13)
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1176,c_97]) ).
tcf(c_3423,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ relation(iPr_def_10)
| ~ relation(sK13)
| ~ function(iPr_def_10)
| ~ function(sK13)
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_3422,c_1177,c_1919]) ).
tcf(c_3424,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ in(X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3423,c_1918,c_1182,c_1917,c_1181]) ).
tcf(c_3525,plain,
! [X0: $i] :
( in(apply(iPr_def_10,X0),relation_dom(sK13))
| ~ relation(iPr_def_10)
| ~ relation(sK13)
| ~ function(iPr_def_10)
| ~ function(sK13)
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1176,c_98]) ).
tcf(c_3526,plain,
! [X0: $i] :
( in(apply(iPr_def_10,X0),iPr_def_13)
| ~ relation(iPr_def_10)
| ~ relation(sK13)
| ~ function(iPr_def_10)
| ~ function(sK13)
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_3525,c_1177,c_1178]) ).
tcf(c_3527,plain,
! [X0: $i] :
( in(apply(iPr_def_10,X0),iPr_def_13)
| ~ in(X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3526,c_1918,c_1182,c_1917,c_1181]) ).
tcf(c_3627,plain,
relation(iPr_def_10),
inference(superposition,[status(thm)],[c_1175,c_71]) ).
tcf(c_3768,plain,
! [X0: $i] :
( in(sK10(iPr_def_12,X0),sK12)
| in(sK10(iPr_def_12,X0),X0)
| ( X0 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_102,c_3424]) ).
tcf(c_4127,plain,
( in(sK10(iPr_def_12,iPr_def_14),sK12)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3768,c_2129]) ).
tcf(c_4136,plain,
in(sK10(iPr_def_12,iPr_def_14),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_4127,c_1180]) ).
tcf(c_4559,plain,
apply(identity_relation(sK12),sK10(iPr_def_12,iPr_def_14)) = sK10(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_4136,c_180]) ).
tcf(c_4563,plain,
apply(iPr_def_10,sK10(iPr_def_12,iPr_def_14)) = sK10(iPr_def_12,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_4559,c_1175]) ).
tcf(c_10342,plain,
( in(sK10(iPr_def_12,iPr_def_14),iPr_def_13)
| ~ in(sK10(iPr_def_12,iPr_def_14),iPr_def_12) ),
inference(superposition,[status(thm)],[c_4563,c_3527]) ).
tcf(c_10436,plain,
( in(sK10(iPr_def_12,iPr_def_14),iPr_def_14)
| in(sK10(iPr_def_12,iPr_def_14),iPr_def_13)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_102,c_10342]) ).
tcf(c_10437,plain,
( in(sK10(iPr_def_12,iPr_def_14),iPr_def_14)
| in(sK10(iPr_def_12,iPr_def_14),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10436,c_1180]) ).
tcf(c_10468,plain,
in(sK10(iPr_def_12,iPr_def_14),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_10437,c_2089]) ).
tcf(c_21195,plain,
( in(sK10(iPr_def_12,iPr_def_14),iPr_def_14)
| ~ in(sK10(iPr_def_12,iPr_def_14),sK12) ),
inference(superposition,[status(thm)],[c_10468,c_2636]) ).
tcf(c_21228,plain,
in(sK10(iPr_def_12,iPr_def_14),iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_21195,c_4136]) ).
tcf(c_33048,plain,
function(iPr_def_10),
inference(superposition,[status(thm)],[c_1175,c_72]) ).
tcf(c_33086,plain,
relation_dom(iPr_def_10) = sK12,
inference(superposition,[status(thm)],[c_1175,c_148]) ).
tcf(c_33093,plain,
set_intersection2(iPr_def_13,sK12) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1179,c_52]) ).
tcf(c_33179,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_33093,c_57]) ).
tcf(c_33241,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ in(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_33093,c_58]) ).
tcf(c_34354,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_10))
| ~ relation(iPr_def_10)
| ~ relation(sK13)
| ~ function(iPr_def_10)
| ~ function(sK13)
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1176,c_97]) ).
tcf(c_34355,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ relation(iPr_def_10)
| ~ relation(sK13)
| ~ function(iPr_def_10)
| ~ function(sK13)
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_34354,c_1177,c_33086]) ).
tcf(c_34356,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ in(X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34355,c_3627,c_1182,c_33048,c_1181]) ).
tcf(c_34442,plain,
! [X0: $i] :
( in(apply(iPr_def_10,X0),relation_dom(sK13))
| ~ relation(iPr_def_10)
| ~ relation(sK13)
| ~ function(iPr_def_10)
| ~ function(sK13)
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1176,c_98]) ).
tcf(c_34443,plain,
! [X0: $i] :
( in(apply(iPr_def_10,X0),iPr_def_13)
| ~ relation(iPr_def_10)
| ~ relation(sK13)
| ~ function(iPr_def_10)
| ~ function(sK13)
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_34442,c_1177,c_1178]) ).
tcf(c_34444,plain,
! [X0: $i] :
( in(apply(iPr_def_10,X0),iPr_def_13)
| ~ in(X0,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34443,c_3627,c_1182,c_33048,c_1181]) ).
tcf(c_34772,plain,
! [X0: $i] :
( in(sK10(iPr_def_12,X0),sK12)
| in(sK10(iPr_def_12,X0),X0)
| ( X0 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_102,c_34356]) ).
tcf(c_34984,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(relation_composition(X0,sK13)))
| ~ relation(sK13)
| ~ function(sK13)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_1178,c_96]) ).
tcf(c_35000,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(relation_composition(X0,sK13)))
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34984,c_1182,c_1181]) ).
tcf(c_35138,plain,
! [X0: $i] :
( in(X0,relation_dom(iPr_def_11))
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ in(X0,relation_dom(iPr_def_10))
| ~ in(apply(iPr_def_10,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_1176,c_35000]) ).
tcf(c_35150,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ~ in(X0,sK12)
| ~ in(apply(iPr_def_10,X0),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_35138,c_1177,c_33086]) ).
tcf(c_35151,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ in(X0,sK12)
| ~ in(apply(iPr_def_10,X0),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35150,c_3627,c_33048]) ).
tcf(c_35532,plain,
( in(sK10(iPr_def_12,iPr_def_14),sK12)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_34772,c_33241]) ).
tcf(c_35541,plain,
in(sK10(iPr_def_12,iPr_def_14),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_35532,c_1180]) ).
tcf(c_39765,plain,
apply(identity_relation(sK12),sK10(iPr_def_12,iPr_def_14)) = sK10(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_35541,c_180]) ).
tcf(c_39769,plain,
apply(iPr_def_10,sK10(iPr_def_12,iPr_def_14)) = sK10(iPr_def_12,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_39765,c_1175]) ).
tcf(c_41798,plain,
( in(sK10(iPr_def_12,iPr_def_14),iPr_def_13)
| ~ in(sK10(iPr_def_12,iPr_def_14),iPr_def_12) ),
inference(superposition,[status(thm)],[c_39769,c_34444]) ).
tcf(c_41977,plain,
~ in(sK10(iPr_def_12,iPr_def_14),iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_41798,c_1180,c_2472,c_21228]) ).
tcf(c_41980,plain,
( in(sK10(iPr_def_12,iPr_def_14),iPr_def_14)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_102,c_41977]) ).
tcf(c_41981,plain,
in(sK10(iPr_def_12,iPr_def_14),iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_41980,c_1180]) ).
tcf(c_41997,plain,
in(sK10(iPr_def_12,iPr_def_14),iPr_def_13),
inference(superposition,[status(thm)],[c_41981,c_33179]) ).
tcf(c_42691,plain,
( in(sK10(iPr_def_12,iPr_def_14),iPr_def_12)
| ~ in(sK10(iPr_def_12,iPr_def_14),iPr_def_13)
| ~ in(sK10(iPr_def_12,iPr_def_14),sK12) ),
inference(superposition,[status(thm)],[c_39769,c_35151]) ).
tcf(c_42697,plain,
~ in(sK10(iPr_def_12,iPr_def_14),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_42691,c_41977,c_35541]) ).
tcf(c_42718,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_42697,c_41997]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU007+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Thu Sep 24 12:32:50 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 0.14/0.47
% 0.14/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.47
% 0.14/0.47 % Detected problem language: tptp
% 0.22/0.49 % Proving...
% 27.05/4.48 % SZS status Started for theBenchmark.p
% 27.05/4.48 % SZS status Theorem for theBenchmark.p
% 27.05/4.48
% 27.05/4.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.05/4.48
% 27.05/4.48 % ------ iProver source info
% 27.05/4.48
% 27.05/4.48 % git: date: 2026-07-19 20:42:38 +0200
% 27.05/4.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.05/4.48 % git: non_committed_changes: false
% 27.05/4.48
% 27.05/4.48 % ------ Parsing...
% 27.05/4.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.05/4.48
% 27.05/4.48 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 27.05/4.48
% 27.05/4.48 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 27.05/4.48
% 27.05/4.48 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.05/4.48 % ------ Proving...
% 27.05/4.48 % ------ Problem Properties
% 27.05/4.48
% 27.05/4.48 %
% 27.05/4.48 % clauses 66
% 27.05/4.48 % conjectures 2
% 27.05/4.48 % EPR 22
% 27.05/4.48 % Horn 60
% 27.05/4.48 % unary 30
% 27.05/4.48 % binary 13
% 27.05/4.48 % lits 140
% 27.05/4.48 % lits eq 21
% 27.05/4.48 % fd_pure 0
% 27.05/4.48 % fd_pseudo 0
% 27.05/4.48 % fd_cond 1
% 27.05/4.48 % fd_pseudo_cond 6
% 27.05/4.48 % AC symbols 0
% 27.05/4.48
% 27.05/4.48 % ------ Schedule dynamic 5 is on
% 27.05/4.48
% 27.05/4.48 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 27.05/4.48
% 27.05/4.48
% 27.05/4.48 % ------
% 27.05/4.48 % Current options:
% 27.05/4.48 % ------
% 27.05/4.48
% 27.05/4.48
% 27.05/4.48 %
% 27.05/4.48
% 27.05/4.48 % ------ Proving...
% 27.05/4.48 %
% 27.05/4.48
% 27.05/4.48 % SZS status Theorem for theBenchmark.p
% 27.05/4.48
% 27.05/4.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.05/4.48
% 27.05/4.48
%------------------------------------------------------------------------------