%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO087+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 1.98s 2.19s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 9 RR)
% Number of literals : 18 ( 0 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 13 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) ),
file('GEO087+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ inner_point(A,B)
| incident_c(A,B) ),
file('GEO087+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ inner_point(A,B)
| ~ end_point(A,B) ),
file('GEO087+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ meet(A,B,C)
| ~ incident_c(D,B)
| ~ incident_c(D,C)
| end_point(D,B) ),
file('GEO087+1.p',unknown),
[] ).
cnf(56,axiom,
inner_point(dollar_f8(A),A),
file('GEO087+1.p',unknown),
[] ).
cnf(58,axiom,
part_of(dollar_c3,dollar_c2),
file('GEO087+1.p',unknown),
[] ).
cnf(59,axiom,
meet(dollar_c1,dollar_c3,dollar_c2),
file('GEO087+1.p',unknown),
[] ).
cnf(86,plain,
incident_c(dollar_f8(A),A),
inference(hyper,[status(thm)],[56,16]),
[iquote('hyper,56,16')] ).
cnf(797,plain,
incident_c(dollar_f8(dollar_c3),dollar_c2),
inference(hyper,[status(thm)],[86,1,58]),
[iquote('hyper,86,1,58')] ).
cnf(920,plain,
end_point(dollar_f8(dollar_c3),dollar_c3),
inference(hyper,[status(thm)],[797,21,59,86]),
[iquote('hyper,797,21,59,86')] ).
cnf(1337,plain,
$false,
inference(hyper,[status(thm)],[920,17,56]),
[iquote('hyper,920,17,56')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO087+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 06:56:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.83/2.03 ----- Otter 3.3f, August 2004 -----
% 1.83/2.03 The process was started by sandbox2 on n022.cluster.edu,
% 1.83/2.03 Wed Jul 27 06:56:50 2022
% 1.83/2.03 The command was "./otter". The process ID is 9905.
% 1.83/2.03
% 1.83/2.03 set(prolog_style_variables).
% 1.83/2.03 set(auto).
% 1.83/2.03 dependent: set(auto1).
% 1.83/2.03 dependent: set(process_input).
% 1.83/2.03 dependent: clear(print_kept).
% 1.83/2.03 dependent: clear(print_new_demod).
% 1.83/2.03 dependent: clear(print_back_demod).
% 1.83/2.03 dependent: clear(print_back_sub).
% 1.83/2.03 dependent: set(control_memory).
% 1.83/2.03 dependent: assign(max_mem, 12000).
% 1.83/2.03 dependent: assign(pick_given_ratio, 4).
% 1.83/2.03 dependent: assign(stats_level, 1).
% 1.83/2.03 dependent: assign(max_seconds, 10800).
% 1.83/2.03 clear(print_given).
% 1.83/2.03
% 1.83/2.03 formula_list(usable).
% 1.83/2.03 all A (A=A).
% 1.83/2.03 all C C1 (part_of(C1,C)<-> (all P (incident_c(P,C1)->incident_c(P,C)))).
% 1.83/2.03 all C C1 C2 (C=sum(C1,C2)<-> (all Q (incident_c(Q,C)<->incident_c(Q,C1)|incident_c(Q,C2)))).
% 1.83/2.03 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)))).
% 1.83/2.03 all P C (inner_point(P,C)<->incident_c(P,C)& -end_point(P,C)).
% 1.83/2.03 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)))).
% 1.83/2.03 all C (closed(C)<-> -(exists P end_point(P,C))).
% 1.83/2.03 all C (open(C)<-> (exists P end_point(P,C))).
% 1.83/2.03 all C C1 (part_of(C1,C)&C1!=C->open(C1)).
% 1.83/2.03 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)).
% 1.83/2.03 all C exists P inner_point(P,C).
% 1.83/2.03 all C P (inner_point(P,C)-> (exists C1 C2 (meet(P,C1,C2)&C=sum(C1,C2)))).
% 1.83/2.03 all C P Q R (end_point(P,C)&end_point(Q,C)&end_point(R,C)->P=Q|P=R|Q=R).
% 1.83/2.03 all C P (end_point(P,C)-> (exists Q (end_point(Q,C)&P!=Q))).
% 1.83/2.03 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)))).
% 1.83/2.03 all C1 C2 ((exists P meet(P,C1,C2))-> (exists C (C=sum(C1,C2)))).
% 1.83/2.03 all C C1 ((all P (incident_c(P,C)<->incident_c(P,C1)))->C=C1).
% 1.83/2.03 -(all C1 C2 (part_of(C1,C2)-> -(exists P meet(P,C1,C2)))).
% 1.83/2.03 end_of_list.
% 1.83/2.03
% 1.83/2.03 -------> usable clausifies to:
% 1.83/2.03
% 1.83/2.03 list(usable).
% 1.83/2.03 0 [] A=A.
% 1.83/2.03 0 [] -part_of(C1,C)| -incident_c(P,C1)|incident_c(P,C).
% 1.83/2.03 0 [] part_of(C1,C)|incident_c($f1(C,C1),C1).
% 1.83/2.03 0 [] part_of(C1,C)| -incident_c($f1(C,C1),C).
% 1.83/2.03 0 [] C!=sum(C1,C2)| -incident_c(Q,C)|incident_c(Q,C1)|incident_c(Q,C2).
% 1.83/2.03 0 [] C!=sum(C1,C2)|incident_c(Q,C)| -incident_c(Q,C1).
% 1.83/2.03 0 [] C!=sum(C1,C2)|incident_c(Q,C)| -incident_c(Q,C2).
% 1.83/2.03 0 [] C=sum(C1,C2)|incident_c($f2(C,C1,C2),C)|incident_c($f2(C,C1,C2),C1)|incident_c($f2(C,C1,C2),C2).
% 1.83/2.03 0 [] C=sum(C1,C2)| -incident_c($f2(C,C1,C2),C)| -incident_c($f2(C,C1,C2),C1).
% 1.83/2.03 0 [] C=sum(C1,C2)| -incident_c($f2(C,C1,C2),C)| -incident_c($f2(C,C1,C2),C2).
% 1.83/2.03 0 [] -end_point(P,C)|incident_c(P,C).
% 1.83/2.03 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).
% 1.83/2.03 0 [] end_point(P,C)| -incident_c(P,C)|part_of($f4(P,C),C).
% 1.83/2.03 0 [] end_point(P,C)| -incident_c(P,C)|part_of($f3(P,C),C).
% 1.83/2.03 0 [] end_point(P,C)| -incident_c(P,C)|incident_c(P,$f4(P,C)).
% 1.83/2.03 0 [] end_point(P,C)| -incident_c(P,C)|incident_c(P,$f3(P,C)).
% 1.83/2.03 0 [] end_point(P,C)| -incident_c(P,C)| -part_of($f4(P,C),$f3(P,C)).
% 1.83/2.03 0 [] end_point(P,C)| -incident_c(P,C)| -part_of($f3(P,C),$f4(P,C)).
% 1.83/2.03 0 [] -inner_point(P,C)|incident_c(P,C).
% 1.83/2.03 0 [] -inner_point(P,C)| -end_point(P,C).
% 1.83/2.03 0 [] inner_point(P,C)| -incident_c(P,C)|end_point(P,C).
% 1.83/2.03 0 [] -meet(P,C,C1)|incident_c(P,C).
% 1.83/2.03 0 [] -meet(P,C,C1)|incident_c(P,C1).
% 1.83/2.03 0 [] -meet(P,C,C1)| -incident_c(Q,C)| -incident_c(Q,C1)|end_point(Q,C).
% 1.83/2.03 0 [] -meet(P,C,C1)| -incident_c(Q,C)| -incident_c(Q,C1)|end_point(Q,C1).
% 1.83/2.03 0 [] meet(P,C,C1)| -incident_c(P,C)| -incident_c(P,C1)|incident_c($f5(P,C,C1),C).
% 1.83/2.03 0 [] meet(P,C,C1)| -incident_c(P,C)| -incident_c(P,C1)|incident_c($f5(P,C,C1),C1).
% 1.83/2.03 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).
% 1.83/2.03 0 [] -closed(C)| -end_point(P,C).
% 1.83/2.03 0 [] closed(C)|end_point($f6(C),C).
% 1.83/2.03 0 [] -open(C)|end_point($f7(C),C).
% 1.83/2.03 0 [] open(C)| -end_point(P,C).
% 1.83/2.03 0 [] -part_of(C1,C)|C1=C|open(C1).
% 1.83/2.03 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).
% 1.83/2.03 0 [] inner_point($f8(C),C).
% 1.83/2.03 0 [] -inner_point(P,C)|meet(P,$f10(C,P),$f9(C,P)).
% 1.83/2.03 0 [] -inner_point(P,C)|C=sum($f10(C,P),$f9(C,P)).
% 1.83/2.03 0 [] -end_point(P,C)| -end_point(Q,C)| -end_point(R,C)|P=Q|P=R|Q=R.
% 1.83/2.03 0 [] -end_point(P,C)|end_point($f11(C,P),C).
% 1.83/2.03 0 [] -end_point(P,C)|P!=$f11(C,P).
% 1.83/2.03 0 [] -closed(C)| -meet(P,C1,C2)|C!=sum(C1,C2)| -end_point(Q,C1)|meet(Q,C1,C2).
% 1.83/2.03 0 [] -meet(P,C1,C2)|$f12(C1,C2)=sum(C1,C2).
% 1.83/2.03 0 [] incident_c($f13(C,C1),C)|incident_c($f13(C,C1),C1)|C=C1.
% 1.83/2.03 0 [] -incident_c($f13(C,C1),C)| -incident_c($f13(C,C1),C1)|C=C1.
% 1.83/2.03 0 [] part_of($c3,$c2).
% 1.83/2.03 0 [] meet($c1,$c3,$c2).
% 1.83/2.03 end_of_list.
% 1.83/2.03
% 1.83/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=12.
% 1.83/2.03
% 1.83/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.83/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.83/2.03 deletion, with positive clauses in sos and nonpositive
% 1.83/2.03 clauses in usable.
% 1.83/2.03
% 1.83/2.03 dependent: set(knuth_bendix).
% 1.83/2.03 dependent: set(anl_eq).
% 1.83/2.03 dependent: set(para_from).
% 1.83/2.03 dependent: set(para_into).
% 1.83/2.03 dependent: clear(para_from_right).
% 1.83/2.03 dependent: clear(para_into_right).
% 1.83/2.03 dependent: set(para_from_vars).
% 1.83/2.03 dependent: set(eq_units_both_ways).
% 1.83/2.03 dependent: set(dynamic_demod_all).
% 1.83/2.03 dependent: set(dynamic_demod).
% 1.83/2.03 dependent: set(order_eq).
% 1.83/2.03 dependent: set(back_demod).
% 1.83/2.03 dependent: set(lrpo).
% 1.83/2.03 dependent: set(hyper_res).
% 1.83/2.03 dependent: set(unit_deletion).
% 1.83/2.03 dependent: set(factor).
% 1.83/2.03
% 1.83/2.03 ------------> process usable:
% 1.83/2.03 ** KEPT (pick-wt=9): 1 [] -part_of(A,B)| -incident_c(C,A)|incident_c(C,B).
% 1.83/2.03 ** KEPT (pick-wt=8): 2 [] part_of(A,B)| -incident_c($f1(B,A),B).
% 1.83/2.03 ** KEPT (pick-wt=14): 3 [] A!=sum(B,C)| -incident_c(D,A)|incident_c(D,B)|incident_c(D,C).
% 1.83/2.03 ** KEPT (pick-wt=11): 4 [] A!=sum(B,C)|incident_c(D,A)| -incident_c(D,B).
% 1.83/2.03 ** KEPT (pick-wt=11): 5 [] A!=sum(B,C)|incident_c(D,A)| -incident_c(D,C).
% 1.83/2.03 ** KEPT (pick-wt=17): 6 [] A=sum(B,C)| -incident_c($f2(A,B,C),A)| -incident_c($f2(A,B,C),B).
% 1.83/2.03 ** KEPT (pick-wt=17): 7 [] A=sum(B,C)| -incident_c($f2(A,B,C),A)| -incident_c($f2(A,B,C),C).
% 1.83/2.04 ** KEPT (pick-wt=6): 8 [] -end_point(A,B)|incident_c(A,B).
% 1.83/2.04 ** 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).
% 1.83/2.04 ** KEPT (pick-wt=11): 10 [] end_point(A,B)| -incident_c(A,B)|part_of($f4(A,B),B).
% 1.83/2.04 ** KEPT (pick-wt=11): 11 [] end_point(A,B)| -incident_c(A,B)|part_of($f3(A,B),B).
% 1.83/2.04 ** KEPT (pick-wt=11): 12 [] end_point(A,B)| -incident_c(A,B)|incident_c(A,$f4(A,B)).
% 1.83/2.04 ** KEPT (pick-wt=11): 13 [] end_point(A,B)| -incident_c(A,B)|incident_c(A,$f3(A,B)).
% 1.83/2.04 ** KEPT (pick-wt=13): 14 [] end_point(A,B)| -incident_c(A,B)| -part_of($f4(A,B),$f3(A,B)).
% 1.83/2.04 ** KEPT (pick-wt=13): 15 [] end_point(A,B)| -incident_c(A,B)| -part_of($f3(A,B),$f4(A,B)).
% 1.83/2.04 ** KEPT (pick-wt=6): 16 [] -inner_point(A,B)|incident_c(A,B).
% 1.83/2.04 ** KEPT (pick-wt=6): 17 [] -inner_point(A,B)| -end_point(A,B).
% 1.83/2.04 ** KEPT (pick-wt=9): 18 [] inner_point(A,B)| -incident_c(A,B)|end_point(A,B).
% 1.83/2.04 ** KEPT (pick-wt=7): 19 [] -meet(A,B,C)|incident_c(A,B).
% 1.83/2.04 ** KEPT (pick-wt=7): 20 [] -meet(A,B,C)|incident_c(A,C).
% 1.83/2.04 ** KEPT (pick-wt=13): 21 [] -meet(A,B,C)| -incident_c(D,B)| -incident_c(D,C)|end_point(D,B).
% 1.83/2.04 ** KEPT (pick-wt=13): 22 [] -meet(A,B,C)| -incident_c(D,B)| -incident_c(D,C)|end_point(D,C).
% 1.83/2.04 ** KEPT (pick-wt=16): 23 [] meet(A,B,C)| -incident_c(A,B)| -incident_c(A,C)|incident_c($f5(A,B,C),B).
% 1.83/2.04 ** KEPT (pick-wt=16): 24 [] meet(A,B,C)| -incident_c(A,B)| -incident_c(A,C)|incident_c($f5(A,B,C),C).
% 1.83/2.04 ** 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).
% 1.83/2.04 ** KEPT (pick-wt=5): 26 [] -closed(A)| -end_point(B,A).
% 1.83/2.04 ** KEPT (pick-wt=6): 27 [] -open(A)|end_point($f7(A),A).
% 1.83/2.04 ** KEPT (pick-wt=5): 28 [] open(A)| -end_point(B,A).
% 1.83/2.04 ** KEPT (pick-wt=8): 29 [] -part_of(A,B)|A=B|open(A).
% 1.83/2.04 ** KEPT (pick-wt=36): 30 [] -part_of(A,B)| -part_of(C,B)| -part_of(D,B)| -end_point(E,A)| -end_point(E,C)| -end_point(E,D)|part_of(C,D)|part_of(D,C)|part_of(A,C)|part_of(C,A)|part_of(A,D)|part_of(D,A).
% 1.83/2.04 ** KEPT (pick-wt=11): 31 [] -inner_point(A,B)|meet(A,$f10(B,A),$f9(B,A)).
% 1.98/2.19 ** KEPT (pick-wt=12): 33 [copy,32,flip.2] -inner_point(A,B)|sum($f10(B,A),$f9(B,A))=B.
% 1.98/2.19 ** KEPT (pick-wt=18): 34 [] -end_point(A,B)| -end_point(C,B)| -end_point(D,B)|A=C|A=D|C=D.
% 1.98/2.19 ** KEPT (pick-wt=8): 35 [] -end_point(A,B)|end_point($f11(B,A),B).
% 1.98/2.19 ** KEPT (pick-wt=8): 37 [copy,36,flip.2] -end_point(A,B)|$f11(B,A)!=A.
% 1.98/2.19 ** KEPT (pick-wt=18): 38 [] -closed(A)| -meet(B,C,D)|A!=sum(C,D)| -end_point(E,C)|meet(E,C,D).
% 1.98/2.19 ** KEPT (pick-wt=11): 40 [copy,39,flip.2] -meet(A,B,C)|sum(B,C)=$f12(B,C).
% 1.98/2.19 ** KEPT (pick-wt=13): 41 [] -incident_c($f13(A,B),A)| -incident_c($f13(A,B),B)|A=B.
% 1.98/2.19
% 1.98/2.19 ------------> process sos:
% 1.98/2.19 ** KEPT (pick-wt=3): 52 [] A=A.
% 1.98/2.19 ** KEPT (pick-wt=8): 53 [] part_of(A,B)|incident_c($f1(B,A),A).
% 1.98/2.19 ** KEPT (pick-wt=23): 54 [] A=sum(B,C)|incident_c($f2(A,B,C),A)|incident_c($f2(A,B,C),B)|incident_c($f2(A,B,C),C).
% 1.98/2.19 ** KEPT (pick-wt=6): 55 [] closed(A)|end_point($f6(A),A).
% 1.98/2.19 ** KEPT (pick-wt=4): 56 [] inner_point($f8(A),A).
% 1.98/2.19 ** KEPT (pick-wt=13): 57 [] incident_c($f13(A,B),A)|incident_c($f13(A,B),B)|A=B.
% 1.98/2.19 ** KEPT (pick-wt=3): 58 [] part_of($c3,$c2).
% 1.98/2.19 ** KEPT (pick-wt=4): 59 [] meet($c1,$c3,$c2).
% 1.98/2.19 Following clause subsumed by 52 during input processing: 0 [copy,52,flip.1] A=A.
% 1.98/2.19 52 back subsumes 51.
% 1.98/2.19 52 back subsumes 50.
% 1.98/2.19
% 1.98/2.19 ======= end of input processing =======
% 1.98/2.19
% 1.98/2.19 =========== start of search ===========
% 1.98/2.19
% 1.98/2.19 -------- PROOF --------
% 1.98/2.19
% 1.98/2.19 -----> EMPTY CLAUSE at 0.16 sec ----> 1337 [hyper,920,17,56] $F.
% 1.98/2.19
% 1.98/2.19 Length of proof is 3. Level of proof is 3.
% 1.98/2.19
% 1.98/2.19 ---------------- PROOF ----------------
% 1.98/2.19 % SZS status Theorem
% 1.98/2.19 % SZS output start Refutation
% See solution above
% 1.98/2.19 ------------ end of proof -------------
% 1.98/2.19
% 1.98/2.19
% 1.98/2.19 Search stopped by max_proofs option.
% 1.98/2.19
% 1.98/2.19
% 1.98/2.19 Search stopped by max_proofs option.
% 1.98/2.19
% 1.98/2.19 ============ end of search ============
% 1.98/2.19
% 1.98/2.19 -------------- statistics -------------
% 1.98/2.19 clauses given 25
% 1.98/2.19 clauses generated 3276
% 1.98/2.19 clauses kept 1331
% 1.98/2.19 clauses forward subsumed 1990
% 1.98/2.19 clauses back subsumed 32
% 1.98/2.19 Kbytes malloced 3906
% 1.98/2.19
% 1.98/2.19 ----------- times (seconds) -----------
% 1.98/2.19 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 1.98/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.19
% 1.98/2.19 That finishes the proof of the theorem.
% 1.98/2.19
% 1.98/2.19 Process 9905 finished Wed Jul 27 06:56:52 2022
% 1.98/2.19 Otter interrupted
% 1.98/2.19 PROOF FOUND
%------------------------------------------------------------------------------