TSTP Solution File: GEO069-3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO069-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %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 : 300s
% DateTime : Wed Jul 27 12:54:19 EDT 2022
% Result : Unsatisfiable 3.92s 4.12s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 11 unt; 2 nHn; 16 RR)
% Number of literals : 25 ( 4 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(77,axiom,
( ~ colinear(A,B,C)
| colinear(C,B,A) ),
file('GEO069-3.p',unknown),
[] ).
cnf(78,axiom,
( ~ colinear(A,B,C)
| colinear(B,C,A) ),
file('GEO069-3.p',unknown),
[] ).
cnf(85,axiom,
( ~ colinear(A,B,C)
| ~ colinear(A,B,D)
| colinear(A,C,D)
| A = B ),
file('GEO069-3.p',unknown),
[] ).
cnf(86,axiom,
( ~ colinear(A,B,C)
| ~ colinear(A,B,D)
| colinear(B,C,D)
| A = B ),
file('GEO069-3.p',unknown),
[] ).
cnf(87,axiom,
u != v,
file('GEO069-3.p',unknown),
[] ).
cnf(88,plain,
v != u,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[87])]),
[iquote('copy,87,flip.1')] ).
cnf(89,axiom,
( ~ colinear(x,w,u)
| ~ colinear(x,w,v) ),
file('GEO069-3.p',unknown),
[] ).
cnf(179,axiom,
colinear(w,v,u),
file('GEO069-3.p',unknown),
[] ).
cnf(180,axiom,
colinear(x,v,u),
file('GEO069-3.p',unknown),
[] ).
cnf(227,plain,
colinear(v,u,w),
inference(hyper,[status(thm)],[179,78]),
[iquote('hyper,179,78')] ).
cnf(321,plain,
colinear(v,u,x),
inference(hyper,[status(thm)],[180,78]),
[iquote('hyper,180,78')] ).
cnf(1227,plain,
colinear(u,w,x),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[321,86,227]),88]),
[iquote('hyper,321,86,227,unit_del,88')] ).
cnf(1229,plain,
colinear(v,w,x),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[321,85,227]),88]),
[iquote('hyper,321,85,227,unit_del,88')] ).
cnf(1434,plain,
colinear(x,w,u),
inference(hyper,[status(thm)],[1227,77]),
[iquote('hyper,1227,77')] ).
cnf(1614,plain,
colinear(x,w,v),
inference(hyper,[status(thm)],[1229,77]),
[iquote('hyper,1229,77')] ).
cnf(2457,plain,
$false,
inference(hyper,[status(thm)],[1614,89,1434]),
[iquote('hyper,1614,89,1434')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO069-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:19:45 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.35/3.52 ----- Otter 3.3f, August 2004 -----
% 3.35/3.52 The process was started by sandbox2 on n013.cluster.edu,
% 3.35/3.52 Wed Jul 27 07:19:45 2022
% 3.35/3.52 The command was "./otter". The process ID is 2147.
% 3.35/3.52
% 3.35/3.52 set(prolog_style_variables).
% 3.35/3.52 set(auto).
% 3.35/3.52 dependent: set(auto1).
% 3.35/3.52 dependent: set(process_input).
% 3.35/3.52 dependent: clear(print_kept).
% 3.35/3.52 dependent: clear(print_new_demod).
% 3.35/3.52 dependent: clear(print_back_demod).
% 3.35/3.52 dependent: clear(print_back_sub).
% 3.35/3.52 dependent: set(control_memory).
% 3.35/3.52 dependent: assign(max_mem, 12000).
% 3.35/3.52 dependent: assign(pick_given_ratio, 4).
% 3.35/3.52 dependent: assign(stats_level, 1).
% 3.35/3.52 dependent: assign(max_seconds, 10800).
% 3.35/3.52 clear(print_given).
% 3.35/3.52
% 3.35/3.52 list(usable).
% 3.35/3.52 0 [] A=A.
% 3.35/3.52 0 [] e_quidistant(X,Y,Y,X).
% 3.35/3.52 0 [] -e_quidistant(X,Y,Z,V)| -e_quidistant(X,Y,V2,W)|e_quidistant(Z,V,V2,W).
% 3.35/3.52 0 [] -e_quidistant(X,Y,Z,Z)|X=Y.
% 3.35/3.52 0 [] between(X,Y,extension(X,Y,W,V)).
% 3.35/3.52 0 [] e_quidistant(Y,extension(X,Y,W,V),W,V).
% 3.35/3.52 0 [] -e_quidistant(X,Y,X1,Y1)| -e_quidistant(Y,Z,Y1,Z1)| -e_quidistant(X,V,X1,V1)| -e_quidistant(Y,V,Y1,V1)| -between(X,Y,Z)| -between(X1,Y1,Z1)|X=Y|e_quidistant(Z,V,Z1,V1).
% 3.35/3.52 0 [] -between(X,Y,X)|X=Y.
% 3.35/3.52 0 [] -between(U,V,W)| -between(Y,X,W)|between(V,inner_pasch(U,V,W,X,Y),Y).
% 3.35/3.52 0 [] -between(U,V,W)| -between(Y,X,W)|between(X,inner_pasch(U,V,W,X,Y),U).
% 3.35/3.52 0 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 3.35/3.52 0 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1).
% 3.35/3.52 0 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2).
% 3.35/3.52 0 [] -e_quidistant(X,W,X,V)| -e_quidistant(Y,W,Y,V)| -e_quidistant(Z,W,Z,V)|between(X,Y,Z)|between(Y,Z,X)|between(Z,X,Y)|W=V.
% 3.35/3.52 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(U,V,euclid1(U,V,W,X,Y)).
% 3.35/3.52 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(U,X,euclid2(U,V,W,X,Y)).
% 3.35/3.52 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(euclid1(U,V,W,X,Y),Y,euclid2(U,V,W,X,Y)).
% 3.35/3.52 0 [] -e_quidistant(U,V,U,V1)| -e_quidistant(U,X,U,X1)| -between(U,V,X)| -between(V,W,X)|between(V1,continuous(U,V,V1,W,X,X1),X1).
% 3.35/3.52 0 [] -e_quidistant(U,V,U,V1)| -e_quidistant(U,X,U,X1)| -between(U,V,X)| -between(V,W,X)|e_quidistant(U,W,U,continuous(U,V,V1,W,X,X1)).
% 3.35/3.52 0 [] -between(X,Y,Z)|colinear(X,Y,Z).
% 3.35/3.52 0 [] -between(Y,Z,X)|colinear(X,Y,Z).
% 3.35/3.52 0 [] -between(Z,X,Y)|colinear(X,Y,Z).
% 3.35/3.52 0 [] -colinear(X,Y,Z)|between(X,Y,Z)|between(Y,Z,X)|between(Z,X,Y).
% 3.35/3.52 0 [] reflection(U,V)=extension(U,V,U,V).
% 3.35/3.52 0 [] insertion(U1,W1,U,V)=extension(extension(W1,U1,lower_dimension_point_1,lower_dimension_point_2),U1,U,V).
% 3.35/3.52 0 [] e_quidistant(U,V,U,V).
% 3.35/3.52 0 [] -e_quidistant(U,V,W,X)|e_quidistant(W,X,U,V).
% 3.35/3.52 0 [] -e_quidistant(U,V,W,X)|e_quidistant(V,U,W,X).
% 3.35/3.52 0 [] -e_quidistant(U,V,W,X)|e_quidistant(U,V,X,W).
% 3.35/3.52 0 [] -e_quidistant(U,V,W,X)|e_quidistant(V,U,X,W).
% 3.35/3.52 0 [] -e_quidistant(U,V,W,X)|e_quidistant(W,X,V,U).
% 3.35/3.52 0 [] -e_quidistant(U,V,W,X)|e_quidistant(X,W,U,V).
% 3.35/3.52 0 [] -e_quidistant(U,V,W,X)|e_quidistant(X,W,V,U).
% 3.35/3.52 0 [] -e_quidistant(U,V,W,X)| -e_quidistant(W,X,Y,Z)|e_quidistant(U,V,Y,Z).
% 3.35/3.52 0 [] V=extension(U,V,W,W).
% 3.35/3.52 0 [] Y!=extension(U,V,W,X)|between(U,V,Y).
% 3.35/3.52 0 [] between(U,V,reflection(U,V)).
% 3.35/3.52 0 [] e_quidistant(V,reflection(U,V),U,V).
% 3.35/3.52 0 [] U!=V|V=reflection(U,V).
% 3.35/3.52 0 [] U=reflection(U,U).
% 3.35/3.52 0 [] V!=reflection(U,V)|U=V.
% 3.35/3.52 0 [] e_quidistant(U,U,V,V).
% 3.35/3.52 0 [] -e_quidistant(U,V,U1,V1)| -e_quidistant(V,W,V1,W1)| -between(U,V,W)| -between(U1,V1,W1)|e_quidistant(U,W,U1,W1).
% 3.35/3.52 0 [] -between(U,V,W)| -between(U,V,X)| -e_quidistant(V,W,V,X)|U=V|W=X.
% 3.35/3.52 0 [] -between(U,V,W)|U=V|W=extension(U,V,V,W).
% 3.35/3.52 0 [] -e_quidistant(W,X,Y,Z)|extension(U,V,W,X)=extension(U,V,Y,Z)|U=V.
% 3.35/3.52 0 [] extension(U,V,U,V)=extension(U,V,V,U)|U=V.
% 3.35/3.52 0 [] e_quidistant(V,U,V,reflection(reflection(U,V),V)).
% 3.35/3.52 0 [] U=reflection(reflection(U,V),V).
% 3.35/3.52 0 [] between(U,V,V).
% 3.35/3.52 0 [] -between(U,W,X)|U!=X|between(V,W,X).
% 3.35/3.52 0 [] -between(U,V,W)|between(W,V,U).
% 3.35/3.52 0 [] between(U,U,V).
% 3.35/3.52 0 [] -between(U,V,W)| -between(V,U,W)|U=V.
% 3.35/3.52 0 [] -between(U,V,W)| -between(U,W,V)|V=W.
% 3.35/3.52 0 [] -between(U,V,W)| -between(V,U,W)|U=V|V=W.
% 3.35/3.52 0 [] -between(U,V,W)| -between(U,W,V)|U=V|V=W.
% 3.35/3.52 0 [] -between(U,V,W)| -between(V,W,X)|between(U,V,W).
% 3.35/3.52 0 [] -between(U,V,W)| -between(U,W,X)|between(V,W,X).
% 3.35/3.52 0 [] -between(U,V,W)| -between(V,W,X)|between(U,W,X)|V=W.
% 3.35/3.52 0 [] -between(U,V,W)| -between(V,W,X)|between(U,V,X)|V=W.
% 3.35/3.52 0 [] -between(U,V,X)| -between(V,W,X)|between(U,W,X).
% 3.35/3.52 0 [] -between(U,V,W)| -between(U,W,X)|between(U,V,X).
% 3.35/3.52 0 [] lower_dimension_point_1!=lower_dimension_point_2.
% 3.35/3.52 0 [] lower_dimension_point_2!=lower_dimension_point_3.
% 3.35/3.52 0 [] lower_dimension_point_1!=lower_dimension_point_3.
% 3.35/3.52 0 [] V!=extension(U,V,lower_dimension_point_1,lower_dimension_point_2).
% 3.35/3.52 0 [] e_quidistant(V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2),X,extension(W,X,lower_dimension_point_1,lower_dimension_point_2)).
% 3.35/3.52 0 [] between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)).
% 3.35/3.52 0 [] -between(U,V,W)| -between(U1,V1,W)| -between(U,X,U1)|between(X,inner_pasch(V1,inner_pasch(U,X,U1,V1,W),U,V,W),W)|between(V,inner_pasch(V1,inner_pasch(U,X,U1,V1,W),U,V,W),V1).
% 3.35/3.52 0 [] -between(U,V,W)| -e_quidistant(U,W,U,W1)| -e_quidistant(V,W,V,W1)|U=V|W=W1.
% 3.35/3.52 0 [] -e_quidistant(U,V,U1,V1)| -e_quidistant(U,W,U1,W1)| -e_quidistant(U,X,U1,X1)| -e_quidistant(W,X,W1,X1)| -between(U,V,W)| -between(U1,V1,W1)|e_quidistant(V,X,V1,X1).
% 3.35/3.52 0 [] -between(U,V,W)| -between(U1,V1,W1)| -e_quidistant(U,V,U1,V1)| -e_quidistant(U,W,U1,W1)|e_quidistant(V,W,V1,W1).
% 3.35/3.52 0 [] -e_quidistant(U,V,U1,V1)| -e_quidistant(V,W,V1,W1)| -e_quidistant(U,X,U1,X1)| -e_quidistant(W,X,W1,X1)| -between(U,V,W)| -between(U1,V1,W1)|e_quidistant(V,X,V1,X1).
% 3.35/3.52 0 [] -between(U,V,W)| -e_quidistant(U,V,U,X)| -e_quidistant(W,V,W,X)|V=X.
% 3.35/3.52 0 [] e_quidistant(U,V,U1,insertion(U1,W1,U,V)).
% 3.35/3.52 0 [] -between(U,V,W)| -e_quidistant(U,W,U1,W1)|between(U1,insertion(U1,W1,U,V),W1).
% 3.35/3.52 0 [] -between(U,V,W)| -e_quidistant(U,W,U1,W1)|e_quidistant(V,W,insertion(U1,W1,U,V),W1).
% 3.35/3.52 0 [] -between(U,V,W)|V=insertion(U,W,U,V).
% 3.35/3.52 0 [] -e_quidistant(W,X,Y,Z)|insertion(U,V,W,X)=insertion(U,V,Y,Z).
% 3.35/3.52 0 [] -e_quidistant(U,V,U1,V1)| -e_quidistant(V,W,V1,W1)| -e_quidistant(U,W,U1,W1)| -between(U,V,W)|between(U1,V1,W1).
% 3.35/3.52 0 [] -between(U,V,W)| -between(U,V,X)|U=V|between(U,W,X)|between(U,X,W).
% 3.35/3.52 0 [] -between(U,V,W)| -between(U,V,X)|U=V|between(V,W,X)|between(V,X,W).
% 3.35/3.52 0 [] -between(U,W,X)| -between(V,W,X)|W=X|between(U,V,W)|between(V,U,W).
% 3.35/3.52 0 [] -between(U,V,X)| -between(U,W,X)|between(U,V,W)|between(U,W,V).
% 3.35/3.52 0 [] -between(U,V,X)| -between(U,W,X)|between(V,W,X)|between(W,V,X).
% 3.35/3.52 0 [] -between(U,V,Y)| -between(V,W,X)| -between(U,X,Y)|between(U,W,Y).
% 3.35/3.52 0 [] -between(U,V,W)| -e_quidistant(U,V,U,W)|V=W.
% 3.35/3.52 0 [] -between(W,V,U)|colinear(U,V,W).
% 3.35/3.52 0 [] -between(U,W,V)|colinear(U,V,W).
% 3.35/3.52 0 [] -between(V,U,W)|colinear(U,V,W).
% 3.35/3.52 0 [] -colinear(U,V,W)|colinear(W,V,U).
% 3.35/3.52 0 [] -colinear(U,V,W)|colinear(V,W,U).
% 3.35/3.52 0 [] -colinear(U,V,W)|colinear(U,W,V).
% 3.35/3.52 0 [] -colinear(U,V,W)|colinear(W,U,V).
% 3.35/3.52 0 [] -colinear(U,V,W)|colinear(V,U,W).
% 3.35/3.52 0 [] -colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 3.35/3.52 0 [] colinear(X,X,Y).
% 3.35/3.52 0 [] colinear(X,Y,X).
% 3.35/3.52 0 [] colinear(Y,X,X).
% 3.35/3.52 0 [] X!=Y|colinear(X,Z,Y).
% 3.35/3.52 0 [] -e_quidistant(U,V,U1,V1)| -e_quidistant(V,W,V1,W1)| -e_quidistant(U,W,U1,W1)| -colinear(U,V,W)|colinear(U1,V1,W1).
% 3.35/3.52 0 [] -colinear(U,V,W)| -colinear(U,V,X)|colinear(U,W,X)|U=V.
% 3.35/3.52 0 [] -colinear(U,V,W)| -colinear(U,V,X)|colinear(V,W,X)|U=V.
% 3.35/3.52 0 [] u!=v.
% 3.35/3.52 0 [] colinear(w,v,u).
% 3.35/3.52 0 [] colinear(x,v,u).
% 3.35/3.52 0 [] -colinear(x,w,u)| -colinear(x,w,v).
% 3.35/3.52 end_of_list.
% 3.35/3.52
% 3.35/3.52 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 3.35/3.52
% 3.35/3.52 This ia a non-Horn set with equality. The strategy will be
% 3.35/3.52 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.35/3.52 deletion, with positive clauses in sos and nonpositive
% 3.35/3.52 clauses in usable.
% 3.35/3.52
% 3.35/3.52 dependent: set(knuth_bendix).
% 3.35/3.52 dependent: set(anl_eq).
% 3.35/3.52 dependent: set(para_from).
% 3.35/3.52 dependent: set(para_into).
% 3.35/3.52 dependent: clear(para_from_right).
% 3.35/3.52 dependent: clear(para_into_right).
% 3.35/3.52 dependent: set(para_from_vars).
% 3.35/3.52 dependent: set(eq_units_both_ways).
% 3.35/3.52 dependent: set(dynamic_demod_all).
% 3.35/3.52 dependent: set(dynamic_demod).
% 3.35/3.52 dependent: set(order_eq).
% 3.35/3.52 dependent: set(back_demod).
% 3.35/3.52 dependent: set(lrpo).
% 3.35/3.52 dependent: set(hyper_res).
% 3.35/3.52 dependent: set(unit_deletion).
% 3.35/3.52 dependent: set(factor).
% 3.35/3.52
% 3.35/3.52 ------------> process usable:
% 3.35/3.52 ** KEPT (pick-wt=15): 1 [] -e_quidistant(A,B,C,D)| -e_quidistant(A,B,E,F)|e_quidistant(C,D,E,F).
% 3.35/3.52 ** KEPT (pick-wt=8): 2 [] -e_quidistant(A,B,C,C)|A=B.
% 3.35/3.52 ** KEPT (pick-wt=36): 3 [] -e_quidistant(A,B,C,D)| -e_quidistant(B,E,D,F)| -e_quidistant(A,G,C,H)| -e_quidistant(B,G,D,H)| -between(A,B,E)| -between(C,D,F)|A=B|e_quidistant(E,G,F,H).
% 3.35/3.52 ** KEPT (pick-wt=7): 4 [] -between(A,B,A)|A=B.
% 3.35/3.52 ** KEPT (pick-wt=17): 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D).
% 3.35/3.52 ** KEPT (pick-wt=17): 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A).
% 3.35/3.52 ** KEPT (pick-wt=4): 7 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 3.35/3.52 ** KEPT (pick-wt=4): 8 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1).
% 3.35/3.52 ** KEPT (pick-wt=4): 9 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2).
% 3.35/3.52 ** KEPT (pick-wt=30): 10 [] -e_quidistant(A,B,A,C)| -e_quidistant(D,B,D,C)| -e_quidistant(E,B,E,C)|between(A,D,E)|between(D,E,A)|between(E,A,D)|B=C.
% 3.35/3.52 ** KEPT (pick-wt=20): 11 [] -between(A,B,C)| -between(D,B,E)|A=B|between(A,D,euclid1(A,D,B,E,C)).
% 3.35/3.52 ** KEPT (pick-wt=20): 12 [] -between(A,B,C)| -between(D,B,E)|A=B|between(A,E,euclid2(A,D,B,E,C)).
% 3.35/3.52 ** KEPT (pick-wt=25): 13 [] -between(A,B,C)| -between(D,B,E)|A=B|between(euclid1(A,D,B,E,C),C,euclid2(A,D,B,E,C)).
% 3.35/3.52 ** KEPT (pick-wt=28): 14 [] -e_quidistant(A,B,A,C)| -e_quidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|between(C,continuous(A,B,C,F,D,E),E).
% 3.35/3.52 ** KEPT (pick-wt=29): 15 [] -e_quidistant(A,B,A,C)| -e_quidistant(A,D,A,E)| -between(A,B,D)| -between(B,F,D)|e_quidistant(A,F,A,continuous(A,B,C,F,D,E)).
% 3.35/3.52 ** KEPT (pick-wt=8): 16 [] -between(A,B,C)|colinear(A,B,C).
% 3.35/3.52 ** KEPT (pick-wt=8): 17 [] -between(A,B,C)|colinear(C,A,B).
% 3.35/3.52 ** KEPT (pick-wt=8): 18 [] -between(A,B,C)|colinear(B,C,A).
% 3.35/3.52 ** KEPT (pick-wt=16): 19 [] -colinear(A,B,C)|between(A,B,C)|between(B,C,A)|between(C,A,B).
% 3.35/3.52 ** KEPT (pick-wt=10): 20 [] -e_quidistant(A,B,C,D)|e_quidistant(C,D,A,B).
% 3.35/3.52 ** KEPT (pick-wt=10): 21 [] -e_quidistant(A,B,C,D)|e_quidistant(B,A,C,D).
% 3.35/3.52 ** KEPT (pick-wt=10): 22 [] -e_quidistant(A,B,C,D)|e_quidistant(A,B,D,C).
% 3.35/3.52 ** KEPT (pick-wt=10): 23 [] -e_quidistant(A,B,C,D)|e_quidistant(B,A,D,C).
% 3.35/3.52 ** KEPT (pick-wt=10): 24 [] -e_quidistant(A,B,C,D)|e_quidistant(C,D,B,A).
% 3.35/3.52 ** KEPT (pick-wt=10): 25 [] -e_quidistant(A,B,C,D)|e_quidistant(D,C,A,B).
% 3.35/3.52 ** KEPT (pick-wt=10): 26 [] -e_quidistant(A,B,C,D)|e_quidistant(D,C,B,A).
% 3.35/3.52 ** KEPT (pick-wt=15): 27 [] -e_quidistant(A,B,C,D)| -e_quidistant(C,D,E,F)|e_quidistant(A,B,E,F).
% 3.35/3.52 ** KEPT (pick-wt=11): 28 [] A!=extension(B,C,D,E)|between(B,C,A).
% 3.35/3.52 ** KEPT (pick-wt=8): 30 [copy,29,flip.2] A!=B|reflection(A,B)=B.
% 3.35/3.52 ** KEPT (pick-wt=8): 32 [copy,31,flip.1] reflection(A,B)!=B|A=B.
% 3.35/3.52 ** KEPT (pick-wt=23): 33 [] -e_quidistant(A,B,C,D)| -e_quidistant(B,E,D,F)| -between(A,B,E)| -between(C,D,F)|e_quidistant(A,E,C,F).
% 3.35/3.52 ** KEPT (pick-wt=19): 34 [] -between(A,B,C)| -between(A,B,D)| -e_quidistant(B,C,B,D)|A=B|C=D.
% 3.35/3.52 ** KEPT (pick-wt=14): 36 [copy,35,flip.3] -between(A,B,C)|A=B|extension(A,B,B,C)=C.
% 3.35/3.52 ** KEPT (pick-wt=19): 37 [] -e_quidistant(A,B,C,D)|extension(E,F,A,B)=extension(E,F,C,D)|E=F.
% 3.35/3.52 ** KEPT (pick-wt=11): 38 [] -between(A,B,C)|A!=C|between(D,B,C).
% 3.35/3.52 ** KEPT (pick-wt=8): 39 [] -between(A,B,C)|between(C,B,A).
% 3.35/3.52 ** KEPT (pick-wt=11): 40 [] -between(A,B,C)| -between(B,A,C)|A=B.
% 3.35/3.52 ** KEPT (pick-wt=11): 41 [] -between(A,B,C)| -between(A,C,B)|B=C.
% 3.35/3.52 Following clause subsumed by 40 during input processing: 0 [] -between(A,B,C)| -between(B,A,C)|A=B|B=C.
% 3.35/3.52 Following clause subsumed by 41 during input processing: 0 [] -between(A,B,C)| -between(A,C,B)|A=B|B=C.
% 3.35/3.52 ** KEPT (pick-wt=12): 42 [] -between(A,B,C)| -between(A,C,D)|between(B,C,D).
% 3.35/3.52 ** KEPT (pick-wt=15): 43 [] -between(A,B,C)| -between(B,C,D)|between(A,C,D)|B=C.
% 3.35/3.52 ** KEPT (pick-wt=15): 44 [] -between(A,B,C)| -between(B,C,D)|between(A,B,D)|B=C.
% 3.35/3.52 ** KEPT (pick-wt=12): 45 [] -between(A,B,C)| -between(B,D,C)|between(A,D,C).
% 3.35/3.52 ** KEPT (pick-wt=12): 46 [] -between(A,B,C)| -between(A,C,D)|between(A,B,D).
% 3.35/3.52 ** KEPT (pick-wt=3): 48 [copy,47,flip.1] lower_dimension_point_2!=lower_dimension_point_1.
% 3.35/3.52 ** KEPT (pick-wt=3): 50 [copy,49,flip.1] lower_dimension_point_3!=lower_dimension_point_2.
% 3.35/3.52 ** KEPT (pick-wt=3): 52 [copy,51,flip.1] lower_dimension_point_3!=lower_dimension_point_1.
% 3.35/3.52 ** KEPT (pick-wt=7): 54 [copy,53,flip.1] extension(A,B,lower_dimension_point_1,lower_dimension_point_2)!=B.
% 3.35/3.52 ** KEPT (pick-wt=40): 55 [] -between(A,B,C)| -between(D,E,C)| -between(A,F,D)|between(F,inner_pasch(E,inner_pasch(A,F,D,E,C),A,B,C),C)|between(B,inner_pasch(E,inner_pasch(A,F,D,E,C),A,B,C),E).
% 3.35/3.52 ** KEPT (pick-wt=20): 56 [] -between(A,B,C)| -e_quidistant(A,C,A,D)| -e_quidistant(B,C,B,D)|A=B|C=D.
% 3.35/3.52 ** KEPT (pick-wt=33): 57 [] -e_quidistant(A,B,C,D)| -e_quidistant(A,E,C,F)| -e_quidistant(A,G,C,H)| -e_quidistant(E,G,F,H)| -between(A,B,E)| -between(C,D,F)|e_quidistant(B,G,D,H).
% 3.35/3.52 ** KEPT (pick-wt=23): 58 [] -between(A,B,C)| -between(D,E,F)| -e_quidistant(A,B,D,E)| -e_quidistant(A,C,D,F)|e_quidistant(B,C,E,F).
% 3.35/3.52 ** KEPT (pick-wt=33): 59 [] -e_quidistant(A,B,C,D)| -e_quidistant(B,E,D,F)| -e_quidistant(A,G,C,H)| -e_quidistant(E,G,F,H)| -between(A,B,E)| -between(C,D,F)|e_quidistant(B,G,D,H).
% 3.35/3.52 ** KEPT (pick-wt=17): 60 [] -between(A,B,C)| -e_quidistant(A,B,A,D)| -e_quidistant(C,B,C,D)|B=D.
% 3.35/3.52 ** KEPT (pick-wt=17): 61 [] -between(A,B,C)| -e_quidistant(A,C,D,E)|between(D,insertion(D,E,A,B),E).
% 3.35/3.52 ** KEPT (pick-wt=18): 62 [] -between(A,B,C)| -e_quidistant(A,C,D,E)|e_quidistant(B,C,insertion(D,E,A,B),E).
% 3.35/3.52 ** KEPT (pick-wt=11): 64 [copy,63,flip.2] -between(A,B,C)|insertion(A,C,A,B)=B.
% 3.35/3.52 ** KEPT (pick-wt=16): 65 [] -e_quidistant(A,B,C,D)|insertion(E,F,A,B)=insertion(E,F,C,D).
% 3.35/3.52 ** KEPT (pick-wt=23): 66 [] -e_quidistant(A,B,C,D)| -e_quidistant(B,E,D,F)| -e_quidistant(A,E,C,F)| -between(A,B,E)|between(C,D,F).
% 3.35/3.52 ** KEPT (pick-wt=19): 67 [] -between(A,B,C)| -between(A,B,D)|A=B|between(A,C,D)|between(A,D,C).
% 3.35/3.52 ** KEPT (pick-wt=19): 68 [] -between(A,B,C)| -between(A,B,D)|A=B|between(B,C,D)|between(B,D,C).
% 3.35/3.52 ** KEPT (pick-wt=19): 69 [] -between(A,B,C)| -between(D,B,C)|B=C|between(A,D,B)|between(D,A,B).
% 3.35/3.52 ** KEPT (pick-wt=16): 70 [] -between(A,B,C)| -between(A,D,C)|between(A,B,D)|between(A,D,B).
% 3.35/3.52 ** KEPT (pick-wt=16): 71 [] -between(A,B,C)| -between(A,D,C)|between(B,D,C)|between(D,B,C).
% 3.35/3.52 ** KEPT (pick-wt=16): 72 [] -between(A,B,C)| -between(B,D,E)| -between(A,E,C)|between(A,D,C).
% 3.35/3.52 ** KEPT (pick-wt=12): 73 [] -between(A,B,C)| -e_quidistant(A,B,A,C)|B=C.
% 3.35/3.52 ** KEPT (pick-wt=8): 74 [] -between(A,B,C)|colinear(C,B,A).
% 3.35/3.52 ** KEPT (pick-wt=8): 75 [] -between(A,B,C)|colinear(A,C,B).
% 3.35/3.52 ** KEPT (pick-wt=8): 76 [] -between(A,B,C)|colinear(B,A,C).
% 3.35/3.52 ** KEPT (pick-wt=8): 77 [] -colinear(A,B,C)|colinear(C,B,A).
% 3.35/3.52 ** KEPT (pick-wt=8): 78 [] -colinear(A,B,C)|colinear(B,C,A).
% 3.35/3.52 ** KEPT (pick-wt=8): 79 [] -colinear(A,B,C)|colinear(A,C,B).
% 3.35/3.52 ** KEPT (pick-wt=8): 80 [] -colinear(A,B,C)|colinear(C,A,B).
% 3.35/3.52 ** KEPT (pick-wt=8): 81 [] -colinear(A,B,C)|colinear(B,A,C).
% 3.35/3.52 ** KEPT (pick-wt=4): 82 [] -colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 3.35/3.52 ** KEPT (pick-wt=7): 83 [] A!=B|colinear(A,C,B).
% 3.35/3.52 ** KEPT (pick-wt=23): 84 [] -e_quidistant(A,B,C,D)| -e_quidistant(B,E,D,F)| -e_quidistant(A,E,C,F)| -colinear(A,B,E)|colinear(C,D,F).
% 3.35/3.52 ** KEPT (pick-wt=15): 85 [] -colinear(A,B,C)| -colinear(A,B,D)|colinear(A,C,D)|A=B.
% 3.35/3.52 ** KEPT (pick-wt=15): 86 [] -colinear(A,B,C)| -colinear(A,B,D)|colinear(B,C,D)|A=B.
% 3.35/3.52 ** KEPT (pick-wt=3): 88 [copy,87,flip.1] v!=u.
% 3.35/3.52 ** KEPT (pick-wt=8): 89 [] -colinear(x,w,u)| -colinear(x,w,v).
% 3.35/3.52 131 back subsumes 108.
% 3.35/3.52
% 3.35/3.52 ------------> process sos:
% 3.35/3.52 ** KEPT (pick-wt=3): 152 [] A=A.
% 3.35/3.52 ** KEPT (pick-wt=5): 153 [] e_quidistant(A,B,B,A).
% 3.35/3.52 ** KEPT (pick-wt=8): 154 [] between(A,B,extension(A,B,C,D)).
% 3.35/3.52 ** KEPT (pick-wt=9): 155 [] e_quidistant(A,extension(B,A,C,D),C,D).
% 3.35/3.52 ** KEPT (pick-wt=9): 156 [] reflection(A,B)=extension(A,B,A,B).
% 3.35/3.52 ---> New Demodulator: 157 [new_demod,156] reflection(A,B)=extension(A,B,A,B).
% 3.35/3.52 ** KEPT (pick-wt=15): 158 [] insertion(A,B,C,D)=extension(extension(B,A,lower_dimension_point_1,lower_dimension_point_2),A,C,D).
% 3.35/3.52 ---> New Demodulator: 159 [new_demod,158] insertion(A,B,C,D)=extension(extension(B,A,lower_dimension_point_1,lower_dimension_point_2),A,C,D).
% 3.35/3.52 ** KEPT (pick-wt=5): 160 [] e_quidistant(A,B,A,B).
% 3.35/3.52 ** KEPT (pick-wt=7): 162 [copy,161,flip.1] extension(A,B,C,C)=B.
% 3.35/3.52 ---> New Demodulator: 163 [new_demod,162] extension(A,B,C,C)=B.
% 3.92/4.12 Following clause subsumed by 154 during input processing: 0 [demod,157] between(A,B,extension(A,B,A,B)).
% 3.92/4.12 Following clause subsumed by 155 during input processing: 0 [demod,157] e_quidistant(A,extension(B,A,B,A),B,A).
% 3.92/4.12 Following clause subsumed by 152 during input processing: 0 [demod,157,163] A=A.
% 3.92/4.12 ** KEPT (pick-wt=5): 164 [] e_quidistant(A,A,B,B).
% 3.92/4.12 ** KEPT (pick-wt=14): 165 [] extension(A,B,A,B)=extension(A,B,B,A)|A=B.
% 3.92/4.12 ** KEPT (pick-wt=17): 167 [copy,166,demod,157,157] e_quidistant(A,B,A,extension(extension(B,A,B,A),A,extension(B,A,B,A),A)).
% 3.92/4.12 ** KEPT (pick-wt=15): 169 [copy,168,demod,157,157,flip.1] extension(extension(A,B,A,B),B,extension(A,B,A,B),B)=A.
% 3.92/4.12 ---> New Demodulator: 170 [new_demod,169] extension(extension(A,B,A,B),B,extension(A,B,A,B),B)=A.
% 3.92/4.12 ** KEPT (pick-wt=4): 171 [] between(A,B,B).
% 3.92/4.12 ** KEPT (pick-wt=4): 172 [] between(A,A,B).
% 3.92/4.12 ** KEPT (pick-wt=13): 173 [] e_quidistant(A,extension(B,A,lower_dimension_point_1,lower_dimension_point_2),C,extension(D,C,lower_dimension_point_1,lower_dimension_point_2)).
% 3.92/4.12 Following clause subsumed by 154 during input processing: 0 [] between(A,B,extension(A,B,lower_dimension_point_1,lower_dimension_point_2)).
% 3.92/4.12 ** KEPT (pick-wt=13): 175 [copy,174,demod,159] e_quidistant(A,B,C,extension(extension(D,C,lower_dimension_point_1,lower_dimension_point_2),C,A,B)).
% 3.92/4.12 ** KEPT (pick-wt=4): 176 [] colinear(A,A,B).
% 3.92/4.12 ** KEPT (pick-wt=4): 177 [] colinear(A,B,A).
% 3.92/4.12 ** KEPT (pick-wt=4): 178 [] colinear(A,B,B).
% 3.92/4.12 ** KEPT (pick-wt=4): 179 [] colinear(w,v,u).
% 3.92/4.12 ** KEPT (pick-wt=4): 180 [] colinear(x,v,u).
% 3.92/4.12 Following clause subsumed by 152 during input processing: 0 [copy,152,flip.1] A=A.
% 3.92/4.12 152 back subsumes 107.
% 3.92/4.12 152 back subsumes 106.
% 3.92/4.12 152 back subsumes 105.
% 3.92/4.12 153 back subsumes 150.
% 3.92/4.12 153 back subsumes 149.
% 3.92/4.12 153 back subsumes 148.
% 3.92/4.12 153 back subsumes 146.
% 3.92/4.12 153 back subsumes 145.
% 3.92/4.12 153 back subsumes 138.
% 3.92/4.12 >>>> Starting back demodulation with 157.
% 3.92/4.12 >> back demodulating 32 with 157.
% 3.92/4.12 >> back demodulating 30 with 157.
% 3.92/4.12 >>>> Starting back demodulation with 159.
% 3.92/4.12 >> back demodulating 65 with 159.
% 3.92/4.12 >> back demodulating 64 with 159.
% 3.92/4.12 >> back demodulating 62 with 159.
% 3.92/4.12 >> back demodulating 61 with 159.
% 3.92/4.12 160 back subsumes 117.
% 3.92/4.12 160 back subsumes 104.
% 3.92/4.12 160 back subsumes 90.
% 3.92/4.12 >>>> Starting back demodulation with 163.
% 3.92/4.12 164 back subsumes 120.
% 3.92/4.12 164 back subsumes 119.
% 3.92/4.12 164 back subsumes 118.
% 3.92/4.12 164 back subsumes 114.
% 3.92/4.12 164 back subsumes 113.
% 3.92/4.12 164 back subsumes 91.
% 3.92/4.12 >>>> Starting back demodulation with 170.
% 3.92/4.12 >> back demodulating 167 with 170.
% 3.92/4.12 171 back subsumes 130.
% 3.92/4.12 171 back subsumes 128.
% 3.92/4.12 171 back subsumes 127.
% 3.92/4.12 171 back subsumes 125.
% 3.92/4.12 171 back subsumes 124.
% 3.92/4.12 171 back subsumes 103.
% 3.92/4.12 171 back subsumes 95.
% 3.92/4.12 171 back subsumes 94.
% 3.92/4.12 172 back subsumes 131.
% 3.92/4.12 172 back subsumes 129.
% 3.92/4.12 172 back subsumes 126.
% 3.92/4.12 172 back subsumes 96.
% 3.92/4.12 176 back subsumes 135.
% 3.92/4.12 176 back subsumes 133.
% 3.92/4.12 178 back subsumes 137.
% 3.92/4.12 178 back subsumes 136.
% 3.92/4.12 178 back subsumes 134.
% 3.92/4.12
% 3.92/4.12 ======= end of input processing =======
% 3.92/4.12
% 3.92/4.12 =========== start of search ===========
% 3.92/4.12
% 3.92/4.12 -------- PROOF --------
% 3.92/4.12
% 3.92/4.12 -----> EMPTY CLAUSE at 0.61 sec ----> 2457 [hyper,1614,89,1434] $F.
% 3.92/4.12
% 3.92/4.12 Length of proof is 7. Level of proof is 3.
% 3.92/4.12
% 3.92/4.12 ---------------- PROOF ----------------
% 3.92/4.12 % SZS status Unsatisfiable
% 3.92/4.12 % SZS output start Refutation
% See solution above
% 3.92/4.12 ------------ end of proof -------------
% 3.92/4.12
% 3.92/4.12
% 3.92/4.12 Search stopped by max_proofs option.
% 3.92/4.12
% 3.92/4.12
% 3.92/4.12 Search stopped by max_proofs option.
% 3.92/4.12
% 3.92/4.12 ============ end of search ============
% 3.92/4.12
% 3.92/4.12 -------------- statistics -------------
% 3.92/4.12 clauses given 37
% 3.92/4.12 clauses generated 7707
% 3.92/4.12 clauses kept 2439
% 3.92/4.12 clauses forward subsumed 5265
% 3.92/4.12 clauses back subsumed 119
% 3.92/4.12 Kbytes malloced 3906
% 3.92/4.12
% 3.92/4.12 ----------- times (seconds) -----------
% 3.92/4.12 user CPU time 0.61 (0 hr, 0 min, 0 sec)
% 3.92/4.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.92/4.12 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 3.92/4.12
% 3.92/4.12 That finishes the proof of the theorem.
% 3.92/4.12
% 3.92/4.12 Process 2147 finished Wed Jul 27 07:19:49 2022
% 3.92/4.12 Otter interrupted
% 3.92/4.12 PROOF FOUND
%------------------------------------------------------------------------------