%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU068+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 02:55:17 PM UTC 2026
% Result : Theorem 47.34s 18.47s
% Output : CNFRefutation 47.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 36
% Syntax : Number of formulae : 244 ( 70 unt; 0 def)
% Number of atoms : 795 ( 104 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 936 ( 385 ~; 399 |; 119 &)
% ( 17 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 12 con; 0-3 aty)
% Number of variables : 477 ( 2 sgn 440 !; 37 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f5,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] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f7,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/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,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(f10,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f12,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f13,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f15,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f16,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f17,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f18,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f19,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f20,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f21,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f22,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f23,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f24,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f25,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f26,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f27,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f28,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f29,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f30,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> subset(relation_image(X2,set_intersection2(X0,relation_inverse_image(X2,X1))),set_intersection2(relation_image(X2,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> subset(relation_image(X2,set_intersection2(X0,relation_inverse_image(X2,X1))),set_intersection2(relation_image(X2,X0),X1)) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f33,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f34,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f37,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] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f39,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f40,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f41,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f18]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f29]) ).
fof(f43,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f28]) ).
fof(f46,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f48,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f49,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f52,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f52]) ).
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(ennf_transformation,[],[f7]) ).
fof(f55,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,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f57,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f58,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f62,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f63,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& ~ subset(relation_image(X2,set_intersection2(X0,relation_inverse_image(X2,X1))),set_intersection2(relation_image(X2,X0),X1)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& ~ subset(relation_image(X2,set_intersection2(X0,relation_inverse_image(X2,X1))),set_intersection2(relation_image(X2,X0),X1)) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f67,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f71,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f38]) ).
fof(f72,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f73,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f74,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f75,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK2(X0,X1,X6)) = X6
& in(sK2(X0,X1,X6),X1)
& in(sK2(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
& in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f75]) ).
fof(f77,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,[],[f55]) ).
fof(f78,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,[],[f77]) ).
fof(f79,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,[],[f78]) ).
fof(f80,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(sK3(X0,X1,X2),X2)
| ( in(apply(X0,sK3(X0,X1,X2)),X1)
& in(sK3(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ~ in(apply(X0,sK3(X0,X1,X2)),X1)
| ~ in(sK3(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f79]) ).
fof(f81,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,[],[f56]) ).
fof(f82,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,[],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK4(X0,X1),X0)
& ~ in(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f85,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,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [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,[],[f85]) ).
fof(f87,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(sK5(X0,X1,X2),X2)
| ( in(sK5(X0,X1,X2),X1)
& in(sK5(X0,X1,X2),X0) ) )
& ( ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f86]) ).
fof(f88,plain,
! [X0] : element(sK6(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f10]) ).
fof(f89,plain,
( function(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f19]) ).
fof(f90,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f20]) ).
fof(f91,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK9(X0))
& element(sK9(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f62]) ).
fof(f92,plain,
empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f22]) ).
fof(f93,plain,
( function(sK11)
& empty(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f23]) ).
fof(f94,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f24]) ).
fof(f95,plain,
! [X0] :
( empty(sK13(X0))
& element(sK13(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X1,sK13(X0))],[f25]) ).
fof(f96,plain,
~ empty(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f26]) ).
fof(f97,plain,
( function(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f46]) ).
fof(f98,plain,
relation(sK16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f43]) ).
fof(f99,plain,
( function(sK19)
& relation(sK19)
& ~ subset(relation_image(sK19,set_intersection2(sK17,relation_inverse_image(sK19,sK18))),set_intersection2(relation_image(sK19,sK17),sK18)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f64]) ).
fof(f100,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f101,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f102,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f103,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f106,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f107,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK2(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f76]) ).
fof(f108,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK2(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f109,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK2(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f110,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK0(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f114,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK0(X0,X1,X2),X2)
| apply(X0,X4) != sK0(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f115,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,[],[f80]) ).
fof(f116,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,[],[f80]) ).
fof(f117,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,[],[f80]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK3(X0,X1,X2),X2)
| in(apply(X0,sK3(X0,X1,X2)),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK3(X0,X1,X2),X2)
| ~ in(apply(X0,sK3(X0,X1,X2)),X1)
| ~ in(sK3(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f122,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f123,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f124,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f127,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f87]) ).
fof(f128,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f87]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f87]) ).
fof(f130,plain,
! [X0] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f88]) ).
fof(f133,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f134,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f136,plain,
relation(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f137,plain,
empty(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f138,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f139,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f140,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f141,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f41]) ).
fof(f142,plain,
function(sK7),
inference(cnf_transformation,[],[f89]) ).
fof(f143,plain,
relation(sK7),
inference(cnf_transformation,[],[f89]) ).
fof(f144,plain,
relation(sK8),
inference(cnf_transformation,[],[f90]) ).
fof(f145,plain,
empty(sK8),
inference(cnf_transformation,[],[f90]) ).
fof(f146,plain,
! [X0] :
( empty(X0)
| ~ empty(sK9(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f147,plain,
! [X0] :
( empty(X0)
| element(sK9(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f148,plain,
empty(sK10),
inference(cnf_transformation,[],[f92]) ).
fof(f149,plain,
function(sK11),
inference(cnf_transformation,[],[f93]) ).
fof(f150,plain,
empty(sK11),
inference(cnf_transformation,[],[f93]) ).
fof(f151,plain,
relation(sK11),
inference(cnf_transformation,[],[f93]) ).
fof(f152,plain,
relation(sK12),
inference(cnf_transformation,[],[f94]) ).
fof(f153,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f94]) ).
fof(f154,plain,
! [X0] : empty(sK13(X0)),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
! [X0] : element(sK13(X0),powerset(X0)),
inference(cnf_transformation,[],[f95]) ).
fof(f156,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f96]) ).
fof(f157,plain,
function(sK15),
inference(cnf_transformation,[],[f97]) ).
fof(f158,plain,
relation(sK15),
inference(cnf_transformation,[],[f97]) ).
fof(f159,plain,
relation(sK16),
inference(cnf_transformation,[],[f98]) ).
fof(f160,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f161,plain,
function(sK19),
inference(cnf_transformation,[],[f99]) ).
fof(f162,plain,
relation(sK19),
inference(cnf_transformation,[],[f99]) ).
fof(f163,plain,
~ subset(relation_image(sK19,set_intersection2(sK17,relation_inverse_image(sK19,sK18))),set_intersection2(relation_image(sK19,sK17),sK18)),
inference(cnf_transformation,[],[f99]) ).
fof(f164,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f165,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f33]) ).
fof(f166,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f167,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f168,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f171,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f71]) ).
fof(f172,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f173,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f174,plain,
! [X2,X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),X2) ),
inference(equality_resolution,[],[f110]) ).
fof(f175,plain,
! [X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),relation_image(X0,X1)) ),
inference(equality_resolution,[],[f174]) ).
fof(f176,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK2(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f109]) ).
fof(f177,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK2(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f108]) ).
fof(f178,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK2(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f107]) ).
fof(f179,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,[],[f117]) ).
fof(f180,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f116]) ).
fof(f181,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f115]) ).
fof(f182,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f126]) ).
fof(f183,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f184,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f124]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_50,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_51,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f106]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ function(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK0(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK1(X0,X1,X2)) = sK0(X0,X1,X2) )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X1,X2,X0),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK2(X1,X2,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ function(X0)
| ~ in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK3(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X0,X1,X2),X2)
| in(apply(X0,sK3(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_64,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,[],[f179]) ).
tcf(c_65,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,[],[f180]) ).
tcf(c_66,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,[],[f181]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_76,plain,
! [X0: $i] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f130]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( relation(set_intersection2(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_80,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f134]) ).
tcf(c_82,plain,
empty(empty_set),
inference(cnf_transformation,[],[f137]) ).
tcf(c_83,plain,
relation(empty_set),
inference(cnf_transformation,[],[f136]) ).
tcf(c_84,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_85,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_86,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_87,plain,
! [X0: $i] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f141]) ).
tcf(c_88,plain,
relation(sK7),
inference(cnf_transformation,[],[f143]) ).
tcf(c_89,plain,
function(sK7),
inference(cnf_transformation,[],[f142]) ).
tcf(c_90,plain,
empty(sK8),
inference(cnf_transformation,[],[f145]) ).
tcf(c_91,plain,
relation(sK8),
inference(cnf_transformation,[],[f144]) ).
tcf(c_92,plain,
! [X0: $i] :
( empty(X0)
| element(sK9(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_93,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK9(X0)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_94,plain,
empty(sK10),
inference(cnf_transformation,[],[f148]) ).
tcf(c_95,plain,
relation(sK11),
inference(cnf_transformation,[],[f151]) ).
tcf(c_96,plain,
empty(sK11),
inference(cnf_transformation,[],[f150]) ).
tcf(c_97,plain,
function(sK11),
inference(cnf_transformation,[],[f149]) ).
tcf(c_98,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f153]) ).
tcf(c_99,plain,
relation(sK12),
inference(cnf_transformation,[],[f152]) ).
tcf(c_100,plain,
! [X0: $i] : element(sK13(X0),powerset(X0)),
inference(cnf_transformation,[],[f155]) ).
tcf(c_101,plain,
! [X0: $i] : empty(sK13(X0)),
inference(cnf_transformation,[],[f154]) ).
tcf(c_102,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f156]) ).
tcf(c_103,plain,
relation(sK15),
inference(cnf_transformation,[],[f158]) ).
tcf(c_104,plain,
function(sK15),
inference(cnf_transformation,[],[f157]) ).
tcf(c_105,plain,
relation(sK16),
inference(cnf_transformation,[],[f159]) ).
tcf(c_106,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f160]) ).
tcf(c_107,negated_conjecture,
~ subset(relation_image(sK19,set_intersection2(sK17,relation_inverse_image(sK19,sK18))),set_intersection2(relation_image(sK19,sK17),sK18)),
inference(cnf_transformation,[],[f163]) ).
tcf(c_108,negated_conjecture,
relation(sK19),
inference(cnf_transformation,[],[f162]) ).
tcf(c_109,negated_conjecture,
function(sK19),
inference(cnf_transformation,[],[f161]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_111,plain,
! [X0: $i] : set_intersection2(X0,empty_set) = empty_set,
inference(cnf_transformation,[],[f165]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_117,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_8219,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1,relation_dom(X0)),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = relation_dom(X0) )
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_factoring,[status(thm)],[c_62]) ).
tcf(c_19175,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = X2 )
| ~ relation(X0)
| ~ function(X0)
| ~ in(sK3(X0,relation_image(X0,X1),X2),X2)
| ~ in(sK3(X0,relation_image(X0,X1),X2),X1)
| ~ in(sK3(X0,relation_image(X0,X1),X2),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_57,c_61]) ).
tcf(c_22522,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse_image(X0,relation_image(X0,X1)) = relation_dom(X0) )
| ~ relation(X0)
| ~ function(X0)
| ~ in(sK3(X0,relation_image(X0,X1),relation_dom(X0)),X1)
| ~ in(sK3(X0,relation_image(X0,X1),relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_8219,c_19175]) ).
tcf(c_27214,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_22522,c_19175,c_8219,c_119,c_118,c_117,c_116,c_115,c_114,c_113,c_112,c_111,c_110,c_109,c_108,c_107,c_106,c_105,c_104,c_103,c_102,c_101,c_100,c_99,c_98,c_97,c_96,c_95,c_94,c_93,c_92,c_91,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_80,c_79,c_83,c_82,c_76,c_75,c_74,c_73,c_72,c_71,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU068+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n007.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 12:39:28 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 47.34/18.47 % SZS status Started for theBenchmark.p
% 47.34/18.47 % SZS status Theorem for theBenchmark.p
% 47.34/18.47
% 47.34/18.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 47.34/18.47
% 47.34/18.47 % ------ iProver source info
% 47.34/18.47
% 47.34/18.47 % git: date: 2026-07-19 20:42:38 +0200
% 47.34/18.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 47.34/18.47 % git: non_committed_changes: false
% 47.34/18.47
% 47.34/18.47 % ------ Parsing...
% 47.34/18.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 47.34/18.47
% 47.34/18.47 % ------ Preprocessing...%
% 47.34/18.47
% 47.34/18.47 % ------ Preprocessing...%
% 47.34/18.47
% 47.34/18.47 % ------ Preprocessing...
% 47.34/18.47 % ------ Proving...
% 47.34/18.47 % ------ Problem Properties
% 47.34/18.47
% 47.34/18.47 %
% 47.34/18.47 % clauses 68
% 47.34/18.47 % conjectures 3
% 47.34/18.47 % EPR 28
% 47.34/18.47 % Horn 58
% 47.34/18.47 % unary 27
% 47.34/18.47 % binary 16
% 47.34/18.47 % lits 161
% 47.34/18.47 % lits eq 18
% 47.34/18.47 % fd_pure 0
% 47.34/18.47 % fd_pseudo 0
% 47.34/18.47 % fd_cond 1
% 47.34/18.47 % fd_pseudo_cond 11
% 47.34/18.47 % AC symbols 0
% 47.34/18.47
% 47.34/18.47 % ------ Input Options Time Limit: Unbounded
% 47.34/18.47
% 47.34/18.47
% 47.34/18.47 % ------
% 47.34/18.47 % Current options:
% 47.34/18.47 % ------
% 47.34/18.47
% 47.34/18.47
% 47.34/18.47 %
% 47.34/18.47
% 47.34/18.47 % ------ Proving...
% 47.34/18.47 %
% 47.34/18.47
% 47.34/18.47 % SZS status Theorem for theBenchmark.p
% 47.34/18.47
% 47.34/18.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 47.34/18.47
% 47.34/18.47
%------------------------------------------------------------------------------