TSTP Solution File: GEO086+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO086+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 12:54:22 EDT 2022
% Result : Theorem 1.67s 1.89s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 6 unt; 1 nHn; 7 RR)
% Number of literals : 9 ( 2 equ; 2 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(29,axiom,
( ~ part_of(A,B)
| A = B
| open(A) ),
file('GEO086+1.p',unknown),
[] ).
cnf(42,axiom,
~ open(dollar_c1),
file('GEO086+1.p',unknown),
[] ).
cnf(59,axiom,
open(dollar_c2),
file('GEO086+1.p',unknown),
[] ).
cnf(60,axiom,
part_of(dollar_c1,dollar_c2),
file('GEO086+1.p',unknown),
[] ).
cnf(75,plain,
dollar_c2 = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[60,29]),42])]),
[iquote('hyper,60,29,unit_del,42,flip.1')] ).
cnf(86,plain,
open(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),75]),
[iquote('back_demod,59,demod,75')] ).
cnf(87,plain,
$false,
inference(binary,[status(thm)],[86,42]),
[iquote('binary,86.1,42.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO086+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 07:30:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox2 on n028.cluster.edu,
% 1.67/1.89 Wed Jul 27 07:30:04 2022
% 1.67/1.89 The command was "./otter". The process ID is 22995.
% 1.67/1.89
% 1.67/1.89 set(prolog_style_variables).
% 1.67/1.89 set(auto).
% 1.67/1.89 dependent: set(auto1).
% 1.67/1.89 dependent: set(process_input).
% 1.67/1.89 dependent: clear(print_kept).
% 1.67/1.89 dependent: clear(print_new_demod).
% 1.67/1.89 dependent: clear(print_back_demod).
% 1.67/1.89 dependent: clear(print_back_sub).
% 1.67/1.89 dependent: set(control_memory).
% 1.67/1.89 dependent: assign(max_mem, 12000).
% 1.67/1.89 dependent: assign(pick_given_ratio, 4).
% 1.67/1.89 dependent: assign(stats_level, 1).
% 1.67/1.89 dependent: assign(max_seconds, 10800).
% 1.67/1.89 clear(print_given).
% 1.67/1.89
% 1.67/1.89 formula_list(usable).
% 1.67/1.89 all A (A=A).
% 1.67/1.89 all C C1 (part_of(C1,C)<-> (all P (incident_c(P,C1)->incident_c(P,C)))).
% 1.67/1.89 all C C1 C2 (C=sum(C1,C2)<-> (all Q (incident_c(Q,C)<->incident_c(Q,C1)|incident_c(Q,C2)))).
% 1.67/1.89 all P C (end_point(P,C)<->incident_c(P,C)& (all C1 C2 (part_of(C1,C)&part_of(C2,C)&incident_c(P,C1)&incident_c(P,C2)->part_of(C1,C2)|part_of(C2,C1)))).
% 1.67/1.89 all P C (inner_point(P,C)<->incident_c(P,C)& -end_point(P,C)).
% 1.67/1.89 all P C C1 (meet(P,C,C1)<->incident_c(P,C)&incident_c(P,C1)& (all Q (incident_c(Q,C)&incident_c(Q,C1)->end_point(Q,C)&end_point(Q,C1)))).
% 1.67/1.89 all C (closed(C)<-> -(exists P end_point(P,C))).
% 1.67/1.89 all C (open(C)<-> (exists P end_point(P,C))).
% 1.67/1.89 all C C1 (part_of(C1,C)&C1!=C->open(C1)).
% 1.67/1.89 all C C1 C2 C3 (part_of(C1,C)&part_of(C2,C)&part_of(C3,C)& (exists P (end_point(P,C1)&end_point(P,C2)&end_point(P,C3)))->part_of(C2,C3)|part_of(C3,C2)|part_of(C1,C2)|part_of(C2,C1)|part_of(C1,C3)|part_of(C3,C1)).
% 1.67/1.89 all C exists P inner_point(P,C).
% 1.67/1.89 all C P (inner_point(P,C)-> (exists C1 C2 (meet(P,C1,C2)&C=sum(C1,C2)))).
% 1.67/1.89 all C P Q R (end_point(P,C)&end_point(Q,C)&end_point(R,C)->P=Q|P=R|Q=R).
% 1.67/1.89 all C P (end_point(P,C)-> (exists Q (end_point(Q,C)&P!=Q))).
% 1.67/1.89 all C C1 C2 P (closed(C)&meet(P,C1,C2)&C=sum(C1,C2)-> (all Q (end_point(Q,C1)->meet(Q,C1,C2)))).
% 1.67/1.89 all C1 C2 ((exists P meet(P,C1,C2))-> (exists C (C=sum(C1,C2)))).
% 1.67/1.89 all C C1 ((all P (incident_c(P,C)<->incident_c(P,C1)))->C=C1).
% 1.67/1.89 -(all C Cpp (open(C)&part_of(Cpp,C)->open(Cpp))).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 -------> usable clausifies to:
% 1.67/1.89
% 1.67/1.89 list(usable).
% 1.67/1.89 0 [] A=A.
% 1.67/1.89 0 [] -part_of(C1,C)| -incident_c(P,C1)|incident_c(P,C).
% 1.67/1.89 0 [] part_of(C1,C)|incident_c($f1(C,C1),C1).
% 1.67/1.89 0 [] part_of(C1,C)| -incident_c($f1(C,C1),C).
% 1.67/1.89 0 [] C!=sum(C1,C2)| -incident_c(Q,C)|incident_c(Q,C1)|incident_c(Q,C2).
% 1.67/1.89 0 [] C!=sum(C1,C2)|incident_c(Q,C)| -incident_c(Q,C1).
% 1.67/1.89 0 [] C!=sum(C1,C2)|incident_c(Q,C)| -incident_c(Q,C2).
% 1.67/1.89 0 [] C=sum(C1,C2)|incident_c($f2(C,C1,C2),C)|incident_c($f2(C,C1,C2),C1)|incident_c($f2(C,C1,C2),C2).
% 1.67/1.89 0 [] C=sum(C1,C2)| -incident_c($f2(C,C1,C2),C)| -incident_c($f2(C,C1,C2),C1).
% 1.67/1.89 0 [] C=sum(C1,C2)| -incident_c($f2(C,C1,C2),C)| -incident_c($f2(C,C1,C2),C2).
% 1.67/1.89 0 [] -end_point(P,C)|incident_c(P,C).
% 1.67/1.89 0 [] -end_point(P,C)| -part_of(C1,C)| -part_of(C2,C)| -incident_c(P,C1)| -incident_c(P,C2)|part_of(C1,C2)|part_of(C2,C1).
% 1.67/1.89 0 [] end_point(P,C)| -incident_c(P,C)|part_of($f4(P,C),C).
% 1.67/1.89 0 [] end_point(P,C)| -incident_c(P,C)|part_of($f3(P,C),C).
% 1.67/1.89 0 [] end_point(P,C)| -incident_c(P,C)|incident_c(P,$f4(P,C)).
% 1.67/1.89 0 [] end_point(P,C)| -incident_c(P,C)|incident_c(P,$f3(P,C)).
% 1.67/1.89 0 [] end_point(P,C)| -incident_c(P,C)| -part_of($f4(P,C),$f3(P,C)).
% 1.67/1.89 0 [] end_point(P,C)| -incident_c(P,C)| -part_of($f3(P,C),$f4(P,C)).
% 1.67/1.89 0 [] -inner_point(P,C)|incident_c(P,C).
% 1.67/1.89 0 [] -inner_point(P,C)| -end_point(P,C).
% 1.67/1.89 0 [] inner_point(P,C)| -incident_c(P,C)|end_point(P,C).
% 1.67/1.89 0 [] -meet(P,C,C1)|incident_c(P,C).
% 1.67/1.89 0 [] -meet(P,C,C1)|incident_c(P,C1).
% 1.67/1.89 0 [] -meet(P,C,C1)| -incident_c(Q,C)| -incident_c(Q,C1)|end_point(Q,C).
% 1.67/1.89 0 [] -meet(P,C,C1)| -incident_c(Q,C)| -incident_c(Q,C1)|end_point(Q,C1).
% 1.67/1.89 0 [] meet(P,C,C1)| -incident_c(P,C)| -incident_c(P,C1)|incident_c($f5(P,C,C1),C).
% 1.67/1.89 0 [] meet(P,C,C1)| -incident_c(P,C)| -incident_c(P,C1)|incident_c($f5(P,C,C1),C1).
% 1.67/1.89 0 [] meet(P,C,C1)| -incident_c(P,C)| -incident_c(P,C1)| -end_point($f5(P,C,C1),C)| -end_point($f5(P,C,C1),C1).
% 1.67/1.89 0 [] -closed(C)| -end_point(P,C).
% 1.67/1.89 0 [] closed(C)|end_point($f6(C),C).
% 1.67/1.89 0 [] -open(C)|end_point($f7(C),C).
% 1.67/1.89 0 [] open(C)| -end_point(P,C).
% 1.67/1.89 0 [] -part_of(C1,C)|C1=C|open(C1).
% 1.67/1.89 0 [] -part_of(C1,C)| -part_of(C2,C)| -part_of(C3,C)| -end_point(P,C1)| -end_point(P,C2)| -end_point(P,C3)|part_of(C2,C3)|part_of(C3,C2)|part_of(C1,C2)|part_of(C2,C1)|part_of(C1,C3)|part_of(C3,C1).
% 1.67/1.89 0 [] inner_point($f8(C),C).
% 1.67/1.89 0 [] -inner_point(P,C)|meet(P,$f10(C,P),$f9(C,P)).
% 1.67/1.89 0 [] -inner_point(P,C)|C=sum($f10(C,P),$f9(C,P)).
% 1.67/1.89 0 [] -end_point(P,C)| -end_point(Q,C)| -end_point(R,C)|P=Q|P=R|Q=R.
% 1.67/1.89 0 [] -end_point(P,C)|end_point($f11(C,P),C).
% 1.67/1.89 0 [] -end_point(P,C)|P!=$f11(C,P).
% 1.67/1.89 0 [] -closed(C)| -meet(P,C1,C2)|C!=sum(C1,C2)| -end_point(Q,C1)|meet(Q,C1,C2).
% 1.67/1.89 0 [] -meet(P,C1,C2)|$f12(C1,C2)=sum(C1,C2).
% 1.67/1.89 0 [] incident_c($f13(C,C1),C)|incident_c($f13(C,C1),C1)|C=C1.
% 1.67/1.89 0 [] -incident_c($f13(C,C1),C)| -incident_c($f13(C,C1),C1)|C=C1.
% 1.67/1.89 0 [] open($c2).
% 1.67/1.89 0 [] part_of($c1,$c2).
% 1.67/1.89 0 [] -open($c1).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=12.
% 1.67/1.89
% 1.67/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.67/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.67/1.89 deletion, with positive clauses in sos and nonpositive
% 1.67/1.89 clauses in usable.
% 1.67/1.89
% 1.67/1.89 dependent: set(knuth_bendix).
% 1.67/1.89 dependent: set(anl_eq).
% 1.67/1.89 dependent: set(para_from).
% 1.67/1.89 dependent: set(para_into).
% 1.67/1.89 dependent: clear(para_from_right).
% 1.67/1.89 dependent: clear(para_into_right).
% 1.67/1.89 dependent: set(para_from_vars).
% 1.67/1.89 dependent: set(eq_units_both_ways).
% 1.67/1.89 dependent: set(dynamic_demod_all).
% 1.67/1.89 dependent: set(dynamic_demod).
% 1.67/1.89 dependent: set(order_eq).
% 1.67/1.89 dependent: set(back_demod).
% 1.67/1.89 dependent: set(lrpo).
% 1.67/1.89 dependent: set(hyper_res).
% 1.67/1.89 dependent: set(unit_deletion).
% 1.67/1.89 dependent: set(factor).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=9): 1 [] -part_of(A,B)| -incident_c(C,A)|incident_c(C,B).
% 1.67/1.89 ** KEPT (pick-wt=8): 2 [] part_of(A,B)| -incident_c($f1(B,A),B).
% 1.67/1.89 ** KEPT (pick-wt=14): 3 [] A!=sum(B,C)| -incident_c(D,A)|incident_c(D,B)|incident_c(D,C).
% 1.67/1.89 ** KEPT (pick-wt=11): 4 [] A!=sum(B,C)|incident_c(D,A)| -incident_c(D,B).
% 1.67/1.89 ** KEPT (pick-wt=11): 5 [] A!=sum(B,C)|incident_c(D,A)| -incident_c(D,C).
% 1.67/1.89 ** KEPT (pick-wt=17): 6 [] A=sum(B,C)| -incident_c($f2(A,B,C),A)| -incident_c($f2(A,B,C),B).
% 1.67/1.89 ** KEPT (pick-wt=17): 7 [] A=sum(B,C)| -incident_c($f2(A,B,C),A)| -incident_c($f2(A,B,C),C).
% 1.67/1.89 ** KEPT (pick-wt=6): 8 [] -end_point(A,B)|incident_c(A,B).
% 1.67/1.89 ** KEPT (pick-wt=21): 9 [] -end_point(A,B)| -part_of(C,B)| -part_of(D,B)| -incident_c(A,C)| -incident_c(A,D)|part_of(C,D)|part_of(D,C).
% 1.67/1.89 ** KEPT (pick-wt=11): 10 [] end_point(A,B)| -incident_c(A,B)|part_of($f4(A,B),B).
% 1.67/1.89 ** KEPT (pick-wt=11): 11 [] end_point(A,B)| -incident_c(A,B)|part_of($f3(A,B),B).
% 1.67/1.89 ** KEPT (pick-wt=11): 12 [] end_point(A,B)| -incident_c(A,B)|incident_c(A,$f4(A,B)).
% 1.67/1.89 ** KEPT (pick-wt=11): 13 [] end_point(A,B)| -incident_c(A,B)|incident_c(A,$f3(A,B)).
% 1.67/1.89 ** KEPT (pick-wt=13): 14 [] end_point(A,B)| -incident_c(A,B)| -part_of($f4(A,B),$f3(A,B)).
% 1.67/1.89 ** KEPT (pick-wt=13): 15 [] end_point(A,B)| -incident_c(A,B)| -part_of($f3(A,B),$f4(A,B)).
% 1.67/1.89 ** KEPT (pick-wt=6): 16 [] -inner_point(A,B)|incident_c(A,B).
% 1.67/1.89 ** KEPT (pick-wt=6): 17 [] -inner_point(A,B)| -end_point(A,B).
% 1.67/1.89 ** KEPT (pick-wt=9): 18 [] inner_point(A,B)| -incident_c(A,B)|end_point(A,B).
% 1.67/1.89 ** KEPT (pick-wt=7): 19 [] -meet(A,B,C)|incident_c(A,B).
% 1.67/1.89 ** KEPT (pick-wt=7): 20 [] -meet(A,B,C)|incident_c(A,C).
% 1.67/1.89 ** KEPT (pick-wt=13): 21 [] -meet(A,B,C)| -incident_c(D,B)| -incident_c(D,C)|end_point(D,B).
% 1.67/1.89 ** KEPT (pick-wt=13): 22 [] -meet(A,B,C)| -incident_c(D,B)| -incident_c(D,C)|end_point(D,C).
% 1.67/1.89 ** KEPT (pick-wt=16): 23 [] meet(A,B,C)| -incident_c(A,B)| -incident_c(A,C)|incident_c($f5(A,B,C),B).
% 1.67/1.89 ** KEPT (pick-wt=16): 24 [] meet(A,B,C)| -incident_c(A,B)| -incident_c(A,C)|incident_c($f5(A,B,C),C).
% 1.67/1.89 ** KEPT (pick-wt=22): 25 [] meet(A,B,C)| -incident_c(A,B)| -incident_c(A,C)| -end_point($f5(A,B,C),B)| -end_point($f5(A,B,C),C).
% 1.67/1.89 ** KEPT (pick-wt=5): 26 [] -closed(A)| -end_point(B,A).
% 1.67/1.89 ** KEPT (pick-wt=6): 27 [] -open(A)|end_point($f7(A),A).
% 1.67/1.89 ** KEPT (pick-wt=5): 28 [] open(A)| -end_point(B,A).
% 1.67/1.89 ** KEPT (pick-wt=8): 29 [] -part_of(A,B)|A=B|open(A).
% 1.67/1.89 ** KEPT (pick-wt=36): 30 [] -part_of(A,B)| -part_of(C,B)| -part_of(D,B)| -end_point(E,A)| -end_point(E,C)| -end_point(E,D)|part_of(C,D)|part_of(D,C)|part_of(A,C)|part_of(C,A)|part_of(A,D)|part_of(D,A).
% 1.67/1.89 ** KEPT (pick-wt=11): 31 [] -inner_point(A,B)|meet(A,$f10(B,A),$f9(B,A)).
% 1.67/1.89 ** KEPT (pick-wt=12): 33 [copy,32,flip.2] -inner_point(A,B)|sum($f10(B,A),$f9(B,A))=B.
% 1.67/1.89 ** KEPT (pick-wt=18): 34 [] -end_point(A,B)| -end_point(C,B)| -end_point(D,B)|A=C|A=D|C=D.
% 1.67/1.89 ** KEPT (pick-wt=8): 35 [] -end_point(A,B)|end_point($f11(B,A),B).
% 1.67/1.89 ** KEPT (pick-wt=8): 37 [copy,36,flip.2] -end_point(A,B)|$f11(B,A)!=A.
% 1.67/1.89 ** KEPT (pick-wt=18): 38 [] -closed(A)| -meet(B,C,D)|A!=sum(C,D)| -end_point(E,C)|meet(E,C,D).
% 1.67/1.89 ** KEPT (pick-wt=11): 40 [copy,39,flip.2] -meet(A,B,C)|sum(B,C)=$f12(B,C).
% 1.67/1.89 ** KEPT (pick-wt=13): 41 [] -incident_c($f13(A,B),A)| -incident_c($f13(A,B),B)|A=B.
% 1.67/1.89 ** KEPT (pick-wt=2): 42 [] -open($c1).
% 1.67/1.89
% 1.67/1.89 ------------> process sos:
% 1.67/1.89 ** KEPT (pick-wt=3): 53 [] A=A.
% 1.67/1.89 ** KEPT (pick-wt=8): 54 [] part_of(A,B)|incident_c($f1(B,A),A).
% 1.67/1.89 ** KEPT (pick-wt=23): 55 [] A=sum(B,C)|incident_c($f2(A,B,C),A)|incident_c($f2(A,B,C),B)|incident_c($f2(A,B,C),C).
% 1.67/1.89 ** KEPT (pick-wt=6): 56 [] closed(A)|end_point($f6(A),A).
% 1.67/1.89 ** KEPT (pick-wt=4): 57 [] inner_point($f8(A),A).
% 1.67/1.89 ** KEPT (pick-wt=13): 58 [] incident_c($f13(A,B),A)|incident_c($f13(A,B),B)|A=B.
% 1.67/1.89 ** KEPT (pick-wt=2): 59 [] open($c2).
% 1.67/1.89 ** KEPT (pick-wt=3): 60 [] part_of($c1,$c2).
% 1.67/1.89 Following clause subsumed by 53 during input processing: 0 [copy,53,flip.1] A=A.
% 1.67/1.89 53 back subsumes 52.
% 1.67/1.89 53 back subsumes 51.
% 1.67/1.89
% 1.67/1.89 ======= end of input processing =======
% 1.67/1.89
% 1.67/1.89 =========== start of search ===========
% 1.67/1.89
% 1.67/1.89 -------- PROOF --------
% 1.67/1.89
% 1.67/1.89 ----> UNIT CONFLICT at 0.01 sec ----> 87 [binary,86.1,42.1] $F.
% 1.67/1.89
% 1.67/1.89 Length of proof is 2. Level of proof is 2.
% 1.67/1.89
% 1.67/1.89 ---------------- PROOF ----------------
% 1.67/1.89 % SZS status Theorem
% 1.67/1.89 % SZS output start Refutation
% See solution above
% 1.67/1.89 ------------ end of proof -------------
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89 ============ end of search ============
% 1.67/1.89
% 1.67/1.89 -------------- statistics -------------
% 1.67/1.89 clauses given 3
% 1.67/1.89 clauses generated 71
% 1.67/1.89 clauses kept 82
% 1.67/1.89 clauses forward subsumed 48
% 1.67/1.89 clauses back subsumed 2
% 1.67/1.89 Kbytes malloced 976
% 1.67/1.89
% 1.67/1.89 ----------- times (seconds) -----------
% 1.67/1.89 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.67/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.89
% 1.67/1.89 That finishes the proof of the theorem.
% 1.67/1.89
% 1.67/1.89 Process 22995 finished Wed Jul 27 07:30:05 2022
% 1.67/1.89 Otter interrupted
% 1.67/1.89 PROOF FOUND
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