%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n006.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 09:39:25 AM UTC 2026
% Result : Theorem 3.12s 1.07s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 75 ( 12 unt; 11 def)
% Number of atoms : 884 ( 86 equ)
% Maximal formula atoms : 96 ( 11 avg)
% Number of connectives : 1013 ( 204 ~; 290 |; 510 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 187 ( 77 !; 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(f23,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(f32,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,[],[f23]) ).
fof(f33,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,[],[f32]) ).
fof(f58,definition,
! [X9] :
( xc = X9
| ( ( aReductOfIn0(X9,xc,xR)
| ? [X13] :
( aElement0(X13)
& aReductOfIn0(X13,xc,xR)
& sdtmndtplgtdt0(X13,xR,X9) ) )
& sdtmndtplgtdt0(xc,xR,X9) )
| ~ sP4(X9) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f59,definition,
! [X9] :
( xb = X9
| ( ( aReductOfIn0(X9,xb,xR)
| ? [X12] :
( aElement0(X12)
& aReductOfIn0(X12,xb,xR)
& sdtmndtplgtdt0(X12,xR,X9) ) )
& sdtmndtplgtdt0(xb,xR,X9) )
| ~ sP5(X9) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f60,definition,
! [X9,X6] :
( X6 = X9
| ( ( aReductOfIn0(X9,X6,xR)
| ? [X10] :
( aElement0(X10)
& aReductOfIn0(X10,X6,xR)
& sdtmndtplgtdt0(X10,xR,X9) ) )
& sdtmndtplgtdt0(X6,xR,X9) )
| ~ sP6(X9,X6) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f61,definition,
! [X6] :
( ? [X9] :
( aElement0(X9)
& sP6(X9,X6)
& sdtmndtasgtdt0(X6,xR,X9)
& ! [X11] : ~ aReductOfIn0(X11,X9,xR)
& aNormalFormOfIn0(X9,X6,xR)
& sP5(X9)
& sdtmndtasgtdt0(xb,xR,X9)
& sP4(X9)
& sdtmndtasgtdt0(xc,xR,X9) )
| ~ sP7(X6) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f62,definition,
! [X6,X4] :
( X4 = X6
| ( ( aReductOfIn0(X6,X4,xR)
| ? [X8] :
( aElement0(X8)
& aReductOfIn0(X8,X4,xR)
& sdtmndtplgtdt0(X8,xR,X6) ) )
& sdtmndtplgtdt0(X4,xR,X6) )
| ~ sP8(X6,X4) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f63,definition,
! [X6,X2] :
( X2 = X6
| ( ( aReductOfIn0(X6,X2,xR)
| ? [X7] :
( aElement0(X7)
& aReductOfIn0(X7,X2,xR)
& sdtmndtplgtdt0(X7,xR,X6) ) )
& sdtmndtplgtdt0(X2,xR,X6) )
| ~ sP9(X6,X2) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f64,definition,
! [X2,X4] :
( ? [X6] :
( aElement0(X6)
& sP9(X6,X2)
& sdtmndtasgtdt0(X2,xR,X6)
& sP8(X6,X4)
& sdtmndtasgtdt0(X4,xR,X6)
& sP7(X6) )
| ~ sP10(X2,X4) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f65,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)
& sP10(X2,X4) )
| ~ sP11(X2) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f66,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)
& sP11(X2) )
| ~ sP12 ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f67,definition,
( ( ~ aReductOfIn0(xc,xa,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR)
| ~ sdtmndtplgtdt0(X1,xR,xc) )
& ~ sdtmndtplgtdt0(xa,xR,xc) )
| ~ sP13 ),
introduced(definition,[new_symbols(definition,[sP13])],[predicate_definition_introduction]) ).
fof(f68,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) )
| ~ sP14(X16) ),
introduced(definition,[new_symbols(definition,[sP14])],[predicate_definition_introduction]) ).
fof(f69,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) )
| sP14(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)
& ( sP12
| ( ~ aReductOfIn0(xb,xa,xR)
& ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(X0,xR,xb) )
& ~ sdtmndtplgtdt0(xa,xR,xb) )
| sP13 ) ),
inference(definition_folding,[],[f33,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58]) ).
fof(f86,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) )
| ~ sP14(X16) ),
inference(nnf_transformation,[],[f68]) ).
fof(f87,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) )
| ~ sP14(X0) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
( ( ~ aReductOfIn0(xc,xa,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR)
| ~ sdtmndtplgtdt0(X1,xR,xc) )
& ~ sdtmndtplgtdt0(xa,xR,xc) )
| ~ sP13 ),
inference(nnf_transformation,[],[f67]) ).
fof(f89,plain,
( ( ~ aReductOfIn0(xc,xa,xR)
& ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(X0,xR,xc) )
& ~ sdtmndtplgtdt0(xa,xR,xc) )
| ~ sP13 ),
inference(rectify,[],[f88]) ).
fof(f90,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)
& sP11(X2) )
| ~ sP12 ),
inference(nnf_transformation,[],[f66]) ).
fof(f91,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)
& sP11(X0) )
| ~ sP12 ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
( ( aElement0(sK23)
& aReductOfIn0(sK23,xa,xR)
& ( xb = sK23
| ( ( aReductOfIn0(xb,sK23,xR)
| ( aElement0(sK24)
& aReductOfIn0(sK24,sK23,xR)
& sdtmndtplgtdt0(sK24,xR,xb) ) )
& sdtmndtplgtdt0(sK23,xR,xb) ) )
& sdtmndtasgtdt0(sK23,xR,xb)
& sP11(sK23) )
| ~ sP12 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24]),skolemize(X0,sK23),skolemize(X1,sK24)],[f91]) ).
fof(f93,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)
& sP10(X2,X4) )
| ~ sP11(X2) ),
inference(nnf_transformation,[],[f65]) ).
fof(f94,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)
& sP10(X0,X1) )
| ~ sP11(X0) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0] :
( ( aElement0(sK25(X0))
& aReductOfIn0(sK25(X0),xa,xR)
& ( xc = sK25(X0)
| ( ( aReductOfIn0(xc,sK25(X0),xR)
| ( aElement0(sK26(X0))
& aReductOfIn0(sK26(X0),sK25(X0),xR)
& sdtmndtplgtdt0(sK26(X0),xR,xc) ) )
& sdtmndtplgtdt0(sK25(X0),xR,xc) ) )
& sdtmndtasgtdt0(sK25(X0),xR,xc)
& sP10(X0,sK25(X0)) )
| ~ sP11(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26]),skolemize(X1,sK25(X0)),skolemize(X2,sK26(X0))],[f94]) ).
fof(f96,plain,
! [X2,X4] :
( ? [X6] :
( aElement0(X6)
& sP9(X6,X2)
& sdtmndtasgtdt0(X2,xR,X6)
& sP8(X6,X4)
& sdtmndtasgtdt0(X4,xR,X6)
& sP7(X6) )
| ~ sP10(X2,X4) ),
inference(nnf_transformation,[],[f64]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2] :
( aElement0(X2)
& sP9(X2,X0)
& sdtmndtasgtdt0(X0,xR,X2)
& sP8(X2,X1)
& sdtmndtasgtdt0(X1,xR,X2)
& sP7(X2) )
| ~ sP10(X0,X1) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ( aElement0(sK27(X0,X1))
& sP9(sK27(X0,X1),X0)
& sdtmndtasgtdt0(X0,xR,sK27(X0,X1))
& sP8(sK27(X0,X1),X1)
& sdtmndtasgtdt0(X1,xR,sK27(X0,X1))
& sP7(sK27(X0,X1)) )
| ~ sP10(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X2,sK27(X0,X1))],[f97]) ).
fof(f105,plain,
! [X6] :
( ? [X9] :
( aElement0(X9)
& sP6(X9,X6)
& sdtmndtasgtdt0(X6,xR,X9)
& ! [X11] : ~ aReductOfIn0(X11,X9,xR)
& aNormalFormOfIn0(X9,X6,xR)
& sP5(X9)
& sdtmndtasgtdt0(xb,xR,X9)
& sP4(X9)
& sdtmndtasgtdt0(xc,xR,X9) )
| ~ sP7(X6) ),
inference(nnf_transformation,[],[f61]) ).
fof(f106,plain,
! [X0] :
( ? [X1] :
( aElement0(X1)
& sP6(X1,X0)
& sdtmndtasgtdt0(X0,xR,X1)
& ! [X2] : ~ aReductOfIn0(X2,X1,xR)
& aNormalFormOfIn0(X1,X0,xR)
& sP5(X1)
& sdtmndtasgtdt0(xb,xR,X1)
& sP4(X1)
& sdtmndtasgtdt0(xc,xR,X1) )
| ~ sP7(X0) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ( aElement0(sK30(X0))
& sP6(sK30(X0),X0)
& sdtmndtasgtdt0(X0,xR,sK30(X0))
& ! [X2] : ~ aReductOfIn0(X2,sK30(X0),xR)
& aNormalFormOfIn0(sK30(X0),X0,xR)
& sP5(sK30(X0))
& sdtmndtasgtdt0(xb,xR,sK30(X0))
& sP4(sK30(X0))
& sdtmndtasgtdt0(xc,xR,sK30(X0)) )
| ~ sP7(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X1,sK30(X0))],[f106]) ).
fof(f117,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) )
| sP14(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)
& ( sP12
| ( ~ aReductOfIn0(xb,xa,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,xa,xR)
| ~ sdtmndtplgtdt0(X4,xR,xb) )
& ~ sdtmndtplgtdt0(xa,xR,xb) )
| sP13 ) ),
inference(rectify,[],[f69]) ).
fof(f118,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) )
| sP14(X0) )
& ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ( aElement0(sK34)
& aReductOfIn0(sK34,xa,xR)
& sdtmndtplgtdt0(sK34,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ( aElement0(sK35)
& aReductOfIn0(sK35,xa,xR)
& sdtmndtplgtdt0(sK35,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& ( sP12
| ( ~ aReductOfIn0(xb,xa,xR)
& ! [X4] :
( ~ aElement0(X4)
| ~ aReductOfIn0(X4,xa,xR)
| ~ sdtmndtplgtdt0(X4,xR,xb) )
& ~ sdtmndtplgtdt0(xa,xR,xb) )
| sP13 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35]),skolemize(X2,sK34),skolemize(X3,sK35)],[f117]) ).
fof(f155,plain,
aElement0(xc),
inference(cnf_transformation,[],[f17]) ).
fof(f156,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f180,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f184,plain,
! [X0] :
( xc != X0
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f185,plain,
( ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sP13 ),
inference(cnf_transformation,[],[f89]) ).
fof(f188,plain,
( sP11(sK23)
| ~ sP12 ),
inference(cnf_transformation,[],[f92]) ).
fof(f196,plain,
! [X0] :
( sP10(X0,sK25(X0))
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f204,plain,
! [X0,X1] :
( sP7(sK27(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f218,plain,
! [X0] :
( sdtmndtasgtdt0(xc,xR,sK30(X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f220,plain,
! [X0] :
( sdtmndtasgtdt0(xb,xR,sK30(X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f226,plain,
! [X0] :
( aElement0(sK30(X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f239,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| sP12
| sP13 ),
inference(cnf_transformation,[],[f118]) ).
fof(f242,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(cnf_transformation,[],[f118]) ).
fof(f243,plain,
( sdtmndtplgtdt0(xa,xR,xc)
| xa = xc ),
inference(cnf_transformation,[],[f118]) ).
fof(f247,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(cnf_transformation,[],[f118]) ).
fof(f248,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| xa = xb ),
inference(cnf_transformation,[],[f118]) ).
fof(f252,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0)
| sP14(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f256,plain,
! [X0] :
( ~ aElement0(X0)
| xb != X0
| sP14(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f292,plain,
~ sP14(xc),
inference(equality_resolution,[],[f184]) ).
fof(f293,plain,
( sP14(xb)
| ~ aElement0(xb) ),
inference(equality_resolution,[],[f256]) ).
fof(f297,plain,
( xa = xb
| sP12
| sP13 ),
inference(resolution,[],[f248,f239]) ).
fof(f304,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xa,xR,X0)
| ~ aElement0(X0)
| sP14(X0)
| sP12
| sP13 ),
inference(superposition,[],[f252,f297]) ).
fof(f308,plain,
( sP14(xc)
| ~ aElement0(xc)
| sP12
| sP13 ),
inference(resolution,[],[f304,f242]) ).
fof(f335,plain,
( ~ aElement0(xc)
| sP12
| sP13 ),
inference(resolution,[],[f292,f308]) ).
fof(f336,plain,
( sP13
| sP12 ),
inference(forward_subsumption_resolution,[],[f335,f155]) ).
fof(f337,plain,
( xa = xc
| ~ sP13 ),
inference(resolution,[],[f185,f243]) ).
fof(f353,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xa,xR,X0)
| ~ sP14(X0)
| ~ sP13 ),
inference(superposition,[],[f180,f337]) ).
fof(f356,plain,
( ~ sP14(xb)
| ~ sP13 ),
inference(resolution,[],[f353,f247]) ).
fof(f361,plain,
( ~ sP13
| ~ aElement0(xb) ),
inference(resolution,[],[f356,f293]) ).
fof(f363,plain,
~ sP13,
inference(forward_subsumption_resolution,[],[f361,f156]) ).
fof(f364,plain,
sP12,
inference(resolution,[],[f363,f336]) ).
fof(f405,plain,
! [X0] :
( ~ sP14(sK30(X0))
| ~ sP7(X0) ),
inference(resolution,[],[f218,f180]) ).
fof(f408,plain,
! [X0] :
( ~ sP7(X0)
| ~ aElement0(sK30(X0))
| sP14(sK30(X0)) ),
inference(resolution,[],[f220,f252]) ).
fof(f411,plain,
! [X0] :
( ~ sP7(X0)
| sP14(sK30(X0)) ),
inference(forward_subsumption_resolution,[],[f408,f226]) ).
fof(f412,plain,
! [X0] : ~ sP7(X0),
inference(forward_subsumption_resolution,[],[f411,f405]) ).
fof(f413,plain,
! [X0,X1] : ~ sP10(X0,X1),
inference(resolution,[],[f412,f204]) ).
fof(f414,plain,
! [X0] : ~ sP11(X0),
inference(resolution,[],[f413,f196]) ).
fof(f415,plain,
~ sP12,
inference(resolution,[],[f414,f188]) ).
fof(f416,plain,
$false,
inference(forward_subsumption_resolution,[],[f415,f364]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.07/0.18 % Computer : n006.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 21:48:32 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.12/1.07 % (238960)Detected formulas, will run a generic FOF schedule.
% 3.12/1.07 % (238965)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2818764337:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.12/1.07 % (238970)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1724273806:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.12/1.07 % (238969)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4007615747:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.12/1.07 % (238971)dis-21_1_sil=8000:lcm=predicate:random_seed=4087872696:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.12/1.07 % (238968)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4038293088:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.12/1.07 % (238966)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1822744705:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.12/1.07 % (238967)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=612571871:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.12/1.07 % (238969)First to succeed.
% 3.12/1.07 % (238969)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-238960"
% 3.12/1.07 % (238968)Instruction limit reached!
% 3.12/1.07 % (238968)------------------------------
% 3.12/1.07 % (238968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.07 % (238968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.07 % (238968)CaDiCaL version: 2.1.3
% 3.12/1.07 % (238968)Termination reason: Instruction limit
% 3.12/1.07 % (238968)Termination phase: Saturation
% 3.12/1.07 % (238968)Time elapsed: 0.065 s
% 3.12/1.07 % (238968)Peak memory usage: 90 MB
% 3.12/1.07 % (238968)Instructions burned: 110 (million)
% 3.12/1.07 % (238971)Instruction limit reached!
% 3.12/1.07 % (238971)------------------------------
% 3.12/1.07 % (238971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.07 % (238971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.07 % (238971)CaDiCaL version: 2.1.3
% 3.12/1.07 % (238971)Termination reason: Instruction limit
% 3.12/1.07 % (238971)Termination phase: Saturation
% 3.12/1.07 % (238971)Time elapsed: 0.074 s
% 3.12/1.07 % (238971)Peak memory usage: 89 MB
% 3.12/1.07 % (238971)Instructions burned: 129 (million)
% 3.12/1.07 % (238970)Instruction limit reached!
% 3.12/1.07 % (238970)------------------------------
% 3.12/1.07 % (238970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.07 % (238970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.07 % (238970)CaDiCaL version: 2.1.3
% 3.12/1.07 % (238970)Termination reason: Instruction limit
% 3.12/1.07 % (238970)Termination phase: Saturation
% 3.12/1.07 % (238970)Time elapsed: 0.095 s
% 3.12/1.07 % (238970)Peak memory usage: 90 MB
% 3.12/1.07 % (238970)Instructions burned: 139 (million)
% 3.12/1.07 % (238979)lrs+10_1_sil=8000:sp=occurrence:random_seed=3708909544:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.12/1.07 % (238980)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1822211928:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.12/1.07 % (238979)Also succeeded, but the first one will report.
% 3.12/1.07 % (238981)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2366756775:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.12/1.07 % (238981)Also succeeded, but the first one will report.
% 3.12/1.07 % (238969)Refutation found. Thanks to Tanya!
% 3.12/1.07 % SZS status Theorem for theBenchmark
% 3.12/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.16 % (238969)------------------------------
% 3.50/1.16 % (238969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.16 % (238969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.16 % (238969)CaDiCaL version: 2.1.3
% 3.50/1.16 % (238969)Termination reason: Refutation
% 3.50/1.16 % (238969)Time elapsed: 0.010 s
% 3.50/1.16 % (238969)Peak memory usage: 88 MB
% 3.50/1.16 % (238969)Instructions burned: 15 (million)
% 3.50/1.16 % (238969)------------------------------
% 3.50/1.16 % (238969)------------------------------
% 3.50/1.16 % (238960)Success in time 0.418 s
% 3.50/1.16 % Vampire exiting
%------------------------------------------------------------------------------