%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU266+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 02:56:25 PM UTC 2026
% Result : Theorem 4.78s 1.41s
% Output : CNFRefutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 123 ( 16 unt; 0 def)
% Number of atoms : 351 ( 76 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 397 ( 169 ~; 175 |; 33 &)
% ( 8 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 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 : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 273 ( 0 sgn 243 !; 30 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f4,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(f14,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
fof(f17,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f25,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f30,conjecture,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) )
<=> relation_rng_as_subset(X0,X1,X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) )
<=> relation_rng_as_subset(X0,X1,X2) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f33,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f36,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f38,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f39,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f40,plain,
? [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
& ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) )
<~> relation_rng_as_subset(X0,X1,X2) = X1 ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f41,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f42,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f33]) ).
fof(f43,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f44,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f45,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f44]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f17]) ).
fof(f56,plain,
? [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
& ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) = X1 )
& ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) != X1 ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f57,plain,
? [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
& ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) = X1 )
& ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) != X1 ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
? [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
& ( ! [X5] :
( ? [X6] : in(ordered_pair(X6,X5),X2)
| ~ in(X5,X1) )
| relation_rng_as_subset(X0,X1,X2) = X1 )
& ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) != X1 ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
( relation_of2_as_subset(sK2,sK0,sK1)
& ( ! [X5] :
( in(ordered_pair(sK4(X5),X5),sK2)
| ~ in(X5,sK1) )
| sK1 = relation_rng_as_subset(sK0,sK1,sK2) )
& ( ( ! [X4] : ~ in(ordered_pair(X4,sK3),sK2)
& in(sK3,sK1) )
| sK1 != relation_rng_as_subset(sK0,sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X6,sK4(X5))],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f42]) ).
fof(f61,plain,
! [X0,X1] :
( ( ( in(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1) )
& ( ~ in(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
& ( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f66,plain,
! [X0] : element(sK9(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f19]) ).
fof(f68,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,[],[f53]) ).
fof(f69,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,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK13(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK11(X0,X1),X1)
| in(ordered_pair(sK12(X0,X1),sK11(X0,X1)),X0) )
& ( ~ in(sK11(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK11(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X2,sK11(X0,X1)),skolemize(X4,sK12(X0,X1)),skolemize(X7,sK13(X0,X5))],[f69]) ).
fof(f71,plain,
relation_of2_as_subset(sK2,sK0,sK1),
inference(cnf_transformation,[],[f59]) ).
fof(f72,plain,
! [X5] :
( in(ordered_pair(sK4(X5),X5),sK2)
| ~ in(X5,sK1)
| sK1 = relation_rng_as_subset(sK0,sK1,sK2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f73,plain,
! [X4] :
( ~ in(ordered_pair(X4,sK3),sK2)
| sK1 != relation_rng_as_subset(sK0,sK1,sK2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f74,plain,
( in(sK3,sK1)
| sK1 != relation_rng_as_subset(sK0,sK1,sK2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f75,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f76,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f77,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f78,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f79,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f92,plain,
! [X0] : element(sK9(X0),X0),
inference(cnf_transformation,[],[f66]) ).
fof(f94,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK13(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f95,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f55]) ).
fof(f100,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f95]) ).
fof(f101,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(ordered_pair(sK13(X0,X5),X5),X0) ),
inference(equality_resolution,[],[f94]) ).
tcf(c_49,negated_conjecture,
( in(sK3,sK1)
| ( relation_rng_as_subset(sK0,sK1,sK2) != sK1 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( ~ in(ordered_pair(X0,sK3),sK2)
| ( relation_rng_as_subset(sK0,sK1,sK2) != sK1 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( in(ordered_pair(sK4(X0),X0),sK2)
| ( relation_rng_as_subset(sK0,sK1,sK2) = sK1 )
| ~ in(X0,sK1) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_52,negated_conjecture,
relation_of2_as_subset(sK2,sK0,sK1),
inference(cnf_transformation,[],[f71]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_as_subset(X1,X2,X0) = relation_rng(X0) )
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_rng_as_subset(X1,X2,X0),powerset(X2))
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_70,plain,
! [X0: $i] : element(sK9(X0),X0),
inference(cnf_transformation,[],[f92]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK13(X1,X0),X0),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_100]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_as_subset(X1,X2,X0) = relation_rng(X0) )
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_rng_as_subset(X1,X2,X0),powerset(X2))
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_61,c_77]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X2,X1,X0)
| ( X2 != sK2 )
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_101]) ).
tcf(c_448,plain,
relation_of2(sK2,sK0,sK1),
inference(unflattening,[status(thm)],[c_447]) ).
tcf(c_478,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_126,c_448]) ).
tcf(c_479,plain,
element(sK2,powerset(cartesian_product2(sK0,sK1))),
inference(unflattening,[status(thm)],[c_478]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_rng_as_subset(X1,X2,X0),powerset(X2))
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_124,c_448]) ).
tcf(c_484,plain,
element(relation_rng_as_subset(sK0,sK1,sK2),powerset(sK1)),
inference(unflattening,[status(thm)],[c_483]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_as_subset(X1,X2,X0) = relation_rng(X0) )
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_122,c_448]) ).
tcf(c_489,plain,
relation_rng_as_subset(sK0,sK1,sK2) = relation_rng(sK2),
inference(unflattening,[status(thm)],[c_488]) ).
tcf(c_964,plain,
( in(sK3,sK1)
| ( relation_rng(sK2) != sK1 ) ),
inference(light_normalisation,[status(thm)],[c_49,c_489]) ).
tcf(c_967,plain,
! [X0: $i] :
( ~ in(ordered_pair(X0,sK3),sK2)
| ( relation_rng(sK2) != sK1 ) ),
inference(light_normalisation,[status(thm)],[c_50,c_489]) ).
tcf(c_974,plain,
! [X0: $i] :
( in(ordered_pair(sK4(X0),X0),sK2)
| ( relation_rng(sK2) = sK1 )
| ~ in(X0,sK1) ),
inference(light_normalisation,[status(thm)],[c_51,c_489]) ).
tcf(c_984,plain,
element(relation_rng(sK2),powerset(sK1)),
inference(light_normalisation,[status(thm)],[c_484,c_489]) ).
tcf(c_1015,plain,
! [X0: $i] :
( empty(X0)
| in(sK9(X0),X0) ),
inference(superposition,[status(thm)],[c_70,c_57]) ).
tcf(c_1098,plain,
relation(sK2),
inference(superposition,[status(thm)],[c_479,c_76]) ).
tcf(c_1123,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_984,c_66]) ).
tcf(c_1149,plain,
! [X0: $i] :
( element(X0,sK1)
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_984,c_69]) ).
tcf(c_1188,plain,
( empty(relation_rng(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_1015,c_1123]) ).
tcf(c_1215,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1188,c_53]) ).
tcf(c_1219,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(sK1) ),
inference(instantiation,[status(thm)],[c_1215]) ).
tcf(c_1239,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_rng(sK2) = sK1 )
| ~ relation(sK2)
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_974,c_74]) ).
tcf(c_1241,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_rng(sK2) = sK1 )
| ~ in(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1239,c_1098]) ).
tcf(c_1265,plain,
! [X0: $i] :
( element(sK5(relation_rng(sK2),X0),sK1)
| in(sK5(relation_rng(sK2),X0),X0)
| ( relation_rng(sK2) = X0 ) ),
inference(superposition,[status(thm)],[c_55,c_1149]) ).
tcf(c_1405,plain,
! [X0: $i] :
( ( relation_rng(sK2) = sK1 )
| ( relation_rng(sK2) = X0 )
| ~ in(sK5(relation_rng(sK2),X0),sK1)
| ~ in(sK5(relation_rng(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_1241,c_54]) ).
tcf(c_1408,plain,
! [X0: $i] :
( ( relation_rng(sK2) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_1241,c_56]) ).
tcf(c_1444,plain,
( ( relation_rng(sK2) = sK1 )
| ~ in(sK5(relation_rng(sK2),sK1),sK1) ),
inference(instantiation,[status(thm)],[c_1405]) ).
tcf(c_1487,plain,
! [X0: $i] :
( ( relation_rng(sK2) = sK1 )
| ~ relation(sK1)
| ~ empty(relation_rng(sK2))
| ~ in(X0,relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_75,c_1408]) ).
tcf(c_3978,plain,
! [X0: $i] :
( empty(sK1)
| in(sK5(relation_rng(sK2),X0),sK1)
| in(sK5(relation_rng(sK2),X0),X0)
| ( relation_rng(sK2) = X0 ) ),
inference(superposition,[status(thm)],[c_1265,c_57]) ).
tcf(c_4042,plain,
( empty(sK1)
| in(sK5(relation_rng(sK2),sK1),sK1)
| ( relation_rng(sK2) = sK1 ) ),
inference(instantiation,[status(thm)],[c_3978]) ).
tcf(c_4087,plain,
relation_rng(sK2) = sK1,
inference(global_subsumption_just,[status(thm)],[c_1487,c_1219,c_1444,c_4042]) ).
tcf(c_4145,plain,
! [X0: $i] :
( ~ in(ordered_pair(X0,sK3),sK2)
| ( sK1 != sK1 ) ),
inference(demodulation,[status(thm)],[c_967,c_4087]) ).
tcf(c_4146,plain,
( in(sK3,sK1)
| ( sK1 != sK1 ) ),
inference(demodulation,[status(thm)],[c_964,c_4087]) ).
tcf(c_4159,plain,
in(sK3,sK1),
inference(equality_resolution_simp,[status(thm)],[c_4146]) ).
tcf(c_4168,plain,
! [X0: $i] : ~ in(ordered_pair(X0,sK3),sK2),
inference(equality_resolution_simp,[status(thm)],[c_4145]) ).
tcf(c_4205,plain,
( ~ relation(sK2)
| ~ in(sK3,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_75,c_4168]) ).
tcf(c_4206,plain,
( ~ relation(sK2)
| ~ in(sK3,sK1) ),
inference(light_normalisation,[status(thm)],[c_4205,c_4087]) ).
tcf(c_4207,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4206,c_1098,c_4159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU266+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.43 % Computer : n014.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 13:27:34 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 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
% 0.16/0.50
% 0.16/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.50
% 0.16/0.50 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 4.78/1.41 % SZS status Started for theBenchmark.p
% 4.78/1.41 % SZS status Theorem for theBenchmark.p
% 4.78/1.41
% 4.78/1.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.78/1.41
% 4.78/1.41 % ------ iProver source info
% 4.78/1.41
% 4.78/1.41 % git: date: 2026-07-19 20:42:38 +0200
% 4.78/1.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.78/1.41 % git: non_committed_changes: false
% 4.78/1.41
% 4.78/1.41 % ------ Parsing...
% 4.78/1.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.78/1.41
% 4.78/1.41 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 4.78/1.41
% 4.78/1.41 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.78/1.41
% 4.78/1.41 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.78/1.41 % ------ Proving...
% 4.78/1.41 % ------ Problem Properties
% 4.78/1.41
% 4.78/1.41 %
% 4.78/1.41 % clauses 30
% 4.78/1.41 % conjectures 3
% 4.78/1.41 % EPR 7
% 4.78/1.41 % Horn 26
% 4.78/1.41 % unary 13
% 4.78/1.41 % binary 6
% 4.78/1.41 % lits 60
% 4.78/1.41 % lits eq 11
% 4.78/1.41 % fd_pure 0
% 4.78/1.41 % fd_pseudo 0
% 4.78/1.41 % fd_cond 0
% 4.78/1.41 % fd_pseudo_cond 5
% 4.78/1.41 % AC symbols 0
% 4.78/1.41
% 4.78/1.41 % ------ Schedule dynamic 5 is on
% 4.78/1.41
% 4.78/1.41 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.78/1.41
% 4.78/1.41
% 4.78/1.41 % ------
% 4.78/1.41 % Current options:
% 4.78/1.41 % ------
% 4.78/1.41
% 4.78/1.41
% 4.78/1.41 %
% 4.78/1.41
% 4.78/1.41 % ------ Proving...
% 4.78/1.41 %
% 4.78/1.41
% 4.78/1.41 % SZS status Theorem for theBenchmark.p
% 4.78/1.41
% 4.78/1.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.78/1.42
% 4.78/1.42
%------------------------------------------------------------------------------