TSTP Solution File: GEO204+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO204+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:25:19 EDT 2022
% Result : Theorem 90.71s 90.87s
% Output : CNFRefutation 90.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 103 ( 27 unt; 0 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 240 ( 91 ~; 109 |; 22 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 94 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(X,Z)
| distinct_points(Y,Z) ) ) ).
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) ).
fof(cu1,axiom,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_lines(U,V) )
=> ( apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ) ) ).
fof(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_points(X,Z)
| apart_point_and_line(Z,Y) ) ) ).
fof(ax1,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& equal_points(Y,Z) )
=> ( distinct_points(X,Z)
& equal_lines(line_connecting(X,Y),line_connecting(X,Z)) ) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& equal_points(Y,Z) )
=> distinct_points(X,Z) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& equal_points(Y,Z)
& distinct_points(X,Z) )
=> equal_lines(line_connecting(X,Y),line_connecting(X,Z)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& equal_points(Y,Z) )
=> distinct_points(X,Z) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y,Z] :
( ~ distinct_points(X,Z)
& distinct_points(X,Y)
& equal_points(Y,Z) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& equal_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
equal_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ distinct_points(X,Y)
<=> equal_points(X,Y) ),
inference(canonicalize,[],[ax1]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ distinct_points(X,Y)
<=> equal_points(X,Y) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) )
& ( distinct_points(X,Y)
| equal_points(X,Y) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
equal_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| ~ equal_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_3,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( equal_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,X_55)
| distinct_points(skolemFOFtoCNF_Y,X_55) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_7,plain,
( distinct_points(skolemFOFtoCNF_X,X_55)
| distinct_points(skolemFOFtoCNF_Y,X_55) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_7:[bind(X_55,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_9,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_8,refute_0_3]) ).
cnf(refute_0_10,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_9,refute_0_10]) ).
fof(negate_1_0,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& equal_points(Y,Z)
& distinct_points(X,Z) )
=> equal_lines(line_connecting(X,Y),line_connecting(X,Z)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_1_1,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_1_3,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_1_5,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_1_7,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[ceq1]) ).
fof(normalize_1_9,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
? [X,Y,Z] :
( ~ equal_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Y)
& distinct_points(X,Z)
& equal_points(Y,Z) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_11,plain,
( ~ equal_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
& distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
& distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
& equal_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) ),
inference(skolemize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
~ equal_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(canonicalize,[],[ax2]) ).
fof(normalize_1_14,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [X,Y] :
( ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) )
& ( distinct_lines(X,Y)
| equal_lines(X,Y) ) ),
inference(clausify,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(conjunct,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_18,plain,
! [U,V,X,Y] :
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[cu1]) ).
fof(normalize_1_19,plain,
! [U,V,X,Y] :
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(specialize,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_21,plain,
equal_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_22,plain,
! [X,Y] :
( ~ distinct_points(X,Y)
<=> equal_points(X,Y) ),
inference(canonicalize,[],[ax1]) ).
fof(normalize_1_23,plain,
! [X,Y] :
( ~ distinct_points(X,Y)
<=> equal_points(X,Y) ),
inference(specialize,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [X,Y] :
( ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) )
& ( distinct_points(X,Y)
| equal_points(X,Y) ) ),
inference(clausify,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
! [X,Y] :
( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ),
inference(conjunct,[],[normalize_1_24]) ).
cnf(refute_1_0,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_2,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_3,plain,
( ~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)
| distinct_points(skolemFOFtoCNF_Y_1,Z)
| distinct_points(skolemFOFtoCNF_Z_1,Z) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_4,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_5,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_6,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_7,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_8,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_9,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_10,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,Z) ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_11,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_12,plain,
~ equal_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_13,plain,
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_14,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| equal_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(subst,[],[refute_1_13:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)))]]) ).
cnf(refute_1_15,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)),
inference(resolve,[$cnf( equal_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) )],[refute_1_14,refute_1_12]) ).
cnf(refute_1_16,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_17,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_18,plain,
( ~ distinct_lines(X_8074,X_8075)
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_8074)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_8075)
| apart_point_and_line(skolemFOFtoCNF_Z_1,X_8074)
| apart_point_and_line(skolemFOFtoCNF_Z_1,X_8075) ),
inference(subst,[],[refute_1_17:[bind(U,$fot(X_8074)),bind(V,$fot(X_8075)),bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_19,plain,
( ~ distinct_lines(X_8074,X_8075)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_8074)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_8075)
| apart_point_and_line(skolemFOFtoCNF_Z_1,X_8074)
| apart_point_and_line(skolemFOFtoCNF_Z_1,X_8075) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) )],[refute_1_16,refute_1_18]) ).
cnf(refute_1_20,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(subst,[],[refute_1_19:[bind(X_8074,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(X_8075,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)))]]) ).
cnf(refute_1_21,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) )],[refute_1_15,refute_1_20]) ).
cnf(refute_1_22,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) )],[refute_1_21,refute_1_11]) ).
cnf(refute_1_23,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) )],[refute_1_16,refute_1_22]) ).
cnf(refute_1_24,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| distinct_points(skolemFOFtoCNF_Z_1,Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_23,refute_1_10]) ).
cnf(refute_1_25,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_24:[bind(Z,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_26,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_25,refute_1_8]) ).
cnf(refute_1_27,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_28,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1))
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_27,refute_1_26]) ).
cnf(refute_1_29,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1)) )],[refute_1_28,refute_1_6]) ).
cnf(refute_1_30,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) )],[refute_1_16,refute_1_29]) ).
cnf(refute_1_31,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_30,refute_1_5]) ).
cnf(refute_1_32,plain,
distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_27,refute_1_31]) ).
cnf(refute_1_33,plain,
( distinct_points(skolemFOFtoCNF_Y_1,Z)
| distinct_points(skolemFOFtoCNF_Z_1,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) )],[refute_1_32,refute_1_3]) ).
cnf(refute_1_34,plain,
( distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1)
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_33:[bind(Z,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_35,plain,
distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1) )],[refute_1_34,refute_1_1]) ).
cnf(refute_1_36,plain,
equal_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_37,plain,
( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_38,plain,
( ~ distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1)
| ~ equal_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_37:[bind(X,$fot(skolemFOFtoCNF_Y_1)),bind(Y,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_39,plain,
~ distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(resolve,[$cnf( equal_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) )],[refute_1_36,refute_1_38]) ).
cnf(refute_1_40,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) )],[refute_1_35,refute_1_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO204+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 18 14:10:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 90.71/90.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 90.71/90.87
% 90.71/90.87 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 90.71/90.87
%------------------------------------------------------------------------------