TSTP Solution File: GEO002-3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 12:54:03 EDT 2022
% Result : Unsatisfiable 1.82s 2.03s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 3 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 7 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(35,axiom,
( ~ between(A,B,C)
| between(C,B,A) ),
file('GEO002-3.p',unknown),
[] ).
cnf(36,axiom,
~ between(a,a,b),
file('GEO002-3.p',unknown),
[] ).
cnf(72,axiom,
between(A,B,B),
file('GEO002-3.p',unknown),
[] ).
cnf(79,plain,
between(A,A,B),
inference(hyper,[status(thm)],[72,35]),
[iquote('hyper,72,35')] ).
cnf(80,plain,
$false,
inference(binary,[status(thm)],[79,36]),
[iquote('binary,79.1,36.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 07:12:09 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.82/2.03 ----- Otter 3.3f, August 2004 -----
% 1.82/2.03 The process was started by sandbox on n010.cluster.edu,
% 1.82/2.03 Wed Jul 27 07:12:10 2022
% 1.82/2.03 The command was "./otter". The process ID is 6488.
% 1.82/2.03
% 1.82/2.03 set(prolog_style_variables).
% 1.82/2.03 set(auto).
% 1.82/2.03 dependent: set(auto1).
% 1.82/2.03 dependent: set(process_input).
% 1.82/2.03 dependent: clear(print_kept).
% 1.82/2.03 dependent: clear(print_new_demod).
% 1.82/2.03 dependent: clear(print_back_demod).
% 1.82/2.03 dependent: clear(print_back_sub).
% 1.82/2.03 dependent: set(control_memory).
% 1.82/2.03 dependent: assign(max_mem, 12000).
% 1.82/2.03 dependent: assign(pick_given_ratio, 4).
% 1.82/2.03 dependent: assign(stats_level, 1).
% 1.82/2.03 dependent: assign(max_seconds, 10800).
% 1.82/2.03 clear(print_given).
% 1.82/2.03
% 1.82/2.03 list(usable).
% 1.82/2.03 0 [] A=A.
% 1.82/2.03 0 [] e_quidistant(X,Y,Y,X).
% 1.82/2.03 0 [] -e_quidistant(X,Y,Z,V)| -e_quidistant(X,Y,V2,W)|e_quidistant(Z,V,V2,W).
% 1.82/2.03 0 [] -e_quidistant(X,Y,Z,Z)|X=Y.
% 1.82/2.03 0 [] between(X,Y,extension(X,Y,W,V)).
% 1.82/2.03 0 [] e_quidistant(Y,extension(X,Y,W,V),W,V).
% 1.82/2.03 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).
% 1.82/2.03 0 [] -between(X,Y,X)|X=Y.
% 1.82/2.03 0 [] -between(U,V,W)| -between(Y,X,W)|between(V,inner_pasch(U,V,W,X,Y),Y).
% 1.82/2.03 0 [] -between(U,V,W)| -between(Y,X,W)|between(X,inner_pasch(U,V,W,X,Y),U).
% 1.82/2.03 0 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 1.82/2.03 0 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1).
% 1.82/2.03 0 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2).
% 1.82/2.03 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.
% 1.82/2.03 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(U,V,euclid1(U,V,W,X,Y)).
% 1.82/2.03 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(U,X,euclid2(U,V,W,X,Y)).
% 1.82/2.03 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)).
% 1.82/2.03 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).
% 1.82/2.03 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)).
% 1.82/2.03 0 [] reflection(U,V)=extension(U,V,U,V).
% 1.82/2.03 0 [] e_quidistant(U,V,U,V).
% 1.82/2.03 0 [] -e_quidistant(U,V,W,X)|e_quidistant(W,X,U,V).
% 1.82/2.03 0 [] -e_quidistant(U,V,W,X)|e_quidistant(V,U,W,X).
% 1.82/2.03 0 [] -e_quidistant(U,V,W,X)|e_quidistant(U,V,X,W).
% 1.82/2.03 0 [] -e_quidistant(U,V,W,X)|e_quidistant(V,U,X,W).
% 1.82/2.03 0 [] -e_quidistant(U,V,W,X)|e_quidistant(W,X,V,U).
% 1.82/2.03 0 [] -e_quidistant(U,V,W,X)|e_quidistant(X,W,U,V).
% 1.82/2.03 0 [] -e_quidistant(U,V,W,X)|e_quidistant(X,W,V,U).
% 1.82/2.03 0 [] -e_quidistant(U,V,W,X)| -e_quidistant(W,X,Y,Z)|e_quidistant(U,V,Y,Z).
% 1.82/2.03 0 [] V=extension(U,V,W,W).
% 1.82/2.03 0 [] Y!=extension(U,V,W,X)|between(U,V,Y).
% 1.82/2.03 0 [] between(U,V,reflection(U,V)).
% 1.82/2.03 0 [] e_quidistant(V,reflection(U,V),U,V).
% 1.82/2.03 0 [] U!=V|V=reflection(U,V).
% 1.82/2.03 0 [] U=reflection(U,U).
% 1.82/2.03 0 [] V!=reflection(U,V)|U=V.
% 1.82/2.03 0 [] e_quidistant(U,U,V,V).
% 1.82/2.03 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).
% 1.82/2.03 0 [] -between(U,V,W)| -between(U,V,X)| -e_quidistant(V,W,V,X)|U=V|W=X.
% 1.82/2.03 0 [] -between(U,V,W)|U=V|W=extension(U,V,V,W).
% 1.82/2.03 0 [] -e_quidistant(W,X,Y,Z)|extension(U,V,W,X)=extension(U,V,Y,Z)|U=V.
% 1.82/2.03 0 [] extension(U,V,U,V)=extension(U,V,V,U)|U=V.
% 1.82/2.03 0 [] e_quidistant(V,U,V,reflection(reflection(U,V),V)).
% 1.82/2.03 0 [] U=reflection(reflection(U,V),V).
% 1.82/2.03 0 [] between(U,V,V).
% 1.82/2.03 0 [] -between(U,W,X)|U!=X|between(V,W,X).
% 1.82/2.03 0 [] -between(U,V,W)|between(W,V,U).
% 1.82/2.03 0 [] -between(a,a,b).
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.82/2.03
% 1.82/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.82/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.82/2.03 deletion, with positive clauses in sos and nonpositive
% 1.82/2.03 clauses in usable.
% 1.82/2.03
% 1.82/2.03 dependent: set(knuth_bendix).
% 1.82/2.03 dependent: set(anl_eq).
% 1.82/2.03 dependent: set(para_from).
% 1.82/2.03 dependent: set(para_into).
% 1.82/2.03 dependent: clear(para_from_right).
% 1.82/2.03 dependent: clear(para_into_right).
% 1.82/2.03 dependent: set(para_from_vars).
% 1.82/2.03 dependent: set(eq_units_both_ways).
% 1.82/2.03 dependent: set(dynamic_demod_all).
% 1.82/2.03 dependent: set(dynamic_demod).
% 1.82/2.03 dependent: set(order_eq).
% 1.82/2.03 dependent: set(back_demod).
% 1.82/2.03 dependent: set(lrpo).
% 1.82/2.03 dependent: set(hyper_res).
% 1.82/2.03 dependent: set(unit_deletion).
% 1.82/2.03 dependent: set(factor).
% 1.82/2.03
% 1.82/2.03 ------------> process usable:
% 1.82/2.03 ** KEPT (pick-wt=15): 1 [] -e_quidistant(A,B,C,D)| -e_quidistant(A,B,E,F)|e_quidistant(C,D,E,F).
% 1.82/2.03 ** KEPT (pick-wt=8): 2 [] -e_quidistant(A,B,C,C)|A=B.
% 1.82/2.03 ** 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).
% 1.82/2.03 ** KEPT (pick-wt=7): 4 [] -between(A,B,A)|A=B.
% 1.82/2.03 ** KEPT (pick-wt=17): 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D).
% 1.82/2.03 ** KEPT (pick-wt=17): 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A).
% 1.82/2.03 ** KEPT (pick-wt=4): 7 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 1.82/2.03 ** KEPT (pick-wt=4): 8 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1).
% 1.82/2.03 ** KEPT (pick-wt=4): 9 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2).
% 1.82/2.03 ** 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.
% 1.82/2.03 ** KEPT (pick-wt=20): 11 [] -between(A,B,C)| -between(D,B,E)|A=B|between(A,D,euclid1(A,D,B,E,C)).
% 1.82/2.03 ** KEPT (pick-wt=20): 12 [] -between(A,B,C)| -between(D,B,E)|A=B|between(A,E,euclid2(A,D,B,E,C)).
% 1.82/2.03 ** 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)).
% 1.82/2.03 ** 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).
% 1.82/2.03 ** 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)).
% 1.82/2.03 ** KEPT (pick-wt=10): 16 [] -e_quidistant(A,B,C,D)|e_quidistant(C,D,A,B).
% 1.82/2.03 ** KEPT (pick-wt=10): 17 [] -e_quidistant(A,B,C,D)|e_quidistant(B,A,C,D).
% 1.82/2.03 ** KEPT (pick-wt=10): 18 [] -e_quidistant(A,B,C,D)|e_quidistant(A,B,D,C).
% 1.82/2.03 ** KEPT (pick-wt=10): 19 [] -e_quidistant(A,B,C,D)|e_quidistant(B,A,D,C).
% 1.82/2.03 ** KEPT (pick-wt=10): 20 [] -e_quidistant(A,B,C,D)|e_quidistant(C,D,B,A).
% 1.82/2.03 ** KEPT (pick-wt=10): 21 [] -e_quidistant(A,B,C,D)|e_quidistant(D,C,A,B).
% 1.82/2.03 ** KEPT (pick-wt=10): 22 [] -e_quidistant(A,B,C,D)|e_quidistant(D,C,B,A).
% 1.82/2.03 ** KEPT (pick-wt=15): 23 [] -e_quidistant(A,B,C,D)| -e_quidistant(C,D,E,F)|e_quidistant(A,B,E,F).
% 1.82/2.03 ** KEPT (pick-wt=11): 24 [] A!=extension(B,C,D,E)|between(B,C,A).
% 1.82/2.03 ** KEPT (pick-wt=8): 26 [copy,25,flip.2] A!=B|reflection(A,B)=B.
% 1.82/2.03 ** KEPT (pick-wt=8): 28 [copy,27,flip.1] reflection(A,B)!=B|A=B.
% 1.82/2.03 ** KEPT (pick-wt=23): 29 [] -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).
% 1.82/2.03 ** KEPT (pick-wt=19): 30 [] -between(A,B,C)| -between(A,B,D)| -e_quidistant(B,C,B,D)|A=B|C=D.
% 1.82/2.03 ** KEPT (pick-wt=14): 32 [copy,31,flip.3] -between(A,B,C)|A=B|extension(A,B,B,C)=C.
% 1.82/2.03 ** KEPT (pick-wt=19): 33 [] -e_quidistant(A,B,C,D)|extension(E,F,A,B)=extension(E,F,C,D)|E=F.
% 1.82/2.03 ** KEPT (pick-wt=11): 34 [] -between(A,B,C)|A!=C|between(D,B,C).
% 1.82/2.03 ** KEPT (pick-wt=8): 35 [] -between(A,B,C)|between(C,B,A).
% 1.82/2.03 ** KEPT (pick-wt=4): 36 [] -between(a,a,b).
% 1.82/2.03
% 1.82/2.03 ------------> process sos:
% 1.82/2.03 ** KEPT (pick-wt=3): 55 [] A=A.
% 1.82/2.03 ** KEPT (pick-wt=5): 56 [] e_quidistant(A,B,B,A).
% 1.82/2.03 ** KEPT (pick-wt=8): 57 [] between(A,B,extension(A,B,C,D)).
% 1.82/2.03 ** KEPT (pick-wt=9): 58 [] e_quidistant(A,extension(B,A,C,D),C,D).
% 1.82/2.03 ** KEPT (pick-wt=9): 59 [] reflection(A,B)=extension(A,B,A,B).
% 1.82/2.03 ---> New Demodulator: 60 [new_demod,59] reflection(A,B)=extension(A,B,A,B).
% 1.82/2.03 ** KEPT (pick-wt=5): 61 [] e_quidistant(A,B,A,B).
% 1.82/2.03 ** KEPT (pick-wt=7): 63 [copy,62,flip.1] extension(A,B,C,C)=B.
% 1.82/2.03 ---> New Demodulator: 64 [new_demod,63] extension(A,B,C,C)=B.
% 1.82/2.03 Following clause subsumed by 57 during input processing: 0 [demod,60] between(A,B,extension(A,B,A,B)).
% 1.82/2.03 Following clause subsumed by 58 during input processing: 0 [demod,60] e_quidistant(A,extension(B,A,B,A),B,A).
% 1.82/2.03 Following clause subsumed by 55 during input processing: 0 [demod,60,64] A=A.
% 1.82/2.03 ** KEPT (pick-wt=5): 65 [] e_quidistant(A,A,B,B).
% 1.82/2.03 ** KEPT (pick-wt=14): 66 [] extension(A,B,A,B)=extension(A,B,B,A)|A=B.
% 1.82/2.03 ** KEPT (pick-wt=17): 68 [copy,67,demod,60,60] e_quidistant(A,B,A,extension(extension(B,A,B,A),A,extension(B,A,B,A),A)).
% 1.82/2.03 ** KEPT (pick-wt=15): 70 [copy,69,demod,60,60,flip.1] extension(extension(A,B,A,B),B,extension(A,B,A,B),B)=A.
% 1.82/2.03 ---> New Demodulator: 71 [new_demod,70] extension(extension(A,B,A,B),B,extension(A,B,A,B),B)=A.
% 1.82/2.03 ** KEPT (pick-wt=4): 72 [] between(A,B,B).
% 1.82/2.03 Following clause subsumed by 55 during input processing: 0 [copy,55,flip.1] A=A.
% 1.82/2.03 55 back subsumes 51.
% 1.82/2.03 56 back subsumes 52.
% 1.82/2.03 >>>> Starting back demodulation with 60.
% 1.82/2.03 >> back demodulating 28 with 60.
% 1.82/2.03 >> back demodulating 26 with 60.
% 1.82/2.03 61 back subsumes 50.
% 1.82/2.03 61 back subsumes 37.
% 1.82/2.03 >>>> Starting back demodulation with 64.
% 1.82/2.03 65 back subsumes 38.
% 1.82/2.03 >>>> Starting back demodulation with 71.
% 1.82/2.03 >> back demodulating 68 with 71.
% 1.82/2.03 72 back subsumes 42.
% 1.82/2.03 72 back subsumes 41.
% 1.82/2.03
% 1.82/2.03 ======= end of input processing =======
% 1.82/2.03
% 1.82/2.03 =========== start of search ===========
% 1.82/2.03
% 1.82/2.03 -------- PROOF --------
% 1.82/2.03
% 1.82/2.03 ----> UNIT CONFLICT at 0.01 sec ----> 80 [binary,79.1,36.1] $F.
% 1.82/2.03
% 1.82/2.03 Length of proof is 1. Level of proof is 1.
% 1.82/2.03
% 1.82/2.03 ---------------- PROOF ----------------
% 1.82/2.03 % SZS status Unsatisfiable
% 1.82/2.03 % SZS output start Refutation
% See solution above
% 1.82/2.03 ------------ end of proof -------------
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Search stopped by max_proofs option.
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Search stopped by max_proofs option.
% 1.82/2.03
% 1.82/2.03 ============ end of search ============
% 1.82/2.03
% 1.82/2.03 -------------- statistics -------------
% 1.82/2.03 clauses given 2
% 1.82/2.03 clauses generated 57
% 1.82/2.03 clauses kept 70
% 1.82/2.03 clauses forward subsumed 30
% 1.82/2.03 clauses back subsumed 7
% 1.82/2.03 Kbytes malloced 976
% 1.82/2.03
% 1.82/2.03 ----------- times (seconds) -----------
% 1.82/2.03 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.82/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.03 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.82/2.03
% 1.82/2.03 That finishes the proof of the theorem.
% 1.82/2.03
% 1.82/2.03 Process 6488 finished Wed Jul 27 07:12:11 2022
% 1.82/2.03 Otter interrupted
% 1.82/2.03 PROOF FOUND
%------------------------------------------------------------------------------