TSTP Solution File: GEO036-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO036-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:54:12 EDT 2022
% Result : Unsatisfiable 3.31s 3.54s
% Output : Refutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 28 ( 13 unt; 4 nHn; 21 RR)
% Number of literals : 50 ( 17 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 43 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ e_quidistant(A,B,C,C)
| A = B ),
file('GEO036-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ between(A,B,A)
| A = B ),
file('GEO036-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ between(A,B,C)
| ~ between(D,E,C)
| between(B,inner_pasch(A,B,C,E,D),D) ),
file('GEO036-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ between(A,B,C)
| ~ between(D,E,C)
| between(E,inner_pasch(A,B,C,E,D),A) ),
file('GEO036-2.p',unknown),
[] ).
cnf(7,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('GEO036-2.p',unknown),
[] ).
cnf(8,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('GEO036-2.p',unknown),
[] ).
cnf(9,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('GEO036-2.p',unknown),
[] ).
cnf(36,axiom,
between(A,B,extension(A,B,C,D)),
file('GEO036-2.p',unknown),
[] ).
cnf(37,axiom,
e_quidistant(A,extension(B,A,C,D),C,D),
file('GEO036-2.p',unknown),
[] ).
cnf(38,axiom,
( lower_dimension_point_1 = lower_dimension_point_2
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_3 ),
file('GEO036-2.p',unknown),
[] ).
cnf(39,plain,
( lower_dimension_point_2 = lower_dimension_point_1
| lower_dimension_point_3 = lower_dimension_point_2
| lower_dimension_point_3 = lower_dimension_point_1 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[38])])])]),
[iquote('copy,38,flip.1,flip.2,flip.3')] ).
cnf(76,plain,
extension(A,B,C,C) = B,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[37,2])]),
[iquote('hyper,37,2,flip.1')] ).
cnf(161,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
| lower_dimension_point_3 = lower_dimension_point_2
| lower_dimension_point_3 = lower_dimension_point_1 ),
inference(para_from,[status(thm),theory(equality)],[39,9]),
[iquote('para_from,39.1.1,9.1.3')] ).
cnf(181,plain,
( A = B
| ~ between(B,A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[76,4]),76,76]),
[iquote('para_into,75.1.1,4.2.1,demod,76,76')] ).
cnf(185,plain,
between(A,B,B),
inference(para_from,[status(thm),theory(equality)],[76,36]),
[iquote('para_from,75.1.1,36.1.3')] ).
cnf(215,plain,
between(A,inner_pasch(B,A,A,A,C),B),
inference(hyper,[status(thm)],[185,6,185]),
[iquote('hyper,185,6,185')] ).
cnf(247,plain,
( ~ between(lower_dimension_point_2,A,lower_dimension_point_1)
| ~ between(A,lower_dimension_point_3,A) ),
inference(para_from,[status(thm),theory(equality)],[181,8]),
[iquote('para_from,181.1.1,8.1.2')] ).
cnf(251,plain,
( ~ between(lower_dimension_point_1,A,lower_dimension_point_3)
| ~ between(A,lower_dimension_point_2,A) ),
inference(para_from,[status(thm),theory(equality)],[181,7]),
[iquote('para_from,181.1.1,7.1.2')] ).
cnf(470,plain,
( ~ between(lower_dimension_point_2,A,B)
| ~ between(A,lower_dimension_point_3,A)
| ~ between(lower_dimension_point_1,B,lower_dimension_point_1) ),
inference(para_into,[status(thm),theory(equality)],[247,4]),
[iquote('para_into,247.1.3,4.2.1')] ).
cnf(509,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_3)
| ~ between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_1) ),
inference(factor,[status(thm)],[470]),
[iquote('factor,470.2.3')] ).
cnf(964,plain,
( ~ between(lower_dimension_point_1,A,B)
| ~ between(A,lower_dimension_point_2,A)
| ~ between(lower_dimension_point_3,B,lower_dimension_point_3) ),
inference(para_into,[status(thm),theory(equality)],[251,4]),
[iquote('para_into,251.1.3,4.2.1')] ).
cnf(1001,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_2)
| ~ between(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_3) ),
inference(factor,[status(thm)],[964]),
[iquote('factor,964.2.3')] ).
cnf(1018,plain,
inner_pasch(A,A,A,A,B) = A,
inference(hyper,[status(thm)],[215,181]),
[iquote('hyper,215,181')] ).
cnf(1020,plain,
between(A,A,B),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1018,5]),185,185]),
[iquote('para_from,1018.1.1,5.3.2,unit_del,185,185')] ).
cnf(1041,plain,
( lower_dimension_point_3 = lower_dimension_point_2
| lower_dimension_point_3 = lower_dimension_point_1 ),
inference(hyper,[status(thm)],[161,185]),
[iquote('hyper,161,185')] ).
cnf(1056,plain,
lower_dimension_point_3 = lower_dimension_point_1,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1041,8]),1020]),
[iquote('para_from,1041.1.1,8.1.2,unit_del,1020')] ).
cnf(1058,plain,
lower_dimension_point_2 = lower_dimension_point_1,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1041,509]),1056,1056]),185,1020])]),
[iquote('para_from,1041.2.1,509.2.2,demod,1056,1056,unit_del,185,1020,flip.1')] ).
cnf(1059,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1001]),1056,1058,1056,1058,1056]),1020,1020]),
[iquote('back_demod,1001,demod,1056,1058,1056,1058,1056,unit_del,1020,1020')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO036-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n026.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 07:24:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.96/2.12 ----- Otter 3.3f, August 2004 -----
% 1.96/2.12 The process was started by sandbox2 on n026.cluster.edu,
% 1.96/2.12 Wed Jul 27 07:24:09 2022
% 1.96/2.12 The command was "./otter". The process ID is 12898.
% 1.96/2.12
% 1.96/2.12 set(prolog_style_variables).
% 1.96/2.12 set(auto).
% 1.96/2.12 dependent: set(auto1).
% 1.96/2.12 dependent: set(process_input).
% 1.96/2.12 dependent: clear(print_kept).
% 1.96/2.12 dependent: clear(print_new_demod).
% 1.96/2.12 dependent: clear(print_back_demod).
% 1.96/2.12 dependent: clear(print_back_sub).
% 1.96/2.12 dependent: set(control_memory).
% 1.96/2.12 dependent: assign(max_mem, 12000).
% 1.96/2.12 dependent: assign(pick_given_ratio, 4).
% 1.96/2.12 dependent: assign(stats_level, 1).
% 1.96/2.12 dependent: assign(max_seconds, 10800).
% 1.96/2.12 clear(print_given).
% 1.96/2.12
% 1.96/2.12 list(usable).
% 1.96/2.12 0 [] A=A.
% 1.96/2.12 0 [] e_quidistant(X,Y,Y,X).
% 1.96/2.12 0 [] -e_quidistant(X,Y,Z,V)| -e_quidistant(X,Y,V2,W)|e_quidistant(Z,V,V2,W).
% 1.96/2.12 0 [] -e_quidistant(X,Y,Z,Z)|X=Y.
% 1.96/2.12 0 [] between(X,Y,extension(X,Y,W,V)).
% 1.96/2.12 0 [] e_quidistant(Y,extension(X,Y,W,V),W,V).
% 1.96/2.12 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).
% 1.96/2.12 0 [] -between(X,Y,X)|X=Y.
% 1.96/2.12 0 [] -between(U,V,W)| -between(Y,X,W)|between(V,inner_pasch(U,V,W,X,Y),Y).
% 1.96/2.12 0 [] -between(U,V,W)| -between(Y,X,W)|between(X,inner_pasch(U,V,W,X,Y),U).
% 1.96/2.12 0 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 1.96/2.12 0 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1).
% 1.96/2.12 0 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2).
% 1.96/2.12 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.
% 1.96/2.12 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(U,V,euclid1(U,V,W,X,Y)).
% 1.96/2.12 0 [] -between(U,W,Y)| -between(V,W,X)|U=W|between(U,X,euclid2(U,V,W,X,Y)).
% 1.96/2.12 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)).
% 1.96/2.12 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).
% 1.96/2.12 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)).
% 1.96/2.12 0 [] lower_dimension_point_1=lower_dimension_point_2|lower_dimension_point_2=lower_dimension_point_3|lower_dimension_point_1=lower_dimension_point_3.
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.96/2.12
% 1.96/2.12 This ia a non-Horn set with equality. The strategy will be
% 1.96/2.12 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.96/2.12 deletion, with positive clauses in sos and nonpositive
% 1.96/2.12 clauses in usable.
% 1.96/2.12
% 1.96/2.12 dependent: set(knuth_bendix).
% 1.96/2.12 dependent: set(anl_eq).
% 1.96/2.12 dependent: set(para_from).
% 1.96/2.12 dependent: set(para_into).
% 1.96/2.12 dependent: clear(para_from_right).
% 1.96/2.12 dependent: clear(para_into_right).
% 1.96/2.12 dependent: set(para_from_vars).
% 1.96/2.12 dependent: set(eq_units_both_ways).
% 1.96/2.12 dependent: set(dynamic_demod_all).
% 1.96/2.12 dependent: set(dynamic_demod).
% 1.96/2.12 dependent: set(order_eq).
% 1.96/2.12 dependent: set(back_demod).
% 1.96/2.12 dependent: set(lrpo).
% 1.96/2.12 dependent: set(hyper_res).
% 1.96/2.12 dependent: set(unit_deletion).
% 1.96/2.12 dependent: set(factor).
% 1.96/2.12
% 1.96/2.12 ------------> process usable:
% 1.96/2.12 ** KEPT (pick-wt=15): 1 [] -e_quidistant(A,B,C,D)| -e_quidistant(A,B,E,F)|e_quidistant(C,D,E,F).
% 1.96/2.12 ** KEPT (pick-wt=8): 2 [] -e_quidistant(A,B,C,C)|A=B.
% 1.96/2.12 ** 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).
% 1.96/2.12 ** KEPT (pick-wt=7): 4 [] -between(A,B,A)|A=B.
% 1.96/2.12 ** KEPT (pick-wt=17): 5 [] -between(A,B,C)| -between(D,E,C)|between(B,inner_pasch(A,B,C,E,D),D).
% 1.96/2.12 ** KEPT (pick-wt=17): 6 [] -between(A,B,C)| -between(D,E,C)|between(E,inner_pasch(A,B,C,E,D),A).
% 1.96/2.12 ** KEPT (pick-wt=4): 7 [] -between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3).
% 1.96/2.12 ** KEPT (pick-wt=4): 8 [] -between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1).
% 1.96/2.12 ** KEPT (pick-wt=4): 9 [] -between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2).
% 1.96/2.12 ** 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.
% 3.31/3.54 ** KEPT (pick-wt=20): 11 [] -between(A,B,C)| -between(D,B,E)|A=B|between(A,D,euclid1(A,D,B,E,C)).
% 3.31/3.54 ** KEPT (pick-wt=20): 12 [] -between(A,B,C)| -between(D,B,E)|A=B|between(A,E,euclid2(A,D,B,E,C)).
% 3.31/3.54 ** 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)).
% 3.31/3.54 ** 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).
% 3.31/3.54 ** 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)).
% 3.31/3.54
% 3.31/3.54 ------------> process sos:
% 3.31/3.54 ** KEPT (pick-wt=3): 34 [] A=A.
% 3.31/3.54 ** KEPT (pick-wt=5): 35 [] e_quidistant(A,B,B,A).
% 3.31/3.54 ** KEPT (pick-wt=8): 36 [] between(A,B,extension(A,B,C,D)).
% 3.31/3.54 ** KEPT (pick-wt=9): 37 [] e_quidistant(A,extension(B,A,C,D),C,D).
% 3.31/3.54 ** KEPT (pick-wt=9): 39 [copy,38,flip.1,flip.2,flip.3] lower_dimension_point_2=lower_dimension_point_1|lower_dimension_point_3=lower_dimension_point_2|lower_dimension_point_3=lower_dimension_point_1.
% 3.31/3.54 Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] A=A.
% 3.31/3.54 35 back subsumes 31.
% 3.31/3.54
% 3.31/3.54 ======= end of input processing =======
% 3.31/3.54
% 3.31/3.54 =========== start of search ===========
% 3.31/3.54
% 3.31/3.54
% 3.31/3.54 Resetting weight limit to 9.
% 3.31/3.54
% 3.31/3.54
% 3.31/3.54 Resetting weight limit to 9.
% 3.31/3.54
% 3.31/3.54 sos_size=900
% 3.31/3.54
% 3.31/3.54 -------- PROOF --------
% 3.31/3.54
% 3.31/3.54 -----> EMPTY CLAUSE at 1.42 sec ----> 1059 [back_demod,1001,demod,1056,1058,1056,1058,1056,unit_del,1020,1020] $F.
% 3.31/3.54
% 3.31/3.54 Length of proof is 17. Level of proof is 7.
% 3.31/3.54
% 3.31/3.54 ---------------- PROOF ----------------
% 3.31/3.54 % SZS status Unsatisfiable
% 3.31/3.54 % SZS output start Refutation
% See solution above
% 3.31/3.54 ------------ end of proof -------------
% 3.31/3.54
% 3.31/3.54
% 3.31/3.54 Search stopped by max_proofs option.
% 3.31/3.54
% 3.31/3.54
% 3.31/3.54 Search stopped by max_proofs option.
% 3.31/3.54
% 3.31/3.54 ============ end of search ============
% 3.31/3.54
% 3.31/3.54 -------------- statistics -------------
% 3.31/3.54 clauses given 107
% 3.31/3.54 clauses generated 38017
% 3.31/3.54 clauses kept 1048
% 3.31/3.54 clauses forward subsumed 6152
% 3.31/3.54 clauses back subsumed 134
% 3.31/3.54 Kbytes malloced 4882
% 3.31/3.54
% 3.31/3.54 ----------- times (seconds) -----------
% 3.31/3.54 user CPU time 1.42 (0 hr, 0 min, 1 sec)
% 3.31/3.54 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.31/3.54 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.31/3.54
% 3.31/3.54 That finishes the proof of the theorem.
% 3.31/3.54
% 3.31/3.54 Process 12898 finished Wed Jul 27 07:24:12 2022
% 3.31/3.54 Otter interrupted
% 3.31/3.54 PROOF FOUND
%------------------------------------------------------------------------------