%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO027-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:54:10 EDT 2022
% Result : Unsatisfiable 2.92s 3.14s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 13 unt; 1 nHn; 12 RR)
% Number of literals : 30 ( 9 equ; 15 neg)
% Maximal clause size : 8 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 40 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ e_quidistant(A,B,C,D)
| ~ e_quidistant(A,B,E,F)
| e_quidistant(C,D,E,F) ),
file('GEO027-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ e_quidistant(A,B,C,C)
| A = B ),
file('GEO027-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ 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) ),
file('GEO027-2.p',unknown),
[] ).
cnf(16,axiom,
u != v,
file('GEO027-2.p',unknown),
[] ).
cnf(17,plain,
v != u,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),
[iquote('copy,16,flip.1')] ).
cnf(18,axiom,
w != extension(u,v,v,w),
file('GEO027-2.p',unknown),
[] ).
cnf(19,plain,
extension(u,v,v,w) != w,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[18])]),
[iquote('copy,18,flip.1')] ).
cnf(20,plain,
( ~ e_quidistant(A,B,C,D)
| e_quidistant(C,D,C,D) ),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(39,axiom,
e_quidistant(A,B,B,A),
file('GEO027-2.p',unknown),
[] ).
cnf(40,axiom,
between(A,B,extension(A,B,C,D)),
file('GEO027-2.p',unknown),
[] ).
cnf(41,axiom,
e_quidistant(A,extension(B,A,C,D),C,D),
file('GEO027-2.p',unknown),
[] ).
cnf(42,axiom,
between(u,v,w),
file('GEO027-2.p',unknown),
[] ).
cnf(104,plain,
e_quidistant(A,B,A,B),
inference(hyper,[status(thm)],[39,20]),
[iquote('hyper,39,20')] ).
cnf(145,plain,
e_quidistant(extension(u,v,v,w),A,w,A),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[41,3,104,104,104,40,42]),17]),
[iquote('hyper,41,3,104,104,104,40,42,unit_del,17')] ).
cnf(148,plain,
extension(A,B,C,C) = B,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[41,2])]),
[iquote('hyper,41,2,flip.1')] ).
cnf(186,plain,
( A = B
| ~ e_quidistant(B,A,C,C) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[148,2]),148]),
[iquote('para_into,147.1.1,2.2.1,demod,148')] ).
cnf(1583,plain,
extension(u,v,v,w) = w,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[145,186])]),
[iquote('hyper,145,186,flip.1')] ).
cnf(1585,plain,
$false,
inference(binary,[status(thm)],[1583,19]),
[iquote('binary,1583.1,19.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO027-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 07:10:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.94 ----- Otter 3.3f, August 2004 -----
% 1.74/1.94 The process was started by sandbox on n014.cluster.edu,
% 1.74/1.94 Wed Jul 27 07:10:24 2022
% 1.74/1.94 The command was "./otter". The process ID is 2838.
% 1.74/1.94
% 1.74/1.94 set(prolog_style_variables).
% 1.74/1.94 set(auto).
% 1.74/1.94 dependent: set(auto1).
% 1.74/1.94 dependent: set(process_input).
% 1.74/1.94 dependent: clear(print_kept).
% 1.74/1.94 dependent: clear(print_new_demod).
% 1.74/1.94 dependent: clear(print_back_demod).
% 1.74/1.94 dependent: clear(print_back_sub).
% 1.74/1.94 dependent: set(control_memory).
% 1.74/1.94 dependent: assign(max_mem, 12000).
% 1.74/1.94 dependent: assign(pick_given_ratio, 4).
% 1.74/1.94 dependent: assign(stats_level, 1).
% 1.74/1.94 dependent: assign(max_seconds, 10800).
% 1.74/1.94 clear(print_given).
% 1.74/1.94
% 1.74/1.94 list(usable).
% 1.74/1.94 0 [] A=A.
% 1.74/1.94 0 [] e_quidistant(X,Y,Y,X).
% 1.74/1.94 0 [] -e_quidistant(X,Y,Z,V)| -e_quidistant(X,Y,V2,W)|e_quidistant(Z,V,V2,W).
% 1.74/1.94 0 [] -e_quidistant(X,Y,Z,Z)|X=Y.
% 1.74/1.94 0 [] between(X,Y,extension(X,Y,W,V)).
% 1.74/1.94 0 [] e_quidistant(Y,extension(X,Y,W,V),W,V).
% 1.74/1.94 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).
% 1.74/1.94 0 [] -between(X,Y,X)|X=Y.
% 1.74/1.94 0 [] -between(U,V,W)| -between(Y,X,W)|between(V,inner_pasch(U,V,W,X,Y),Y).
% 1.74/1.94 0 [] -between(U,V,W)| -between(Y,X,W)|between(X,inner_pasch(U,V,W,X,Y),U).
% 1.74/1.94 0 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 1.74/1.94 0 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1).
% 1.74/1.94 0 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2).
% 1.74/1.94 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.
% 1.74/1.94 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(U,V,euclid1(U,V,W,X,Y)).
% 1.74/1.94 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(U,X,euclid2(U,V,W,X,Y)).
% 1.74/1.94 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)).
% 1.74/1.94 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).
% 1.74/1.94 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)).
% 1.74/1.94 0 [] between(u,v,w).
% 1.74/1.94 0 [] u!=v.
% 1.74/1.94 0 [] w!=extension(u,v,v,w).
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.74/1.94
% 1.74/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.94 deletion, with positive clauses in sos and nonpositive
% 1.74/1.94 clauses in usable.
% 1.74/1.94
% 1.74/1.94 dependent: set(knuth_bendix).
% 1.74/1.94 dependent: set(anl_eq).
% 1.74/1.94 dependent: set(para_from).
% 1.74/1.94 dependent: set(para_into).
% 1.74/1.94 dependent: clear(para_from_right).
% 1.74/1.94 dependent: clear(para_into_right).
% 1.74/1.94 dependent: set(para_from_vars).
% 1.74/1.94 dependent: set(eq_units_both_ways).
% 1.74/1.94 dependent: set(dynamic_demod_all).
% 1.74/1.94 dependent: set(dynamic_demod).
% 1.74/1.94 dependent: set(order_eq).
% 1.74/1.94 dependent: set(back_demod).
% 1.74/1.94 dependent: set(lrpo).
% 1.74/1.94 dependent: set(hyper_res).
% 1.74/1.94 dependent: set(unit_deletion).
% 1.74/1.94 dependent: set(factor).
% 1.74/1.94
% 1.74/1.94 ------------> process usable:
% 1.74/1.94 ** KEPT (pick-wt=15): 1 [] -e_quidistant(A,B,C,D)| -e_quidistant(A,B,E,F)|e_quidistant(C,D,E,F).
% 1.74/1.94 ** KEPT (pick-wt=8): 2 [] -e_quidistant(A,B,C,C)|A=B.
% 1.74/1.94 ** 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).
% 1.74/1.94 ** KEPT (pick-wt=7): 4 [] -between(A,B,A)|A=B.
% 1.74/1.94 ** KEPT (pick-wt=17): 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D).
% 1.74/1.94 ** KEPT (pick-wt=17): 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A).
% 1.74/1.94 ** KEPT (pick-wt=4): 7 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 1.74/1.94 ** KEPT (pick-wt=4): 8 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1).
% 1.74/1.94 ** KEPT (pick-wt=4): 9 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2).
% 1.74/1.94 ** 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.
% 1.74/1.94 ** KEPT (pick-wt=20): 11 [] -between(A,B,C)| -between(D,B,E)|A=B|between(A,D,euclid1(A,D,B,E,C)).
% 2.92/3.14 ** KEPT (pick-wt=20): 12 [] -between(A,B,C)| -between(D,B,E)|A=B|between(A,E,euclid2(A,D,B,E,C)).
% 2.92/3.14 ** 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)).
% 2.92/3.14 ** 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).
% 2.92/3.14 ** 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)).
% 2.92/3.14 ** KEPT (pick-wt=3): 17 [copy,16,flip.1] v!=u.
% 2.92/3.14 ** KEPT (pick-wt=7): 19 [copy,18,flip.1] extension(u,v,v,w)!=w.
% 2.92/3.14
% 2.92/3.14 ------------> process sos:
% 2.92/3.14 ** KEPT (pick-wt=3): 38 [] A=A.
% 2.92/3.14 ** KEPT (pick-wt=5): 39 [] e_quidistant(A,B,B,A).
% 2.92/3.14 ** KEPT (pick-wt=8): 40 [] between(A,B,extension(A,B,C,D)).
% 2.92/3.14 ** KEPT (pick-wt=9): 41 [] e_quidistant(A,extension(B,A,C,D),C,D).
% 2.92/3.14 ** KEPT (pick-wt=4): 42 [] between(u,v,w).
% 2.92/3.14 Following clause subsumed by 38 during input processing: 0 [copy,38,flip.1] A=A.
% 2.92/3.14 39 back subsumes 35.
% 2.92/3.14
% 2.92/3.14 ======= end of input processing =======
% 2.92/3.14
% 2.92/3.14 =========== start of search ===========
% 2.92/3.14
% 2.92/3.14
% 2.92/3.14 Resetting weight limit to 11.
% 2.92/3.14
% 2.92/3.14
% 2.92/3.14 Resetting weight limit to 11.
% 2.92/3.14
% 2.92/3.14 sos_size=1454
% 2.92/3.14
% 2.92/3.14 -------- PROOF --------
% 2.92/3.14
% 2.92/3.14 ----> UNIT CONFLICT at 1.20 sec ----> 1585 [binary,1583.1,19.1] $F.
% 2.92/3.14
% 2.92/3.14 Length of proof is 8. Level of proof is 4.
% 2.92/3.14
% 2.92/3.14 ---------------- PROOF ----------------
% 2.92/3.14 % SZS status Unsatisfiable
% 2.92/3.14 % SZS output start Refutation
% See solution above
% 2.92/3.14 ------------ end of proof -------------
% 2.92/3.14
% 2.92/3.14
% 2.92/3.14 Search stopped by max_proofs option.
% 2.92/3.14
% 2.92/3.14
% 2.92/3.14 Search stopped by max_proofs option.
% 2.92/3.14
% 2.92/3.14 ============ end of search ============
% 2.92/3.14
% 2.92/3.14 -------------- statistics -------------
% 2.92/3.14 clauses given 62
% 2.92/3.14 clauses generated 8244
% 2.92/3.14 clauses kept 1580
% 2.92/3.14 clauses forward subsumed 3466
% 2.92/3.14 clauses back subsumed 71
% 2.92/3.14 Kbytes malloced 4882
% 2.92/3.14
% 2.92/3.14 ----------- times (seconds) -----------
% 2.92/3.14 user CPU time 1.20 (0 hr, 0 min, 1 sec)
% 2.92/3.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.92/3.14 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.92/3.14
% 2.92/3.14 That finishes the proof of the theorem.
% 2.92/3.14
% 2.92/3.14 Process 2838 finished Wed Jul 27 07:10:27 2022
% 2.92/3.14 Otter interrupted
% 2.92/3.15 PROOF FOUND
%------------------------------------------------------------------------------