%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM022+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 : Tue Sep 29 09:40:10 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 28
% Syntax : Number of formulae : 149 ( 29 unt; 26 def)
% Number of atoms : 1048 ( 90 equ)
% Maximal formula atoms : 96 ( 7 avg)
% Number of connectives : 1173 ( 274 ~; 365 |; 510 &)
% ( 15 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 18 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 190 ( 0 sgn 80 !; 110 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(f19,conjecture,
( ( ( ( aReductOfIn0(xb,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xb) )
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xc,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xc) )
| sdtmndtplgtdt0(xa,xR,xc) ) )
=> ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& ( X0 = xb
| ( ( aReductOfIn0(xb,X0,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,X0,xR)
& sdtmndtplgtdt0(X1,xR,xb) ) )
& sdtmndtplgtdt0(X0,xR,xb) ) )
& sdtmndtasgtdt0(X0,xR,xb)
& ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& ( X1 = xc
| ( ( aReductOfIn0(xc,X1,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,X1,xR)
& sdtmndtplgtdt0(X2,xR,xc) ) )
& sdtmndtplgtdt0(X1,xR,xc) ) )
& sdtmndtasgtdt0(X1,xR,xc)
& ? [X2] :
( aElement0(X2)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2)
& ( X1 = X2
| ( ( aReductOfIn0(X2,X1,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X1,xR)
& sdtmndtplgtdt0(X3,xR,X2) ) )
& sdtmndtplgtdt0(X1,xR,X2) ) )
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aElement0(X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X2,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3)
& ~ ? [X4] : aReductOfIn0(X4,X3,xR)
& aNormalFormOfIn0(X3,X2,xR)
& ( xb = X3
| ( ( aReductOfIn0(X3,xb,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xb,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(xb,xR,X3) ) )
& sdtmndtasgtdt0(xb,xR,X3)
& ( xc = X3
| ( ( aReductOfIn0(X3,xc,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xc,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(xc,xR,X3) ) )
& sdtmndtasgtdt0(xc,xR,X3) ) ) ) ) )
=> ( ( ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [X0] :
( aElement0(X0)
& ( xb = X0
| aReductOfIn0(X0,xb,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xb,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xb,xR,X0)
| sdtmndtasgtdt0(xb,xR,X0) )
& ( xc = X0
| aReductOfIn0(X0,xc,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xc,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xc,xR,X0)
| sdtmndtasgtdt0(xc,xR,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
~ ( ( ( ( aReductOfIn0(xb,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xb) )
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xc,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xc) )
| sdtmndtplgtdt0(xa,xR,xc) ) )
=> ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& ( X0 = xb
| ( ( aReductOfIn0(xb,X0,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,X0,xR)
& sdtmndtplgtdt0(X1,xR,xb) ) )
& sdtmndtplgtdt0(X0,xR,xb) ) )
& sdtmndtasgtdt0(X0,xR,xb)
& ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& ( X1 = xc
| ( ( aReductOfIn0(xc,X1,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,X1,xR)
& sdtmndtplgtdt0(X2,xR,xc) ) )
& sdtmndtplgtdt0(X1,xR,xc) ) )
& sdtmndtasgtdt0(X1,xR,xc)
& ? [X2] :
( aElement0(X2)
& ( X0 = X2
| ( ( aReductOfIn0(X2,X0,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,xR)
& sdtmndtplgtdt0(X3,xR,X2) ) )
& sdtmndtplgtdt0(X0,xR,X2) ) )
& sdtmndtasgtdt0(X0,xR,X2)
& ( X1 = X2
| ( ( aReductOfIn0(X2,X1,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X1,xR)
& sdtmndtplgtdt0(X3,xR,X2) ) )
& sdtmndtplgtdt0(X1,xR,X2) ) )
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aElement0(X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X2,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3)
& ~ ? [X4] : aReductOfIn0(X4,X3,xR)
& aNormalFormOfIn0(X3,X2,xR)
& ( xb = X3
| ( ( aReductOfIn0(X3,xb,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xb,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(xb,xR,X3) ) )
& sdtmndtasgtdt0(xb,xR,X3)
& ( xc = X3
| ( ( aReductOfIn0(X3,xc,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xc,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(xc,xR,X3) ) )
& sdtmndtasgtdt0(xc,xR,X3) ) ) ) ) )
=> ( ( ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [X0] :
( aElement0(X0)
& ( xb = X0
| aReductOfIn0(X0,xb,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xb,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xb,xR,X0)
| sdtmndtasgtdt0(xb,xR,X0) )
& ( xc = X0
| aReductOfIn0(X0,xc,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xc,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xc,xR,X0)
| sdtmndtasgtdt0(xc,xR,X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f27,plain,
~ ( ( ( ( aReductOfIn0(xb,xa,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtplgtdt0(X0,xR,xb) )
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xc,xa,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtplgtdt0(X1,xR,xc) )
| sdtmndtplgtdt0(xa,xR,xc) ) )
=> ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& ( xb = X2
| ( ( aReductOfIn0(xb,X2,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X2,xR)
& sdtmndtplgtdt0(X3,xR,xb) ) )
& sdtmndtplgtdt0(X2,xR,xb) ) )
& sdtmndtasgtdt0(X2,xR,xb)
& ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xa,xR)
& ( xc = X4
| ( ( aReductOfIn0(xc,X4,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X4,xR)
& sdtmndtplgtdt0(X5,xR,xc) ) )
& sdtmndtplgtdt0(X4,xR,xc) ) )
& sdtmndtasgtdt0(X4,xR,xc)
& ? [X6] :
( aElement0(X6)
& ( X2 = X6
| ( ( aReductOfIn0(X6,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X6) ) )
& sdtmndtplgtdt0(X2,xR,X6) ) )
& sdtmndtasgtdt0(X2,xR,X6)
& ( X4 = X6
| ( ( aReductOfIn0(X6,X4,xR)
| ? [X8] :
( aElement0(X8)
& aReductOfIn0(X8,X4,xR)
& sdtmndtplgtdt0(X8,xR,X6) ) )
& sdtmndtplgtdt0(X4,xR,X6) ) )
& sdtmndtasgtdt0(X4,xR,X6)
& ? [X9] :
( aElement0(X9)
& ( X6 = X9
| ( ( aReductOfIn0(X9,X6,xR)
| ? [X10] :
( aElement0(X10)
& aReductOfIn0(X10,X6,xR)
& sdtmndtplgtdt0(X10,xR,X9) ) )
& sdtmndtplgtdt0(X6,xR,X9) ) )
& sdtmndtasgtdt0(X6,xR,X9)
& ~ ? [X11] : aReductOfIn0(X11,X9,xR)
& aNormalFormOfIn0(X9,X6,xR)
& ( xb = X9
| ( ( aReductOfIn0(X9,xb,xR)
| ? [X12] :
( aElement0(X12)
& aReductOfIn0(X12,xb,xR)
& sdtmndtplgtdt0(X12,xR,X9) ) )
& sdtmndtplgtdt0(xb,xR,X9) ) )
& sdtmndtasgtdt0(xb,xR,X9)
& ( xc = X9
| ( ( aReductOfIn0(X9,xc,xR)
| ? [X13] :
( aElement0(X13)
& aReductOfIn0(X13,xc,xR)
& sdtmndtplgtdt0(X13,xR,X9) ) )
& sdtmndtplgtdt0(xc,xR,X9) ) )
& sdtmndtasgtdt0(xc,xR,X9) ) ) ) ) )
=> ( ( ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [X14] :
( aElement0(X14)
& aReductOfIn0(X14,xa,xR)
& sdtmndtplgtdt0(X14,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [X15] :
( aElement0(X15)
& aReductOfIn0(X15,xa,xR)
& sdtmndtplgtdt0(X15,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [X16] :
( aElement0(X16)
& ( xb = X16
| aReductOfIn0(X16,xb,xR)
| ? [X17] :
( aElement0(X17)
& aReductOfIn0(X17,xb,xR)
& sdtmndtplgtdt0(X17,xR,X16) )
| sdtmndtplgtdt0(xb,xR,X16)
| sdtmndtasgtdt0(xb,xR,X16) )
& ( xc = X16
| aReductOfIn0(X16,xc,xR)
| ? [X18] :
( aElement0(X18)
& aReductOfIn0(X18,xc,xR)
& sdtmndtplgtdt0(X18,xR,X16) )
| sdtmndtplgtdt0(xc,xR,X16)
| sdtmndtasgtdt0(xc,xR,X16) ) ) ) ),
inference(rectify,[],[f20]) ).
fof(f52,plain,
( ! [X16] :
( ~ aElement0(X16)
| ( xb != X16
& ~ aReductOfIn0(X16,xb,xR)
& ! [X17] :
( ~ aElement0(X17)
| ~ aReductOfIn0(X17,xb,xR)
| ~ sdtmndtplgtdt0(X17,xR,X16) )
& ~ sdtmndtplgtdt0(xb,xR,X16)
& ~ sdtmndtasgtdt0(xb,xR,X16) )
| ( xc != X16
& ~ aReductOfIn0(X16,xc,xR)
& ! [X18] :
( ~ aElement0(X18)
| ~ aReductOfIn0(X18,xc,xR)
| ~ sdtmndtplgtdt0(X18,xR,X16) )
& ~ sdtmndtplgtdt0(xc,xR,X16)
& ~ sdtmndtasgtdt0(xc,xR,X16) ) )
& ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [X14] :
( aElement0(X14)
& aReductOfIn0(X14,xa,xR)
& sdtmndtplgtdt0(X14,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [X15] :
( aElement0(X15)
& aReductOfIn0(X15,xa,xR)
& sdtmndtplgtdt0(X15,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& ( ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& ( xb = X2
| ( ( aReductOfIn0(xb,X2,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X2,xR)
& sdtmndtplgtdt0(X3,xR,xb) ) )
& sdtmndtplgtdt0(X2,xR,xb) ) )
& sdtmndtasgtdt0(X2,xR,xb)
& ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xa,xR)
& ( xc = X4
| ( ( aReductOfIn0(xc,X4,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X4,xR)
& sdtmndtplgtdt0(X5,xR,xc) ) )
& sdtmndtplgtdt0(X4,xR,xc) ) )
& sdtmndtasgtdt0(X4,xR,xc)
& ? [X6] :
( aElement0(X6)
& ( X2 = X6
| ( ( aReductOfIn0(X6,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X6) ) )
& sdtmndtplgtdt0(X2,xR,X6) ) )
& sdtmndtasgtdt0(X2,xR,X6)
& ( X4 = X6
| ( ( aReductOfIn0(X6,X4,xR)
| ? [X8] :
( aElement0(X8)
& aReductOfIn0(X8,X4,xR)
& sdtmndtplgtdt0(X8,xR,X6) ) )
& sdtmndtplgtdt0(X4,xR,X6) ) )
& sdtmndtasgtdt0(X4,xR,X6)
& ? [X9] :
( aElement0(X9)
& ( X6 = X9
| ( ( aReductOfIn0(X9,X6,xR)
| ? [X10] :
( aElement0(X10)
& aReductOfIn0(X10,X6,xR)
& sdtmndtplgtdt0(X10,xR,X9) ) )
& sdtmndtplgtdt0(X6,xR,X9) ) )
& sdtmndtasgtdt0(X6,xR,X9)
& ! [X11] : ~ aReductOfIn0(X11,X9,xR)
& aNormalFormOfIn0(X9,X6,xR)
& ( xb = X9
| ( ( aReductOfIn0(X9,xb,xR)
| ? [X12] :
( aElement0(X12)
& aReductOfIn0(X12,xb,xR)
& sdtmndtplgtdt0(X12,xR,X9) ) )
& sdtmndtplgtdt0(xb,xR,X9) ) )
& sdtmndtasgtdt0(xb,xR,X9)
& ( xc = X9
| ( ( aReductOfIn0(X9,xc,xR)
| ? [X13] :
( aElement0(X13)
& aReductOfIn0(X13,xc,xR)
& sdtmndtplgtdt0(X13,xR,X9) ) )
& sdtmndtplgtdt0(xc,xR,X9) ) )
& sdtmndtasgtdt0(xc,xR,X9) ) ) ) )
| ( ~ aReductOfIn0(xb,xa,xR)
& ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(X0,xR,xb) )
& ~ sdtmndtplgtdt0(xa,xR,xb) )
| ( ~ aReductOfIn0(xc,xa,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR)
| ~ sdtmndtplgtdt0(X1,xR,xc) )
& ~ sdtmndtplgtdt0(xa,xR,xc) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f53,plain,
( ! [X16] :
( ~ aElement0(X16)
| ( xb != X16
& ~ aReductOfIn0(X16,xb,xR)
& ! [X17] :
( ~ aElement0(X17)
| ~ aReductOfIn0(X17,xb,xR)
| ~ sdtmndtplgtdt0(X17,xR,X16) )
& ~ sdtmndtplgtdt0(xb,xR,X16)
& ~ sdtmndtasgtdt0(xb,xR,X16) )
| ( xc != X16
& ~ aReductOfIn0(X16,xc,xR)
& ! [X18] :
( ~ aElement0(X18)
| ~ aReductOfIn0(X18,xc,xR)
| ~ sdtmndtplgtdt0(X18,xR,X16) )
& ~ sdtmndtplgtdt0(xc,xR,X16)
& ~ sdtmndtasgtdt0(xc,xR,X16) ) )
& ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [X14] :
( aElement0(X14)
& aReductOfIn0(X14,xa,xR)
& sdtmndtplgtdt0(X14,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [X15] :
( aElement0(X15)
& aReductOfIn0(X15,xa,xR)
& sdtmndtplgtdt0(X15,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& ( ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& ( xb = X2
| ( ( aReductOfIn0(xb,X2,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X2,xR)
& sdtmndtplgtdt0(X3,xR,xb) ) )
& sdtmndtplgtdt0(X2,xR,xb) ) )
& sdtmndtasgtdt0(X2,xR,xb)
& ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xa,xR)
& ( xc = X4
| ( ( aReductOfIn0(xc,X4,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X4,xR)
& sdtmndtplgtdt0(X5,xR,xc) ) )
& sdtmndtplgtdt0(X4,xR,xc) ) )
& sdtmndtasgtdt0(X4,xR,xc)
& ? [X6] :
( aElement0(X6)
& ( X2 = X6
| ( ( aReductOfIn0(X6,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X6) ) )
& sdtmndtplgtdt0(X2,xR,X6) ) )
& sdtmndtasgtdt0(X2,xR,X6)
& ( X4 = X6
| ( ( aReductOfIn0(X6,X4,xR)
| ? [X8] :
( aElement0(X8)
& aReductOfIn0(X8,X4,xR)
& sdtmndtplgtdt0(X8,xR,X6) ) )
& sdtmndtplgtdt0(X4,xR,X6) ) )
& sdtmndtasgtdt0(X4,xR,X6)
& ? [X9] :
( aElement0(X9)
& ( X6 = X9
| ( ( aReductOfIn0(X9,X6,xR)
| ? [X10] :
( aElement0(X10)
& aReductOfIn0(X10,X6,xR)
& sdtmndtplgtdt0(X10,xR,X9) ) )
& sdtmndtplgtdt0(X6,xR,X9) ) )
& sdtmndtasgtdt0(X6,xR,X9)
& ! [X11] : ~ aReductOfIn0(X11,X9,xR)
& aNormalFormOfIn0(X9,X6,xR)
& ( xb = X9
| ( ( aReductOfIn0(X9,xb,xR)
| ? [X12] :
( aElement0(X12)
& aReductOfIn0(X12,xb,xR)
& sdtmndtplgtdt0(X12,xR,X9) ) )
& sdtmndtplgtdt0(xb,xR,X9) ) )
& sdtmndtasgtdt0(xb,xR,X9)
& ( xc = X9
| ( ( aReductOfIn0(X9,xc,xR)
| ? [X13] :
( aElement0(X13)
& aReductOfIn0(X13,xc,xR)
& sdtmndtplgtdt0(X13,xR,X9) ) )
& sdtmndtplgtdt0(xc,xR,X9) ) )
& sdtmndtasgtdt0(xc,xR,X9) ) ) ) )
| ( ~ aReductOfIn0(xb,xa,xR)
& ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(X0,xR,xb) )
& ~ sdtmndtplgtdt0(xa,xR,xb) )
| ( ~ aReductOfIn0(xc,xa,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR)
| ~ sdtmndtplgtdt0(X1,xR,xc) )
& ~ sdtmndtplgtdt0(xa,xR,xc) ) ) ),
inference(flattening,[],[f52]) ).
fof(f66,definition,
! [X9] :
( xc = X9
| ( ( aReductOfIn0(X9,xc,xR)
| ? [X13] :
( aElement0(X13)
& aReductOfIn0(X13,xc,xR)
& sdtmndtplgtdt0(X13,xR,X9) ) )
& sdtmndtplgtdt0(xc,xR,X9) )
| ~ sP8(X9) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f67,definition,
! [X9] :
( xb = X9
| ( ( aReductOfIn0(X9,xb,xR)
| ? [X12] :
( aElement0(X12)
& aReductOfIn0(X12,xb,xR)
& sdtmndtplgtdt0(X12,xR,X9) ) )
& sdtmndtplgtdt0(xb,xR,X9) )
| ~ sP9(X9) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f68,definition,
! [X9,X6] :
( X6 = X9
| ( ( aReductOfIn0(X9,X6,xR)
| ? [X10] :
( aElement0(X10)
& aReductOfIn0(X10,X6,xR)
& sdtmndtplgtdt0(X10,xR,X9) ) )
& sdtmndtplgtdt0(X6,xR,X9) )
| ~ sP10(X9,X6) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f69,definition,
! [X6] :
( ? [X9] :
( aElement0(X9)
& sP10(X9,X6)
& sdtmndtasgtdt0(X6,xR,X9)
& ! [X11] : ~ aReductOfIn0(X11,X9,xR)
& aNormalFormOfIn0(X9,X6,xR)
& sP9(X9)
& sdtmndtasgtdt0(xb,xR,X9)
& sP8(X9)
& sdtmndtasgtdt0(xc,xR,X9) )
| ~ sP11(X6) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f70,definition,
! [X6,X4] :
( X4 = X6
| ( ( aReductOfIn0(X6,X4,xR)
| ? [X8] :
( aElement0(X8)
& aReductOfIn0(X8,X4,xR)
& sdtmndtplgtdt0(X8,xR,X6) ) )
& sdtmndtplgtdt0(X4,xR,X6) )
| ~ sP12(X6,X4) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f71,definition,
! [X6,X2] :
( X2 = X6
| ( ( aReductOfIn0(X6,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X6) ) )
& sdtmndtplgtdt0(X2,xR,X6) )
| ~ sP13(X6,X2) ),
introduced(definition,[new_symbols(definition,[sP13])],[predicate_definition_introduction]) ).
fof(f72,definition,
! [X2,X4] :
( ? [X6] :
( aElement0(X6)
& sP13(X6,X2)
& sdtmndtasgtdt0(X2,xR,X6)
& sP12(X6,X4)
& sdtmndtasgtdt0(X4,xR,X6)
& sP11(X6) )
| ~ sP14(X2,X4) ),
introduced(definition,[new_symbols(definition,[sP14])],[predicate_definition_introduction]) ).
fof(f73,definition,
! [X2] :
( ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xa,xR)
& ( xc = X4
| ( ( aReductOfIn0(xc,X4,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X4,xR)
& sdtmndtplgtdt0(X5,xR,xc) ) )
& sdtmndtplgtdt0(X4,xR,xc) ) )
& sdtmndtasgtdt0(X4,xR,xc)
& sP14(X2,X4) )
| ~ sP15(X2) ),
introduced(definition,[new_symbols(definition,[sP15])],[predicate_definition_introduction]) ).
fof(f74,definition,
( ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& ( xb = X2
| ( ( aReductOfIn0(xb,X2,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X2,xR)
& sdtmndtplgtdt0(X3,xR,xb) ) )
& sdtmndtplgtdt0(X2,xR,xb) ) )
& sdtmndtasgtdt0(X2,xR,xb)
& sP15(X2) )
| ~ sP16 ),
introduced(definition,[new_symbols(definition,[sP16])],[predicate_definition_introduction]) ).
fof(f75,definition,
( ( ~ aReductOfIn0(xc,xa,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR)
| ~ sdtmndtplgtdt0(X1,xR,xc) )
& ~ sdtmndtplgtdt0(xa,xR,xc) )
| ~ sP17 ),
introduced(definition,[new_symbols(definition,[sP17])],[predicate_definition_introduction]) ).
fof(f76,definition,
! [X16] :
( ( xc != X16
& ~ aReductOfIn0(X16,xc,xR)
& ! [X18] :
( ~ aElement0(X18)
| ~ aReductOfIn0(X18,xc,xR)
| ~ sdtmndtplgtdt0(X18,xR,X16) )
& ~ sdtmndtplgtdt0(xc,xR,X16)
& ~ sdtmndtasgtdt0(xc,xR,X16) )
| ~ sP18(X16) ),
introduced(definition,[new_symbols(definition,[sP18])],[predicate_definition_introduction]) ).
fof(f77,plain,
( ! [X16] :
( ~ aElement0(X16)
| ( xb != X16
& ~ aReductOfIn0(X16,xb,xR)
& ! [X17] :
( ~ aElement0(X17)
| ~ aReductOfIn0(X17,xb,xR)
| ~ sdtmndtplgtdt0(X17,xR,X16) )
& ~ sdtmndtplgtdt0(xb,xR,X16)
& ~ sdtmndtasgtdt0(xb,xR,X16) )
| sP18(X16) )
& ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [X14] :
( aElement0(X14)
& aReductOfIn0(X14,xa,xR)
& sdtmndtplgtdt0(X14,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [X15] :
( aElement0(X15)
& aReductOfIn0(X15,xa,xR)
& sdtmndtplgtdt0(X15,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& ( sP16
| ( ~ aReductOfIn0(xb,xa,xR)
& ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(X0,xR,xb) )
& ~ sdtmndtplgtdt0(xa,xR,xb) )
| sP17 ) ),
inference(definition_folding,[],[f53,f76,f75,f74,f73,f72,f71,f70,f69,f68,f67,f66]) ).
fof(f113,plain,
! [X16] :
( ( xc != X16
& ~ aReductOfIn0(X16,xc,xR)
& ! [X18] :
( ~ aElement0(X18)
| ~ aReductOfIn0(X18,xc,xR)
| ~ sdtmndtplgtdt0(X18,xR,X16) )
& ~ sdtmndtplgtdt0(xc,xR,X16)
& ~ sdtmndtasgtdt0(xc,xR,X16) )
| ~ sP18(X16) ),
inference(nnf_transformation,[],[f76]) ).
fof(f114,plain,
! [X0] :
( ( xc != X0
& ~ aReductOfIn0(X0,xc,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xc,xR)
| ~ sdtmndtplgtdt0(X1,xR,X0) )
& ~ sdtmndtplgtdt0(xc,xR,X0)
& ~ sdtmndtasgtdt0(xc,xR,X0) )
| ~ sP18(X0) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
( ( ~ aReductOfIn0(xc,xa,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR)
| ~ sdtmndtplgtdt0(X1,xR,xc) )
& ~ sdtmndtplgtdt0(xa,xR,xc) )
| ~ sP17 ),
inference(nnf_transformation,[],[f75]) ).
fof(f116,plain,
( ( ~ aReductOfIn0(xc,xa,xR)
& ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(X0,xR,xc) )
& ~ sdtmndtplgtdt0(xa,xR,xc) )
| ~ sP17 ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
( ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& ( xb = X2
| ( ( aReductOfIn0(xb,X2,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X2,xR)
& sdtmndtplgtdt0(X3,xR,xb) ) )
& sdtmndtplgtdt0(X2,xR,xb) ) )
& sdtmndtasgtdt0(X2,xR,xb)
& sP15(X2) )
| ~ sP16 ),
inference(nnf_transformation,[],[f74]) ).
fof(f118,plain,
( ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& ( xb = X0
| ( ( aReductOfIn0(xb,X0,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,X0,xR)
& sdtmndtplgtdt0(X1,xR,xb) ) )
& sdtmndtplgtdt0(X0,xR,xb) ) )
& sdtmndtasgtdt0(X0,xR,xb)
& sP15(X0) )
| ~ sP16 ),
inference(rectify,[],[f117]) ).
fof(f119,plain,
( ( aElement0(sK38)
& aReductOfIn0(sK38,xa,xR)
& ( xb = sK38
| ( ( aReductOfIn0(xb,sK38,xR)
| ( aElement0(sK39)
& aReductOfIn0(sK39,sK38,xR)
& sdtmndtplgtdt0(sK39,xR,xb) ) )
& sdtmndtplgtdt0(sK38,xR,xb) ) )
& sdtmndtasgtdt0(sK38,xR,xb)
& sP15(sK38) )
| ~ sP16 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38,sK39]),skolemize(X0,sK38),skolemize(X1,sK39)],[f118]) ).
fof(f120,plain,
! [X2] :
( ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,xa,xR)
& ( xc = X4
| ( ( aReductOfIn0(xc,X4,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X4,xR)
& sdtmndtplgtdt0(X5,xR,xc) ) )
& sdtmndtplgtdt0(X4,xR,xc) ) )
& sdtmndtasgtdt0(X4,xR,xc)
& sP14(X2,X4) )
| ~ sP15(X2) ),
inference(nnf_transformation,[],[f73]) ).
fof(f121,plain,
! [X0] :
( ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& ( xc = X1
| ( ( aReductOfIn0(xc,X1,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,X1,xR)
& sdtmndtplgtdt0(X2,xR,xc) ) )
& sdtmndtplgtdt0(X1,xR,xc) ) )
& sdtmndtasgtdt0(X1,xR,xc)
& sP14(X0,X1) )
| ~ sP15(X0) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0] :
( ( aElement0(sK40(X0))
& aReductOfIn0(sK40(X0),xa,xR)
& ( xc = sK40(X0)
| ( ( aReductOfIn0(xc,sK40(X0),xR)
| ( aElement0(sK41(X0))
& aReductOfIn0(sK41(X0),sK40(X0),xR)
& sdtmndtplgtdt0(sK41(X0),xR,xc) ) )
& sdtmndtplgtdt0(sK40(X0),xR,xc) ) )
& sdtmndtasgtdt0(sK40(X0),xR,xc)
& sP14(X0,sK40(X0)) )
| ~ sP15(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X1,sK40(X0)),skolemize(X2,sK41(X0))],[f121]) ).
fof(f123,plain,
! [X2,X4] :
( ? [X6] :
( aElement0(X6)
& sP13(X6,X2)
& sdtmndtasgtdt0(X2,xR,X6)
& sP12(X6,X4)
& sdtmndtasgtdt0(X4,xR,X6)
& sP11(X6) )
| ~ sP14(X2,X4) ),
inference(nnf_transformation,[],[f72]) ).
fof(f124,plain,
! [X0,X1] :
( ? [X2] :
( aElement0(X2)
& sP13(X2,X0)
& sdtmndtasgtdt0(X0,xR,X2)
& sP12(X2,X1)
& sdtmndtasgtdt0(X1,xR,X2)
& sP11(X2) )
| ~ sP14(X0,X1) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ( aElement0(sK42(X0,X1))
& sP13(sK42(X0,X1),X0)
& sdtmndtasgtdt0(X0,xR,sK42(X0,X1))
& sP12(sK42(X0,X1),X1)
& sdtmndtasgtdt0(X1,xR,sK42(X0,X1))
& sP11(sK42(X0,X1)) )
| ~ sP14(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(X2,sK42(X0,X1))],[f124]) ).
fof(f132,plain,
! [X6] :
( ? [X9] :
( aElement0(X9)
& sP10(X9,X6)
& sdtmndtasgtdt0(X6,xR,X9)
& ! [X11] : ~ aReductOfIn0(X11,X9,xR)
& aNormalFormOfIn0(X9,X6,xR)
& sP9(X9)
& sdtmndtasgtdt0(xb,xR,X9)
& sP8(X9)
& sdtmndtasgtdt0(xc,xR,X9) )
| ~ sP11(X6) ),
inference(nnf_transformation,[],[f69]) ).
fof(f133,plain,
! [X0] :
( ? [X1] :
( aElement0(X1)
& sP10(X1,X0)
& sdtmndtasgtdt0(X0,xR,X1)
& ! [X2] : ~ aReductOfIn0(X2,X1,xR)
& aNormalFormOfIn0(X1,X0,xR)
& sP9(X1)
& sdtmndtasgtdt0(xb,xR,X1)
& sP8(X1)
& sdtmndtasgtdt0(xc,xR,X1) )
| ~ sP11(X0) ),
inference(rectify,[],[f132]) ).
fof(f134,plain,
! [X0] :
( ( aElement0(sK45(X0))
& sP10(sK45(X0),X0)
& sdtmndtasgtdt0(X0,xR,sK45(X0))
& ! [X2] : ~ aReductOfIn0(X2,sK45(X0),xR)
& aNormalFormOfIn0(sK45(X0),X0,xR)
& sP9(sK45(X0))
& sdtmndtasgtdt0(xb,xR,sK45(X0))
& sP8(sK45(X0))
& sdtmndtasgtdt0(xc,xR,sK45(X0)) )
| ~ sP11(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(X1,sK45(X0))],[f133]) ).
fof(f144,plain,
( ! [X0] :
( ~ aElement0(X0)
| ( xb != X0
& ~ aReductOfIn0(X0,xb,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xb,xR)
| ~ sdtmndtplgtdt0(X1,xR,X0) )
& ~ sdtmndtplgtdt0(xb,xR,X0)
& ~ sdtmndtasgtdt0(xb,xR,X0) )
| sP18(X0) )
& ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& sdtmndtplgtdt0(X2,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,xa,xR)
& sdtmndtplgtdt0(X3,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& ( sP16
| ( ~ aReductOfIn0(xb,xa,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,xa,xR)
| ~ sdtmndtplgtdt0(X4,xR,xb) )
& ~ sdtmndtplgtdt0(xa,xR,xb) )
| sP17 ) ),
inference(rectify,[],[f77]) ).
fof(f145,plain,
( ! [X0] :
( ~ aElement0(X0)
| ( xb != X0
& ~ aReductOfIn0(X0,xb,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xb,xR)
| ~ sdtmndtplgtdt0(X1,xR,X0) )
& ~ sdtmndtplgtdt0(xb,xR,X0)
& ~ sdtmndtasgtdt0(xb,xR,X0) )
| sP18(X0) )
& ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ( aElement0(sK49)
& aReductOfIn0(sK49,xa,xR)
& sdtmndtplgtdt0(sK49,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ( aElement0(sK50)
& aReductOfIn0(sK50,xa,xR)
& sdtmndtplgtdt0(sK50,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& ( sP16
| ( ~ aReductOfIn0(xb,xa,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,xa,xR)
| ~ sdtmndtplgtdt0(X4,xR,xb) )
& ~ sdtmndtplgtdt0(xa,xR,xb) )
| sP17 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50]),skolemize(X2,sK49),skolemize(X3,sK50)],[f144]) ).
fof(f209,plain,
aElement0(xc),
inference(cnf_transformation,[],[f17]) ).
fof(f210,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f234,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sP18(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f238,plain,
! [X0] :
( xc != X0
| ~ sP18(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f239,plain,
( ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sP17 ),
inference(cnf_transformation,[],[f116]) ).
fof(f242,plain,
( sP15(sK38)
| ~ sP16 ),
inference(cnf_transformation,[],[f119]) ).
fof(f250,plain,
! [X0] :
( sP14(X0,sK40(X0))
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f258,plain,
! [X0,X1] :
( sP11(sK42(X0,X1))
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f272,plain,
! [X0] :
( sdtmndtasgtdt0(xc,xR,sK45(X0))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f274,plain,
! [X0] :
( sdtmndtasgtdt0(xb,xR,sK45(X0))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f280,plain,
! [X0] :
( aElement0(sK45(X0))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f294,plain,
! [X4] :
( sP16
| ~ aElement0(X4)
| ~ aReductOfIn0(X4,xa,xR)
| ~ sdtmndtplgtdt0(X4,xR,xb)
| sP17 ),
inference(cnf_transformation,[],[f145]) ).
fof(f295,plain,
( sP16
| ~ aReductOfIn0(xb,xa,xR)
| sP17 ),
inference(cnf_transformation,[],[f145]) ).
fof(f296,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(cnf_transformation,[],[f145]) ).
fof(f297,plain,
( xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(cnf_transformation,[],[f145]) ).
fof(f301,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(cnf_transformation,[],[f145]) ).
fof(f303,plain,
( xa = xb
| aReductOfIn0(xb,xa,xR)
| sdtmndtplgtdt0(sK49,xR,xb) ),
inference(cnf_transformation,[],[f145]) ).
fof(f304,plain,
( xa = xb
| aReductOfIn0(xb,xa,xR)
| aReductOfIn0(sK49,xa,xR) ),
inference(cnf_transformation,[],[f145]) ).
fof(f305,plain,
( xa = xb
| aReductOfIn0(xb,xa,xR)
| aElement0(sK49) ),
inference(cnf_transformation,[],[f145]) ).
fof(f306,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0)
| sP18(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f310,plain,
! [X0] :
( ~ aElement0(X0)
| xb != X0
| sP18(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f314,plain,
~ sP18(xc),
inference(equality_resolution,[],[f238]) ).
fof(f315,plain,
( ~ aElement0(xb)
| sP18(xb) ),
inference(equality_resolution,[],[f310]) ).
fof(f319,definition,
( spl51_1
<=> sP17 ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f327,definition,
( spl51_3
<=> sP16 ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
fof(f332,definition,
( spl51_4
<=> ! [X4] :
( ~ aElement0(X4)
| ~ sdtmndtplgtdt0(X4,xR,xb)
| ~ aReductOfIn0(X4,xa,xR) ) ),
introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).
fof(f333,plain,
( ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,xb)
| ~ aElement0(X4)
| ~ aReductOfIn0(X4,xa,xR) )
| ~ spl51_4 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f334,plain,
( spl51_1
| spl51_4
| spl51_3 ),
inference(avatar_split_clause,[],[f294,f327,f332,f319]) ).
fof(f336,definition,
( spl51_5
<=> aReductOfIn0(xb,xa,xR) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
fof(f339,plain,
( spl51_1
| ~ spl51_5
| spl51_3 ),
inference(avatar_split_clause,[],[f295,f327,f336,f319]) ).
fof(f341,definition,
( spl51_6
<=> sdtmndtplgtdt0(xa,xR,xc) ),
introduced(definition,[new_symbols(definition,[spl51_6])],[avatar_definition]) ).
fof(f345,definition,
( spl51_7
<=> xa = xc ),
introduced(definition,[new_symbols(definition,[spl51_7])],[avatar_definition]) ).
fof(f347,plain,
( xa = xc
| ~ spl51_7 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f348,plain,
( spl51_6
| spl51_7 ),
inference(avatar_split_clause,[],[f297,f345,f341]) ).
fof(f369,definition,
( spl51_12
<=> xa = xb ),
introduced(definition,[new_symbols(definition,[spl51_12])],[avatar_definition]) ).
fof(f371,plain,
( xa = xb
| ~ spl51_12 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f374,definition,
( spl51_13
<=> sdtmndtplgtdt0(sK49,xR,xb) ),
introduced(definition,[new_symbols(definition,[spl51_13])],[avatar_definition]) ).
fof(f376,plain,
( sdtmndtplgtdt0(sK49,xR,xb)
| ~ spl51_13 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f377,plain,
( spl51_13
| spl51_5
| spl51_12 ),
inference(avatar_split_clause,[],[f303,f369,f336,f374]) ).
fof(f379,definition,
( spl51_14
<=> aReductOfIn0(sK49,xa,xR) ),
introduced(definition,[new_symbols(definition,[spl51_14])],[avatar_definition]) ).
fof(f381,plain,
( aReductOfIn0(sK49,xa,xR)
| ~ spl51_14 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f382,plain,
( spl51_14
| spl51_5
| spl51_12 ),
inference(avatar_split_clause,[],[f304,f369,f336,f379]) ).
fof(f384,definition,
( spl51_15
<=> aElement0(sK49) ),
introduced(definition,[new_symbols(definition,[spl51_15])],[avatar_definition]) ).
fof(f386,plain,
( aElement0(sK49)
| ~ spl51_15 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f387,plain,
( spl51_15
| spl51_5
| spl51_12 ),
inference(avatar_split_clause,[],[f305,f369,f336,f384]) ).
fof(f389,definition,
( spl51_16
<=> sP18(xb) ),
introduced(definition,[new_symbols(definition,[spl51_16])],[avatar_definition]) ).
fof(f391,plain,
( sP18(xb)
| ~ spl51_16 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f393,definition,
( spl51_17
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[spl51_17])],[avatar_definition]) ).
fof(f396,plain,
( spl51_16
| ~ spl51_17 ),
inference(avatar_split_clause,[],[f315,f393,f389]) ).
fof(f398,definition,
( spl51_18
<=> sP15(sK38) ),
introduced(definition,[new_symbols(definition,[spl51_18])],[avatar_definition]) ).
fof(f400,plain,
( sP15(sK38)
| ~ spl51_18 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f401,plain,
( ~ spl51_3
| spl51_18 ),
inference(avatar_split_clause,[],[f242,f398,f327]) ).
fof(f445,plain,
( ~ spl51_1
| ~ spl51_6 ),
inference(avatar_split_clause,[],[f239,f341,f319]) ).
fof(f451,plain,
spl51_17,
inference(avatar_split_clause,[],[f210,f393]) ).
fof(f469,plain,
( ~ aElement0(sK49)
| ~ aReductOfIn0(sK49,xa,xR)
| ~ spl51_4
| ~ spl51_13 ),
inference(resolution,[],[f333,f376]) ).
fof(f470,plain,
( ~ aReductOfIn0(sK49,xa,xR)
| ~ spl51_4
| ~ spl51_13
| ~ spl51_15 ),
inference(forward_subsumption_resolution,[],[f469,f386]) ).
fof(f472,plain,
( $false
| ~ spl51_4
| ~ spl51_13
| ~ spl51_14
| ~ spl51_15 ),
inference(forward_subsumption_resolution,[],[f470,f381]) ).
fof(f473,plain,
( ~ spl51_4
| ~ spl51_13
| ~ spl51_14
| ~ spl51_15 ),
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f498,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(xa,xR,X0)
| ~ sP18(X0) )
| ~ spl51_7 ),
inference(forward_demodulation,[],[f234,f347]) ).
fof(f500,plain,
( ~ sP18(xb)
| ~ spl51_7 ),
inference(resolution,[],[f498,f301]) ).
fof(f501,plain,
( $false
| ~ spl51_7
| ~ spl51_16 ),
inference(forward_subsumption_resolution,[],[f500,f391]) ).
fof(f502,plain,
( ~ spl51_7
| ~ spl51_16 ),
inference(avatar_contradiction_clause,[],[f501]) ).
fof(f516,definition,
( spl51_33
<=> sP18(xc) ),
introduced(definition,[new_symbols(definition,[spl51_33])],[avatar_definition]) ).
fof(f517,plain,
( ~ sP18(xc)
| spl51_33 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f520,definition,
( spl51_34
<=> aElement0(xc) ),
introduced(definition,[new_symbols(definition,[spl51_34])],[avatar_definition]) ).
fof(f521,plain,
( aElement0(xc)
| ~ spl51_34 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f537,plain,
spl51_34,
inference(avatar_split_clause,[],[f209,f520]) ).
fof(f538,plain,
~ spl51_33,
inference(avatar_split_clause,[],[f314,f516]) ).
fof(f550,plain,
! [X0] :
( ~ sP18(sK45(X0))
| ~ sP11(X0) ),
inference(resolution,[],[f272,f234]) ).
fof(f552,plain,
! [X0] :
( ~ sP11(X0)
| ~ aElement0(sK45(X0))
| sP18(sK45(X0)) ),
inference(resolution,[],[f274,f306]) ).
fof(f554,plain,
! [X0] :
( ~ sP11(X0)
| sP18(sK45(X0)) ),
inference(forward_subsumption_resolution,[],[f552,f280]) ).
fof(f555,plain,
! [X0] : ~ sP11(X0),
inference(forward_subsumption_resolution,[],[f554,f550]) ).
fof(f556,plain,
! [X0,X1] : ~ sP14(X0,X1),
inference(resolution,[],[f555,f258]) ).
fof(f557,plain,
! [X0] : ~ sP15(X0),
inference(resolution,[],[f556,f250]) ).
fof(f558,plain,
( $false
| ~ spl51_18 ),
inference(resolution,[],[f557,f400]) ).
fof(f561,plain,
~ spl51_18,
inference(avatar_contradiction_clause,[],[f558]) ).
fof(f567,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| sP18(X0) )
| ~ spl51_12 ),
inference(superposition,[],[f306,f371]) ).
fof(f593,plain,
( ~ aElement0(xc)
| sP18(xc)
| ~ spl51_12 ),
inference(resolution,[],[f567,f296]) ).
fof(f595,plain,
( sP18(xc)
| ~ spl51_12
| ~ spl51_34 ),
inference(forward_subsumption_resolution,[],[f593,f521]) ).
fof(f596,plain,
( $false
| ~ spl51_12
| spl51_33
| ~ spl51_34 ),
inference(forward_subsumption_resolution,[],[f595,f517]) ).
fof(f597,plain,
( ~ spl51_12
| spl51_33
| ~ spl51_34 ),
inference(avatar_contradiction_clause,[],[f596]) ).
cnf(s2,plain,
( spl51_1
| spl51_3
| spl51_4 ),
inference(sat_conversion,[],[f334]) ).
cnf(s3,plain,
( spl51_1
| spl51_3
| ~ spl51_5 ),
inference(sat_conversion,[],[f339]) ).
cnf(s4,plain,
( spl51_6
| spl51_7 ),
inference(sat_conversion,[],[f348]) ).
cnf(s9,plain,
( spl51_5
| spl51_12
| spl51_13 ),
inference(sat_conversion,[],[f377]) ).
cnf(s10,plain,
( spl51_5
| spl51_12
| spl51_14 ),
inference(sat_conversion,[],[f382]) ).
cnf(s11,plain,
( spl51_5
| spl51_12
| spl51_15 ),
inference(sat_conversion,[],[f387]) ).
cnf(s12,plain,
( spl51_16
| ~ spl51_17 ),
inference(sat_conversion,[],[f396]) ).
cnf(s13,plain,
( ~ spl51_3
| spl51_18 ),
inference(sat_conversion,[],[f401]) ).
cnf(s21,plain,
( ~ spl51_1
| ~ spl51_6 ),
inference(sat_conversion,[],[f445]) ).
cnf(s24,plain,
spl51_17,
inference(sat_conversion,[],[f451]) ).
cnf(s26,plain,
( ~ spl51_4
| ~ spl51_13
| ~ spl51_14
| ~ spl51_15 ),
inference(sat_conversion,[],[f473]) ).
cnf(s29,plain,
( ~ spl51_7
| ~ spl51_16 ),
inference(sat_conversion,[],[f502]) ).
cnf(s35,plain,
spl51_34,
inference(sat_conversion,[],[f537]) ).
cnf(s36,plain,
~ spl51_33,
inference(sat_conversion,[],[f538]) ).
cnf(s38,plain,
~ spl51_18,
inference(sat_conversion,[],[f561]) ).
cnf(s43,plain,
( ~ spl51_12
| spl51_33
| ~ spl51_34 ),
inference(sat_conversion,[],[f597]) ).
cnf(s44,plain,
~ spl51_12,
inference(rat,[],[s43,s36,s35]) ).
cnf(s48,plain,
~ spl51_3,
inference(rat,[],[s13,s38]) ).
cnf(s49,plain,
spl51_16,
inference(rat,[],[s12,s24]) ).
cnf(s50,plain,
~ spl51_7,
inference(rat,[],[s29,s49]) ).
cnf(s51,plain,
( spl51_5
| spl51_15 ),
inference(rat,[],[s11,s44]) ).
cnf(s52,plain,
( spl51_5
| spl51_14 ),
inference(rat,[],[s10,s44]) ).
cnf(s53,plain,
( spl51_5
| spl51_13 ),
inference(rat,[],[s9,s44]) ).
cnf(s58,plain,
spl51_6,
inference(rat,[],[s4,s50]) ).
cnf(s60,plain,
~ spl51_1,
inference(rat,[],[s21,s58]) ).
cnf(s61,plain,
~ spl51_5,
inference(rat,[],[s3,s48,s60]) ).
cnf(s62,plain,
spl51_15,
inference(rat,[],[s51,s61]) ).
cnf(s63,plain,
spl51_14,
inference(rat,[],[s52,s61]) ).
cnf(s64,plain,
spl51_13,
inference(rat,[],[s53,s61]) ).
cnf(s65,plain,
~ spl51_4,
inference(rat,[],[s26,s62,s63,s64]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s2,s65,s48,s60]) ).
fof(f598,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM022+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:48:13 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.27 % (1614998)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (1615006)dis+10_1_sil=32000:sp=arity:random_seed=2955913888:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (1615004)% WARNING: option uhcvi not known.
% 0.18/0.27 % (1615006) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1614998-1615006"...
% 0.18/0.27 % (1615003)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1463203314_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % (1615004)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3182895855:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (1615005)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=60697836:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (1615006)...printing done.
% 0.18/0.27 % (1615007)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2741887313:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (1615009)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1002177599:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.27 % (1615008)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2488971350:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % (1615006)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (1615006)------------------------------
% 0.18/0.27 % (1615006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (1615006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (1615006)CaDiCaL version: 2.1.3
% 0.18/0.27 % (1615006)Termination reason: Refutation
% 0.18/0.27 % (1615006)Time elapsed: 0.007 s
% 0.18/0.27 % (1615006)Peak memory usage: 13 MB
% 0.18/0.27 % (1615006)Instructions burned: 18 (million)
% 0.18/0.27 % (1614998)Success in time 0.042 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------