%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU201+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 : n014.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 02:55:52 PM UTC 2026
% Result : Theorem 26.58s 4.33s
% Output : CNFRefutation 26.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 97 ( 9 unt; 0 def)
% Number of atoms : 405 ( 49 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 522 ( 214 ~; 225 |; 61 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 250 ( 0 sgn 229 !; 21 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f18,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f38,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
fof(f39,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f40,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f54,plain,
? [X0,X1] :
( relation(X1)
& relation_rng(relation_rng_restriction(X0,X1)) != set_intersection2(relation_rng(X1),X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(flattening,[],[f56]) ).
fof(f60,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f61,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f62,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f63,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f68,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f79,plain,
( relation(sK1)
& relation_rng(relation_rng_restriction(sK0,sK1)) != set_intersection2(relation_rng(sK1),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f54]) ).
fof(f80,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,[],[f8]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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(sK2(X0,X1,X2),X2)
| ( in(sK2(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f85,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2)
| ( in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X1)
& in(sK4(X0,X1,X2),X0) ) )
& ( ~ in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X1)
| ~ in(sK4(X0,X1,X2),X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X4,sK4(X0,X1,X2))],[f86]) ).
fof(f90,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f91,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK9(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK7(X0,X1),X1)
| in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0) )
& ( ~ in(sK7(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK7(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f91]) ).
fof(f96,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,[],[f69]) ).
fof(f97,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,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK12(X0,X1),X0)
& ~ in(sK12(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f97]) ).
fof(f104,plain,
relation(sK1),
inference(cnf_transformation,[],[f79]) ).
fof(f105,plain,
relation_rng(relation_rng_restriction(sK0,sK1)) != set_intersection2(relation_rng(sK1),sK0),
inference(cnf_transformation,[],[f79]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f116,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f117,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f118,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f119,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f122,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f134,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK9(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f135,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f136,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK7(X0,X1),X1)
| in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f137,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK7(X0,X1),X1)
| ~ in(ordered_pair(X3,sK7(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f143,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f163,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f111]) ).
fof(f164,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f110]) ).
fof(f165,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[],[f122]) ).
fof(f168,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f135]) ).
fof(f169,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(ordered_pair(sK9(X0,X5),X5),X0) ),
inference(equality_resolution,[],[f134]) ).
tcf(c_49,negated_conjecture,
relation_rng(relation_rng_restriction(sK0,sK1)) != set_intersection2(relation_rng(sK1),sK0),
inference(cnf_transformation,[],[f105]) ).
tcf(c_50,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f104]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f116]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X1),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ relation(relation_rng_restriction(X3,X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X1) = X2 )
| ~ relation(X1)
| ~ in(sK7(X1,X2),X2)
| ~ in(ordered_pair(X0,sK7(X1,X2)),X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( in(sK7(X0,X1),X1)
| in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(X1,X0),X0),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(ordered_pair(X0,X1),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_166]) ).
tcf(c_671,plain,
relation_rng(relation_rng_restriction(sK0,sK1)) != set_intersection2(sK0,relation_rng(sK1)),
inference(demodulation,[status(thm)],[c_49,c_61]) ).
tcf(c_3325,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(sK0,sK1)) = set_intersection2(sK0,relation_rng(sK1)) )
| ~ relation(relation_rng_restriction(sK0,sK1))
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),set_intersection2(sK0,relation_rng(sK1)))
| ~ in(ordered_pair(X0,sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_3327,plain,
( in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),set_intersection2(sK0,relation_rng(sK1)))
| in(ordered_pair(sK8(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(sK0,sK1))
| ( relation_rng(relation_rng_restriction(sK0,sK1)) = set_intersection2(sK0,relation_rng(sK1)) )
| ~ relation(relation_rng_restriction(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_3426,plain,
( subset(relation_rng(relation_rng_restriction(sK0,sK1)),set_intersection2(sK0,relation_rng(sK1)))
| ~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),sK0)
| ~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),relation_rng(sK1)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_3483,plain,
( relation(relation_rng_restriction(sK0,sK1))
| ~ relation(sK1) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_5896,plain,
( in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),relation_rng(sK1))
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),set_intersection2(sK0,relation_rng(sK1))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_5897,plain,
( in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),sK0)
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),set_intersection2(sK0,relation_rng(sK1))) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_6563,plain,
( subset(relation_rng(relation_rng_restriction(sK0,sK1)),relation_rng(sK1))
| ~ relation(sK1) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_6565,plain,
( subset(relation_rng(relation_rng_restriction(sK0,sK1)),sK0)
| ~ relation(sK1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_6795,plain,
! [X0: $i] :
( in(sK7(relation_rng_restriction(sK0,sK1),X0),relation_rng(relation_rng_restriction(sK0,sK1)))
| ~ relation(relation_rng_restriction(sK0,sK1))
| ~ in(ordered_pair(sK8(relation_rng_restriction(sK0,sK1),X0),sK7(relation_rng_restriction(sK0,sK1),X0)),relation_rng_restriction(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_17070,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(relation_rng_restriction(X1,X2),X0),X0),relation_rng_restriction(X1,X2))
| ~ relation(relation_rng_restriction(X1,X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_19245,plain,
( in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),relation_rng(relation_rng_restriction(sK0,sK1)))
| ~ relation(relation_rng_restriction(sK0,sK1))
| ~ in(ordered_pair(sK8(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_6795]) ).
tcf(c_41229,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK9(relation_rng_restriction(X0,X1),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),relation_rng(relation_rng_restriction(X0,X1))) ),
inference(instantiation,[status(thm)],[c_17070]) ).
tcf(c_45123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK7(X0,X1),X3)
| ~ subset(X2,X3)
| ~ in(sK7(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_64658,plain,
( in(ordered_pair(sK9(relation_rng_restriction(sK0,sK1),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(sK0,sK1))
| ~ relation(relation_rng_restriction(sK0,sK1))
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),relation_rng(relation_rng_restriction(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_41229]) ).
tcf(c_74031,plain,
( ( relation_rng(relation_rng_restriction(sK0,sK1)) = set_intersection2(sK0,relation_rng(sK1)) )
| ~ relation(relation_rng_restriction(sK0,sK1))
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),set_intersection2(sK0,relation_rng(sK1)))
| ~ in(ordered_pair(sK9(relation_rng_restriction(sK0,sK1),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_3325]) ).
tcf(c_78926,plain,
! [X0: $i] :
( in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),set_intersection2(sK0,relation_rng(sK1)))
| ~ subset(X0,set_intersection2(sK0,relation_rng(sK1)))
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),X0) ),
inference(instantiation,[status(thm)],[c_45123]) ).
tcf(c_90006,plain,
( in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),set_intersection2(sK0,relation_rng(sK1)))
| ~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),set_intersection2(sK0,relation_rng(sK1)))
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),relation_rng(relation_rng_restriction(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_78926]) ).
tcf(c_92601,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(sK9(X2,sK7(X0,set_intersection2(X1,relation_rng(X2)))),sK7(X0,set_intersection2(X1,relation_rng(X2)))),X2)
| ~ relation(X2)
| ~ in(sK7(X0,set_intersection2(X1,relation_rng(X2))),relation_rng(X2)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_92618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X0,sK7(X1,set_intersection2(X2,X3))),relation_rng_restriction(X2,X4))
| ~ relation(X4)
| ~ in(sK7(X1,set_intersection2(X2,X3)),X2)
| ~ in(ordered_pair(X0,sK7(X1,set_intersection2(X2,X3))),X4) ),
inference(instantiation,[status(thm)],[c_360]) ).
tcf(c_95489,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(sK0,X1))
| ~ relation(X1)
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),sK0)
| ~ in(ordered_pair(X0,sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),X1) ),
inference(instantiation,[status(thm)],[c_92618]) ).
tcf(c_95517,plain,
( in(ordered_pair(sK9(sK1,sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),relation_rng(sK1)) ),
inference(instantiation,[status(thm)],[c_92601]) ).
tcf(c_100457,plain,
( in(ordered_pair(sK9(sK1,sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(sK0,sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),sK0)
| ~ in(ordered_pair(sK9(sK1,sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK1) ),
inference(instantiation,[status(thm)],[c_95489]) ).
tcf(c_107726,plain,
( in(sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1))),relation_rng(relation_rng_restriction(sK0,sK1)))
| ~ relation(relation_rng_restriction(sK0,sK1))
| ~ in(ordered_pair(sK9(sK1,sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),sK7(relation_rng_restriction(sK0,sK1),set_intersection2(sK0,relation_rng(sK1)))),relation_rng_restriction(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_107727,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_107726,c_100457,c_95517,c_90006,c_74031,c_64658,c_19245,c_6565,c_6563,c_5896,c_5897,c_3483,c_3426,c_3327,c_671,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU201+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:09:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 26.58/4.33 % SZS status Started for theBenchmark.p
% 26.58/4.33 % SZS status Theorem for theBenchmark.p
% 26.58/4.33
% 26.58/4.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.58/4.33
% 26.58/4.33 % ------ iProver source info
% 26.58/4.33
% 26.58/4.33 % git: date: 2026-07-19 20:42:38 +0200
% 26.58/4.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.58/4.33 % git: non_committed_changes: false
% 26.58/4.33
% 26.58/4.33 % ------ Parsing...
% 26.58/4.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.58/4.33
% 26.58/4.33 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 26.58/4.33
% 26.58/4.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.58/4.33
% 26.58/4.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 26.58/4.33 % ------ Proving...
% 26.58/4.33 % ------ Problem Properties
% 26.58/4.33
% 26.58/4.33 %
% 26.58/4.33 % clauses 56
% 26.58/4.33 % conjectures 1
% 26.58/4.33 % EPR 18
% 26.58/4.33 % Horn 48
% 26.58/4.33 % unary 16
% 26.58/4.33 % binary 17
% 26.58/4.33 % lits 130
% 26.58/4.33 % lits eq 13
% 26.58/4.33 % fd_pure 0
% 26.58/4.33 % fd_pseudo 0
% 26.58/4.33 % fd_cond 0
% 26.58/4.33 % fd_pseudo_cond 10
% 26.58/4.33 % AC symbols 0
% 26.58/4.33
% 26.58/4.33 % ------ Schedule dynamic 5 is on
% 26.58/4.33
% 26.58/4.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 26.58/4.33
% 26.58/4.33
% 26.58/4.33 % ------
% 26.58/4.33 % Current options:
% 26.58/4.33 % ------
% 26.58/4.33
% 26.58/4.33
% 26.58/4.33 %
% 26.58/4.33
% 26.58/4.33 % ------ Proving...
% 26.58/4.33 %
% 26.58/4.33
% 26.58/4.33 % SZS status Theorem for theBenchmark.p
% 26.58/4.33
% 26.58/4.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.58/4.33
% 26.58/4.33
%------------------------------------------------------------------------------