%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN723+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 03:41:28 PM UTC 2026
% Result : Theorem 1.91s 1.36s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 331 ( 1 unt; 5 def)
% Number of atoms : 1754 ( 0 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 2225 ( 823 ~;1172 |; 150 &)
% ( 78 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 30 ( 29 usr; 26 prp; 0-1 aty)
% Number of functors : 42 ( 42 usr; 35 con; 0-1 aty)
% Number of variables : 547 ( 0 sgn 415 !; 132 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
! [X1] :
( p(X0)
<=> p(X1) )
<=> ( ( ? [X0] : q(X0)
<=> ! [X1] : r(X1) )
<=> ( ( ? [X0] :
! [X1] :
( q(X0)
<=> q(X1) )
<=> ( ? [X0] : r(X0)
<=> ! [X1] : s(X1) ) )
<=> ( ? [X0] :
! [X1] :
( r(X0)
<=> r(X1) )
<=> ( ( ? [X0] : s(X0)
<=> ! [X1] : p(X1) )
<=> ( ? [X0] :
! [X1] :
( s(X0)
<=> s(X1) )
<=> ( ? [X0] : p(X0)
<=> ! [X1] : q(X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm138) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( p(X0)
<=> p(X1) )
<=> ( ( ? [X0] : q(X0)
<=> ! [X1] : r(X1) )
<=> ( ( ? [X0] :
! [X1] :
( q(X0)
<=> q(X1) )
<=> ( ? [X0] : r(X0)
<=> ! [X1] : s(X1) ) )
<=> ( ? [X0] :
! [X1] :
( r(X0)
<=> r(X1) )
<=> ( ( ? [X0] : s(X0)
<=> ! [X1] : p(X1) )
<=> ( ? [X0] :
! [X1] :
( s(X0)
<=> s(X1) )
<=> ( ? [X0] : p(X0)
<=> ! [X1] : q(X1) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
! [X1] :
( p(X0)
<=> p(X1) )
<=> ( ( ? [X2] : q(X2)
<=> ! [X3] : r(X3) )
<=> ( ( ? [X4] :
! [X5] :
( q(X4)
<=> q(X5) )
<=> ( ? [X6] : r(X6)
<=> ! [X7] : s(X7) ) )
<=> ( ? [X8] :
! [X9] :
( r(X8)
<=> r(X9) )
<=> ( ( ? [X10] : s(X10)
<=> ! [X11] : p(X11) )
<=> ( ? [X12] :
! [X13] :
( s(X12)
<=> s(X13) )
<=> ( ? [X14] : p(X14)
<=> ! [X15] : q(X15) ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
! [X1] :
( p(X0)
<=> p(X1) )
<~> ( ( ? [X2] : q(X2)
<=> ! [X3] : r(X3) )
<=> ( ( ? [X4] :
! [X5] :
( q(X4)
<=> q(X5) )
<=> ( ? [X6] : r(X6)
<=> ! [X7] : s(X7) ) )
<=> ( ? [X8] :
! [X9] :
( r(X8)
<=> r(X9) )
<=> ( ( ? [X10] : s(X10)
<=> ! [X11] : p(X11) )
<=> ( ? [X12] :
! [X13] :
( s(X12)
<=> s(X13) )
<=> ( ? [X14] : p(X14)
<=> ! [X15] : q(X15) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
( ( ~ sP4
| ( ( ( ( ? [X2] : q(X2)
| ! [X3] : r(X3) )
& ( ! [X2] : ~ q(X2)
| ? [X3] : ~ r(X3) ) )
| ( ( ~ sP2
| sP3 )
& ( ~ sP3
| sP2 ) ) )
& ( ( ( sP2
| sP3 )
& ( ~ sP2
| ~ sP3 ) )
| ( ( ! [X2] : ~ q(X2)
| ! [X3] : r(X3) )
& ( ? [X3] : ~ r(X3)
| ? [X2] : q(X2) ) ) ) ) )
& ( ( ( ( ( ! [X2] : ~ q(X2)
| ! [X3] : r(X3) )
& ( ? [X3] : ~ r(X3)
| ? [X2] : q(X2) ) )
| ( ( ~ sP2
| sP3 )
& ( ~ sP3
| sP2 ) ) )
& ( ( ( ? [X2] : q(X2)
| ! [X3] : r(X3) )
& ( ! [X2] : ~ q(X2)
| ? [X3] : ~ r(X3) ) )
| ( ( sP2
| sP3 )
& ( ~ sP2
| ~ sP3 ) ) ) )
| sP4 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
( ( ~ sP4
| ( ( ( ( ? [X15] : q(X15)
| ! [X14] : r(X14) )
& ( ! [X13] : ~ q(X13)
| ? [X12] : ~ r(X12) ) )
| ( ( ~ sP2
| sP3 )
& ( ~ sP3
| sP2 ) ) )
& ( ( ( sP2
| sP3 )
& ( ~ sP2
| ~ sP3 ) )
| ( ( ! [X11] : ~ q(X11)
| ! [X10] : r(X10) )
& ( ? [X9] : ~ r(X9)
| ? [X8] : q(X8) ) ) ) ) )
& ( ( ( ( ( ! [X7] : ~ q(X7)
| ! [X6] : r(X6) )
& ( ? [X5] : ~ r(X5)
| ? [X4] : q(X4) ) )
| ( ( ~ sP2
| sP3 )
& ( ~ sP3
| sP2 ) ) )
& ( ( ( ? [X3] : q(X3)
| ! [X2] : r(X2) )
& ( ! [X1] : ~ q(X1)
| ? [X0] : ~ r(X0) ) )
| ( ( sP2
| sP3 )
& ( ~ sP2
| ~ sP3 ) ) ) )
| sP4 ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
( ( ~ sP4
| ( ( ( ( q(sK12)
| ! [X14] : r(X14) )
& ( ! [X13] : ~ q(X13)
| ~ r(sK11) ) )
| ( ( ~ sP2
| sP3 )
& ( ~ sP3
| sP2 ) ) )
& ( ( ( sP2
| sP3 )
& ( ~ sP2
| ~ sP3 ) )
| ( ( ! [X11] : ~ q(X11)
| ! [X10] : r(X10) )
& ( ~ r(sK10)
| q(sK9) ) ) ) ) )
& ( ( ( ( ( ! [X7] : ~ q(X7)
| ! [X6] : r(X6) )
& ( ~ r(sK8)
| q(sK7) ) )
| ( ( ~ sP2
| sP3 )
& ( ~ sP3
| sP2 ) ) )
& ( ( ( q(sK6)
| ! [X2] : r(X2) )
& ( ! [X1] : ~ q(X1)
| ~ r(sK5) ) )
| ( ( sP2
| sP3 )
& ( ~ sP2
| ~ sP3 ) ) ) )
| sP4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK5),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8),skolemize(X8,sK9),skolemize(X9,sK10),skolemize(X12,sK11),skolemize(X15,sK12)],[f12]) ).
fof(f14,plain,
( ( ~ sP3
| ( ( ! [X8] :
? [X9] :
( ( r(X8)
| r(X9) )
& ( ~ r(X8)
| ~ r(X9) ) )
| sP1 )
& ( ~ sP1
| ? [X8] :
! [X9] :
( ( ~ r(X8)
| r(X9) )
& ( ~ r(X9)
| r(X8) ) ) ) ) )
& ( ( ( ? [X8] :
! [X9] :
( ( ~ r(X8)
| r(X9) )
& ( ~ r(X9)
| r(X8) ) )
| sP1 )
& ( ! [X8] :
? [X9] :
( ( r(X8)
| r(X9) )
& ( ~ r(X8)
| ~ r(X9) ) )
| ~ sP1 ) )
| sP3 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f15,plain,
( ( ~ sP3
| ( ( ! [X6] :
? [X7] :
( ( r(X6)
| r(X7) )
& ( ~ r(X6)
| ~ r(X7) ) )
| sP1 )
& ( ~ sP1
| ? [X4] :
! [X5] :
( ( ~ r(X4)
| r(X5) )
& ( ~ r(X5)
| r(X4) ) ) ) ) )
& ( ( ( ? [X2] :
! [X3] :
( ( ~ r(X2)
| r(X3) )
& ( ~ r(X3)
| r(X2) ) )
| sP1 )
& ( ! [X0] :
? [X1] :
( ( r(X0)
| r(X1) )
& ( ~ r(X0)
| ~ r(X1) ) )
| ~ sP1 ) )
| sP3 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
( ( ~ sP3
| ( ( ! [X6] :
( ( r(X6)
| r(sK16(X6)) )
& ( ~ r(X6)
| ~ r(sK16(X6)) ) )
| sP1 )
& ( ~ sP1
| ! [X5] :
( ( ~ r(sK15)
| r(X5) )
& ( ~ r(X5)
| r(sK15) ) ) ) ) )
& ( ( ( ! [X3] :
( ( ~ r(sK14)
| r(X3) )
& ( ~ r(X3)
| r(sK14) ) )
| sP1 )
& ( ! [X0] :
( ( r(X0)
| r(sK13(X0)) )
& ( ~ r(X0)
| ~ r(sK13(X0)) ) )
| ~ sP1 ) )
| sP3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X1,sK13(X0)),skolemize(X2,sK14),skolemize(X4,sK15),skolemize(X7,sK16(X6))],[f15]) ).
fof(f17,plain,
( ( ~ sP2
| ( ( ! [X4] :
? [X5] :
( ( q(X4)
| q(X5) )
& ( ~ q(X4)
| ~ q(X5) ) )
| ( ( ! [X6] : ~ r(X6)
| ! [X7] : s(X7) )
& ( ? [X7] : ~ s(X7)
| ? [X6] : r(X6) ) ) )
& ( ( ( ? [X6] : r(X6)
| ! [X7] : s(X7) )
& ( ! [X6] : ~ r(X6)
| ? [X7] : ~ s(X7) ) )
| ? [X4] :
! [X5] :
( ( ~ q(X4)
| q(X5) )
& ( ~ q(X5)
| q(X4) ) ) ) ) )
& ( ( ( ? [X4] :
! [X5] :
( ( ~ q(X4)
| q(X5) )
& ( ~ q(X5)
| q(X4) ) )
| ( ( ! [X6] : ~ r(X6)
| ! [X7] : s(X7) )
& ( ? [X7] : ~ s(X7)
| ? [X6] : r(X6) ) ) )
& ( ! [X4] :
? [X5] :
( ( q(X4)
| q(X5) )
& ( ~ q(X4)
| ~ q(X5) ) )
| ( ( ? [X6] : r(X6)
| ! [X7] : s(X7) )
& ( ! [X6] : ~ r(X6)
| ? [X7] : ~ s(X7) ) ) ) )
| sP2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f18,plain,
( ( ~ sP2
| ( ( ! [X22] :
? [X23] :
( ( q(X22)
| q(X23) )
& ( ~ q(X22)
| ~ q(X23) ) )
| ( ( ! [X21] : ~ r(X21)
| ! [X20] : s(X20) )
& ( ? [X19] : ~ s(X19)
| ? [X18] : r(X18) ) ) )
& ( ( ( ? [X17] : r(X17)
| ! [X16] : s(X16) )
& ( ! [X15] : ~ r(X15)
| ? [X14] : ~ s(X14) ) )
| ? [X12] :
! [X13] :
( ( ~ q(X12)
| q(X13) )
& ( ~ q(X13)
| q(X12) ) ) ) ) )
& ( ( ( ? [X10] :
! [X11] :
( ( ~ q(X10)
| q(X11) )
& ( ~ q(X11)
| q(X10) ) )
| ( ( ! [X9] : ~ r(X9)
| ! [X8] : s(X8) )
& ( ? [X7] : ~ s(X7)
| ? [X6] : r(X6) ) ) )
& ( ! [X4] :
? [X5] :
( ( q(X4)
| q(X5) )
& ( ~ q(X4)
| ~ q(X5) ) )
| ( ( ? [X3] : r(X3)
| ! [X2] : s(X2) )
& ( ! [X1] : ~ r(X1)
| ? [X0] : ~ s(X0) ) ) ) )
| sP2 ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
( ( ~ sP2
| ( ( ! [X22] :
( ( q(X22)
| q(sK28(X22)) )
& ( ~ q(X22)
| ~ q(sK28(X22)) ) )
| ( ( ! [X21] : ~ r(X21)
| ! [X20] : s(X20) )
& ( ~ s(sK27)
| r(sK26) ) ) )
& ( ( ( r(sK25)
| ! [X16] : s(X16) )
& ( ! [X15] : ~ r(X15)
| ~ s(sK24) ) )
| ! [X13] :
( ( ~ q(sK23)
| q(X13) )
& ( ~ q(X13)
| q(sK23) ) ) ) ) )
& ( ( ( ! [X11] :
( ( ~ q(sK22)
| q(X11) )
& ( ~ q(X11)
| q(sK22) ) )
| ( ( ! [X9] : ~ r(X9)
| ! [X8] : s(X8) )
& ( ~ s(sK21)
| r(sK20) ) ) )
& ( ! [X4] :
( ( q(X4)
| q(sK19(X4)) )
& ( ~ q(X4)
| ~ q(sK19(X4)) ) )
| ( ( r(sK18)
| ! [X2] : s(X2) )
& ( ! [X1] : ~ r(X1)
| ~ s(sK17) ) ) ) )
| sP2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28]),skolemize(X0,sK17),skolemize(X3,sK18),skolemize(X5,sK19(X4)),skolemize(X6,sK20),skolemize(X7,sK21),skolemize(X10,sK22),skolemize(X12,sK23),skolemize(X14,sK24),skolemize(X17,sK25),skolemize(X18,sK26),skolemize(X19,sK27),skolemize(X23,sK28(X22))],[f18]) ).
fof(f20,plain,
( ( ~ sP1
| ( ( ( ( ? [X10] : s(X10)
| ! [X11] : p(X11) )
& ( ! [X10] : ~ s(X10)
| ? [X11] : ~ p(X11) ) )
| sP0 )
& ( ~ sP0
| ( ( ! [X10] : ~ s(X10)
| ! [X11] : p(X11) )
& ( ? [X11] : ~ p(X11)
| ? [X10] : s(X10) ) ) ) ) )
& ( ( ( ( ( ! [X10] : ~ s(X10)
| ! [X11] : p(X11) )
& ( ? [X11] : ~ p(X11)
| ? [X10] : s(X10) ) )
| sP0 )
& ( ( ( ? [X10] : s(X10)
| ! [X11] : p(X11) )
& ( ! [X10] : ~ s(X10)
| ? [X11] : ~ p(X11) ) )
| ~ sP0 ) )
| sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f21,plain,
( ( ~ sP1
| ( ( ( ( ? [X15] : s(X15)
| ! [X14] : p(X14) )
& ( ! [X13] : ~ s(X13)
| ? [X12] : ~ p(X12) ) )
| sP0 )
& ( ~ sP0
| ( ( ! [X11] : ~ s(X11)
| ! [X10] : p(X10) )
& ( ? [X9] : ~ p(X9)
| ? [X8] : s(X8) ) ) ) ) )
& ( ( ( ( ( ! [X7] : ~ s(X7)
| ! [X6] : p(X6) )
& ( ? [X5] : ~ p(X5)
| ? [X4] : s(X4) ) )
| sP0 )
& ( ( ( ? [X3] : s(X3)
| ! [X2] : p(X2) )
& ( ! [X1] : ~ s(X1)
| ? [X0] : ~ p(X0) ) )
| ~ sP0 ) )
| sP1 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
( ( ~ sP1
| ( ( ( ( s(sK36)
| ! [X14] : p(X14) )
& ( ! [X13] : ~ s(X13)
| ~ p(sK35) ) )
| sP0 )
& ( ~ sP0
| ( ( ! [X11] : ~ s(X11)
| ! [X10] : p(X10) )
& ( ~ p(sK34)
| s(sK33) ) ) ) ) )
& ( ( ( ( ( ! [X7] : ~ s(X7)
| ! [X6] : p(X6) )
& ( ~ p(sK32)
| s(sK31) ) )
| sP0 )
& ( ( ( s(sK30)
| ! [X2] : p(X2) )
& ( ! [X1] : ~ s(X1)
| ~ p(sK29) ) )
| ~ sP0 ) )
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32,sK33,sK34,sK35,sK36]),skolemize(X0,sK29),skolemize(X3,sK30),skolemize(X4,sK31),skolemize(X5,sK32),skolemize(X8,sK33),skolemize(X9,sK34),skolemize(X12,sK35),skolemize(X15,sK36)],[f21]) ).
fof(f26,plain,
( ( ? [X0] :
! [X1] :
( ( ~ p(X0)
| p(X1) )
& ( ~ p(X1)
| p(X0) ) )
| sP4 )
& ( ! [X0] :
? [X1] :
( ( p(X0)
| p(X1) )
& ( ~ p(X0)
| ~ p(X1) ) )
| ~ sP4 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f27,plain,
( ( ? [X2] :
! [X3] :
( ( ~ p(X2)
| p(X3) )
& ( ~ p(X3)
| p(X2) ) )
| sP4 )
& ( ! [X0] :
? [X1] :
( ( p(X0)
| p(X1) )
& ( ~ p(X0)
| ~ p(X1) ) )
| ~ sP4 ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
( ( ! [X3] :
( ( ~ p(sK50)
| p(X3) )
& ( ~ p(X3)
| p(sK50) ) )
| sP4 )
& ( ! [X0] :
( ( p(X0)
| p(sK49(X0)) )
& ( ~ p(X0)
| ~ p(sK49(X0)) ) )
| ~ sP4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50]),skolemize(X1,sK49(X0)),skolemize(X2,sK50)],[f27]) ).
fof(f29,plain,
! [X14] :
( ~ sP4
| q(sK12)
| r(X14)
| ~ sP2
| sP3 ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X13] :
( ~ sP4
| ~ q(X13)
| ~ r(sK11)
| ~ sP2
| sP3 ),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
! [X14] :
( ~ sP4
| q(sK12)
| r(X14)
| ~ sP3
| sP2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
! [X13] :
( ~ sP4
| ~ q(X13)
| ~ r(sK11)
| ~ sP3
| sP2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f33,plain,
! [X10,X11] :
( ~ sP4
| sP2
| sP3
| ~ q(X11)
| r(X10) ),
inference(cnf_transformation,[],[f13]) ).
fof(f34,plain,
! [X10,X11] :
( ~ sP4
| ~ sP2
| ~ sP3
| ~ q(X11)
| r(X10) ),
inference(cnf_transformation,[],[f13]) ).
fof(f35,plain,
( ~ sP4
| sP2
| sP3
| ~ r(sK10)
| q(sK9) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
( ~ sP4
| ~ sP2
| ~ sP3
| ~ r(sK10)
| q(sK9) ),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
! [X6,X7] :
( ~ q(X7)
| r(X6)
| ~ sP2
| sP3
| sP4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
( ~ r(sK8)
| q(sK7)
| ~ sP2
| sP3
| sP4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f39,plain,
! [X6,X7] :
( ~ q(X7)
| r(X6)
| ~ sP3
| sP2
| sP4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
( ~ r(sK8)
| q(sK7)
| ~ sP3
| sP2
| sP4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f41,plain,
! [X2] :
( q(sK6)
| r(X2)
| sP2
| sP3
| sP4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f42,plain,
! [X1] :
( ~ q(X1)
| ~ r(sK5)
| sP2
| sP3
| sP4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f43,plain,
! [X2] :
( q(sK6)
| r(X2)
| ~ sP2
| ~ sP3
| sP4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f44,plain,
! [X1] :
( ~ q(X1)
| ~ r(sK5)
| ~ sP2
| ~ sP3
| sP4 ),
inference(cnf_transformation,[],[f13]) ).
fof(f45,plain,
! [X6] :
( ~ sP3
| r(X6)
| r(sK16(X6))
| sP1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X6] :
( ~ sP3
| ~ r(X6)
| ~ r(sK16(X6))
| sP1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f47,plain,
! [X5] :
( ~ sP3
| ~ sP1
| ~ r(sK15)
| r(X5) ),
inference(cnf_transformation,[],[f16]) ).
fof(f48,plain,
! [X5] :
( ~ sP3
| ~ sP1
| ~ r(X5)
| r(sK15) ),
inference(cnf_transformation,[],[f16]) ).
fof(f49,plain,
! [X3] :
( ~ r(sK14)
| r(X3)
| sP1
| sP3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f50,plain,
! [X3] :
( ~ r(X3)
| r(sK14)
| sP1
| sP3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f51,plain,
! [X0] :
( r(X0)
| r(sK13(X0))
| ~ sP1
| sP3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f52,plain,
! [X0] :
( ~ r(X0)
| ~ r(sK13(X0))
| ~ sP1
| sP3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f53,plain,
! [X21,X22,X20] :
( ~ sP2
| q(X22)
| q(sK28(X22))
| ~ r(X21)
| s(X20) ),
inference(cnf_transformation,[],[f19]) ).
fof(f54,plain,
! [X21,X22,X20] :
( ~ sP2
| ~ q(X22)
| ~ q(sK28(X22))
| ~ r(X21)
| s(X20) ),
inference(cnf_transformation,[],[f19]) ).
fof(f55,plain,
! [X22] :
( ~ sP2
| q(X22)
| q(sK28(X22))
| ~ s(sK27)
| r(sK26) ),
inference(cnf_transformation,[],[f19]) ).
fof(f56,plain,
! [X22] :
( ~ sP2
| ~ q(X22)
| ~ q(sK28(X22))
| ~ s(sK27)
| r(sK26) ),
inference(cnf_transformation,[],[f19]) ).
fof(f57,plain,
! [X16,X13] :
( ~ sP2
| r(sK25)
| s(X16)
| ~ q(sK23)
| q(X13) ),
inference(cnf_transformation,[],[f19]) ).
fof(f58,plain,
! [X15,X13] :
( ~ sP2
| ~ r(X15)
| ~ s(sK24)
| ~ q(sK23)
| q(X13) ),
inference(cnf_transformation,[],[f19]) ).
fof(f59,plain,
! [X16,X13] :
( ~ sP2
| r(sK25)
| s(X16)
| ~ q(X13)
| q(sK23) ),
inference(cnf_transformation,[],[f19]) ).
fof(f60,plain,
! [X15,X13] :
( ~ sP2
| ~ r(X15)
| ~ s(sK24)
| ~ q(X13)
| q(sK23) ),
inference(cnf_transformation,[],[f19]) ).
fof(f61,plain,
! [X11,X8,X9] :
( ~ q(sK22)
| q(X11)
| ~ r(X9)
| s(X8)
| sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f62,plain,
! [X11,X8,X9] :
( ~ q(X11)
| q(sK22)
| ~ r(X9)
| s(X8)
| sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f63,plain,
! [X11] :
( ~ q(sK22)
| q(X11)
| ~ s(sK21)
| r(sK20)
| sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f64,plain,
! [X11] :
( ~ q(X11)
| q(sK22)
| ~ s(sK21)
| r(sK20)
| sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f65,plain,
! [X2,X4] :
( q(X4)
| q(sK19(X4))
| r(sK18)
| s(X2)
| sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f66,plain,
! [X2,X4] :
( ~ q(X4)
| ~ q(sK19(X4))
| r(sK18)
| s(X2)
| sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f67,plain,
! [X1,X4] :
( q(X4)
| q(sK19(X4))
| ~ r(X1)
| ~ s(sK17)
| sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f68,plain,
! [X1,X4] :
( ~ q(X4)
| ~ q(sK19(X4))
| ~ r(X1)
| ~ s(sK17)
| sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f69,plain,
! [X14] :
( ~ sP1
| s(sK36)
| p(X14)
| sP0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f70,plain,
! [X13] :
( ~ sP1
| ~ s(X13)
| ~ p(sK35)
| sP0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f71,plain,
! [X10,X11] :
( ~ sP1
| ~ sP0
| ~ s(X11)
| p(X10) ),
inference(cnf_transformation,[],[f22]) ).
fof(f72,plain,
( ~ sP1
| ~ sP0
| ~ p(sK34)
| s(sK33) ),
inference(cnf_transformation,[],[f22]) ).
fof(f73,plain,
! [X6,X7] :
( ~ s(X7)
| p(X6)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f74,plain,
( ~ p(sK32)
| s(sK31)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f75,plain,
! [X2] :
( s(sK30)
| p(X2)
| ~ sP0
| sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f76,plain,
! [X1] :
( ~ s(X1)
| ~ p(sK29)
| ~ sP0
| sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f93,plain,
! [X3] :
( ~ p(sK50)
| p(X3)
| sP4 ),
inference(cnf_transformation,[],[f28]) ).
fof(f94,plain,
! [X3] :
( ~ p(X3)
| p(sK50)
| sP4 ),
inference(cnf_transformation,[],[f28]) ).
fof(f95,plain,
! [X0] :
( p(X0)
| p(sK49(X0))
| ~ sP4 ),
inference(cnf_transformation,[],[f28]) ).
fof(f96,plain,
! [X0] :
( ~ p(X0)
| ~ p(sK49(X0))
| ~ sP4 ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,plain,
! [X0: $i] :
( sP4
| ~ sP2
| ~ sP3
| ~ r(sK5)
| ~ q(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_50,plain,
! [X0: $i] :
( sP4
| q(sK6)
| r(X0)
| ~ sP2
| ~ sP3 ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_51,plain,
! [X0: $i] :
( sP2
| sP3
| sP4
| ~ r(sK5)
| ~ q(X0) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_52,plain,
! [X0: $i] :
( sP2
| sP3
| sP4
| q(sK6)
| r(X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_53,plain,
( sP2
| sP4
| q(sK7)
| ~ sP3
| ~ r(sK8) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( sP2
| sP4
| r(X1)
| ~ sP3
| ~ q(X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_55,plain,
( sP3
| sP4
| q(sK7)
| ~ sP2
| ~ r(sK8) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( sP3
| sP4
| r(X1)
| ~ sP2
| ~ q(X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_57,plain,
( q(sK9)
| ~ sP2
| ~ sP3
| ~ sP4
| ~ r(sK10) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_58,plain,
( sP2
| sP3
| q(sK9)
| ~ sP4
| ~ r(sK10) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( r(X1)
| ~ sP2
| ~ sP3
| ~ sP4
| ~ q(X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( sP2
| sP3
| r(X1)
| ~ sP4
| ~ q(X0) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_61,plain,
! [X0: $i] :
( sP2
| ~ sP3
| ~ sP4
| ~ r(sK11)
| ~ q(X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_62,plain,
! [X0: $i] :
( sP2
| q(sK12)
| r(X0)
| ~ sP3
| ~ sP4 ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_63,plain,
! [X0: $i] :
( sP3
| ~ sP2
| ~ sP4
| ~ r(sK11)
| ~ q(X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_64,plain,
! [X0: $i] :
( sP3
| q(sK12)
| r(X0)
| ~ sP2
| ~ sP4 ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_65,plain,
! [X0: $i] :
( sP3
| ~ sP1
| ~ r(X0)
| ~ r(sK13(X0)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_66,plain,
! [X0: $i] :
( sP3
| r(X0)
| r(sK13(X0))
| ~ sP1 ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_67,plain,
! [X0: $i] :
( sP1
| sP3
| r(sK14)
| ~ r(X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_68,plain,
! [X0: $i] :
( sP1
| sP3
| r(X0)
| ~ r(sK14) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_69,plain,
! [X0: $i] :
( r(sK15)
| ~ sP1
| ~ sP3
| ~ r(X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_70,plain,
! [X0: $i] :
( r(X0)
| ~ sP1
| ~ sP3
| ~ r(sK15) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_71,plain,
! [X0: $i] :
( sP1
| ~ sP3
| ~ r(X0)
| ~ r(sK16(X0)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_72,plain,
! [X0: $i] :
( sP1
| r(X0)
| r(sK16(X0))
| ~ sP3 ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sP2
| ~ s(sK17)
| ~ q(X0)
| ~ r(X1)
| ~ q(sK19(X0)) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( sP2
| q(X1)
| q(sK19(X1))
| ~ s(sK17)
| ~ r(X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( sP2
| r(sK18)
| s(X1)
| ~ q(X0)
| ~ q(sK19(X0)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( sP2
| r(sK18)
| s(X1)
| q(X0)
| q(sK19(X0)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_77,plain,
! [X0: $i] :
( sP2
| q(sK22)
| r(sK20)
| ~ s(sK21)
| ~ q(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_78,plain,
! [X0: $i] :
( sP2
| r(sK20)
| q(X0)
| ~ s(sK21)
| ~ q(sK22) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2
| q(sK22)
| s(X2)
| ~ q(X1)
| ~ r(X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2
| s(X2)
| q(X1)
| ~ q(sK22)
| ~ r(X0) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( q(sK23)
| ~ sP2
| ~ s(sK24)
| ~ q(X1)
| ~ r(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( q(sK23)
| r(sK25)
| s(X1)
| ~ sP2
| ~ q(X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( q(X1)
| ~ sP2
| ~ s(sK24)
| ~ q(sK23)
| ~ r(X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( r(sK25)
| s(X1)
| q(X0)
| ~ sP2
| ~ q(sK23) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_85,plain,
! [X0: $i] :
( r(sK26)
| ~ sP2
| ~ s(sK27)
| ~ q(X0)
| ~ q(sK28(X0)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_86,plain,
! [X0: $i] :
( r(sK26)
| q(X0)
| q(sK28(X0))
| ~ sP2
| ~ s(sK27) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( s(X2)
| ~ sP2
| ~ q(X0)
| ~ r(X1)
| ~ q(sK28(X0)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( s(X2)
| q(X1)
| q(sK28(X1))
| ~ sP2
| ~ r(X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_89,plain,
! [X0: $i] :
( sP1
| ~ sP0
| ~ p(sK29)
| ~ s(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_90,plain,
! [X0: $i] :
( sP1
| s(sK30)
| p(X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_91,plain,
( sP0
| sP1
| s(sK31)
| ~ p(sK32) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( sP0
| sP1
| p(X1)
| ~ s(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_93,plain,
( s(sK33)
| ~ sP0
| ~ sP1
| ~ p(sK34) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( p(X1)
| ~ sP0
| ~ sP1
| ~ s(X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_95,plain,
! [X0: $i] :
( sP0
| ~ sP1
| ~ p(sK35)
| ~ s(X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_96,plain,
! [X0: $i] :
( sP0
| s(sK36)
| p(X0)
| ~ sP1 ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_113,negated_conjecture,
! [X0: $i] :
( ~ sP4
| ~ p(X0)
| ~ p(sK49(X0)) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_114,negated_conjecture,
! [X0: $i] :
( p(X0)
| p(sK49(X0))
| ~ sP4 ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_115,negated_conjecture,
! [X0: $i] :
( sP4
| p(sK50)
| ~ p(X0) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_116,negated_conjecture,
! [X0: $i] :
( sP4
| p(X0)
| ~ p(sK50) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_118,plain,
( sP4
| p(sK50)
| ~ p(sK22) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_119,plain,
( p(sK22)
| p(sK49(sK22))
| ~ sP4 ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_121,plain,
( sP0
| sP1
| p(sK22)
| ~ s(sK22) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_129,plain,
( sP0
| ~ sP1
| ~ p(sK35)
| ~ s(sK22) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_130,plain,
( p(sK22)
| ~ sP0
| ~ sP1
| ~ s(sK22) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_134,plain,
( sP3
| q(sK12)
| r(sK22)
| ~ sP2
| ~ sP4 ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_136,plain,
( sP2
| sP3
| r(sK22)
| ~ sP4
| ~ q(sK22) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_137,plain,
( sP3
| sP4
| r(sK22)
| ~ sP2
| ~ q(sK22) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_138,plain,
( sP2
| sP4
| r(sK22)
| ~ sP3
| ~ q(sK22) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_155,plain,
( r(sK22)
| ~ sP2
| ~ sP3
| ~ sP4
| ~ q(sK22) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_156,plain,
( sP4
| ~ sP2
| ~ sP3
| ~ q(sK22)
| ~ r(sK5) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_162,plain,
( q(sK22)
| r(sK26)
| q(sK28(sK22))
| ~ sP2
| ~ s(sK27) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_173,plain,
( r(sK26)
| ~ sP2
| ~ s(sK27)
| ~ q(sK22)
| ~ q(sK28(sK22)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_174,plain,
( sP2
| ~ s(sK17)
| ~ q(sK22)
| ~ r(sK22)
| ~ q(sK19(sK22)) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_2500,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2
| r(X2)
| ~ sP3
| ~ p(X0)
| ~ q(X1)
| ~ p(sK49(X0)) ),
inference(resolution,[status(thm)],[c_54,c_113]) ).
tcf(c_2501,plain,
( sP2
| r(sK22)
| ~ sP3
| ~ p(sK22)
| ~ q(sK22)
| ~ p(sK49(sK22)) ),
inference(instantiation,[status(thm)],[c_2500]) ).
tcf(c_2910,plain,
! [X0: $i,X1: $i] :
( p(X1)
| p(sK49(X1))
| ~ sP2
| ~ sP3
| ~ r(sK5)
| ~ q(X0) ),
inference(resolution,[status(thm)],[c_49,c_114]) ).
tcf(c_2911,plain,
( p(sK22)
| p(sK49(sK22))
| ~ sP2
| ~ sP3
| ~ q(sK22)
| ~ r(sK5) ),
inference(instantiation,[status(thm)],[c_2910]) ).
tcf(c_3290,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_3291,negated_conjecture,
( iPr_def_10
| sP4
| ~ p(sK50) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_3292,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ~ p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_115]) ).
tcf(c_3293,negated_conjecture,
( iPr_def_11
| sP4
| p(sK50) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_115]) ).
tcf(c_3317,plain,
( iPr_def_10
| sP0
| s(sK36)
| ~ sP1 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_96]) ).
tcf(c_3318,plain,
( iPr_def_16
| sP0
| ~ sP1
| ~ p(sK35) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_95]) ).
tcf(c_3319,plain,
( iPr_def_16
| iPr_def_10
| ~ sP0
| ~ sP1 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_94]) ).
tcf(c_3320,plain,
( iPr_def_16
| iPr_def_10
| sP0
| sP1 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_92]) ).
tcf(c_3321,plain,
( iPr_def_10
| sP1
| s(sK30)
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_90]) ).
tcf(c_3322,plain,
( iPr_def_16
| sP1
| ~ sP0
| ~ p(sK29) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_89]) ).
tcf(c_3323,plain,
! [X0: $i] :
( ~ iPr_def_19
| q(sK28(X0))
| q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_19])],[c_88]) ).
tcf(c_3324,plain,
! [X0: $i] :
( ~ iPr_def_20
| ~ r(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_20])],[c_88]) ).
tcf(c_3325,plain,
( iPr_def_20
| iPr_def_19
| iPr_def_15
| ~ sP2 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_88]) ).
tcf(c_3326,plain,
! [X0: $i] :
( ~ iPr_def_21
| ~ q(sK28(X0))
| ~ q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_21])],[c_87]) ).
tcf(c_3327,plain,
( iPr_def_21
| iPr_def_20
| iPr_def_15
| ~ sP2 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_87]) ).
tcf(c_3330,plain,
( iPr_def_15
| iPr_def_12
| r(sK25)
| ~ sP2
| ~ q(sK23) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_84]) ).
tcf(c_3331,plain,
( iPr_def_20
| iPr_def_12
| ~ sP2
| ~ s(sK24)
| ~ q(sK23) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_83]) ).
tcf(c_3332,plain,
! [X0: $i] :
( ~ iPr_def_22
| ~ q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_22])],[c_82]) ).
tcf(c_3333,plain,
( iPr_def_22
| iPr_def_15
| q(sK23)
| r(sK25)
| ~ sP2 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_82]) ).
tcf(c_3334,plain,
( iPr_def_22
| iPr_def_20
| q(sK23)
| ~ sP2
| ~ s(sK24) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_81]) ).
tcf(c_3335,plain,
( iPr_def_20
| iPr_def_15
| iPr_def_12
| sP2
| ~ q(sK22) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_80]) ).
tcf(c_3336,plain,
( iPr_def_22
| iPr_def_20
| iPr_def_15
| sP2
| q(sK22) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_79]) ).
tcf(c_3337,plain,
( iPr_def_12
| sP2
| r(sK20)
| ~ s(sK21)
| ~ q(sK22) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_78]) ).
tcf(c_3338,plain,
( iPr_def_22
| sP2
| q(sK22)
| r(sK20)
| ~ s(sK21) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_77]) ).
tcf(c_3339,plain,
! [X0: $i] :
( ~ iPr_def_23
| q(sK19(X0))
| q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_23])],[c_76]) ).
tcf(c_3340,plain,
( iPr_def_23
| iPr_def_15
| sP2
| r(sK18) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_76]) ).
tcf(c_3341,plain,
! [X0: $i] :
( ~ iPr_def_24
| ~ q(sK19(X0))
| ~ q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_24])],[c_75]) ).
tcf(c_3342,plain,
( iPr_def_24
| iPr_def_15
| sP2
| r(sK18) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_75]) ).
tcf(c_3343,plain,
( iPr_def_23
| iPr_def_20
| sP2
| ~ s(sK17) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_74]) ).
tcf(c_3344,plain,
( iPr_def_24
| iPr_def_20
| sP2
| ~ s(sK17) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_73]) ).
tcf(c_3349,plain,
! [X0: $i] :
( ~ iPr_def_27
| r(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_27])],[c_70]) ).
tcf(c_3350,plain,
( iPr_def_27
| ~ sP1
| ~ sP3
| ~ r(sK15) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_70]) ).
tcf(c_3351,plain,
( iPr_def_20
| r(sK15)
| ~ sP1
| ~ sP3 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_69]) ).
tcf(c_3352,plain,
( iPr_def_27
| sP1
| sP3
| ~ r(sK14) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_68]) ).
tcf(c_3353,plain,
( iPr_def_20
| sP1
| sP3
| r(sK14) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_67]) ).
tcf(c_3358,plain,
( iPr_def_27
| sP3
| q(sK12)
| ~ sP2
| ~ sP4 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_64]) ).
tcf(c_3359,plain,
( iPr_def_22
| sP3
| ~ sP2
| ~ sP4
| ~ r(sK11) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_63]) ).
tcf(c_3360,plain,
( iPr_def_27
| sP2
| q(sK12)
| ~ sP3
| ~ sP4 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_62]) ).
tcf(c_3361,plain,
( iPr_def_22
| sP2
| ~ sP3
| ~ sP4
| ~ r(sK11) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_61]) ).
tcf(c_3362,plain,
( iPr_def_27
| iPr_def_22
| sP2
| sP3
| ~ sP4 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_60]) ).
tcf(c_3363,plain,
( iPr_def_27
| iPr_def_22
| ~ sP2
| ~ sP3
| ~ sP4 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_59]) ).
tcf(c_3364,plain,
( iPr_def_27
| iPr_def_22
| sP3
| sP4
| ~ sP2 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_56]) ).
tcf(c_3365,plain,
( iPr_def_27
| iPr_def_22
| sP2
| sP4
| ~ sP3 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_54]) ).
tcf(c_3366,plain,
( iPr_def_27
| sP2
| sP3
| sP4
| q(sK6) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_52]) ).
tcf(c_3367,plain,
( iPr_def_22
| sP2
| sP3
| sP4
| ~ r(sK5) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_51]) ).
tcf(c_3368,plain,
( iPr_def_27
| sP4
| q(sK6)
| ~ sP2
| ~ sP3 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_50]) ).
tcf(c_3369,plain,
( iPr_def_22
| sP4
| ~ sP2
| ~ sP3
| ~ r(sK5) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_49]) ).
tcf(c_3370,negated_conjecture,
( iPr_def_10
| sP4
| ~ p(sK50) ),
inference(demodulation,[status(thm)],[c_3291]) ).
tcf(c_3372,negated_conjecture,
( iPr_def_11
| sP4
| p(sK50) ),
inference(demodulation,[status(thm)],[c_3293]) ).
tcf(c_3383,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ~ p(X0) ),
inference(demodulation,[status(thm)],[c_3292]) ).
tcf(c_3387,negated_conjecture,
! [X0: $i] :
( p(X0)
| ~ iPr_def_10 ),
inference(demodulation,[status(thm)],[c_3290]) ).
tcf(c_3392,plain,
( ~ iPr_def_11
| ~ p(sK22) ),
inference(instantiation,[status(thm)],[c_3383]) ).
tcf(c_3394,plain,
( ~ iPr_def_20
| ~ r(sK22) ),
inference(instantiation,[status(thm)],[c_3324]) ).
tcf(c_3395,plain,
( ~ iPr_def_22
| ~ q(sK22) ),
inference(instantiation,[status(thm)],[c_3332]) ).
tcf(c_3398,plain,
( q(sK22)
| q(sK28(sK22))
| ~ iPr_def_19 ),
inference(instantiation,[status(thm)],[c_3323]) ).
tcf(c_3399,plain,
( q(sK22)
| q(sK19(sK22))
| ~ iPr_def_23 ),
inference(instantiation,[status(thm)],[c_3339]) ).
tcf(c_3408,plain,
( ~ iPr_def_11
| ~ p(sK45) ),
inference(instantiation,[status(thm)],[c_3383]) ).
tcf(c_3413,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ p(sK49(X0)) ),
inference(instantiation,[status(thm)],[c_3383]) ).
tcf(c_3414,plain,
( ~ iPr_def_11
| ~ p(sK49(sK22)) ),
inference(instantiation,[status(thm)],[c_3413]) ).
tcf(c_3418,plain,
( ~ iPr_def_22
| ~ q(sK12) ),
inference(instantiation,[status(thm)],[c_3332]) ).
tcf(c_3425,plain,
( ~ iPr_def_20
| ~ r(sK18) ),
inference(instantiation,[status(thm)],[c_3324]) ).
tcf(c_3441,plain,
( r(sK8)
| ~ iPr_def_27 ),
inference(instantiation,[status(thm)],[c_3349]) ).
tcf(c_3442,plain,
( r(sK10)
| ~ iPr_def_27 ),
inference(instantiation,[status(thm)],[c_3349]) ).
tcf(c_3455,plain,
( ~ iPr_def_22
| ~ q(sK9) ),
inference(instantiation,[status(thm)],[c_3332]) ).
tcf(c_3471,plain,
! [X0: $i] :
( ~ iPr_def_22
| ~ q(sK28(X0)) ),
inference(instantiation,[status(thm)],[c_3332]) ).
tcf(c_3472,plain,
( ~ iPr_def_22
| ~ q(sK28(sK22)) ),
inference(instantiation,[status(thm)],[c_3471]) ).
tcf(c_3486,plain,
( r(sK11)
| ~ iPr_def_27 ),
inference(instantiation,[status(thm)],[c_3349]) ).
tcf(c_3570,plain,
( p(sK29)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_3387]) ).
tcf(c_3571,plain,
( p(sK32)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_3387]) ).
tcf(c_3573,plain,
! [X0: $i] :
( p(sK49(X0))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_3387]) ).
tcf(c_3574,plain,
( p(sK49(sK22))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_3573]) ).
tcf(c_3651,plain,
( p(sK35)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_3387]) ).
tcf(c_3654,plain,
! [X0: $i] :
( r(sK13(X0))
| ~ iPr_def_27 ),
inference(instantiation,[status(thm)],[c_3349]) ).
tcf(c_3674,plain,
! [X0: $i] :
( ~ iPr_def_22
| ~ q(sK19(X0)) ),
inference(instantiation,[status(thm)],[c_3332]) ).
tcf(c_3675,plain,
( ~ iPr_def_22
| ~ q(sK19(sK22)) ),
inference(instantiation,[status(thm)],[c_3674]) ).
tcf(c_3705,plain,
( ~ iPr_def_20
| ~ r(sK25) ),
inference(instantiation,[status(thm)],[c_3324]) ).
tcf(c_3706,plain,
( ~ iPr_def_20
| ~ r(sK26) ),
inference(instantiation,[status(thm)],[c_3324]) ).
tcf(c_3708,plain,
! [X0: $i] :
( ~ iPr_def_20
| ~ r(sK13(X0)) ),
inference(instantiation,[status(thm)],[c_3324]) ).
tcf(c_3743,plain,
( ~ iPr_def_24
| ~ q(sK12)
| ~ q(sK19(sK12)) ),
inference(instantiation,[status(thm)],[c_3341]) ).
tcf(c_3766,plain,
( ~ iPr_def_20
| ~ r(sK20) ),
inference(instantiation,[status(thm)],[c_3324]) ).
tcf(c_3942,plain,
! [X0: $i] :
( r(sK16(X0))
| ~ iPr_def_27 ),
inference(instantiation,[status(thm)],[c_3349]) ).
tcf(c_4050,plain,
! [X0: $i] :
( ~ iPr_def_20
| ~ r(sK16(X0)) ),
inference(instantiation,[status(thm)],[c_3324]) ).
tcf(c_4516,plain,
( ~ iPr_def_11
| ~ p(sK38) ),
inference(instantiation,[status(thm)],[c_3383]) ).
tcf(c_4517,plain,
( ~ iPr_def_11
| ~ p(sK46) ),
inference(instantiation,[status(thm)],[c_3383]) ).
tcf(c_4575,plain,
( r(sK5)
| ~ iPr_def_27 ),
inference(instantiation,[status(thm)],[c_3349]) ).
tcf(c_4587,plain,
( ~ iPr_def_11
| ~ p(sK40) ),
inference(instantiation,[status(thm)],[c_3383]) ).
tcf(c_4639,plain,
( p(sK34)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_3387]) ).
tcf(c_4758,plain,
( ~ iPr_def_22
| ~ q(sK6) ),
inference(instantiation,[status(thm)],[c_3332]) ).
tcf(c_4759,plain,
( ~ iPr_def_22
| ~ q(sK7) ),
inference(instantiation,[status(thm)],[c_3332]) ).
fof(f5,definition,
( sP0
<=> ( ? [X12] :
! [X13] :
( s(X12)
<=> s(X13) )
<=> ( ? [X14] : p(X14)
<=> ! [X15] : q(X15) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,definition,
( sP1
<=> ( ( ? [X10] : s(X10)
<=> ! [X11] : p(X11) )
<=> sP0 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f7,definition,
( sP2
<=> ( ? [X4] :
! [X5] :
( q(X4)
<=> q(X5) )
<=> ( ? [X6] : r(X6)
<=> ! [X7] : s(X7) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f8,definition,
( sP3
<=> ( ? [X8] :
! [X9] :
( r(X8)
<=> r(X9) )
<=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f9,definition,
( sP4
<=> ( ( ? [X2] : q(X2)
<=> ! [X3] : r(X3) )
<=> ( sP2
<=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f10,plain,
( ? [X0] :
! [X1] :
( p(X0)
<=> p(X1) )
<~> sP4 ),
inference(definition_folding,[],[f4,f9,f8,f7,f6,f5]) ).
fof(f23,plain,
( ( ~ sP0
| ( ( ! [X12] :
? [X13] :
( ( s(X12)
| s(X13) )
& ( ~ s(X12)
| ~ s(X13) ) )
| ( ( ! [X14] : ~ p(X14)
| ! [X15] : q(X15) )
& ( ? [X15] : ~ q(X15)
| ? [X14] : p(X14) ) ) )
& ( ( ( ? [X14] : p(X14)
| ! [X15] : q(X15) )
& ( ! [X14] : ~ p(X14)
| ? [X15] : ~ q(X15) ) )
| ? [X12] :
! [X13] :
( ( ~ s(X12)
| s(X13) )
& ( ~ s(X13)
| s(X12) ) ) ) ) )
& ( ( ( ? [X12] :
! [X13] :
( ( ~ s(X12)
| s(X13) )
& ( ~ s(X13)
| s(X12) ) )
| ( ( ! [X14] : ~ p(X14)
| ! [X15] : q(X15) )
& ( ? [X15] : ~ q(X15)
| ? [X14] : p(X14) ) ) )
& ( ! [X12] :
? [X13] :
( ( s(X12)
| s(X13) )
& ( ~ s(X12)
| ~ s(X13) ) )
| ( ( ? [X14] : p(X14)
| ! [X15] : q(X15) )
& ( ! [X14] : ~ p(X14)
| ? [X15] : ~ q(X15) ) ) ) )
| sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
( ( ~ sP0
| ( ( ! [X22] :
? [X23] :
( ( s(X22)
| s(X23) )
& ( ~ s(X22)
| ~ s(X23) ) )
| ( ( ! [X21] : ~ p(X21)
| ! [X20] : q(X20) )
& ( ? [X19] : ~ q(X19)
| ? [X18] : p(X18) ) ) )
& ( ( ( ? [X17] : p(X17)
| ! [X16] : q(X16) )
& ( ! [X15] : ~ p(X15)
| ? [X14] : ~ q(X14) ) )
| ? [X12] :
! [X13] :
( ( ~ s(X12)
| s(X13) )
& ( ~ s(X13)
| s(X12) ) ) ) ) )
& ( ( ( ? [X10] :
! [X11] :
( ( ~ s(X10)
| s(X11) )
& ( ~ s(X11)
| s(X10) ) )
| ( ( ! [X9] : ~ p(X9)
| ! [X8] : q(X8) )
& ( ? [X7] : ~ q(X7)
| ? [X6] : p(X6) ) ) )
& ( ! [X4] :
? [X5] :
( ( s(X4)
| s(X5) )
& ( ~ s(X4)
| ~ s(X5) ) )
| ( ( ? [X3] : p(X3)
| ! [X2] : q(X2) )
& ( ! [X1] : ~ p(X1)
| ? [X0] : ~ q(X0) ) ) ) )
| sP0 ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
( ( ~ sP0
| ( ( ! [X22] :
( ( s(X22)
| s(sK48(X22)) )
& ( ~ s(X22)
| ~ s(sK48(X22)) ) )
| ( ( ! [X21] : ~ p(X21)
| ! [X20] : q(X20) )
& ( ~ q(sK47)
| p(sK46) ) ) )
& ( ( ( p(sK45)
| ! [X16] : q(X16) )
& ( ! [X15] : ~ p(X15)
| ~ q(sK44) ) )
| ! [X13] :
( ( ~ s(sK43)
| s(X13) )
& ( ~ s(X13)
| s(sK43) ) ) ) ) )
& ( ( ( ! [X11] :
( ( ~ s(sK42)
| s(X11) )
& ( ~ s(X11)
| s(sK42) ) )
| ( ( ! [X9] : ~ p(X9)
| ! [X8] : q(X8) )
& ( ~ q(sK41)
| p(sK40) ) ) )
& ( ! [X4] :
( ( s(X4)
| s(sK39(X4)) )
& ( ~ s(X4)
| ~ s(sK39(X4)) ) )
| ( ( p(sK38)
| ! [X2] : q(X2) )
& ( ! [X1] : ~ p(X1)
| ~ q(sK37) ) ) ) )
| sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38,sK39,sK40,sK41,sK42,sK43,sK44,sK45,sK46,sK47,sK48]),skolemize(X0,sK37),skolemize(X3,sK38),skolemize(X5,sK39(X4)),skolemize(X6,sK40),skolemize(X7,sK41),skolemize(X10,sK42),skolemize(X12,sK43),skolemize(X14,sK44),skolemize(X17,sK45),skolemize(X18,sK46),skolemize(X19,sK47),skolemize(X23,sK48(X22))],[f24]) ).
fof(f77,plain,
! [X21,X22,X20] :
( ~ sP0
| s(X22)
| s(sK48(X22))
| ~ p(X21)
| q(X20) ),
inference(cnf_transformation,[],[f25]) ).
fof(f78,plain,
! [X21,X22,X20] :
( ~ sP0
| ~ s(X22)
| ~ s(sK48(X22))
| ~ p(X21)
| q(X20) ),
inference(cnf_transformation,[],[f25]) ).
fof(f79,plain,
! [X22] :
( ~ sP0
| s(X22)
| s(sK48(X22))
| ~ q(sK47)
| p(sK46) ),
inference(cnf_transformation,[],[f25]) ).
fof(f80,plain,
! [X22] :
( ~ sP0
| ~ s(X22)
| ~ s(sK48(X22))
| ~ q(sK47)
| p(sK46) ),
inference(cnf_transformation,[],[f25]) ).
fof(f81,plain,
! [X16,X13] :
( ~ sP0
| p(sK45)
| q(X16)
| ~ s(sK43)
| s(X13) ),
inference(cnf_transformation,[],[f25]) ).
fof(f82,plain,
! [X15,X13] :
( ~ sP0
| ~ p(X15)
| ~ q(sK44)
| ~ s(sK43)
| s(X13) ),
inference(cnf_transformation,[],[f25]) ).
fof(f83,plain,
! [X16,X13] :
( ~ sP0
| p(sK45)
| q(X16)
| ~ s(X13)
| s(sK43) ),
inference(cnf_transformation,[],[f25]) ).
fof(f84,plain,
! [X15,X13] :
( ~ sP0
| ~ p(X15)
| ~ q(sK44)
| ~ s(X13)
| s(sK43) ),
inference(cnf_transformation,[],[f25]) ).
fof(f85,plain,
! [X11,X8,X9] :
( ~ s(sK42)
| s(X11)
| ~ p(X9)
| q(X8)
| sP0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f86,plain,
! [X11,X8,X9] :
( ~ s(X11)
| s(sK42)
| ~ p(X9)
| q(X8)
| sP0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f87,plain,
! [X11] :
( ~ s(sK42)
| s(X11)
| ~ q(sK41)
| p(sK40)
| sP0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f88,plain,
! [X11] :
( ~ s(X11)
| s(sK42)
| ~ q(sK41)
| p(sK40)
| sP0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f89,plain,
! [X2,X4] :
( s(X4)
| s(sK39(X4))
| p(sK38)
| q(X2)
| sP0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f90,plain,
! [X2,X4] :
( ~ s(X4)
| ~ s(sK39(X4))
| p(sK38)
| q(X2)
| sP0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f91,plain,
! [X1,X4] :
( s(X4)
| s(sK39(X4))
| ~ p(X1)
| ~ q(sK37)
| sP0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f92,plain,
! [X1,X4] :
( ~ s(X4)
| ~ s(sK39(X4))
| ~ p(X1)
| ~ q(sK37)
| sP0 ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( sP0
| ~ q(sK37)
| ~ p(X1)
| ~ s(X0)
| ~ s(sK39(X0)) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( sP0
| s(X1)
| s(sK39(X1))
| ~ q(sK37)
| ~ p(X0) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( sP0
| p(sK38)
| q(X1)
| ~ s(X0)
| ~ s(sK39(X0)) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( sP0
| p(sK38)
| s(X0)
| q(X1)
| s(sK39(X0)) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_101,plain,
! [X0: $i] :
( sP0
| p(sK40)
| s(sK42)
| ~ q(sK41)
| ~ s(X0) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_102,plain,
! [X0: $i] :
( sP0
| p(sK40)
| s(X0)
| ~ s(sK42)
| ~ q(sK41) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0
| s(sK42)
| q(X2)
| ~ p(X1)
| ~ s(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0
| s(X2)
| q(X1)
| ~ s(sK42)
| ~ p(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( s(sK43)
| ~ sP0
| ~ q(sK44)
| ~ p(X1)
| ~ s(X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( p(sK45)
| s(sK43)
| q(X1)
| ~ sP0
| ~ s(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( s(X1)
| ~ sP0
| ~ s(sK43)
| ~ q(sK44)
| ~ p(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( p(sK45)
| s(X1)
| q(X0)
| ~ sP0
| ~ s(sK43) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_109,plain,
! [X0: $i] :
( p(sK46)
| ~ sP0
| ~ q(sK47)
| ~ s(X0)
| ~ s(sK48(X0)) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_110,plain,
! [X0: $i] :
( p(sK46)
| s(X0)
| s(sK48(X0))
| ~ sP0
| ~ q(sK47) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( q(X2)
| ~ sP0
| ~ p(X1)
| ~ s(X0)
| ~ s(sK48(X0)) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( s(X1)
| q(X2)
| s(sK48(X1))
| ~ sP0
| ~ p(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_158,plain,
( p(sK46)
| s(sK22)
| s(sK48(sK22))
| ~ sP0
| ~ q(sK47) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_159,plain,
( sP0
| p(sK38)
| q(sK22)
| ~ s(sK22)
| ~ s(sK39(sK22)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_160,plain,
( sP0
| s(sK22)
| s(sK39(sK22))
| ~ p(sK22)
| ~ q(sK37) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_169,plain,
( q(sK22)
| ~ sP0
| ~ p(sK22)
| ~ s(sK22)
| ~ s(sK48(sK22)) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_3294,plain,
! [X0: $i] :
( ~ iPr_def_12
| q(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_112]) ).
tcf(c_3295,plain,
! [X0: $i] :
( ~ iPr_def_13
| s(sK48(X0))
| s(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_112]) ).
tcf(c_3296,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_112]) ).
tcf(c_3297,plain,
! [X0: $i] :
( ~ iPr_def_14
| ~ s(sK48(X0))
| ~ s(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_111]) ).
tcf(c_3298,plain,
( iPr_def_14
| iPr_def_12
| iPr_def_11
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_111]) ).
tcf(c_3300,plain,
( iPr_def_14
| p(sK46)
| ~ sP0
| ~ q(sK47) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_109]) ).
tcf(c_3301,plain,
! [X0: $i] :
( ~ iPr_def_15
| s(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_108]) ).
tcf(c_3302,plain,
( iPr_def_15
| iPr_def_12
| p(sK45)
| ~ sP0
| ~ s(sK43) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_108]) ).
tcf(c_3303,plain,
( iPr_def_15
| iPr_def_11
| ~ sP0
| ~ s(sK43)
| ~ q(sK44) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_107]) ).
tcf(c_3304,plain,
! [X0: $i] :
( ~ iPr_def_16
| ~ s(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_16])],[c_106]) ).
tcf(c_3305,plain,
( iPr_def_16
| iPr_def_12
| p(sK45)
| s(sK43)
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_106]) ).
tcf(c_3306,plain,
( iPr_def_16
| iPr_def_11
| s(sK43)
| ~ sP0
| ~ q(sK44) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_105]) ).
tcf(c_3307,plain,
( iPr_def_15
| iPr_def_12
| iPr_def_11
| sP0
| ~ s(sK42) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_3308,plain,
( iPr_def_16
| iPr_def_12
| iPr_def_11
| sP0
| s(sK42) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_103]) ).
tcf(c_3309,plain,
( iPr_def_15
| sP0
| p(sK40)
| ~ s(sK42)
| ~ q(sK41) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_102]) ).
tcf(c_3310,plain,
( iPr_def_16
| sP0
| p(sK40)
| s(sK42)
| ~ q(sK41) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_101]) ).
tcf(c_3311,plain,
! [X0: $i] :
( ~ iPr_def_17
| s(sK39(X0))
| s(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_17])],[c_100]) ).
tcf(c_3312,plain,
( iPr_def_17
| iPr_def_12
| sP0
| p(sK38) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_100]) ).
tcf(c_3313,plain,
! [X0: $i] :
( ~ iPr_def_18
| ~ s(sK39(X0))
| ~ s(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_18])],[c_99]) ).
tcf(c_3314,plain,
( iPr_def_18
| iPr_def_12
| sP0
| p(sK38) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_99]) ).
tcf(c_3315,plain,
( iPr_def_17
| iPr_def_11
| sP0
| ~ q(sK37) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_98]) ).
tcf(c_3316,plain,
( iPr_def_18
| iPr_def_11
| sP0
| ~ q(sK37) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_97]) ).
tcf(c_3388,plain,
( q(sK22)
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_3389,plain,
( s(sK22)
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3301]) ).
tcf(c_3393,plain,
( ~ iPr_def_16
| ~ s(sK22) ),
inference(instantiation,[status(thm)],[c_3304]) ).
tcf(c_3397,plain,
( s(sK22)
| s(sK39(sK22))
| ~ iPr_def_17 ),
inference(instantiation,[status(thm)],[c_3311]) ).
tcf(c_3513,plain,
( s(sK27)
| s(sK48(sK27))
| ~ iPr_def_13 ),
inference(instantiation,[status(thm)],[c_3295]) ).
tcf(c_3517,plain,
( s(sK17)
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3301]) ).
tcf(c_3518,plain,
( s(sK24)
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3301]) ).
tcf(c_3519,plain,
( s(sK27)
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3301]) ).
tcf(c_3520,plain,
! [X0: $i] :
( s(sK48(X0))
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3301]) ).
tcf(c_3521,plain,
( s(sK48(sK22))
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3520]) ).
tcf(c_3632,plain,
! [X0: $i] :
( s(sK39(X0))
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3301]) ).
tcf(c_3635,plain,
( s(sK39(sK22))
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3632]) ).
tcf(c_3747,plain,
( s(sK21)
| ~ iPr_def_15 ),
inference(instantiation,[status(thm)],[c_3301]) ).
tcf(c_3808,plain,
( ~ iPr_def_16
| ~ s(sK27) ),
inference(instantiation,[status(thm)],[c_3304]) ).
tcf(c_3809,plain,
( ~ iPr_def_16
| ~ s(sK30) ),
inference(instantiation,[status(thm)],[c_3304]) ).
tcf(c_3810,plain,
( ~ iPr_def_16
| ~ s(sK36) ),
inference(instantiation,[status(thm)],[c_3304]) ).
tcf(c_3811,plain,
! [X0: $i] :
( ~ iPr_def_16
| ~ s(sK39(X0)) ),
inference(instantiation,[status(thm)],[c_3304]) ).
tcf(c_3812,plain,
( ~ iPr_def_16
| ~ s(sK39(sK22)) ),
inference(instantiation,[status(thm)],[c_3811]) ).
tcf(c_3813,plain,
! [X0: $i] :
( ~ iPr_def_16
| ~ s(sK48(X0)) ),
inference(instantiation,[status(thm)],[c_3304]) ).
tcf(c_3814,plain,
( ~ iPr_def_16
| ~ s(sK48(sK22)) ),
inference(instantiation,[status(thm)],[c_3813]) ).
tcf(c_4247,plain,
! [X0: $i] :
( q(sK28(X0))
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_4248,plain,
( q(sK28(sK22))
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_4247]) ).
tcf(c_4249,plain,
( q(sK37)
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_4250,plain,
( q(sK41)
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_4251,plain,
( q(sK44)
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_4253,plain,
( q(sK19(sK12))
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_4260,plain,
( q(sK47)
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_4459,plain,
( q(sK12)
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_4475,plain,
! [X0: $i] :
( q(sK19(X0))
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_3294]) ).
tcf(c_4476,plain,
( q(sK19(sK22))
| ~ iPr_def_12 ),
inference(instantiation,[status(thm)],[c_4475]) ).
tcf(c_4661,plain,
( ~ iPr_def_16
| ~ s(sK48(sK27)) ),
inference(instantiation,[status(thm)],[c_3813]) ).
tcf(c_4731,plain,
( ~ iPr_def_16
| ~ s(sK33) ),
inference(instantiation,[status(thm)],[c_3304]) ).
tcf(c_4788,plain,
( ~ iPr_def_16
| ~ s(sK31) ),
inference(instantiation,[status(thm)],[c_3304]) ).
tcf(c_4797,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4788,c_4759,c_4758,c_4731,c_4661,c_4639,c_4587,c_4575,c_4517,c_4516,c_4476,c_4459,c_4260,c_4253,c_4251,c_4250,c_4249,c_4248,c_4247,c_4050,c_3942,c_3814,c_3813,c_3812,c_3811,c_3810,c_3809,c_3808,c_3766,c_3747,c_3743,c_3708,c_3706,c_3705,c_3675,c_3674,c_3654,c_3651,c_3635,c_3632,c_3574,c_3573,c_3571,c_3570,c_3521,c_3520,c_3519,c_3518,c_3517,c_3513,c_3486,c_3472,c_3471,c_3455,c_3442,c_3441,c_3425,c_3418,c_3414,c_3413,c_3408,c_3337,c_3331,c_3309,c_3303,c_3369,c_3361,c_3359,c_3338,c_3334,c_3330,c_3326,c_3313,c_3310,c_3306,c_3302,c_3297,c_3368,c_3363,c_3360,c_3358,c_3350,c_3333,c_3305,c_3300,c_3367,c_3351,c_3399,c_3339,c_3335,c_3398,c_3323,c_3322,c_3318,c_3397,c_3311,c_3307,c_3295,c_3366,c_3365,c_3364,c_3362,c_3352,c_3344,c_3343,c_3336,c_3321,c_3319,c_3317,c_3316,c_3315,c_3308,c_3353,c_3342,c_3340,c_3395,c_3332,c_3327,c_3325,c_3394,c_3324,c_3314,c_3312,c_3393,c_3304,c_3298,c_3296,c_3392,c_3383,c_3370,c_3387,c_3349,c_3320,c_3389,c_3301,c_3388,c_3294,c_3372,c_2911,c_2501,c_174,c_173,c_85,c_97,c_169,c_162,c_160,c_159,c_158,c_156,c_49,c_57,c_155,c_61,c_63,c_65,c_71,c_50,c_51,c_53,c_138,c_55,c_137,c_58,c_136,c_62,c_134,c_89,c_93,c_130,c_129,c_95,c_113,c_66,c_72,c_90,c_91,c_121,c_92,c_119,c_114,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN723+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 % Computer : n004.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 02:11:21 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 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
% 0.21/0.48
% 0.21/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.48
% 0.21/0.48 % Detected problem language: tptp
% 0.21/0.50 % Proving...
% 1.91/1.36 % SZS status Started for theBenchmark.p
% 1.91/1.36 % SZS status Theorem for theBenchmark.p
% 1.91/1.36
% 1.91/1.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.91/1.36
% 1.91/1.36 % ------ iProver source info
% 1.91/1.36
% 1.91/1.36 % git: date: 2026-07-19 20:42:38 +0200
% 1.91/1.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.91/1.36 % git: non_committed_changes: false
% 1.91/1.36
% 1.91/1.36 % ------ Parsing...
% 1.91/1.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.91/1.36
% 1.91/1.36 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.91/1.36
% 1.91/1.36 % ------ Preprocessing... gs_s sp: 98 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.91/1.36 % ------ Proving...
% 1.91/1.36 % ------ Problem Properties
% 1.91/1.36
% 1.91/1.36 %
% 1.91/1.36 % clauses 88
% 1.91/1.36 % conjectures 6
% 1.91/1.36 % EPR 74
% 1.91/1.36 % Horn 18
% 1.91/1.36 % unary 0
% 1.91/1.36 % binary 8
% 1.91/1.36 % lits 348
% 1.91/1.36 % lits eq 0
% 1.91/1.36 % fd_pure 0
% 1.91/1.36 % fd_pseudo 0
% 1.91/1.36 % fd_cond 0
% 1.91/1.36 % fd_pseudo_cond 0
% 1.91/1.36 % AC symbols 0
% 1.91/1.36
% 1.91/1.36 % ------ Schedule dynamic 5 is on
% 1.91/1.36
% 1.91/1.36 % ------ no equalities: superposition off
% 1.91/1.36
% 1.91/1.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.91/1.36
% 1.91/1.36
% 1.91/1.36 % ------
% 1.91/1.36 % Current options:
% 1.91/1.36 % ------
% 1.91/1.36
% 1.91/1.36
% 1.91/1.36 %
% 1.91/1.36
% 1.91/1.36 % ------ Proving...
% 1.91/1.36 %
% 1.91/1.36
% 1.91/1.36 % SZS status Theorem for theBenchmark.p
% 1.91/1.36
% 1.91/1.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.91/1.36
% 1.91/1.36
%------------------------------------------------------------------------------