%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL674+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n031.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 : Mon Sep 7 12:43:14 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 61 ( 17 unt; 0 def)
% Number of atoms : 1218 ( 0 equ)
% Maximal formula atoms : 250 ( 19 avg)
% Number of connectives : 1996 ( 839 ~; 700 |; 454 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 66 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-1 aty)
% Number of variables : 203 ( 0 sgn 149 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X) ).
fof(transitivity,axiom,
! [X,Y,Z] :
( ( r1(X,Y)
& r1(Y,Z) )
=> r1(X,Z) ) ).
fof(main,conjecture,
~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
| ~ ( ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p6(X)
& ~ p106(X)
& p105(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p6(X)
& ~ p106(X)
& p105(X) ) ) )
| ~ ( ~ p105(Y)
& p104(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p5(X)
& ~ p105(X)
& p104(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p5(X)
& ~ p105(X)
& p104(X) ) ) )
| ~ ( ~ p104(Y)
& p103(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p4(X)
& ~ p104(X)
& p103(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p4(X)
& ~ p104(X)
& p103(X) ) ) )
| ~ ( ~ p103(Y)
& p102(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p3(X)
& ~ p103(X)
& p102(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p3(X)
& ~ p103(X)
& p102(X) ) ) )
| ~ ( ~ p102(Y)
& p101(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p6(X)
| ~ p105(X) )
| p6(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p6(X)
| ~ p105(X) )
| ~ p6(Y) ) )
| ~ p105(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p5(X)
| ~ p104(X) )
| p5(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p5(X)
| ~ p104(X) )
| ~ p5(Y) ) )
| ~ p104(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p4(X)
| ~ p103(X) )
| p4(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p4(X)
| ~ p103(X) )
| ~ p4(Y) ) )
| ~ p103(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p3(X)
| ~ p102(X) )
| p3(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p3(X)
| ~ p102(X) )
| ~ p3(Y) ) )
| ~ p102(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p105(Y)
| ~ p106(Y) )
& ( p104(Y)
| ~ p105(Y) )
& ( p103(Y)
| ~ p104(Y) )
& ( p102(Y)
| ~ p103(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ~ p101(X)
& p100(X) ) ) ).
fof(subgoal_0,plain,
! [X] :
( ( ~ ~ ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p6(X)
& ~ p106(X)
& p105(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p6(X)
& ~ p106(X)
& p105(X) ) ) )
| ~ ( ~ p105(Y)
& p104(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p5(X)
& ~ p105(X)
& p104(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p5(X)
& ~ p105(X)
& p104(X) ) ) )
| ~ ( ~ p104(Y)
& p103(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p4(X)
& ~ p104(X)
& p103(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p4(X)
& ~ p104(X)
& p103(X) ) ) )
| ~ ( ~ p103(Y)
& p102(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p3(X)
& ~ p103(X)
& p102(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p3(X)
& ~ p103(X)
& p102(X) ) ) )
| ~ ( ~ p102(Y)
& p101(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p6(X)
| ~ p105(X) )
| p6(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p6(X)
| ~ p105(X) )
| ~ p6(Y) ) )
| ~ p105(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p5(X)
| ~ p104(X) )
| p5(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p5(X)
| ~ p104(X) )
| ~ p5(Y) ) )
| ~ p104(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p4(X)
| ~ p103(X) )
| p4(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p4(X)
| ~ p103(X) )
| ~ p4(Y) ) )
| ~ p103(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p3(X)
| ~ p102(X) )
| p3(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p3(X)
| ~ p102(X) )
| ~ p3(Y) ) )
| ~ p102(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p105(Y)
| ~ p106(Y) )
& ( p104(Y)
| ~ p105(Y) )
& ( p103(Y)
| ~ p104(Y) )
& ( p102(Y)
| ~ p103(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ~ p101(X) )
=> ~ p100(X) ),
inference(strip,[],[main]) ).
fof(negate_0_0,plain,
~ ! [X] :
( ( ~ ~ ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p6(X)
& ~ p106(X)
& p105(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p6(X)
& ~ p106(X)
& p105(X) ) ) )
| ~ ( ~ p105(Y)
& p104(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p5(X)
& ~ p105(X)
& p104(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p5(X)
& ~ p105(X)
& p104(X) ) ) )
| ~ ( ~ p104(Y)
& p103(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p4(X)
& ~ p104(X)
& p103(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p4(X)
& ~ p104(X)
& p103(X) ) ) )
| ~ ( ~ p103(Y)
& p102(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p3(X)
& ~ p103(X)
& p102(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p3(X)
& ~ p103(X)
& p102(X) ) ) )
| ~ ( ~ p102(Y)
& p101(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p6(X)
| ~ p105(X) )
| p6(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p6(X)
| ~ p105(X) )
| ~ p6(Y) ) )
| ~ p105(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p5(X)
| ~ p104(X) )
| p5(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p5(X)
| ~ p104(X) )
| ~ p5(Y) ) )
| ~ p104(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p4(X)
| ~ p103(X) )
| p4(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p4(X)
| ~ p103(X) )
| ~ p4(Y) ) )
| ~ p103(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p3(X)
| ~ p102(X) )
| p3(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p3(X)
| ~ p102(X) )
| ~ p3(Y) ) )
| ~ p102(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p105(Y)
| ~ p106(Y) )
& ( p104(Y)
| ~ p105(Y) )
& ( p103(Y)
| ~ p104(Y) )
& ( p102(Y)
| ~ p103(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ~ p101(X) )
=> ~ p100(X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( ~ p101(X)
& p100(X)
& ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(X,Y)
| ( ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| ~ r1(Y,X)
| p1(X) ) )
& ( p1(Y)
| ! [X] :
( ~ p1(X)
| ~ p100(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| p100(Y) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| ~ r1(Y,X)
| p2(X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p102(Y)
| ( ( ~ p3(Y)
| ! [X] :
( ~ p102(X)
| ~ r1(Y,X)
| p3(X) ) )
& ( p3(Y)
| ! [X] :
( ~ p102(X)
| ~ p3(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p103(Y)
| p102(Y) )
& ( ~ p103(Y)
| ( ( ~ p4(Y)
| ! [X] :
( ~ p103(X)
| ~ r1(Y,X)
| p4(X) ) )
& ( p4(Y)
| ! [X] :
( ~ p103(X)
| ~ p4(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p104(Y)
| p103(Y) )
& ( ~ p104(Y)
| ( ( ~ p5(Y)
| ! [X] :
( ~ p104(X)
| ~ r1(Y,X)
| p5(X) ) )
& ( p5(Y)
| ! [X] :
( ~ p104(X)
| ~ p5(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p105(Y)
| p104(Y) )
& ( ~ p105(Y)
| ( ( ~ p6(Y)
| ! [X] :
( ~ p105(X)
| ~ r1(Y,X)
| p6(X) ) )
& ( p6(Y)
| ! [X] :
( ~ p105(X)
| ~ p6(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p106(Y)
| p105(Y) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( ~ p102(X)
& ~ p2(X)
& p101(X)
& r1(Y,X) )
& ? [X] :
( ~ p102(X)
& p101(X)
& p2(X)
& r1(Y,X) ) ) )
& ( ~ p101(Y)
| p102(Y)
| ( ? [X] :
( ~ p103(X)
& ~ p3(X)
& p102(X)
& r1(Y,X) )
& ? [X] :
( ~ p103(X)
& p102(X)
& p3(X)
& r1(Y,X) ) ) )
& ( ~ p102(Y)
| p103(Y)
| ( ? [X] :
( ~ p104(X)
& ~ p4(X)
& p103(X)
& r1(Y,X) )
& ? [X] :
( ~ p104(X)
& p103(X)
& p4(X)
& r1(Y,X) ) ) )
& ( ~ p103(Y)
| p104(Y)
| ( ? [X] :
( ~ p105(X)
& ~ p5(X)
& p104(X)
& r1(Y,X) )
& ? [X] :
( ~ p105(X)
& p104(X)
& p5(X)
& r1(Y,X) ) ) )
& ( ~ p104(Y)
| p105(Y)
| ( ? [X] :
( ~ p106(X)
& ~ p6(X)
& p105(X)
& r1(Y,X) )
& ? [X] :
( ~ p106(X)
& p105(X)
& p6(X)
& r1(Y,X) ) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ p101(skolemFOFtoCNF_X)
& p100(skolemFOFtoCNF_X)
& ! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| ( ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| ~ r1(Y,X)
| p1(X) ) )
& ( p1(Y)
| ! [X] :
( ~ p1(X)
| ~ p100(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| p100(Y) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| ~ r1(Y,X)
| p2(X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p102(Y)
| ( ( ~ p3(Y)
| ! [X] :
( ~ p102(X)
| ~ r1(Y,X)
| p3(X) ) )
& ( p3(Y)
| ! [X] :
( ~ p102(X)
| ~ p3(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p103(Y)
| p102(Y) )
& ( ~ p103(Y)
| ( ( ~ p4(Y)
| ! [X] :
( ~ p103(X)
| ~ r1(Y,X)
| p4(X) ) )
& ( p4(Y)
| ! [X] :
( ~ p103(X)
| ~ p4(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p104(Y)
| p103(Y) )
& ( ~ p104(Y)
| ( ( ~ p5(Y)
| ! [X] :
( ~ p104(X)
| ~ r1(Y,X)
| p5(X) ) )
& ( p5(Y)
| ! [X] :
( ~ p104(X)
| ~ p5(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p105(Y)
| p104(Y) )
& ( ~ p105(Y)
| ( ( ~ p6(Y)
| ! [X] :
( ~ p105(X)
| ~ r1(Y,X)
| p6(X) ) )
& ( p6(Y)
| ! [X] :
( ~ p105(X)
| ~ p6(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p106(Y)
| p105(Y) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( ~ p102(X)
& ~ p2(X)
& p101(X)
& r1(Y,X) )
& ? [X] :
( ~ p102(X)
& p101(X)
& p2(X)
& r1(Y,X) ) ) )
& ( ~ p101(Y)
| p102(Y)
| ( ? [X] :
( ~ p103(X)
& ~ p3(X)
& p102(X)
& r1(Y,X) )
& ? [X] :
( ~ p103(X)
& p102(X)
& p3(X)
& r1(Y,X) ) ) )
& ( ~ p102(Y)
| p103(Y)
| ( ? [X] :
( ~ p104(X)
& ~ p4(X)
& p103(X)
& r1(Y,X) )
& ? [X] :
( ~ p104(X)
& p103(X)
& p4(X)
& r1(Y,X) ) ) )
& ( ~ p103(Y)
| p104(Y)
| ( ? [X] :
( ~ p105(X)
& ~ p5(X)
& p104(X)
& r1(Y,X) )
& ? [X] :
( ~ p105(X)
& p104(X)
& p5(X)
& r1(Y,X) ) ) )
& ( ~ p104(Y)
| p105(Y)
| ( ? [X] :
( ~ p106(X)
& ~ p6(X)
& p105(X)
& r1(Y,X) )
& ? [X] :
( ~ p106(X)
& p105(X)
& p6(X)
& r1(Y,X) ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| p3(Y) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| p3(Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : r1(X,X),
inference(canonicalize,[],[reflexivity]) ).
fof(normalize_0_5,plain,
! [X] : r1(X,X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| ( ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| ~ r1(Y,X)
| p1(X) ) )
& ( p1(Y)
| ! [X] :
( ~ p1(X)
| ~ p100(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| p100(Y) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| ~ r1(Y,X)
| p2(X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p102(Y)
| ( ( ~ p3(Y)
| ! [X] :
( ~ p102(X)
| ~ r1(Y,X)
| p3(X) ) )
& ( p3(Y)
| ! [X] :
( ~ p102(X)
| ~ p3(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p103(Y)
| p102(Y) )
& ( ~ p103(Y)
| ( ( ~ p4(Y)
| ! [X] :
( ~ p103(X)
| ~ r1(Y,X)
| p4(X) ) )
& ( p4(Y)
| ! [X] :
( ~ p103(X)
| ~ p4(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p104(Y)
| p103(Y) )
& ( ~ p104(Y)
| ( ( ~ p5(Y)
| ! [X] :
( ~ p104(X)
| ~ r1(Y,X)
| p5(X) ) )
& ( p5(Y)
| ! [X] :
( ~ p104(X)
| ~ p5(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p105(Y)
| p104(Y) )
& ( ~ p105(Y)
| ( ( ~ p6(Y)
| ! [X] :
( ~ p105(X)
| ~ r1(Y,X)
| p6(X) ) )
& ( p6(Y)
| ! [X] :
( ~ p105(X)
| ~ p6(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p106(Y)
| p105(Y) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( ~ p102(X)
& ~ p2(X)
& p101(X)
& r1(Y,X) )
& ? [X] :
( ~ p102(X)
& p101(X)
& p2(X)
& r1(Y,X) ) ) )
& ( ~ p101(Y)
| p102(Y)
| ( ? [X] :
( ~ p103(X)
& ~ p3(X)
& p102(X)
& r1(Y,X) )
& ? [X] :
( ~ p103(X)
& p102(X)
& p3(X)
& r1(Y,X) ) ) )
& ( ~ p102(Y)
| p103(Y)
| ( ? [X] :
( ~ p104(X)
& ~ p4(X)
& p103(X)
& r1(Y,X) )
& ? [X] :
( ~ p104(X)
& p103(X)
& p4(X)
& r1(Y,X) ) ) )
& ( ~ p103(Y)
| p104(Y)
| ( ? [X] :
( ~ p105(X)
& ~ p5(X)
& p104(X)
& r1(Y,X) )
& ? [X] :
( ~ p105(X)
& p104(X)
& p5(X)
& r1(Y,X) ) ) )
& ( ~ p104(Y)
| p105(Y)
| ( ? [X] :
( ~ p106(X)
& ~ p6(X)
& p105(X)
& r1(Y,X) )
& ? [X] :
( ~ p106(X)
& p105(X)
& p6(X)
& r1(Y,X) ) ) ) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_7,plain,
! [Y] :
( ~ r1(skolemFOFtoCNF_X,Y)
| ( ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| ~ r1(Y,X)
| p1(X) ) )
& ( p1(Y)
| ! [X] :
( ~ p1(X)
| ~ p100(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| p100(Y) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| ~ r1(Y,X)
| p2(X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p102(Y)
| ( ( ~ p3(Y)
| ! [X] :
( ~ p102(X)
| ~ r1(Y,X)
| p3(X) ) )
& ( p3(Y)
| ! [X] :
( ~ p102(X)
| ~ p3(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p103(Y)
| p102(Y) )
& ( ~ p103(Y)
| ( ( ~ p4(Y)
| ! [X] :
( ~ p103(X)
| ~ r1(Y,X)
| p4(X) ) )
& ( p4(Y)
| ! [X] :
( ~ p103(X)
| ~ p4(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p104(Y)
| p103(Y) )
& ( ~ p104(Y)
| ( ( ~ p5(Y)
| ! [X] :
( ~ p104(X)
| ~ r1(Y,X)
| p5(X) ) )
& ( p5(Y)
| ! [X] :
( ~ p104(X)
| ~ p5(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p105(Y)
| p104(Y) )
& ( ~ p105(Y)
| ( ( ~ p6(Y)
| ! [X] :
( ~ p105(X)
| ~ r1(Y,X)
| p6(X) ) )
& ( p6(Y)
| ! [X] :
( ~ p105(X)
| ~ p6(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p106(Y)
| p105(Y) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( ~ p102(X)
& ~ p2(X)
& p101(X)
& r1(Y,X) )
& ? [X] :
( ~ p102(X)
& p101(X)
& p2(X)
& r1(Y,X) ) ) )
& ( ~ p101(Y)
| p102(Y)
| ( ? [X] :
( ~ p103(X)
& ~ p3(X)
& p102(X)
& r1(Y,X) )
& ? [X] :
( ~ p103(X)
& p102(X)
& p3(X)
& r1(Y,X) ) ) )
& ( ~ p102(Y)
| p103(Y)
| ( ? [X] :
( ~ p104(X)
& ~ p4(X)
& p103(X)
& r1(Y,X) )
& ? [X] :
( ~ p104(X)
& p103(X)
& p4(X)
& r1(Y,X) ) ) )
& ( ~ p103(Y)
| p104(Y)
| ( ? [X] :
( ~ p105(X)
& ~ p5(X)
& p104(X)
& r1(Y,X) )
& ? [X] :
( ~ p105(X)
& p104(X)
& p5(X)
& r1(Y,X) ) ) )
& ( ~ p104(Y)
| p105(Y)
| ( ? [X] :
( ~ p106(X)
& ~ p6(X)
& p105(X)
& r1(Y,X) )
& ? [X] :
( ~ p106(X)
& p105(X)
& p6(X)
& r1(Y,X) ) ) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p100(Y) )
& ( ~ p102(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) )
& ( ~ p103(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y) )
& ( ~ p104(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y) )
& ( ~ p105(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y) )
& ( ~ p106(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y) )
& ( ~ p100(Y)
| ~ p102(skolemFOFtoCNF_X_10(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) )
& ( ~ p100(Y)
| ~ p102(skolemFOFtoCNF_X_9(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) )
& ( ~ p100(Y)
| ~ p2(skolemFOFtoCNF_X_10(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| p101(skolemFOFtoCNF_X_10(Y)) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| p101(skolemFOFtoCNF_X_9(Y)) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| p2(skolemFOFtoCNF_X_9(Y)) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| r1(Y,skolemFOFtoCNF_X_10(Y)) )
& ( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| r1(Y,skolemFOFtoCNF_X_9(Y)) )
& ( ~ p101(Y)
| ~ p103(skolemFOFtoCNF_X_7(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y) )
& ( ~ p101(Y)
| ~ p103(skolemFOFtoCNF_X_8(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y) )
& ( ~ p101(Y)
| ~ p3(skolemFOFtoCNF_X_8(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y) )
& ( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y)
| p102(skolemFOFtoCNF_X_7(Y)) )
& ( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y)
| p102(skolemFOFtoCNF_X_8(Y)) )
& ( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y)
| p3(skolemFOFtoCNF_X_7(Y)) )
& ( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y)
| r1(Y,skolemFOFtoCNF_X_7(Y)) )
& ( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y)
| r1(Y,skolemFOFtoCNF_X_8(Y)) )
& ( ~ p102(Y)
| ~ p104(skolemFOFtoCNF_X_5(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y) )
& ( ~ p102(Y)
| ~ p104(skolemFOFtoCNF_X_6(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y) )
& ( ~ p102(Y)
| ~ p4(skolemFOFtoCNF_X_6(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y) )
& ( ~ p102(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y)
| p103(skolemFOFtoCNF_X_5(Y)) )
& ( ~ p102(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y)
| p103(skolemFOFtoCNF_X_6(Y)) )
& ( ~ p102(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y)
| p4(skolemFOFtoCNF_X_5(Y)) )
& ( ~ p102(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y)
| r1(Y,skolemFOFtoCNF_X_5(Y)) )
& ( ~ p102(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p103(Y)
| r1(Y,skolemFOFtoCNF_X_6(Y)) )
& ( ~ p103(Y)
| ~ p105(skolemFOFtoCNF_X_3(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y) )
& ( ~ p103(Y)
| ~ p105(skolemFOFtoCNF_X_4(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y) )
& ( ~ p103(Y)
| ~ p5(skolemFOFtoCNF_X_4(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y) )
& ( ~ p103(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y)
| p104(skolemFOFtoCNF_X_3(Y)) )
& ( ~ p103(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y)
| p104(skolemFOFtoCNF_X_4(Y)) )
& ( ~ p103(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y)
| p5(skolemFOFtoCNF_X_3(Y)) )
& ( ~ p103(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y)
| r1(Y,skolemFOFtoCNF_X_3(Y)) )
& ( ~ p103(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p104(Y)
| r1(Y,skolemFOFtoCNF_X_4(Y)) )
& ( ~ p104(Y)
| ~ p106(skolemFOFtoCNF_X_1(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y) )
& ( ~ p104(Y)
| ~ p106(skolemFOFtoCNF_X_2(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y) )
& ( ~ p104(Y)
| ~ p6(skolemFOFtoCNF_X_2(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y) )
& ( ~ p104(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y)
| p105(skolemFOFtoCNF_X_1(Y)) )
& ( ~ p104(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y)
| p105(skolemFOFtoCNF_X_2(Y)) )
& ( ~ p104(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y)
| p6(skolemFOFtoCNF_X_1(Y)) )
& ( ~ p104(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y)
| r1(Y,skolemFOFtoCNF_X_1(Y)) )
& ( ~ p104(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p105(Y)
| r1(Y,skolemFOFtoCNF_X_2(Y)) )
& ( ~ p1(X)
| ~ p100(X)
| ~ p100(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p1(Y) )
& ( ~ p1(Y)
| ~ p100(X)
| ~ p100(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p1(X) )
& ( ~ p101(X)
| ~ p101(Y)
| ~ p2(X)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p2(Y) )
& ( ~ p101(X)
| ~ p101(Y)
| ~ p2(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p2(X) )
& ( ~ p102(X)
| ~ p102(Y)
| ~ p3(X)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p3(Y) )
& ( ~ p102(X)
| ~ p102(Y)
| ~ p3(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p3(X) )
& ( ~ p103(X)
| ~ p103(Y)
| ~ p4(X)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p4(Y) )
& ( ~ p103(X)
| ~ p103(Y)
| ~ p4(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p4(X) )
& ( ~ p104(X)
| ~ p104(Y)
| ~ p5(X)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p5(Y) )
& ( ~ p104(X)
| ~ p104(Y)
| ~ p5(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p5(X) )
& ( ~ p105(X)
| ~ p105(Y)
| ~ p6(X)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p6(Y) )
& ( ~ p105(X)
| ~ p105(Y)
| ~ p6(Y)
| ~ r1(Y,X)
| ~ r1(skolemFOFtoCNF_X,Y)
| p6(X) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y] :
( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| r1(Y,skolemFOFtoCNF_X_10(Y)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
p100(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
~ p101(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_12,plain,
! [Y] :
( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y)
| r1(Y,skolemFOFtoCNF_X_8(Y)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_13,plain,
! [Y] :
( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| p101(skolemFOFtoCNF_X_10(Y)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_14,plain,
! [Y] :
( ~ p100(Y)
| ~ p102(skolemFOFtoCNF_X_10(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ r1(X,Y)
| ~ r1(Y,Z)
| r1(X,Z) ),
inference(canonicalize,[],[transitivity]) ).
fof(normalize_0_16,plain,
! [X,Y,Z] :
( ~ r1(X,Y)
| ~ r1(Y,Z)
| r1(X,Z) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [Y] :
( ~ p101(Y)
| ~ p3(skolemFOFtoCNF_X_8(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y) ),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( ~ r1(skolemFOFtoCNF_X,Y)
| p3(Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)))
| p3(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_2,plain,
r1(X,X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_4,plain,
( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| r1(Y,skolemFOFtoCNF_X_10(Y)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ p100(skolemFOFtoCNF_X)
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X)
| r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_4:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_6,plain,
( ~ p100(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X)
| r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
p100(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( p101(skolemFOFtoCNF_X)
| r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( p100(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
~ p101(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( p101(skolemFOFtoCNF_X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ p101(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y)
| r1(Y,skolemFOFtoCNF_X_8(Y)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
( ~ p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| r1(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X),skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_0_11:[bind(Y,$fot(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_13,plain,
( ~ p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| r1(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X),skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ p100(Y)
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y)
| p101(skolemFOFtoCNF_X_10(Y)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ p100(skolemFOFtoCNF_X)
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_14:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_16,plain,
( ~ p100(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( p101(skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( p100(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( p101(skolemFOFtoCNF_X) )],[refute_0_17,refute_0_9]) ).
cnf(refute_0_19,plain,
( p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| r1(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X),skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) ),
inference(resolve,[$cnf( p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) )],[refute_0_18,refute_0_13]) ).
cnf(refute_0_20,plain,
( ~ p100(Y)
| ~ p102(skolemFOFtoCNF_X_10(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p101(Y) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_21,plain,
( ~ p100(skolemFOFtoCNF_X)
| ~ p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| p101(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_20:[bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_22,plain,
( ~ p100(skolemFOFtoCNF_X)
| ~ p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| p101(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_3,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| p101(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( p100(skolemFOFtoCNF_X) )],[refute_0_7,refute_0_22]) ).
cnf(refute_0_24,plain,
~ p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( p101(skolemFOFtoCNF_X) )],[refute_0_23,refute_0_9]) ).
cnf(refute_0_25,plain,
r1(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X),skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))),
inference(resolve,[$cnf( p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) )],[refute_0_19,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ r1(X,Y)
| ~ r1(Y,Z)
| r1(X,Z) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_27,plain,
( ~ r1(X_48,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| ~ r1(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X),skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)))
| r1(X_48,skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_48)),bind(Y,$fot(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))),bind(Z,$fot(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))))]]) ).
cnf(refute_0_28,plain,
( ~ r1(X_48,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| r1(X_48,skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X),skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_0_28:[bind(X_48,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_30,plain,
r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) )],[refute_0_10,refute_0_29]) ).
cnf(refute_0_31,plain,
p3(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) )],[refute_0_30,refute_0_1]) ).
cnf(refute_0_32,plain,
( ~ p101(Y)
| ~ p3(skolemFOFtoCNF_X_8(Y))
| ~ r1(skolemFOFtoCNF_X,Y)
| p102(Y) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_33,plain,
( ~ p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| ~ p3(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)))
| ~ r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_32:[bind(Y,$fot(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_34,plain,
( ~ p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))
| ~ p3(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)))
| p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_X,skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) )],[refute_0_10,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ p3(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)))
| p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( p101(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) )],[refute_0_18,refute_0_34]) ).
cnf(refute_0_36,plain,
~ p3(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))),
inference(resolve,[$cnf( p102(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X)) )],[refute_0_35,refute_0_24]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( p3(skolemFOFtoCNF_X_8(skolemFOFtoCNF_X_10(skolemFOFtoCNF_X))) )],[refute_0_31,refute_0_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL674+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.38 % Computer : n031.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 5 02:08:54 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.11/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.47
%------------------------------------------------------------------------------