%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU078+1 : 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 : n001.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 02:55:19 PM UTC 2026
% Result : Theorem 17.44s 3.63s
% Output : CNFRefutation 17.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 21
% Syntax : Number of formulae : 209 ( 42 unt; 2 def)
% Number of atoms : 808 ( 197 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 873 ( 354 ~; 399 |; 88 &)
% ( 20 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 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 : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 324 ( 1 sgn 288 !; 36 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f7,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f8,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f13,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f17,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f28,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f30,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1] :
~ ( ! [X2] : relation_inverse_image(X0,singleton(X1)) != singleton(X2)
& in(X1,relation_rng(X0)) )
<=> one_to_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
fof(f31,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f37,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f42,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f45,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f28]) ).
fof(f49,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f53,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f54,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f56,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f55]) ).
fof(f61,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f62,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f65,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ! [X1] :
( ? [X2] : relation_inverse_image(X0,singleton(X1)) = singleton(X2)
| ~ in(X1,relation_rng(X0)) )
<=> one_to_one(X0) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f66,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ! [X1] :
( ? [X2] : relation_inverse_image(X0,singleton(X1)) = singleton(X2)
| ~ in(X1,relation_rng(X0)) )
<=> one_to_one(X0) ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
? [X0] :
( function(X0)
& relation(X0)
& ( one_to_one(X0)
<~> ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f68,plain,
? [X0] :
( function(X0)
& relation(X0)
& ( one_to_one(X0)
<~> ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
inference(flattening,[],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f72,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f71]) ).
fof(f77,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f42]) ).
fof(f78,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f80,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f81,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(apply(X0,sK0(X0,X1,X2)),X1)
& in(sK0(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(apply(X0,sK0(X0,X1,X2)),X1)
| ~ in(sK0(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f85,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| sK1(X0,X1) = X0 )
& ( ~ in(sK1(X0,X1),X1)
| sK1(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f85]) ).
fof(f87,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f88,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK4(X0,X5)) = X5
& in(sK4(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| ( sK2(X0,X1) = apply(X0,sK3(X0,X1))
& in(sK3(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK2(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK2(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f88]) ).
fof(f90,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f8]) ).
fof(f101,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ? [X1] :
( ! [X2] : relation_inverse_image(X0,singleton(X1)) != singleton(X2)
& in(X1,relation_rng(X0)) )
| one_to_one(X0) )
& ( ~ one_to_one(X0)
| ! [X1] :
( ? [X2] : relation_inverse_image(X0,singleton(X1)) = singleton(X2)
| ~ in(X1,relation_rng(X0)) ) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f102,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ? [X3] :
( ! [X4] : relation_inverse_image(X0,singleton(X3)) != singleton(X4)
& in(X3,relation_rng(X0)) )
| one_to_one(X0) )
& ( ~ one_to_one(X0)
| ! [X1] :
( ? [X2] : relation_inverse_image(X0,singleton(X1)) = singleton(X2)
| ~ in(X1,relation_rng(X0)) ) ) ) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ( ! [X4] : singleton(X4) != relation_inverse_image(X0,singleton(sK17(X0)))
& in(sK17(X0),relation_rng(X0)) )
| one_to_one(X0) )
& ( ~ one_to_one(X0)
| ! [X1] :
( relation_inverse_image(X0,singleton(X1)) = singleton(sK16(X0,X1))
| ~ in(X1,relation_rng(X0)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X2,sK16(X0,X1)),skolemize(X3,sK17(X0))],[f102]) ).
fof(f104,plain,
? [X0] :
( function(X0)
& relation(X0)
& ( one_to_one(X0)
| ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) )
& ( ~ one_to_one(X0)
| ? [X1] :
! [X2] : ~ subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f105,plain,
? [X0] :
( function(X0)
& relation(X0)
& ( one_to_one(X0)
| ! [X1] :
? [X2] : subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) )
& ( ~ one_to_one(X0)
| ? [X1] :
! [X2] : ~ subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
? [X0] :
( function(X0)
& relation(X0)
& ( one_to_one(X0)
| ! [X3] :
? [X4] : subset(relation_inverse_image(X0,singleton(X3)),singleton(X4)) )
& ( ~ one_to_one(X0)
| ? [X1] :
! [X2] : ~ subset(relation_inverse_image(X0,singleton(X1)),singleton(X2)) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
( function(sK18)
& relation(sK18)
& ( one_to_one(sK18)
| ! [X3] : subset(relation_inverse_image(sK18,singleton(X3)),singleton(sK20(X3))) )
& ( ~ one_to_one(sK18)
| ! [X2] : ~ subset(relation_inverse_image(sK18,singleton(sK19)),singleton(X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X4,sK20(X3))],[f106]) ).
fof(f109,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f110,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f109]) ).
fof(f113,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f118,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(apply(X0,X4),X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f119,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,relation_dom(X0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f120,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f124,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f86]) ).
fof(f125,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f128,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| apply(X0,sK4(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f89]) ).
fof(f129,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(sK4(X0,X5),relation_dom(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f130,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| in(X5,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f134,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f90]) ).
fof(f140,plain,
relation(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f141,plain,
empty(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f145,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f147,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f167,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f45]) ).
fof(f169,plain,
! [X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| singleton(X4) != relation_inverse_image(X0,singleton(sK17(X0)))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f170,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK17(X0),relation_rng(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f171,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_inverse_image(X0,singleton(X1)) = singleton(sK16(X0,X1))
| ~ in(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f172,plain,
function(sK18),
inference(cnf_transformation,[],[f107]) ).
fof(f173,plain,
relation(sK18),
inference(cnf_transformation,[],[f107]) ).
fof(f174,plain,
! [X3] :
( one_to_one(sK18)
| subset(relation_inverse_image(sK18,singleton(X3)),singleton(sK20(X3))) ),
inference(cnf_transformation,[],[f107]) ).
fof(f175,plain,
! [X2] :
( ~ one_to_one(sK18)
| ~ subset(relation_inverse_image(sK18,singleton(sK19)),singleton(X2)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f179,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f181,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f110]) ).
fof(f183,plain,
! [X0,X1] :
( empty_set != X0
| subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f189,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f77]) ).
fof(f190,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f192,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f120]) ).
fof(f193,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f119]) ).
fof(f194,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f195,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f125]) ).
fof(f196,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f195]) ).
fof(f197,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f124]) ).
fof(f198,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),X1) ),
inference(equality_resolution,[],[f130]) ).
fof(f199,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f198]) ).
fof(f200,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(sK4(X0,X5),relation_dom(X0)) ),
inference(equality_resolution,[],[f129]) ).
fof(f201,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| apply(X0,sK4(X0,X5)) = X5 ),
inference(equality_resolution,[],[f128]) ).
fof(f202,plain,
! [X1] : subset(empty_set,singleton(X1)),
inference(equality_resolution,[],[f183]) ).
tcf(c_50,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_61,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f196]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( in(sK4(X1,X0),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK4(X1,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_69,plain,
! [X0: $i] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f134]) ).
tcf(c_75,plain,
empty(empty_set),
inference(cnf_transformation,[],[f141]) ).
tcf(c_76,plain,
relation(empty_set),
inference(cnf_transformation,[],[f140]) ).
tcf(c_79,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_81,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_102,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f167]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X1,singleton(X0)) = singleton(sK16(X1,X0)) )
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_105,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK17(X0),relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ( relation_inverse_image(X0,singleton(sK17(X0))) != singleton(X1) ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_107,negated_conjecture,
! [X0: $i] :
( ~ one_to_one(sK18)
| ~ subset(relation_inverse_image(sK18,singleton(sK19)),singleton(X0)) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_108,negated_conjecture,
! [X0: $i] :
( one_to_one(sK18)
| subset(relation_inverse_image(sK18,singleton(X0)),singleton(sK20(X0))) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_109,negated_conjecture,
relation(sK18),
inference(cnf_transformation,[],[f173]) ).
tcf(c_110,negated_conjecture,
function(sK18),
inference(cnf_transformation,[],[f172]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_116,plain,
! [X0: $i] : subset(empty_set,singleton(X0)),
inference(cnf_transformation,[],[f202]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( singleton(X1) = X0 )
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_124,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_129,plain,
subset(empty_set,singleton(empty_set)),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_142,plain,
( ( empty_set = empty_set )
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_2385,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK17(X0),relation_rng(X0))
| ~ relation(X0)
| ( X0 != sK18 ) ),
inference(resolution_lifted,[status(thm)],[c_105,c_110]) ).
tcf(c_2386,plain,
( one_to_one(sK18)
| in(sK17(sK18),relation_rng(sK18))
| ~ relation(sK18) ),
inference(unflattening,[status(thm)],[c_2385]) ).
tcf(c_11289,definition,
iPr_def_10 = singleton(sK19),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_11290,definition,
iPr_def_11 = relation_inverse_image(sK18,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_11291,negated_conjecture,
function(sK18),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_11292,negated_conjecture,
relation(sK18),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_11293,negated_conjecture,
! [X0: $i] :
( one_to_one(sK18)
| subset(relation_inverse_image(sK18,singleton(X0)),singleton(sK20(X0))) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_11294,negated_conjecture,
! [X0: $i] :
( ~ one_to_one(sK18)
| ~ subset(iPr_def_11,singleton(X0)) ),
inference(demodulation,[status(thm)],[c_107,c_11289,c_11290]) ).
tcf(c_11295,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_11297,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_11305,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = singleton(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_11307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| ~ subset(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_11311,plain,
( ( singleton(empty_set) = singleton(empty_set) )
| ( empty_set != empty_set ) ),
inference(instantiation,[status(thm)],[c_11305]) ).
tcf(c_11314,plain,
( ~ one_to_one(sK18)
| ~ subset(iPr_def_11,singleton(empty_set)) ),
inference(instantiation,[status(thm)],[c_11294]) ).
tcf(c_12586,plain,
( one_to_one(sK18)
| subset(relation_inverse_image(sK18,iPr_def_10),singleton(sK20(sK19))) ),
inference(superposition,[status(thm)],[c_11289,c_11293]) ).
tcf(c_12590,plain,
( one_to_one(sK18)
| subset(iPr_def_11,singleton(sK20(sK19))) ),
inference(light_normalisation,[status(thm)],[c_12586,c_11290]) ).
tcf(c_12608,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_75,c_50]) ).
tcf(c_12777,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_79,c_124]) ).
tcf(c_12778,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_81,c_124]) ).
tcf(c_12929,plain,
! [X0: $i] :
( ( X0 = sK19 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_11289,c_62]) ).
tcf(c_12960,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_75,c_12777]) ).
tcf(c_12983,plain,
relation_rng(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_75,c_12778]) ).
tcf(c_13044,plain,
! [X0: $i] :
( empty(X0)
| in(sK5(X0),X0) ),
inference(superposition,[status(thm)],[c_69,c_114]) ).
tcf(c_13252,plain,
! [X0: $i] :
( in(X0,relation_dom(sK18))
| ~ relation(sK18)
| ~ function(sK18)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_11290,c_57]) ).
tcf(c_13253,plain,
! [X0: $i] :
( in(X0,relation_dom(sK18))
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13252,c_11292,c_11291]) ).
tcf(c_13292,plain,
! [X0: $i] :
( one_to_one(sK18)
| ( relation_inverse_image(sK18,singleton(X0)) = empty_set )
| ( relation_inverse_image(sK18,singleton(X0)) = singleton(sK20(X0)) ) ),
inference(superposition,[status(thm)],[c_11293,c_118]) ).
tcf(c_13296,plain,
( one_to_one(sK18)
| ( empty_set = iPr_def_11 )
| ( singleton(sK20(sK19)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_12590,c_118]) ).
tcf(c_13383,plain,
! [X0: $i] :
( in(apply(sK18,X0),iPr_def_10)
| ~ relation(sK18)
| ~ function(sK18)
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_11290,c_58]) ).
tcf(c_13384,plain,
! [X0: $i] :
( in(apply(sK18,X0),iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13383,c_11292,c_11291]) ).
tcf(c_13422,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(iPr_def_11,singleton(X0))
| ~ subset(X2,X1)
| ( iPr_def_11 != X2 )
| ( singleton(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_11307]) ).
tcf(c_13436,plain,
! [X0: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_12983,c_66]) ).
tcf(c_13446,plain,
! [X0: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_13436,c_12960]) ).
tcf(c_13447,plain,
! [X0: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13446,c_76,c_12608]) ).
tcf(c_13572,plain,
! [X0: $i] :
( ( apply(sK18,X0) = sK19 )
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_13384,c_12929]) ).
tcf(c_13856,plain,
( empty(iPr_def_11)
| ( apply(sK18,sK5(iPr_def_11)) = sK19 ) ),
inference(superposition,[status(thm)],[c_13044,c_13572]) ).
tcf(c_13967,plain,
( ( iPr_def_11 = empty_set )
| ~ empty(iPr_def_11) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_13971,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_11295]) ).
tcf(c_13973,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_11 = X0 )
| ( iPr_def_11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_11297]) ).
tcf(c_13999,plain,
( ( empty_set = iPr_def_11 )
| ( apply(sK18,sK5(iPr_def_11)) = sK19 ) ),
inference(superposition,[status(thm)],[c_13856,c_124]) ).
tcf(c_14489,plain,
! [X0: $i] :
( ~ empty(empty_set)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_13447,c_125]) ).
tcf(c_14493,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_14489,c_75]) ).
tcf(c_17344,plain,
( in(sK19,relation_rng(sK18))
| ( empty_set = iPr_def_11 )
| ~ relation(sK18)
| ~ function(sK18)
| ~ in(sK5(iPr_def_11),relation_dom(sK18)) ),
inference(superposition,[status(thm)],[c_13999,c_66]) ).
tcf(c_17349,plain,
( in(sK19,relation_rng(sK18))
| ( empty_set = iPr_def_11 )
| ~ in(sK5(iPr_def_11),relation_dom(sK18)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17344,c_11292,c_11291]) ).
tcf(c_17578,plain,
( in(sK19,relation_rng(sK18))
| ( empty_set = iPr_def_11 )
| ~ in(sK5(iPr_def_11),iPr_def_11) ),
inference(superposition,[status(thm)],[c_13253,c_17349]) ).
tcf(c_17600,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(iPr_def_11,singleton(X0))
| ~ subset(X2,singleton(X1))
| ( iPr_def_11 != X2 )
| ( singleton(X0) != singleton(X1) ) ),
inference(instantiation,[status(thm)],[c_13422]) ).
tcf(c_17601,plain,
( subset(iPr_def_11,singleton(empty_set))
| ~ subset(empty_set,singleton(empty_set))
| ( iPr_def_11 != empty_set )
| ( singleton(empty_set) != singleton(empty_set) ) ),
inference(instantiation,[status(thm)],[c_17600]) ).
tcf(c_18692,plain,
( empty(iPr_def_11)
| in(sK19,relation_rng(sK18))
| ( empty_set = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_13044,c_17578]) ).
tcf(c_18993,plain,
( empty(iPr_def_11)
| ( empty_set = iPr_def_11 )
| ( relation_inverse_image(sK18,singleton(sK19)) = singleton(sK16(sK18,sK19)) )
| ~ one_to_one(sK18)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(superposition,[status(thm)],[c_18692,c_104]) ).
tcf(c_19016,plain,
( empty(iPr_def_11)
| ( empty_set = iPr_def_11 )
| ( singleton(sK16(sK18,sK19)) = iPr_def_11 )
| ~ one_to_one(sK18)
| ~ relation(sK18)
| ~ function(sK18) ),
inference(light_normalisation,[status(thm)],[c_18993,c_11289,c_11290]) ).
tcf(c_19017,plain,
( empty(iPr_def_11)
| ( empty_set = iPr_def_11 )
| ( singleton(sK16(sK18,sK19)) = iPr_def_11 )
| ~ one_to_one(sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19016,c_11292,c_11291]) ).
tcf(c_19115,plain,
( ~ one_to_one(sK18)
| ( singleton(sK16(sK18,sK19)) = iPr_def_11 )
| ( empty_set = iPr_def_11 ) ),
inference(global_subsumption_just,[status(thm)],[c_19017,c_75,c_129,c_142,c_11311,c_11314,c_13967,c_17601,c_19017]) ).
tcf(c_19116,plain,
( ( empty_set = iPr_def_11 )
| ( singleton(sK16(sK18,sK19)) = iPr_def_11 )
| ~ one_to_one(sK18) ),
inference(renaming,[status(thm)],[c_19115]) ).
tcf(c_19123,plain,
( ( empty_set = iPr_def_11 )
| ( singleton(sK20(sK19)) = iPr_def_11 )
| ( singleton(sK16(sK18,sK19)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_13296,c_19116]) ).
tcf(c_20951,plain,
! [X0: $i] :
( ( iPr_def_11 = X0 )
| ( iPr_def_11 != iPr_def_11 )
| ( X0 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_13973]) ).
tcf(c_20952,plain,
( ( iPr_def_11 = empty_set )
| ( iPr_def_11 != iPr_def_11 )
| ( empty_set != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_20951]) ).
tcf(c_22805,plain,
( one_to_one(sK18)
| subset(relation_inverse_image(sK18,iPr_def_11),singleton(sK20(sK16(sK18,sK19))))
| ( empty_set = iPr_def_11 )
| ( singleton(sK20(sK19)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_19123,c_11293]) ).
tcf(c_22806,plain,
( ( empty_set = iPr_def_11 )
| ( singleton(sK20(sK19)) = iPr_def_11 )
| ~ one_to_one(sK18)
| ~ subset(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_19123,c_11294]) ).
tcf(c_22828,plain,
( ( empty_set = iPr_def_11 )
| ( singleton(sK20(sK19)) = iPr_def_11 )
| ~ one_to_one(sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22806,c_102]) ).
tcf(c_23024,plain,
( ( empty_set = iPr_def_11 )
| ( singleton(sK20(sK19)) = iPr_def_11 ) ),
inference(global_subsumption_just,[status(thm)],[c_22805,c_13296,c_22828]) ).
tcf(c_23056,plain,
( ( empty_set = iPr_def_11 )
| ~ one_to_one(sK18)
| ~ subset(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_23024,c_11294]) ).
tcf(c_23077,plain,
( ( empty_set = iPr_def_11 )
| ~ one_to_one(sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23056,c_102]) ).
tcf(c_23258,plain,
~ one_to_one(sK18),
inference(global_subsumption_just,[status(thm)],[c_23077,c_75,c_129,c_142,c_11311,c_11314,c_13971,c_17601,c_20952,c_23077]) ).
tcf(c_23260,plain,
! [X0: $i] :
( ( relation_inverse_image(sK18,singleton(X0)) = empty_set )
| ( relation_inverse_image(sK18,singleton(X0)) = singleton(sK20(X0)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_13292,c_23258]) ).
tcf(c_24202,plain,
! [X0: $i] :
( one_to_one(sK18)
| ( relation_inverse_image(sK18,singleton(sK17(sK18))) = empty_set )
| ~ relation(sK18)
| ~ function(sK18)
| ( singleton(sK20(sK17(sK18))) != singleton(X0) ) ),
inference(superposition,[status(thm)],[c_23260,c_106]) ).
tcf(c_24232,plain,
! [X0: $i] :
( ( relation_inverse_image(sK18,singleton(sK17(sK18))) = empty_set )
| ( singleton(sK20(sK17(sK18))) != singleton(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24202,c_23258,c_11292,c_11291]) ).
tcf(c_24788,plain,
relation_inverse_image(sK18,singleton(sK17(sK18))) = empty_set,
inference(equality_resolution,[status(thm)],[c_24232]) ).
tcf(c_28196,plain,
( in(sK4(sK18,sK17(sK18)),relation_dom(sK18))
| ~ relation(sK18)
| ~ function(sK18)
| ~ in(sK17(sK18),relation_rng(sK18)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_54512,negated_conjecture,
~ one_to_one(sK18),
inference(global_subsumption_just,[status(thm)],[c_11294,c_75,c_129,c_142,c_11311,c_11314,c_13971,c_17601,c_20952,c_23077]) ).
tcf(c_54514,negated_conjecture,
! [X0: $i] : subset(relation_inverse_image(sK18,singleton(X0)),singleton(sK20(X0))),
inference(global_subsumption_just,[status(thm)],[c_11293,c_108,c_23258]) ).
tcf(c_54530,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_75,c_50]) ).
tcf(c_54631,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_79,c_124]) ).
tcf(c_54632,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_81,c_124]) ).
tcf(c_54767,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_75,c_54631]) ).
tcf(c_54783,plain,
relation_rng(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_75,c_54632]) ).
tcf(c_54914,plain,
! [X0: $i] :
( ( relation_inverse_image(sK18,singleton(X0)) = empty_set )
| ( relation_inverse_image(sK18,singleton(X0)) = singleton(sK20(X0)) ) ),
inference(superposition,[status(thm)],[c_54514,c_118]) ).
tcf(c_54971,plain,
! [X0: $i] :
( one_to_one(sK18)
| ( relation_inverse_image(sK18,singleton(sK17(sK18))) = empty_set )
| ~ relation(sK18)
| ~ function(sK18)
| ( singleton(sK20(sK17(sK18))) != singleton(X0) ) ),
inference(superposition,[status(thm)],[c_54914,c_106]) ).
tcf(c_54978,plain,
! [X0: $i] :
( ( relation_inverse_image(sK18,singleton(sK17(sK18))) = empty_set )
| ( singleton(sK20(sK17(sK18))) != singleton(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54971,c_54512,c_11292,c_11291]) ).
tcf(c_54981,plain,
relation_inverse_image(sK18,singleton(sK17(sK18))) = empty_set,
inference(global_subsumption_just,[status(thm)],[c_54978,c_24788]) ).
tcf(c_55136,plain,
! [X0: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_54783,c_66]) ).
tcf(c_55144,plain,
! [X0: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_55136,c_54767]) ).
tcf(c_55145,plain,
! [X0: $i] :
( in(apply(empty_set,X0),empty_set)
| ~ in(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55144,c_76,c_54530]) ).
tcf(c_55156,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_55145,c_14493]) ).
tcf(c_55375,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK4(X0,sK17(X0))) = sK17(X0) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_105,c_68]) ).
tcf(c_59897,plain,
( one_to_one(sK18)
| ( apply(sK18,sK4(sK18,sK17(sK18))) = sK17(sK18) )
| ~ relation(sK18) ),
inference(superposition,[status(thm)],[c_11291,c_55375]) ).
tcf(c_59901,plain,
apply(sK18,sK4(sK18,sK17(sK18))) = sK17(sK18),
inference(forward_subsumption_resolution,[status(thm)],[c_59897,c_54512,c_11292]) ).
tcf(c_59917,plain,
! [X0: $i] :
( in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0))
| ~ relation(sK18)
| ~ function(sK18)
| ~ in(sK17(sK18),X0)
| ~ in(sK4(sK18,sK17(sK18)),relation_dom(sK18)) ),
inference(superposition,[status(thm)],[c_59901,c_56]) ).
tcf(c_59947,plain,
! [X0: $i] :
( in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0))
| ~ in(sK17(sK18),X0)
| ~ in(sK4(sK18,sK17(sK18)),relation_dom(sK18)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_59917,c_11292,c_11291]) ).
tcf(c_59972,plain,
! [X0: $i] :
( in(sK4(sK18,sK17(sK18)),relation_inverse_image(sK18,X0))
| ~ in(sK17(sK18),X0) ),
inference(global_subsumption_just,[status(thm)],[c_59947,c_110,c_109,c_75,c_129,c_142,c_2386,c_11311,c_11314,c_13971,c_17601,c_20952,c_23077,c_28196,c_59947]) ).
tcf(c_59980,plain,
( in(sK4(sK18,sK17(sK18)),empty_set)
| ~ in(sK17(sK18),singleton(sK17(sK18))) ),
inference(superposition,[status(thm)],[c_54981,c_59972]) ).
tcf(c_59994,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_59980,c_55156,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU078+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:47:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 17.44/3.63 % SZS status Started for theBenchmark.p
% 17.44/3.63 % SZS status Theorem for theBenchmark.p
% 17.44/3.63
% 17.44/3.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.44/3.63
% 17.44/3.63 % ------ iProver source info
% 17.44/3.63
% 17.44/3.63 % git: date: 2026-07-19 20:42:38 +0200
% 17.44/3.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.44/3.63 % git: non_committed_changes: false
% 17.44/3.63
% 17.44/3.63 % ------ Parsing...
% 17.44/3.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.44/3.63
% 17.44/3.63 % ------ Preprocessing... sup_sim: 0 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 %
% 17.44/3.63
% 17.44/3.63 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.44/3.63
% 17.44/3.63 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.44/3.63 % ------ Proving...
% 17.44/3.63 % ------ Problem Properties
% 17.44/3.63
% 17.44/3.63 %
% 17.44/3.63 % clauses 75
% 17.44/3.63 % conjectures 4
% 17.44/3.63 % EPR 33
% 17.44/3.63 % Horn 64
% 17.44/3.63 % unary 29
% 17.44/3.63 % binary 20
% 17.44/3.63 % lits 172
% 17.44/3.63 % lits eq 24
% 17.44/3.63 % fd_pure 0
% 17.44/3.63 % fd_pseudo 0
% 17.44/3.63 % fd_cond 1
% 17.44/3.63 % fd_pseudo_cond 10
% 17.44/3.63 % AC symbols 0
% 17.44/3.63
% 17.44/3.63 % ------ Schedule dynamic 5 is on
% 17.44/3.63
% 17.44/3.63 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.44/3.63
% 17.44/3.63
% 17.44/3.63 % ------
% 17.44/3.63 % Current options:
% 17.44/3.63 % ------
% 17.44/3.63
% 17.44/3.63
% 17.44/3.63 %
% 17.44/3.63
% 17.44/3.63 % ------ Proving...
% 17.44/3.63 %
% 17.44/3.63
% 17.44/3.63 % SZS status Theorem for theBenchmark.p
% 17.44/3.63
% 17.44/3.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.44/3.63
% 17.44/3.63
%------------------------------------------------------------------------------