%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU384+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:57:18 PM UTC 2026
% Result : Theorem 16.11s 3.33s
% Output : CNFRefutation 16.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of formulae : 169 ( 31 unt; 6 def)
% Number of atoms : 973 ( 120 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 913 ( 345 ~; 430 |; 105 &)
% ( 13 <=>; 19 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 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 : 17 ( 15 usr; 5 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-4 aty)
% Number of variables : 325 ( 0 sgn 299 !; 26 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( ( net_str(X3,X0)
& strict_net_str(X3,X0) )
=> ( X3 = netstr_restr_to_element(X0,X1,X2)
<=> ( the_mapping(X0,X3) = partfun_dom_restriction(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X3))
& the_InternalRel(X3) = relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X3))
& ! [X4] :
( in(X4,the_carrier(X3))
<=> ? [X5] :
( related(X1,X2,X5)
& X5 = X4
& element(X5,the_carrier(X1)) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_waybel_9) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X1))
& net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( net_str(netstr_restr_to_element(X0,X1,X2),X0)
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_waybel_9) ).
fof(f25,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f27,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(f43,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f47,axiom,
! [X0,X1,X2,X3] :
( ( element(X3,the_carrier(X2))
& net_str(X2,X1)
& ~ empty_carrier(X2)
& one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ( in(X0,a_3_0_waybel_9(X1,X2,X3))
<=> ? [X4] :
( related(X2,X3,X4)
& X0 = X4
& element(X4,the_carrier(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_waybel_9) ).
fof(f65,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> the_carrier(netstr_restr_to_element(X0,X1,X2)) = a_3_0_waybel_9(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_waybel_9) ).
fof(f66,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> the_carrier(netstr_restr_to_element(X0,X1,X2)) = a_3_0_waybel_9(X0,X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f67,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f68,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f69,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f98,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ~ net_str(X3,X0)
| ~ strict_net_str(X3,X0)
| ( X3 = netstr_restr_to_element(X0,X1,X2)
<=> ( the_mapping(X0,X3) = partfun_dom_restriction(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X3))
& the_InternalRel(X3) = relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X3))
& ! [X4] :
( in(X4,the_carrier(X3))
<=> ? [X5] :
( related(X1,X2,X5)
& X5 = X4
& element(X5,the_carrier(X1)) ) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f99,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ~ net_str(X3,X0)
| ~ strict_net_str(X3,X0)
| ( X3 = netstr_restr_to_element(X0,X1,X2)
<=> ( the_mapping(X0,X3) = partfun_dom_restriction(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X3))
& the_InternalRel(X3) = relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X3))
& ! [X4] :
( in(X4,the_carrier(X3))
<=> ? [X5] :
( related(X1,X2,X5)
& X5 = X4
& element(X5,the_carrier(X1)) ) ) ) ) ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( net_str(netstr_restr_to_element(X0,X1,X2),X0)
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( net_str(netstr_restr_to_element(X0,X1,X2),X0)
& strict_net_str(netstr_restr_to_element(X0,X1,X2),X0) ) ),
inference(flattening,[],[f106]) ).
fof(f109,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f110,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| rel_str(X1) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f120,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f121,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(flattening,[],[f120]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ( in(X0,a_3_0_waybel_9(X1,X2,X3))
<=> ? [X4] :
( related(X2,X3,X4)
& X0 = X4
& element(X4,the_carrier(X2)) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ( in(X0,a_3_0_waybel_9(X1,X2,X3))
<=> ? [X4] :
( related(X2,X3,X4)
& X0 = X4
& element(X4,the_carrier(X2)) ) ) ),
inference(flattening,[],[f126]) ).
fof(f138,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( net_str(X1,X0)
& ~ empty_carrier(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& the_carrier(netstr_restr_to_element(X0,X1,X2)) != a_3_0_waybel_9(X0,X1,X2) ) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f139,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( net_str(X1,X0)
& ~ empty_carrier(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& the_carrier(netstr_restr_to_element(X0,X1,X2)) != a_3_0_waybel_9(X0,X1,X2) ) ) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f141,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f142,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f141]) ).
fof(f143,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f69]) ).
fof(f158,plain,
! [X0,X3,X2,X1] :
( ~ sP1(X0,X3,X2,X1)
| ( ( netstr_restr_to_element(X0,X1,X2) != X3
| sP0(X1,X2,X3,X0) )
& ( ~ sP0(X1,X2,X3,X0)
| X3 = netstr_restr_to_element(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f151]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( ~ sP1(X0,X1,X2,X3)
| ( ( netstr_restr_to_element(X0,X3,X2) != X1
| sP0(X3,X2,X1,X0) )
& ( ~ sP0(X3,X2,X1,X0)
| netstr_restr_to_element(X0,X3,X2) = X1 ) ) ),
inference(rectify,[],[f158]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ( ( ~ in(X0,a_3_0_waybel_9(X1,X2,X3))
| ? [X4] :
( related(X2,X3,X4)
& X0 = X4
& element(X4,the_carrier(X2)) ) )
& ( ! [X4] :
( ~ related(X2,X3,X4)
| X0 != X4
| ~ element(X4,the_carrier(X2)) )
| in(X0,a_3_0_waybel_9(X1,X2,X3)) ) ) ),
inference(nnf_transformation,[],[f127]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ( ( ~ in(X0,a_3_0_waybel_9(X1,X2,X3))
| ? [X5] :
( related(X2,X3,X5)
& X0 = X5
& element(X5,the_carrier(X2)) ) )
& ( ! [X4] :
( ~ related(X2,X3,X4)
| X0 != X4
| ~ element(X4,the_carrier(X2)) )
| in(X0,a_3_0_waybel_9(X1,X2,X3)) ) ) ),
inference(rectify,[],[f170]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ( ( ~ in(X0,a_3_0_waybel_9(X1,X2,X3))
| ( related(X2,X3,sK12(X0,X2,X3))
& sK12(X0,X2,X3) = X0
& element(sK12(X0,X2,X3),the_carrier(X2)) ) )
& ( ! [X4] :
( ~ related(X2,X3,X4)
| X0 != X4
| ~ element(X4,the_carrier(X2)) )
| in(X0,a_3_0_waybel_9(X1,X2,X3)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X5,sK12(X0,X2,X3))],[f171]) ).
fof(f186,plain,
( one_sorted_str(sK25)
& ~ empty_carrier(sK25)
& net_str(sK26,sK25)
& ~ empty_carrier(sK26)
& element(sK27,the_carrier(sK26))
& the_carrier(netstr_restr_to_element(sK25,sK26,sK27)) != a_3_0_waybel_9(sK25,sK26,sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X0,sK25),skolemize(X1,sK26),skolemize(X2,sK27)],[f139]) ).
fof(f187,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f143]) ).
fof(f188,plain,
! [X0,X1] :
( ( ( in(sK28(X0,X1),X0)
| in(sK28(X0,X1),X1) )
& ( ~ in(sK28(X0,X1),X0)
| ~ in(sK28(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(X2,sK28(X0,X1))],[f187]) ).
fof(f216,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1,X2,X3)
| netstr_restr_to_element(X0,X3,X2) != X1
| sP0(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ net_str(X3,X0)
| ~ strict_net_str(X3,X0)
| sP1(X0,X3,X2,X1) ),
inference(cnf_transformation,[],[f152]) ).
fof(f235,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| net_str(netstr_restr_to_element(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| strict_net_str(netstr_restr_to_element(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f238,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f239,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| rel_str(X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f260,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f266,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ in(X0,a_3_0_waybel_9(X1,X2,X3))
| related(X2,X3,sK12(X0,X2,X3)) ),
inference(cnf_transformation,[],[f172]) ).
fof(f267,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ in(X0,a_3_0_waybel_9(X1,X2,X3))
| sK12(X0,X2,X3) = X0 ),
inference(cnf_transformation,[],[f172]) ).
fof(f268,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ in(X0,a_3_0_waybel_9(X1,X2,X3))
| element(sK12(X0,X2,X3),the_carrier(X2)) ),
inference(cnf_transformation,[],[f172]) ).
fof(f269,plain,
! [X2,X3,X0,X1,X4] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ related(X2,X3,X4)
| X0 != X4
| ~ element(X4,the_carrier(X2))
| in(X0,a_3_0_waybel_9(X1,X2,X3)) ),
inference(cnf_transformation,[],[f172]) ).
fof(f306,plain,
one_sorted_str(sK25),
inference(cnf_transformation,[],[f186]) ).
fof(f307,plain,
~ empty_carrier(sK25),
inference(cnf_transformation,[],[f186]) ).
fof(f308,plain,
net_str(sK26,sK25),
inference(cnf_transformation,[],[f186]) ).
fof(f309,plain,
~ empty_carrier(sK26),
inference(cnf_transformation,[],[f186]) ).
fof(f310,plain,
element(sK27,the_carrier(sK26)),
inference(cnf_transformation,[],[f186]) ).
fof(f311,plain,
the_carrier(netstr_restr_to_element(sK25,sK26,sK27)) != a_3_0_waybel_9(sK25,sK26,sK27),
inference(cnf_transformation,[],[f186]) ).
fof(f312,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f313,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f314,plain,
! [X0,X1] :
( in(sK28(X0,X1),X0)
| in(sK28(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f188]) ).
fof(f315,plain,
! [X0,X1] :
( ~ in(sK28(X0,X1),X0)
| ~ in(sK28(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f188]) ).
fof(f325,plain,
! [X2,X3,X0] :
( ~ sP1(X0,netstr_restr_to_element(X0,X3,X2),X2,X3)
| sP0(X3,X2,netstr_restr_to_element(X0,X3,X2),X0) ),
inference(equality_resolution,[],[f216]) ).
fof(f328,plain,
! [X2,X3,X1,X4] :
( ~ element(X3,the_carrier(X2))
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ related(X2,X3,X4)
| ~ element(X4,the_carrier(X2))
| in(X4,a_3_0_waybel_9(X1,X2,X3)) ),
inference(equality_resolution,[],[f269]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X2,netstr_restr_to_element(X0,X1,X2),X0)
| ~ sP1(X0,netstr_restr_to_element(X0,X1,X2),X2,X1) ),
inference(cnf_transformation,[],[f325]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X3)
| empty_carrier(X1)
| sP1(X3,X2,X0,X1)
| ~ one_sorted_str(X3)
| ~ net_str(X2,X3)
| ~ net_str(X1,X3)
| ~ strict_net_str(X2,X3)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| strict_net_str(netstr_restr_to_element(X2,X1,X0),X2)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| net_str(netstr_restr_to_element(X2,X1,X0),X2)
| ~ one_sorted_str(X2)
| ~ net_str(X1,X2)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_90,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( rel_str(X0)
| ~ one_sorted_str(X1)
| ~ net_str(X0,X1) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_112,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f260]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X3)
| empty_carrier(X0)
| in(X2,a_3_0_waybel_9(X3,X0,X1))
| ~ one_sorted_str(X3)
| ~ net_str(X0,X3)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ related(X0,X1,X2) ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| element(sK12(X0,X2,X3),the_carrier(X2))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ element(X3,the_carrier(X2))
| ~ in(X0,a_3_0_waybel_9(X1,X2,X3)) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| ( sK12(X0,X2,X3) = X0 )
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ element(X3,the_carrier(X2))
| ~ in(X0,a_3_0_waybel_9(X1,X2,X3)) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty_carrier(X2)
| empty_carrier(X1)
| related(X2,X3,sK12(X0,X2,X3))
| ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| ~ element(X3,the_carrier(X2))
| ~ in(X0,a_3_0_waybel_9(X1,X2,X3)) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_158,negated_conjecture,
the_carrier(netstr_restr_to_element(sK25,sK26,sK27)) != a_3_0_waybel_9(sK25,sK26,sK27),
inference(cnf_transformation,[],[f311]) ).
tcf(c_159,negated_conjecture,
element(sK27,the_carrier(sK26)),
inference(cnf_transformation,[],[f310]) ).
tcf(c_160,negated_conjecture,
~ empty_carrier(sK26),
inference(cnf_transformation,[],[f309]) ).
tcf(c_161,negated_conjecture,
net_str(sK26,sK25),
inference(cnf_transformation,[],[f308]) ).
tcf(c_162,negated_conjecture,
~ empty_carrier(sK25),
inference(cnf_transformation,[],[f307]) ).
tcf(c_163,negated_conjecture,
one_sorted_str(sK25),
inference(cnf_transformation,[],[f306]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK28(X0,X1),X1)
| ~ in(sK28(X0,X1),X0) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( in(sK28(X0,X1),X1)
| in(sK28(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_10965,definition,
iPr_def_10 = the_carrier(sK26),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_10966,definition,
iPr_def_11 = netstr_restr_to_element(sK25,sK26,sK27),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_10967,definition,
iPr_def_12 = the_carrier(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_10968,definition,
iPr_def_13 = a_3_0_waybel_9(sK25,sK26,sK27),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_10969,negated_conjecture,
one_sorted_str(sK25),
inference(demodulation,[status(thm)],[c_163]) ).
tcf(c_10970,negated_conjecture,
~ empty_carrier(sK25),
inference(demodulation,[status(thm)],[c_162]) ).
tcf(c_10971,negated_conjecture,
net_str(sK26,sK25),
inference(demodulation,[status(thm)],[c_161]) ).
tcf(c_10972,negated_conjecture,
~ empty_carrier(sK26),
inference(demodulation,[status(thm)],[c_160]) ).
tcf(c_10973,negated_conjecture,
element(sK27,iPr_def_10),
inference(demodulation,[status(thm)],[c_159,c_10965]) ).
tcf(c_10974,negated_conjecture,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_158,c_10968,c_10966,c_10967]) ).
tcf(c_13363,plain,
( rel_str(sK26)
| ~ one_sorted_str(sK25) ),
inference(superposition,[status(thm)],[c_10971,c_91]) ).
tcf(c_13364,plain,
rel_str(sK26),
inference(forward_subsumption_resolution,[status(thm)],[c_13363,c_10969]) ).
tcf(c_13371,plain,
one_sorted_str(sK26),
inference(superposition,[status(thm)],[c_13364,c_90]) ).
tcf(c_13454,plain,
( empty_carrier(sK26)
| ~ empty(iPr_def_10)
| ~ one_sorted_str(sK26) ),
inference(superposition,[status(thm)],[c_10965,c_112]) ).
tcf(c_13459,plain,
~ empty(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_13454,c_10972,c_13371]) ).
tcf(c_14096,plain,
( sP0(sK26,sK27,netstr_restr_to_element(sK25,sK26,sK27),sK25)
| ~ sP1(sK25,iPr_def_11,sK27,sK26) ),
inference(superposition,[status(thm)],[c_10966,c_69]) ).
tcf(c_14097,plain,
( sP0(sK26,sK27,iPr_def_11,sK25)
| ~ sP1(sK25,iPr_def_11,sK27,sK26) ),
inference(light_normalisation,[status(thm)],[c_14096,c_10966]) ).
tcf(c_14207,plain,
( empty_carrier(sK26)
| empty_carrier(sK25)
| strict_net_str(iPr_def_11,sK25)
| ~ one_sorted_str(sK25)
| ~ net_str(sK26,sK25)
| ~ element(sK27,the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_10966,c_87]) ).
tcf(c_14209,plain,
( empty_carrier(sK26)
| empty_carrier(sK25)
| strict_net_str(iPr_def_11,sK25)
| ~ one_sorted_str(sK25)
| ~ element(sK27,iPr_def_10)
| ~ net_str(sK26,sK25) ),
inference(light_normalisation,[status(thm)],[c_14207,c_10965]) ).
tcf(c_14210,plain,
strict_net_str(iPr_def_11,sK25),
inference(forward_subsumption_resolution,[status(thm)],[c_14209,c_10972,c_10970,c_10969,c_10973,c_10971]) ).
tcf(c_14291,plain,
( empty_carrier(sK26)
| empty_carrier(sK25)
| net_str(iPr_def_11,sK25)
| ~ one_sorted_str(sK25)
| ~ net_str(sK26,sK25)
| ~ element(sK27,the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_10966,c_88]) ).
tcf(c_14294,plain,
( empty_carrier(sK26)
| empty_carrier(sK25)
| net_str(iPr_def_11,sK25)
| ~ one_sorted_str(sK25)
| ~ element(sK27,iPr_def_10)
| ~ net_str(sK26,sK25) ),
inference(light_normalisation,[status(thm)],[c_14291,c_10965]) ).
tcf(c_14295,plain,
net_str(iPr_def_11,sK25),
inference(forward_subsumption_resolution,[status(thm)],[c_14294,c_10972,c_10970,c_10969,c_10973,c_10971]) ).
tcf(c_14502,plain,
( ( iPr_def_12 = iPr_def_13 )
| ~ in(sK28(iPr_def_12,iPr_def_13),iPr_def_13)
| ~ in(sK28(iPr_def_12,iPr_def_13),iPr_def_12) ),
inference(instantiation,[status(thm)],[c_166]) ).
tcf(c_14549,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_13)
| in(sK28(iPr_def_12,iPr_def_13),iPr_def_12)
| ( iPr_def_12 = iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_167]) ).
tcf(c_14671,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| element(sK12(X0,sK26,sK27),the_carrier(sK26))
| ~ one_sorted_str(sK25)
| ~ net_str(sK26,sK25)
| ~ in(X0,iPr_def_13)
| ~ element(sK27,the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_10968,c_119]) ).
tcf(c_14672,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| element(sK12(X0,sK26,sK27),iPr_def_10)
| ~ one_sorted_str(sK25)
| ~ element(sK27,iPr_def_10)
| ~ net_str(sK26,sK25)
| ~ in(X0,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_14671,c_10965]) ).
tcf(c_14673,plain,
! [X0: $i] :
( element(sK12(X0,sK26,sK27),iPr_def_10)
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14672,c_10972,c_10970,c_10969,c_10973,c_10971]) ).
tcf(c_14739,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| ( sK12(X0,sK26,sK27) = X0 )
| ~ one_sorted_str(sK25)
| ~ net_str(sK26,sK25)
| ~ in(X0,iPr_def_13)
| ~ element(sK27,the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_10968,c_120]) ).
tcf(c_14740,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| ( sK12(X0,sK26,sK27) = X0 )
| ~ one_sorted_str(sK25)
| ~ element(sK27,iPr_def_10)
| ~ net_str(sK26,sK25)
| ~ in(X0,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_14739,c_10965]) ).
tcf(c_14741,plain,
! [X0: $i] :
( ( sK12(X0,sK26,sK27) = X0 )
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14740,c_10972,c_10970,c_10969,c_10973,c_10971]) ).
tcf(c_14803,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| related(sK26,sK27,sK12(X0,sK26,sK27))
| ~ one_sorted_str(sK25)
| ~ net_str(sK26,sK25)
| ~ in(X0,iPr_def_13)
| ~ element(sK27,the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_10968,c_121]) ).
tcf(c_14804,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| related(sK26,sK27,sK12(X0,sK26,sK27))
| ~ one_sorted_str(sK25)
| ~ element(sK27,iPr_def_10)
| ~ net_str(sK26,sK25)
| ~ in(X0,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_14803,c_10965]) ).
tcf(c_14805,plain,
! [X0: $i] :
( related(sK26,sK27,sK12(X0,sK26,sK27))
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14804,c_10972,c_10970,c_10969,c_10973,c_10971]) ).
tcf(c_14962,plain,
! [X0: $i] :
( empty(iPr_def_10)
| in(sK12(X0,sK26,sK27),iPr_def_10)
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_14673,c_165]) ).
tcf(c_14963,plain,
! [X0: $i] :
( in(sK12(X0,sK26,sK27),iPr_def_10)
| ~ in(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14962,c_13459]) ).
tcf(c_14972,plain,
! [X0: $i] :
( in(sK28(X0,iPr_def_13),X0)
| ( X0 = iPr_def_13 )
| ( sK12(sK28(X0,iPr_def_13),sK26,sK27) = sK28(X0,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_167,c_14741]) ).
tcf(c_15101,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| in(X0,iPr_def_13)
| ~ one_sorted_str(sK25)
| ~ net_str(sK26,sK25)
| ~ element(sK27,the_carrier(sK26))
| ~ related(sK26,sK27,X0)
| ~ element(X0,the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_10968,c_118]) ).
tcf(c_15112,plain,
! [X0: $i] :
( empty_carrier(sK26)
| empty_carrier(sK25)
| in(X0,iPr_def_13)
| ~ one_sorted_str(sK25)
| ~ element(sK27,iPr_def_10)
| ~ net_str(sK26,sK25)
| ~ element(X0,iPr_def_10)
| ~ related(sK26,sK27,X0) ),
inference(light_normalisation,[status(thm)],[c_15101,c_10965]) ).
tcf(c_15113,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| ~ element(X0,iPr_def_10)
| ~ related(sK26,sK27,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15112,c_10972,c_10970,c_10969,c_10973,c_10971]) ).
tcf(c_18845,plain,
( empty_carrier(sK26)
| empty_carrier(sK25)
| sP0(sK26,sK27,iPr_def_11,sK25)
| ~ one_sorted_str(sK25)
| ~ net_str(iPr_def_11,sK25)
| ~ net_str(sK26,sK25)
| ~ strict_net_str(iPr_def_11,sK25)
| ~ element(sK27,the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_80,c_14097]) ).
tcf(c_18846,plain,
( empty_carrier(sK26)
| empty_carrier(sK25)
| sP0(sK26,sK27,iPr_def_11,sK25)
| ~ one_sorted_str(sK25)
| ~ element(sK27,iPr_def_10)
| ~ net_str(iPr_def_11,sK25)
| ~ net_str(sK26,sK25)
| ~ strict_net_str(iPr_def_11,sK25) ),
inference(light_normalisation,[status(thm)],[c_18845,c_10965]) ).
tcf(c_18847,plain,
sP0(sK26,sK27,iPr_def_11,sK25),
inference(forward_subsumption_resolution,[status(thm)],[c_18846,c_10972,c_10970,c_10969,c_10973,c_14295,c_10971,c_14210]) ).
fof(f150,definition,
! [X1,X2,X3,X0] :
( sP0(X1,X2,X3,X0)
<=> ( the_mapping(X0,X3) = partfun_dom_restriction(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X3))
& the_InternalRel(X3) = relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X3))
& ! [X4] :
( in(X4,the_carrier(X3))
<=> ? [X5] :
( related(X1,X2,X5)
& X5 = X4
& element(X5,the_carrier(X1)) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f151,definition,
! [X0,X3,X2,X1] :
( ~ sP1(X0,X3,X2,X1)
| ( X3 = netstr_restr_to_element(X0,X1,X2)
<=> sP0(X1,X2,X3,X0) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f152,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ net_str(X1,X0)
| empty_carrier(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ~ net_str(X3,X0)
| ~ strict_net_str(X3,X0)
| sP1(X0,X3,X2,X1) ) ) ) ),
inference(definition_folding,[],[f99,f151,f150]) ).
fof(f160,plain,
! [X1,X2,X3,X0] :
( ( ~ sP0(X1,X2,X3,X0)
| ( the_mapping(X0,X3) = partfun_dom_restriction(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X3))
& the_InternalRel(X3) = relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X3))
& ! [X4] :
( ( ~ in(X4,the_carrier(X3))
| ? [X5] :
( related(X1,X2,X5)
& X5 = X4
& element(X5,the_carrier(X1)) ) )
& ( ! [X5] :
( ~ related(X1,X2,X5)
| X4 != X5
| ~ element(X5,the_carrier(X1)) )
| in(X4,the_carrier(X3)) ) ) ) )
& ( the_mapping(X0,X3) != partfun_dom_restriction(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X3))
| the_InternalRel(X3) != relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X3))
| ? [X4] :
( ( in(X4,the_carrier(X3))
| ? [X5] :
( related(X1,X2,X5)
& X5 = X4
& element(X5,the_carrier(X1)) ) )
& ( ~ in(X4,the_carrier(X3))
| ! [X5] :
( ~ related(X1,X2,X5)
| X4 != X5
| ~ element(X5,the_carrier(X1)) ) ) )
| sP0(X1,X2,X3,X0) ) ),
inference(nnf_transformation,[],[f150]) ).
fof(f161,plain,
! [X1,X2,X3,X0] :
( ( ~ sP0(X1,X2,X3,X0)
| ( the_mapping(X0,X3) = partfun_dom_restriction(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X3))
& the_InternalRel(X3) = relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X3))
& ! [X4] :
( ( ~ in(X4,the_carrier(X3))
| ? [X5] :
( related(X1,X2,X5)
& X5 = X4
& element(X5,the_carrier(X1)) ) )
& ( ! [X5] :
( ~ related(X1,X2,X5)
| X4 != X5
| ~ element(X5,the_carrier(X1)) )
| in(X4,the_carrier(X3)) ) ) ) )
& ( the_mapping(X0,X3) != partfun_dom_restriction(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X3))
| the_InternalRel(X3) != relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X3))
| ? [X4] :
( ( in(X4,the_carrier(X3))
| ? [X5] :
( related(X1,X2,X5)
& X5 = X4
& element(X5,the_carrier(X1)) ) )
& ( ~ in(X4,the_carrier(X3))
| ! [X5] :
( ~ related(X1,X2,X5)
| X4 != X5
| ~ element(X5,the_carrier(X1)) ) ) )
| sP0(X1,X2,X3,X0) ) ),
inference(flattening,[],[f160]) ).
fof(f162,plain,
! [X0,X1,X2,X3] :
( ( ~ sP0(X0,X1,X2,X3)
| ( the_mapping(X3,X2) = partfun_dom_restriction(the_carrier(X0),the_carrier(X3),the_mapping(X3,X0),the_carrier(X2))
& the_InternalRel(X2) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X2))
& ! [X7] :
( ( ~ in(X7,the_carrier(X2))
| ? [X9] :
( related(X0,X1,X9)
& X7 = X9
& element(X9,the_carrier(X0)) ) )
& ( ! [X8] :
( ~ related(X0,X1,X8)
| X7 != X8
| ~ element(X8,the_carrier(X0)) )
| in(X7,the_carrier(X2)) ) ) ) )
& ( the_mapping(X3,X2) != partfun_dom_restriction(the_carrier(X0),the_carrier(X3),the_mapping(X3,X0),the_carrier(X2))
| the_InternalRel(X2) != relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X2))
| ? [X4] :
( ( in(X4,the_carrier(X2))
| ? [X6] :
( related(X0,X1,X6)
& X4 = X6
& element(X6,the_carrier(X0)) ) )
& ( ~ in(X4,the_carrier(X2))
| ! [X5] :
( ~ related(X0,X1,X5)
| X4 != X5
| ~ element(X5,the_carrier(X0)) ) ) )
| sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f161]) ).
fof(f163,plain,
! [X0,X1,X2,X3] :
( ( ~ sP0(X0,X1,X2,X3)
| ( the_mapping(X3,X2) = partfun_dom_restriction(the_carrier(X0),the_carrier(X3),the_mapping(X3,X0),the_carrier(X2))
& the_InternalRel(X2) = relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X2))
& ! [X7] :
( ( ~ in(X7,the_carrier(X2))
| ( related(X0,X1,sK5(X0,X1,X7))
& sK5(X0,X1,X7) = X7
& element(sK5(X0,X1,X7),the_carrier(X0)) ) )
& ( ! [X8] :
( ~ related(X0,X1,X8)
| X7 != X8
| ~ element(X8,the_carrier(X0)) )
| in(X7,the_carrier(X2)) ) ) ) )
& ( the_mapping(X3,X2) != partfun_dom_restriction(the_carrier(X0),the_carrier(X3),the_mapping(X3,X0),the_carrier(X2))
| the_InternalRel(X2) != relation_restriction_as_relation_of(the_InternalRel(X0),the_carrier(X2))
| ( ( in(sK3(X0,X1,X2),the_carrier(X2))
| ( related(X0,X1,sK4(X0,X1,X2))
& sK3(X0,X1,X2) = sK4(X0,X1,X2)
& element(sK4(X0,X1,X2),the_carrier(X0)) ) )
& ( ~ in(sK3(X0,X1,X2),the_carrier(X2))
| ! [X5] :
( ~ related(X0,X1,X5)
| sK3(X0,X1,X2) != X5
| ~ element(X5,the_carrier(X0)) ) ) )
| sP0(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X4,sK3(X0,X1,X2)),skolemize(X6,sK4(X0,X1,X2)),skolemize(X9,sK5(X0,X1,X7))],[f162]) ).
fof(f220,plain,
! [X2,X3,X0,X1,X7] :
( ~ sP0(X0,X1,X2,X3)
| ~ in(X7,the_carrier(X2))
| related(X0,X1,sK5(X0,X1,X7)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f221,plain,
! [X2,X3,X0,X1,X7] :
( ~ sP0(X0,X1,X2,X3)
| ~ in(X7,the_carrier(X2))
| sK5(X0,X1,X7) = X7 ),
inference(cnf_transformation,[],[f163]) ).
fof(f222,plain,
! [X2,X3,X0,X1,X7] :
( ~ sP0(X0,X1,X2,X3)
| ~ in(X7,the_carrier(X2))
| element(sK5(X0,X1,X7),the_carrier(X0)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f223,plain,
! [X2,X3,X0,X1,X8,X7] :
( ~ sP0(X0,X1,X2,X3)
| ~ related(X0,X1,X8)
| X7 != X8
| ~ element(X8,the_carrier(X0))
| in(X7,the_carrier(X2)) ),
inference(cnf_transformation,[],[f163]) ).
fof(f327,plain,
! [X2,X3,X0,X1,X8] :
( ~ sP0(X0,X1,X2,X3)
| ~ related(X0,X1,X8)
| ~ element(X8,the_carrier(X0))
| in(X8,the_carrier(X2)) ),
inference(equality_resolution,[],[f223]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X4,the_carrier(X2))
| ~ element(X4,the_carrier(X0))
| ~ related(X0,X1,X4)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK5(X0,X1,X4),the_carrier(X0))
| ~ in(X4,the_carrier(X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(X0,X1,X4) = X4 )
| ~ in(X4,the_carrier(X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( related(X0,X1,sK5(X0,X1,X4))
| ~ in(X4,the_carrier(X2))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_18849,plain,
! [X0: $i] :
( in(X0,the_carrier(iPr_def_11))
| ~ related(sK26,sK27,X0)
| ~ element(X0,the_carrier(sK26)) ),
inference(superposition,[status(thm)],[c_18847,c_74]) ).
tcf(c_18850,plain,
! [X0: $i] :
( related(sK26,sK27,sK5(sK26,sK27,X0))
| ~ in(X0,the_carrier(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_18847,c_77]) ).
tcf(c_18851,plain,
! [X0: $i] :
( ( sK5(sK26,sK27,X0) = X0 )
| ~ in(X0,the_carrier(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_18847,c_76]) ).
tcf(c_18852,plain,
! [X0: $i] :
( element(sK5(sK26,sK27,X0),the_carrier(sK26))
| ~ in(X0,the_carrier(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_18847,c_75]) ).
tcf(c_18855,plain,
! [X0: $i] :
( element(sK5(sK26,sK27,X0),iPr_def_10)
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_18852,c_10965,c_10967]) ).
tcf(c_18858,plain,
! [X0: $i] :
( ( sK5(sK26,sK27,X0) = X0 )
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_18851,c_10967]) ).
tcf(c_18861,plain,
! [X0: $i] :
( related(sK26,sK27,sK5(sK26,sK27,X0))
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_18850,c_10967]) ).
tcf(c_18864,plain,
! [X0: $i] :
( in(X0,iPr_def_12)
| ~ element(X0,iPr_def_10)
| ~ related(sK26,sK27,X0) ),
inference(light_normalisation,[status(thm)],[c_18849,c_10965,c_10967]) ).
tcf(c_20252,plain,
( ( iPr_def_12 = iPr_def_13 )
| ( sK12(sK28(iPr_def_12,iPr_def_13),sK26,sK27) = sK28(iPr_def_12,iPr_def_13) )
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_14972,c_18858]) ).
tcf(c_20276,plain,
( ( sK12(sK28(iPr_def_12,iPr_def_13),sK26,sK27) = sK28(iPr_def_12,iPr_def_13) )
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20252,c_10974]) ).
tcf(c_20329,plain,
! [X0: $i] :
( in(sK5(sK26,sK27,X0),iPr_def_13)
| ~ in(X0,iPr_def_12)
| ~ element(sK5(sK26,sK27,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_18861,c_15113]) ).
tcf(c_20564,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_10)
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) )
| ~ in(sK28(iPr_def_12,iPr_def_13),iPr_def_13) ),
inference(superposition,[status(thm)],[c_20276,c_14963]) ).
tcf(c_20565,plain,
( related(sK26,sK27,sK28(iPr_def_12,iPr_def_13))
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) )
| ~ in(sK28(iPr_def_12,iPr_def_13),iPr_def_13) ),
inference(superposition,[status(thm)],[c_20276,c_14805]) ).
tcf(c_20631,plain,
! [X0: $i] :
( in(sK5(sK26,sK27,X0),iPr_def_13)
| ~ in(X0,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_20329,c_18855,c_20329]) ).
tcf(c_20645,plain,
! [X0: $i] :
( ( sK12(sK5(sK26,sK27,X0),sK26,sK27) = sK5(sK26,sK27,X0) )
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_20631,c_14741]) ).
tcf(c_20683,plain,
( ( iPr_def_12 = iPr_def_13 )
| ( sK12(sK28(iPr_def_12,iPr_def_13),sK26,sK27) = sK28(iPr_def_12,iPr_def_13) )
| ( sK12(sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)),sK26,sK27) = sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_14972,c_20645]) ).
tcf(c_20707,plain,
( ( sK12(sK28(iPr_def_12,iPr_def_13),sK26,sK27) = sK28(iPr_def_12,iPr_def_13) )
| ( sK12(sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)),sK26,sK27) = sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20683,c_10974]) ).
tcf(c_21249,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_12)
| in(sK28(iPr_def_12,iPr_def_13),iPr_def_10)
| ( iPr_def_12 = iPr_def_13 )
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_167,c_20564]) ).
tcf(c_21250,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_12)
| in(sK28(iPr_def_12,iPr_def_13),iPr_def_10)
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21249,c_10974]) ).
tcf(c_21257,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_10)
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21250,c_18858]) ).
tcf(c_21269,plain,
( element(sK28(iPr_def_12,iPr_def_13),iPr_def_10)
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_21257,c_164]) ).
tcf(c_26066,plain,
! [X0: $i] :
( in(sK12(X0,sK26,sK27),iPr_def_12)
| ~ in(X0,iPr_def_13)
| ~ element(sK12(X0,sK26,sK27),iPr_def_10) ),
inference(superposition,[status(thm)],[c_14805,c_18864]) ).
tcf(c_26073,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_12)
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) )
| ~ element(sK28(iPr_def_12,iPr_def_13),iPr_def_10)
| ~ in(sK28(iPr_def_12,iPr_def_13),iPr_def_13) ),
inference(superposition,[status(thm)],[c_20565,c_18864]) ).
tcf(c_26248,plain,
! [X0: $i] :
( in(sK12(X0,sK26,sK27),iPr_def_12)
| ~ in(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_26066,c_14673,c_26066]) ).
tcf(c_26261,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_12)
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) )
| ~ in(sK28(iPr_def_12,iPr_def_13),iPr_def_13) ),
inference(superposition,[status(thm)],[c_20276,c_26248]) ).
tcf(c_26428,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_12)
| ( sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13) ) ),
inference(global_subsumption_just,[status(thm)],[c_26261,c_10974,c_14549,c_21269,c_26073]) ).
tcf(c_26432,plain,
sK5(sK26,sK27,sK28(iPr_def_12,iPr_def_13)) = sK28(iPr_def_12,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_26428,c_18858]) ).
tcf(c_26438,plain,
sK12(sK28(iPr_def_12,iPr_def_13),sK26,sK27) = sK28(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_20707,c_26432]) ).
tcf(c_26441,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_13)
| ~ in(sK28(iPr_def_12,iPr_def_13),iPr_def_12) ),
inference(superposition,[status(thm)],[c_26432,c_20631]) ).
tcf(c_26460,plain,
( in(sK28(iPr_def_12,iPr_def_13),iPr_def_12)
| ~ in(sK28(iPr_def_12,iPr_def_13),iPr_def_13) ),
inference(superposition,[status(thm)],[c_26438,c_26248]) ).
tcf(c_26940,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_26460,c_26441,c_14549,c_14502,c_10974]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU384+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 13:56:09 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 16.11/3.33 % SZS status Started for theBenchmark.p
% 16.11/3.33 % SZS status Theorem for theBenchmark.p
% 16.11/3.33
% 16.11/3.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.11/3.33
% 16.11/3.33 % ------ iProver source info
% 16.11/3.33
% 16.11/3.33 % git: date: 2026-07-19 20:42:38 +0200
% 16.11/3.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.11/3.33 % git: non_committed_changes: false
% 16.11/3.33
% 16.11/3.33 % ------ Parsing...
% 16.11/3.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.11/3.33
% 16.11/3.33 % ------ Preprocessing... sup_sim: 0 sf_s rm: 17 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 16.11/3.33
% 16.11/3.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.11/3.33
% 16.11/3.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.11/3.33 % ------ Proving...
% 16.11/3.33 % ------ Problem Properties
% 16.11/3.33
% 16.11/3.33 %
% 16.11/3.33 % clauses 109
% 16.11/3.33 % conjectures 6
% 16.11/3.33 % EPR 38
% 16.11/3.33 % Horn 90
% 16.11/3.33 % unary 34
% 16.11/3.33 % binary 29
% 16.11/3.33 % lits 301
% 16.11/3.33 % lits eq 35
% 16.11/3.33 % fd_pure 0
% 16.11/3.33 % fd_pseudo 0
% 16.11/3.33 % fd_cond 1
% 16.11/3.33 % fd_pseudo_cond 9
% 16.11/3.33 % AC symbols 0
% 16.11/3.33
% 16.11/3.33 % ------ Schedule dynamic 5 is on
% 16.11/3.33
% 16.11/3.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 16.11/3.33
% 16.11/3.33
% 16.11/3.33 % ------
% 16.11/3.33 % Current options:
% 16.11/3.33 % ------
% 16.11/3.33
% 16.11/3.33
% 16.11/3.33 %
% 16.11/3.33
% 16.11/3.33 % ------ Proving...
% 16.11/3.33 %
% 16.11/3.33
% 16.11/3.33 % SZS status Theorem for theBenchmark.p
% 16.11/3.33
% 16.11/3.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.11/3.34
% 16.11/3.34
%------------------------------------------------------------------------------