TSTP Solution File: SEU367+2 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU367+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:06:38 EDT 2023
% Result : Theorem 73.04s 10.82s
% Output : CNFRefutation 73.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 154 ( 28 unt; 0 def)
% Number of atoms : 841 ( 66 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 1093 ( 406 ~; 493 |; 156 &)
% ( 11 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 415 ( 6 sgn; 206 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f47,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f57,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( element(X4,the_carrier(X1))
=> ( related(X1,X3,X4)
=> in(apply_netmap(X0,X1,X4),X2) ) )
& element(X3,the_carrier(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_waybel_0) ).
fof(f62,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X1))
=> ? [X4] :
( in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_waybel_0) ).
fof(f113,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f133,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f515,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f613,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f619,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f647,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f702,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2,X3] :
( subset(X2,X3)
=> ( ( is_often_in(X0,X1,X2)
=> is_often_in(X0,X1,X3) )
& ( is_eventually_in(X0,X1,X2)
=> is_eventually_in(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_waybel_0) ).
fof(f703,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2,X3] :
( subset(X2,X3)
=> ( ( is_often_in(X0,X1,X2)
=> is_often_in(X0,X1,X3) )
& ( is_eventually_in(X0,X1,X2)
=> is_eventually_in(X0,X1,X3) ) ) ) ) ),
inference(negated_conjecture,[],[f702]) ).
fof(f856,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X1)) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f857,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_eventually_in(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X1)) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f856]) ).
fof(f863,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( ? [X4] :
( in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) )
| ~ element(X3,the_carrier(X1)) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f62]) ).
fof(f864,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_often_in(X0,X1,X2)
<=> ! [X3] :
( ? [X4] :
( in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) )
| ~ element(X3,the_carrier(X1)) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f863]) ).
fof(f1372,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f515]) ).
fof(f1617,plain,
? [X0] :
( ? [X1] :
( ? [X2,X3] :
( ( ( ~ is_often_in(X0,X1,X3)
& is_often_in(X0,X1,X2) )
| ( ~ is_eventually_in(X0,X1,X3)
& is_eventually_in(X0,X1,X2) ) )
& subset(X2,X3) )
& net_str(X1,X0)
& ~ empty_carrier(X1) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f703]) ).
fof(f1618,plain,
? [X0] :
( ? [X1] :
( ? [X2,X3] :
( ( ( ~ is_often_in(X0,X1,X3)
& is_often_in(X0,X1,X2) )
| ( ~ is_eventually_in(X0,X1,X3)
& is_eventually_in(X0,X1,X2) ) )
& subset(X2,X3) )
& net_str(X1,X0)
& ~ empty_carrier(X1) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f1617]) ).
fof(f1752,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ? [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) )
| ~ element(X3,the_carrier(X1)) ) )
& ( ? [X3] :
( ! [X4] :
( in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X1)) )
| ~ is_eventually_in(X0,X1,X2) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f857]) ).
fof(f1753,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ? [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) )
| ~ element(X3,the_carrier(X1)) ) )
& ( ? [X5] :
( ! [X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,X5,X6)
| ~ element(X6,the_carrier(X1)) )
& element(X5,the_carrier(X1)) )
| ~ is_eventually_in(X0,X1,X2) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f1752]) ).
fof(f1754,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) )
=> ( ~ in(apply_netmap(X0,X1,sK69(X0,X1,X2,X3)),X2)
& related(X1,X3,sK69(X0,X1,X2,X3))
& element(sK69(X0,X1,X2,X3),the_carrier(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1755,plain,
! [X0,X1,X2] :
( ? [X5] :
( ! [X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,X5,X6)
| ~ element(X6,the_carrier(X1)) )
& element(X5,the_carrier(X1)) )
=> ( ! [X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,sK70(X0,X1,X2),X6)
| ~ element(X6,the_carrier(X1)) )
& element(sK70(X0,X1,X2),the_carrier(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1756,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_eventually_in(X0,X1,X2)
| ! [X3] :
( ( ~ in(apply_netmap(X0,X1,sK69(X0,X1,X2,X3)),X2)
& related(X1,X3,sK69(X0,X1,X2,X3))
& element(sK69(X0,X1,X2,X3),the_carrier(X1)) )
| ~ element(X3,the_carrier(X1)) ) )
& ( ( ! [X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,sK70(X0,X1,X2),X6)
| ~ element(X6,the_carrier(X1)) )
& element(sK70(X0,X1,X2),the_carrier(X1)) )
| ~ is_eventually_in(X0,X1,X2) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f1753,f1755,f1754]) ).
fof(f1769,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_often_in(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X1)) ) )
& ( ! [X3] :
( ? [X4] :
( in(apply_netmap(X0,X1,X4),X2)
& related(X1,X3,X4)
& element(X4,the_carrier(X1)) )
| ~ element(X3,the_carrier(X1)) )
| ~ is_often_in(X0,X1,X2) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f864]) ).
fof(f1770,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_often_in(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X1)) ) )
& ( ! [X5] :
( ? [X6] :
( in(apply_netmap(X0,X1,X6),X2)
& related(X1,X5,X6)
& element(X6,the_carrier(X1)) )
| ~ element(X5,the_carrier(X1)) )
| ~ is_often_in(X0,X1,X2) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f1769]) ).
fof(f1771,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,X3,X4)
| ~ element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X1)) )
=> ( ! [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,sK76(X0,X1,X2),X4)
| ~ element(X4,the_carrier(X1)) )
& element(sK76(X0,X1,X2),the_carrier(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1772,plain,
! [X0,X1,X2,X5] :
( ? [X6] :
( in(apply_netmap(X0,X1,X6),X2)
& related(X1,X5,X6)
& element(X6,the_carrier(X1)) )
=> ( in(apply_netmap(X0,X1,sK77(X0,X1,X2,X5)),X2)
& related(X1,X5,sK77(X0,X1,X2,X5))
& element(sK77(X0,X1,X2,X5),the_carrier(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1773,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_often_in(X0,X1,X2)
| ( ! [X4] :
( ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,sK76(X0,X1,X2),X4)
| ~ element(X4,the_carrier(X1)) )
& element(sK76(X0,X1,X2),the_carrier(X1)) ) )
& ( ! [X5] :
( ( in(apply_netmap(X0,X1,sK77(X0,X1,X2,X5)),X2)
& related(X1,X5,sK77(X0,X1,X2,X5))
& element(sK77(X0,X1,X2,X5),the_carrier(X1)) )
| ~ element(X5,the_carrier(X1)) )
| ~ is_often_in(X0,X1,X2) ) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76,sK77])],[f1770,f1772,f1771]) ).
fof(f1941,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f113]) ).
fof(f1942,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f1941]) ).
fof(f1943,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f1942]) ).
fof(f1944,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK132(X0,X1,X2),X1)
& ~ in(sK132(X0,X1,X2),X0) )
| ~ in(sK132(X0,X1,X2),X2) )
& ( in(sK132(X0,X1,X2),X1)
| in(sK132(X0,X1,X2),X0)
| in(sK132(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1945,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK132(X0,X1,X2),X1)
& ~ in(sK132(X0,X1,X2),X0) )
| ~ in(sK132(X0,X1,X2),X2) )
& ( in(sK132(X0,X1,X2),X1)
| in(sK132(X0,X1,X2),X0)
| in(sK132(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK132])],[f1943,f1944]) ).
fof(f2005,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f133]) ).
fof(f2006,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f2005]) ).
fof(f2007,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f2006]) ).
fof(f2008,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK157(X0,X1,X2),X1)
| ~ in(sK157(X0,X1,X2),X0)
| ~ in(sK157(X0,X1,X2),X2) )
& ( ( ~ in(sK157(X0,X1,X2),X1)
& in(sK157(X0,X1,X2),X0) )
| in(sK157(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f2009,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK157(X0,X1,X2),X1)
| ~ in(sK157(X0,X1,X2),X0)
| ~ in(sK157(X0,X1,X2),X2) )
& ( ( ~ in(sK157(X0,X1,X2),X1)
& in(sK157(X0,X1,X2),X0) )
| in(sK157(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f2007,f2008]) ).
fof(f2795,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f613]) ).
fof(f2854,plain,
( ? [X0] :
( ? [X1] :
( ? [X2,X3] :
( ( ( ~ is_often_in(X0,X1,X3)
& is_often_in(X0,X1,X2) )
| ( ~ is_eventually_in(X0,X1,X3)
& is_eventually_in(X0,X1,X2) ) )
& subset(X2,X3) )
& net_str(X1,X0)
& ~ empty_carrier(X1) )
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X3,X2] :
( ( ( ~ is_often_in(sK554,X1,X3)
& is_often_in(sK554,X1,X2) )
| ( ~ is_eventually_in(sK554,X1,X3)
& is_eventually_in(sK554,X1,X2) ) )
& subset(X2,X3) )
& net_str(X1,sK554)
& ~ empty_carrier(X1) )
& one_sorted_str(sK554)
& ~ empty_carrier(sK554) ) ),
introduced(choice_axiom,[]) ).
fof(f2855,plain,
( ? [X1] :
( ? [X3,X2] :
( ( ( ~ is_often_in(sK554,X1,X3)
& is_often_in(sK554,X1,X2) )
| ( ~ is_eventually_in(sK554,X1,X3)
& is_eventually_in(sK554,X1,X2) ) )
& subset(X2,X3) )
& net_str(X1,sK554)
& ~ empty_carrier(X1) )
=> ( ? [X3,X2] :
( ( ( ~ is_often_in(sK554,sK555,X3)
& is_often_in(sK554,sK555,X2) )
| ( ~ is_eventually_in(sK554,sK555,X3)
& is_eventually_in(sK554,sK555,X2) ) )
& subset(X2,X3) )
& net_str(sK555,sK554)
& ~ empty_carrier(sK555) ) ),
introduced(choice_axiom,[]) ).
fof(f2856,plain,
( ? [X3,X2] :
( ( ( ~ is_often_in(sK554,sK555,X3)
& is_often_in(sK554,sK555,X2) )
| ( ~ is_eventually_in(sK554,sK555,X3)
& is_eventually_in(sK554,sK555,X2) ) )
& subset(X2,X3) )
=> ( ( ( ~ is_often_in(sK554,sK555,sK557)
& is_often_in(sK554,sK555,sK556) )
| ( ~ is_eventually_in(sK554,sK555,sK557)
& is_eventually_in(sK554,sK555,sK556) ) )
& subset(sK556,sK557) ) ),
introduced(choice_axiom,[]) ).
fof(f2857,plain,
( ( ( ~ is_often_in(sK554,sK555,sK557)
& is_often_in(sK554,sK555,sK556) )
| ( ~ is_eventually_in(sK554,sK555,sK557)
& is_eventually_in(sK554,sK555,sK556) ) )
& subset(sK556,sK557)
& net_str(sK555,sK554)
& ~ empty_carrier(sK555)
& one_sorted_str(sK554)
& ~ empty_carrier(sK554) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK554,sK555,sK556,sK557])],[f1618,f2856,f2855,f2854]) ).
fof(f2953,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f45]) ).
fof(f2955,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f2981,plain,
! [X2,X0,X1] :
( element(sK70(X0,X1,X2),the_carrier(X1))
| ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f2982,plain,
! [X2,X0,X1,X6] :
( in(apply_netmap(X0,X1,X6),X2)
| ~ related(X1,sK70(X0,X1,X2),X6)
| ~ element(X6,the_carrier(X1))
| ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f2983,plain,
! [X2,X3,X0,X1] :
( is_eventually_in(X0,X1,X2)
| element(sK69(X0,X1,X2,X3),the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f2984,plain,
! [X2,X3,X0,X1] :
( is_eventually_in(X0,X1,X2)
| related(X1,X3,sK69(X0,X1,X2,X3))
| ~ element(X3,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f2985,plain,
! [X2,X3,X0,X1] :
( is_eventually_in(X0,X1,X2)
| ~ in(apply_netmap(X0,X1,sK69(X0,X1,X2,X3)),X2)
| ~ element(X3,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1756]) ).
fof(f3003,plain,
! [X2,X0,X1,X5] :
( element(sK77(X0,X1,X2,X5),the_carrier(X1))
| ~ element(X5,the_carrier(X1))
| ~ is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f3004,plain,
! [X2,X0,X1,X5] :
( related(X1,X5,sK77(X0,X1,X2,X5))
| ~ element(X5,the_carrier(X1))
| ~ is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f3005,plain,
! [X2,X0,X1,X5] :
( in(apply_netmap(X0,X1,sK77(X0,X1,X2,X5)),X2)
| ~ element(X5,the_carrier(X1))
| ~ is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f3006,plain,
! [X2,X0,X1] :
( is_often_in(X0,X1,X2)
| element(sK76(X0,X1,X2),the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f3007,plain,
! [X2,X0,X1,X4] :
( is_often_in(X0,X1,X2)
| ~ in(apply_netmap(X0,X1,X4),X2)
| ~ related(X1,sK76(X0,X1,X2),X4)
| ~ element(X4,the_carrier(X1))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f3216,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f1945]) ).
fof(f3300,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f2009]) ).
fof(f4518,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f4699,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2795]) ).
fof(f4710,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f619]) ).
fof(f4761,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f647]) ).
fof(f4856,plain,
~ empty_carrier(sK554),
inference(cnf_transformation,[],[f2857]) ).
fof(f4857,plain,
one_sorted_str(sK554),
inference(cnf_transformation,[],[f2857]) ).
fof(f4858,plain,
~ empty_carrier(sK555),
inference(cnf_transformation,[],[f2857]) ).
fof(f4859,plain,
net_str(sK555,sK554),
inference(cnf_transformation,[],[f2857]) ).
fof(f4860,plain,
subset(sK556,sK557),
inference(cnf_transformation,[],[f2857]) ).
fof(f4861,plain,
( is_often_in(sK554,sK555,sK556)
| is_eventually_in(sK554,sK555,sK556) ),
inference(cnf_transformation,[],[f2857]) ).
fof(f4862,plain,
( is_often_in(sK554,sK555,sK556)
| ~ is_eventually_in(sK554,sK555,sK557) ),
inference(cnf_transformation,[],[f2857]) ).
fof(f4863,plain,
( ~ is_often_in(sK554,sK555,sK557)
| is_eventually_in(sK554,sK555,sK556) ),
inference(cnf_transformation,[],[f2857]) ).
fof(f4864,plain,
( ~ is_often_in(sK554,sK555,sK557)
| ~ is_eventually_in(sK554,sK555,sK557) ),
inference(cnf_transformation,[],[f2857]) ).
fof(f4906,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f2955,f4761,f4761]) ).
fof(f5698,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f3216]) ).
fof(f5721,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f3300]) ).
cnf(c_123,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2953]) ).
cnf(c_125,plain,
set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f4906]) ).
cnf(c_151,plain,
( ~ in(apply_netmap(X0,X1,sK69(X0,X1,X2,X3)),X2)
| ~ element(X3,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| is_eventually_in(X0,X1,X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f2985]) ).
cnf(c_152,plain,
( ~ element(X0,the_carrier(X1))
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2)
| related(X1,X0,sK69(X2,X1,X3,X0))
| is_eventually_in(X2,X1,X3)
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(cnf_transformation,[],[f2984]) ).
cnf(c_153,plain,
( ~ element(X0,the_carrier(X1))
| ~ net_str(X1,X2)
| ~ one_sorted_str(X2)
| element(sK69(X2,X1,X3,X0),the_carrier(X1))
| is_eventually_in(X2,X1,X3)
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(cnf_transformation,[],[f2983]) ).
cnf(c_154,plain,
( ~ related(X0,sK70(X1,X0,X2),X3)
| ~ is_eventually_in(X1,X0,X2)
| ~ element(X3,the_carrier(X0))
| ~ net_str(X0,X1)
| ~ one_sorted_str(X1)
| in(apply_netmap(X1,X0,X3),X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f2982]) ).
cnf(c_155,plain,
( ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| element(sK70(X0,X1,X2),the_carrier(X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f2981]) ).
cnf(c_173,plain,
( ~ related(X0,sK76(X1,X0,X2),X3)
| ~ in(apply_netmap(X1,X0,X3),X2)
| ~ element(X3,the_carrier(X0))
| ~ net_str(X0,X1)
| ~ one_sorted_str(X1)
| is_often_in(X1,X0,X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f3007]) ).
cnf(c_174,plain,
( ~ net_str(X0,X1)
| ~ one_sorted_str(X1)
| element(sK76(X1,X0,X2),the_carrier(X0))
| is_often_in(X1,X0,X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f3006]) ).
cnf(c_175,plain,
( ~ is_often_in(X0,X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| in(apply_netmap(X0,X1,sK77(X0,X1,X2,X3)),X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f3005]) ).
cnf(c_176,plain,
( ~ is_often_in(X0,X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| related(X1,X3,sK77(X0,X1,X2,X3))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f3004]) ).
cnf(c_177,plain,
( ~ is_often_in(X0,X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| element(sK77(X0,X1,X2,X3),the_carrier(X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f3003]) ).
cnf(c_386,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f5698]) ).
cnf(c_474,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f5721]) ).
cnf(c_1684,plain,
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f4518]) ).
cnf(c_1864,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f4699]) ).
cnf(c_1876,plain,
set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f4710]) ).
cnf(c_2020,negated_conjecture,
( ~ is_eventually_in(sK554,sK555,sK557)
| ~ is_often_in(sK554,sK555,sK557) ),
inference(cnf_transformation,[],[f4864]) ).
cnf(c_2021,negated_conjecture,
( ~ is_often_in(sK554,sK555,sK557)
| is_eventually_in(sK554,sK555,sK556) ),
inference(cnf_transformation,[],[f4863]) ).
cnf(c_2022,negated_conjecture,
( ~ is_eventually_in(sK554,sK555,sK557)
| is_often_in(sK554,sK555,sK556) ),
inference(cnf_transformation,[],[f4862]) ).
cnf(c_2023,negated_conjecture,
( is_eventually_in(sK554,sK555,sK556)
| is_often_in(sK554,sK555,sK556) ),
inference(cnf_transformation,[],[f4861]) ).
cnf(c_2024,negated_conjecture,
subset(sK556,sK557),
inference(cnf_transformation,[],[f4860]) ).
cnf(c_2025,negated_conjecture,
net_str(sK555,sK554),
inference(cnf_transformation,[],[f4859]) ).
cnf(c_2026,negated_conjecture,
~ empty_carrier(sK555),
inference(cnf_transformation,[],[f4858]) ).
cnf(c_2027,negated_conjecture,
one_sorted_str(sK554),
inference(cnf_transformation,[],[f4857]) ).
cnf(c_2028,negated_conjecture,
~ empty_carrier(sK554),
inference(cnf_transformation,[],[f4856]) ).
cnf(c_54366,plain,
( X0 != sK554
| X1 != sK555
| ~ is_often_in(X0,X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ one_sorted_str(X0)
| element(sK77(X0,X1,X2,X3),the_carrier(X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_177,c_2025]) ).
cnf(c_54367,plain,
( ~ element(X0,the_carrier(sK555))
| ~ is_often_in(sK554,sK555,X1)
| ~ one_sorted_str(sK554)
| element(sK77(sK554,sK555,X1,X0),the_carrier(sK555))
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54366]) ).
cnf(c_54369,plain,
( ~ is_often_in(sK554,sK555,X1)
| ~ element(X0,the_carrier(sK555))
| element(sK77(sK554,sK555,X1,X0),the_carrier(sK555)) ),
inference(global_subsumption_just,[status(thm)],[c_54367,c_2027,c_2028,c_2026,c_54367]) ).
cnf(c_54370,plain,
( ~ element(X0,the_carrier(sK555))
| ~ is_often_in(sK554,sK555,X1)
| element(sK77(sK554,sK555,X1,X0),the_carrier(sK555)) ),
inference(renaming,[status(thm)],[c_54369]) ).
cnf(c_54381,plain,
( X0 != sK554
| X1 != sK555
| ~ is_often_in(X0,X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ one_sorted_str(X0)
| related(X1,X3,sK77(X0,X1,X2,X3))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_176,c_2025]) ).
cnf(c_54382,plain,
( ~ element(X0,the_carrier(sK555))
| ~ is_often_in(sK554,sK555,X1)
| ~ one_sorted_str(sK554)
| related(sK555,X0,sK77(sK554,sK555,X1,X0))
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54381]) ).
cnf(c_54384,plain,
( ~ is_often_in(sK554,sK555,X1)
| ~ element(X0,the_carrier(sK555))
| related(sK555,X0,sK77(sK554,sK555,X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_54382,c_2027,c_2028,c_2026,c_54382]) ).
cnf(c_54385,plain,
( ~ element(X0,the_carrier(sK555))
| ~ is_often_in(sK554,sK555,X1)
| related(sK555,X0,sK77(sK554,sK555,X1,X0)) ),
inference(renaming,[status(thm)],[c_54384]) ).
cnf(c_54396,plain,
( X0 != sK554
| X1 != sK555
| ~ is_often_in(X0,X1,X2)
| ~ element(X3,the_carrier(X1))
| ~ one_sorted_str(X0)
| in(apply_netmap(X0,X1,sK77(X0,X1,X2,X3)),X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_175,c_2025]) ).
cnf(c_54397,plain,
( ~ element(X0,the_carrier(sK555))
| ~ is_often_in(sK554,sK555,X1)
| ~ one_sorted_str(sK554)
| in(apply_netmap(sK554,sK555,sK77(sK554,sK555,X1,X0)),X1)
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54396]) ).
cnf(c_54399,plain,
( ~ is_often_in(sK554,sK555,X1)
| ~ element(X0,the_carrier(sK555))
| in(apply_netmap(sK554,sK555,sK77(sK554,sK555,X1,X0)),X1) ),
inference(global_subsumption_just,[status(thm)],[c_54397,c_2027,c_2028,c_2026,c_54397]) ).
cnf(c_54400,plain,
( ~ element(X0,the_carrier(sK555))
| ~ is_often_in(sK554,sK555,X1)
| in(apply_netmap(sK554,sK555,sK77(sK554,sK555,X1,X0)),X1) ),
inference(renaming,[status(thm)],[c_54399]) ).
cnf(c_54411,plain,
( X0 != sK554
| X1 != sK555
| ~ is_eventually_in(X0,X1,X2)
| ~ one_sorted_str(X0)
| element(sK70(X0,X1,X2),the_carrier(X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_155,c_2025]) ).
cnf(c_54412,plain,
( ~ is_eventually_in(sK554,sK555,X0)
| ~ one_sorted_str(sK554)
| element(sK70(sK554,sK555,X0),the_carrier(sK555))
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54411]) ).
cnf(c_54414,plain,
( ~ is_eventually_in(sK554,sK555,X0)
| element(sK70(sK554,sK555,X0),the_carrier(sK555)) ),
inference(global_subsumption_just,[status(thm)],[c_54412,c_2027,c_2028,c_2026,c_54412]) ).
cnf(c_54423,plain,
( X0 != sK554
| X1 != sK555
| ~ in(apply_netmap(X0,X1,sK69(X0,X1,X2,X3)),X2)
| ~ element(X3,the_carrier(X1))
| ~ one_sorted_str(X0)
| is_eventually_in(X0,X1,X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_151,c_2025]) ).
cnf(c_54424,plain,
( ~ in(apply_netmap(sK554,sK555,sK69(sK554,sK555,X0,X1)),X0)
| ~ element(X1,the_carrier(sK555))
| ~ one_sorted_str(sK554)
| is_eventually_in(sK554,sK555,X0)
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54423]) ).
cnf(c_54426,plain,
( ~ element(X1,the_carrier(sK555))
| ~ in(apply_netmap(sK554,sK555,sK69(sK554,sK555,X0,X1)),X0)
| is_eventually_in(sK554,sK555,X0) ),
inference(global_subsumption_just,[status(thm)],[c_54424,c_2027,c_2028,c_2026,c_54424]) ).
cnf(c_54427,plain,
( ~ in(apply_netmap(sK554,sK555,sK69(sK554,sK555,X0,X1)),X0)
| ~ element(X1,the_carrier(sK555))
| is_eventually_in(sK554,sK555,X0) ),
inference(renaming,[status(thm)],[c_54426]) ).
cnf(c_54540,plain,
( X0 != sK555
| X1 != sK554
| ~ element(X2,the_carrier(X0))
| ~ one_sorted_str(X1)
| element(sK69(X1,X0,X3,X2),the_carrier(X0))
| is_eventually_in(X1,X0,X3)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_153,c_2025]) ).
cnf(c_54541,plain,
( ~ element(X0,the_carrier(sK555))
| ~ one_sorted_str(sK554)
| element(sK69(sK554,sK555,X1,X0),the_carrier(sK555))
| is_eventually_in(sK554,sK555,X1)
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54540]) ).
cnf(c_54543,plain,
( ~ element(X0,the_carrier(sK555))
| element(sK69(sK554,sK555,X1,X0),the_carrier(sK555))
| is_eventually_in(sK554,sK555,X1) ),
inference(global_subsumption_just,[status(thm)],[c_54541,c_2027,c_2028,c_2026,c_54541]) ).
cnf(c_54555,plain,
( X0 != sK555
| X1 != sK554
| ~ element(X2,the_carrier(X0))
| ~ one_sorted_str(X1)
| related(X0,X2,sK69(X1,X0,X3,X2))
| is_eventually_in(X1,X0,X3)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_152,c_2025]) ).
cnf(c_54556,plain,
( ~ element(X0,the_carrier(sK555))
| ~ one_sorted_str(sK554)
| related(sK555,X0,sK69(sK554,sK555,X1,X0))
| is_eventually_in(sK554,sK555,X1)
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54555]) ).
cnf(c_54558,plain,
( ~ element(X0,the_carrier(sK555))
| related(sK555,X0,sK69(sK554,sK555,X1,X0))
| is_eventually_in(sK554,sK555,X1) ),
inference(global_subsumption_just,[status(thm)],[c_54556,c_2027,c_2028,c_2026,c_54556]) ).
cnf(c_54700,plain,
( X0 != sK555
| X1 != sK554
| ~ one_sorted_str(X1)
| element(sK76(X1,X0,X2),the_carrier(X0))
| is_often_in(X1,X0,X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_174,c_2025]) ).
cnf(c_54701,plain,
( ~ one_sorted_str(sK554)
| element(sK76(sK554,sK555,X0),the_carrier(sK555))
| is_often_in(sK554,sK555,X0)
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54700]) ).
cnf(c_54703,plain,
( element(sK76(sK554,sK555,X0),the_carrier(sK555))
| is_often_in(sK554,sK555,X0) ),
inference(global_subsumption_just,[status(thm)],[c_54701,c_2027,c_2028,c_2026,c_54701]) ).
cnf(c_54712,plain,
( X0 != sK555
| X1 != sK554
| ~ related(X0,sK76(X1,X0,X2),X3)
| ~ in(apply_netmap(X1,X0,X3),X2)
| ~ element(X3,the_carrier(X0))
| ~ one_sorted_str(X1)
| is_often_in(X1,X0,X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_173,c_2025]) ).
cnf(c_54713,plain,
( ~ related(sK555,sK76(sK554,sK555,X0),X1)
| ~ in(apply_netmap(sK554,sK555,X1),X0)
| ~ element(X1,the_carrier(sK555))
| ~ one_sorted_str(sK554)
| is_often_in(sK554,sK555,X0)
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54712]) ).
cnf(c_54715,plain,
( ~ element(X1,the_carrier(sK555))
| ~ in(apply_netmap(sK554,sK555,X1),X0)
| ~ related(sK555,sK76(sK554,sK555,X0),X1)
| is_often_in(sK554,sK555,X0) ),
inference(global_subsumption_just,[status(thm)],[c_54713,c_2027,c_2028,c_2026,c_54713]) ).
cnf(c_54716,plain,
( ~ related(sK555,sK76(sK554,sK555,X0),X1)
| ~ in(apply_netmap(sK554,sK555,X1),X0)
| ~ element(X1,the_carrier(sK555))
| is_often_in(sK554,sK555,X0) ),
inference(renaming,[status(thm)],[c_54715]) ).
cnf(c_54730,plain,
( X0 != sK555
| X1 != sK554
| ~ related(X0,sK70(X1,X0,X2),X3)
| ~ is_eventually_in(X1,X0,X2)
| ~ element(X3,the_carrier(X0))
| ~ one_sorted_str(X1)
| in(apply_netmap(X1,X0,X3),X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_154,c_2025]) ).
cnf(c_54731,plain,
( ~ related(sK555,sK70(sK554,sK555,X0),X1)
| ~ element(X1,the_carrier(sK555))
| ~ is_eventually_in(sK554,sK555,X0)
| ~ one_sorted_str(sK554)
| in(apply_netmap(sK554,sK555,X1),X0)
| empty_carrier(sK554)
| empty_carrier(sK555) ),
inference(unflattening,[status(thm)],[c_54730]) ).
cnf(c_54733,plain,
( ~ is_eventually_in(sK554,sK555,X0)
| ~ element(X1,the_carrier(sK555))
| ~ related(sK555,sK70(sK554,sK555,X0),X1)
| in(apply_netmap(sK554,sK555,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_54731,c_2027,c_2028,c_2026,c_54731]) ).
cnf(c_54734,plain,
( ~ related(sK555,sK70(sK554,sK555,X0),X1)
| ~ element(X1,the_carrier(sK555))
| ~ is_eventually_in(sK554,sK555,X0)
| in(apply_netmap(sK554,sK555,X1),X0) ),
inference(renaming,[status(thm)],[c_54733]) ).
cnf(c_313819,plain,
( ~ in(apply_netmap(sK554,sK555,sK77(sK554,sK555,X0,sK76(sK554,sK555,X1))),X1)
| ~ element(sK77(sK554,sK555,X0,sK76(sK554,sK555,X1)),the_carrier(sK555))
| ~ element(sK76(sK554,sK555,X1),the_carrier(sK555))
| ~ is_often_in(sK554,sK555,X0)
| is_often_in(sK554,sK555,X1) ),
inference(superposition,[status(thm)],[c_54385,c_54716]) ).
cnf(c_313841,plain,
( ~ element(sK69(sK554,sK555,X0,sK70(sK554,sK555,X1)),the_carrier(sK555))
| ~ element(sK70(sK554,sK555,X1),the_carrier(sK555))
| ~ is_eventually_in(sK554,sK555,X1)
| in(apply_netmap(sK554,sK555,sK69(sK554,sK555,X0,sK70(sK554,sK555,X1))),X1)
| is_eventually_in(sK554,sK555,X0) ),
inference(superposition,[status(thm)],[c_54558,c_54734]) ).
cnf(c_313868,plain,
( ~ element(sK70(sK554,sK555,X0),the_carrier(sK555))
| ~ is_eventually_in(sK554,sK555,X0)
| in(apply_netmap(sK554,sK555,sK69(sK554,sK555,X1,sK70(sK554,sK555,X0))),X0)
| is_eventually_in(sK554,sK555,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_313841,c_54543]) ).
cnf(c_313879,plain,
( ~ in(apply_netmap(sK554,sK555,sK77(sK554,sK555,X0,sK76(sK554,sK555,X1))),X1)
| ~ element(sK76(sK554,sK555,X1),the_carrier(sK555))
| ~ is_often_in(sK554,sK555,X0)
| is_often_in(sK554,sK555,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_313819,c_54370]) ).
cnf(c_320508,plain,
( ~ in(apply_netmap(sK554,sK555,sK69(sK554,sK555,set_union2(X0,X1),X2)),X1)
| ~ element(X2,the_carrier(sK555))
| is_eventually_in(sK554,sK555,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_386,c_54427]) ).
cnf(c_320753,plain,
( ~ element(sK70(sK554,sK555,X0),the_carrier(sK555))
| ~ is_eventually_in(sK554,sK555,X0)
| is_eventually_in(sK554,sK555,set_union2(X1,X0)) ),
inference(superposition,[status(thm)],[c_313868,c_320508]) ).
cnf(c_321159,plain,
( ~ is_often_in(sK554,sK555,set_difference(X0,X1))
| ~ element(X2,the_carrier(sK555))
| in(apply_netmap(sK554,sK555,sK77(sK554,sK555,set_difference(X0,X1),X2)),X0) ),
inference(superposition,[status(thm)],[c_54400,c_474]) ).
cnf(c_321304,plain,
( ~ element(sK76(sK554,sK555,X0),the_carrier(sK555))
| ~ is_often_in(sK554,sK555,set_difference(X0,X1))
| is_often_in(sK554,sK555,X0) ),
inference(superposition,[status(thm)],[c_321159,c_313879]) ).
cnf(c_321397,plain,
( ~ is_eventually_in(sK554,sK555,X0)
| is_eventually_in(sK554,sK555,set_union2(X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_320753,c_54414,c_320753]) ).
cnf(c_321425,plain,
( ~ is_often_in(sK554,sK555,set_difference(X0,X1))
| is_often_in(sK554,sK555,X0) ),
inference(global_subsumption_just,[status(thm)],[c_321304,c_54703,c_321304]) ).
cnf(c_341817,plain,
set_union2(sK556,sK557) = sK557,
inference(superposition,[status(thm)],[c_2024,c_1684]) ).
cnf(c_342135,plain,
set_union2(sK557,sK556) = sK557,
inference(demodulation,[status(thm)],[c_341817,c_123]) ).
cnf(c_342161,plain,
( ~ is_eventually_in(sK554,sK555,sK556)
| is_eventually_in(sK554,sK555,sK557) ),
inference(superposition,[status(thm)],[c_342135,c_321397]) ).
cnf(c_342761,plain,
set_difference(sK556,sK557) = empty_set,
inference(superposition,[status(thm)],[c_2024,c_1864]) ).
cnf(c_343104,plain,
set_difference(sK557,set_difference(sK557,sK556)) = set_difference(sK556,empty_set),
inference(superposition,[status(thm)],[c_342761,c_125]) ).
cnf(c_343137,plain,
set_difference(sK557,set_difference(sK557,sK556)) = sK556,
inference(demodulation,[status(thm)],[c_343104,c_1876]) ).
cnf(c_343148,plain,
( ~ is_often_in(sK554,sK555,sK556)
| is_often_in(sK554,sK555,sK557) ),
inference(superposition,[status(thm)],[c_343137,c_321425]) ).
cnf(c_344581,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_343148,c_342161,c_2020,c_2021,c_2022,c_2023]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU367+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 01:51:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 73.04/10.82 % SZS status Started for theBenchmark.p
% 73.04/10.82 % SZS status Theorem for theBenchmark.p
% 73.04/10.82
% 73.04/10.82 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 73.04/10.82
% 73.04/10.82 ------ iProver source info
% 73.04/10.82
% 73.04/10.82 git: date: 2023-05-31 18:12:56 +0000
% 73.04/10.82 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 73.04/10.82 git: non_committed_changes: false
% 73.04/10.82 git: last_make_outside_of_git: false
% 73.04/10.82
% 73.04/10.82 ------ Parsing...
% 73.04/10.82 ------ Clausification by vclausify_rel & Parsing by iProver...
% 73.04/10.82
% 73.04/10.82 ------ Preprocessing... sup_sim: 109 sf_s rm: 96 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 5 sf_s rm: 27 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 27 0s sf_e pe_s pe_e
% 73.04/10.82
% 73.04/10.82 ------ Preprocessing... gs_s sp: 18 0s gs_e snvd_s sp: 0 0s snvd_e
% 73.04/10.82
% 73.04/10.82 ------ Preprocessing... sf_s rm: 5 0s sf_e sf_s rm: 0 0s sf_e
% 73.04/10.82 ------ Proving...
% 73.04/10.82 ------ Problem Properties
% 73.04/10.82
% 73.04/10.82
% 73.04/10.82 clauses 1762
% 73.04/10.82 conjectures 8
% 73.04/10.82 EPR 233
% 73.04/10.82 Horn 1193
% 73.04/10.82 unary 205
% 73.04/10.82 binary 441
% 73.04/10.82 lits 5980
% 73.04/10.82 lits eq 684
% 73.04/10.82 fd_pure 0
% 73.04/10.82 fd_pseudo 0
% 73.04/10.82 fd_cond 51
% 73.04/10.82 fd_pseudo_cond 147
% 73.04/10.82 AC symbols 0
% 73.04/10.82
% 73.04/10.82 ------ Schedule dynamic 5 is on
% 73.04/10.82
% 73.04/10.82 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 73.04/10.82
% 73.04/10.82
% 73.04/10.82 ------
% 73.04/10.82 Current options:
% 73.04/10.82 ------
% 73.04/10.82
% 73.04/10.82
% 73.04/10.82
% 73.04/10.82
% 73.04/10.82 ------ Proving...
% 73.04/10.82
% 73.04/10.82
% 73.04/10.82 % SZS status Theorem for theBenchmark.p
% 73.04/10.82
% 73.04/10.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 73.04/10.82
% 73.04/10.83
%------------------------------------------------------------------------------