TSTP Solution File: GRA003+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:55:41 EDT 2022
% Result : Theorem 2.04s 2.23s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 12 unt; 2 nHn; 23 RR)
% Number of literals : 43 ( 6 equ; 21 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 35 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(18,axiom,
( ~ path(A,B,C)
| vertex(A) ),
file('GRA003+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ path(A,B,C)
| vertex(B) ),
file('GRA003+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ path(A,B,C)
| ~ on_path(D,C)
| edge(D) ),
file('GRA003+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ path(A,B,C)
| ~ precedes(D,E,C)
| on_path(D,C) ),
file('GRA003+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ path(A,B,C)
| ~ precedes(D,E,C)
| on_path(E,C) ),
file('GRA003+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ shortest_path(A,B,C)
| path(A,B,C) ),
file('GRA003+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ shortest_path(A,B,C)
| A != B ),
file('GRA003+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ shortest_path(A,B,C)
| ~ precedes(D,E,C)
| ~ precedes(E,D,C) ),
file('GRA003+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ vertex(dollar_c5)
| ~ vertex(dollar_c4)
| dollar_c5 = dollar_c4
| ~ edge(dollar_c3)
| ~ edge(dollar_c2)
| dollar_c3 = dollar_c2
| ~ path(dollar_c5,dollar_c4,dollar_c1) ),
file('GRA003+1.p',unknown),
[] ).
cnf(89,plain,
( ~ shortest_path(A,B,C)
| ~ precedes(D,D,C) ),
inference(factor,[status(thm)],[58]),
[iquote('factor,58.2.3')] ).
cnf(97,axiom,
shortest_path(dollar_c5,dollar_c4,dollar_c1),
file('GRA003+1.p',unknown),
[] ).
cnf(98,axiom,
precedes(dollar_c3,dollar_c2,dollar_c1),
file('GRA003+1.p',unknown),
[] ).
cnf(99,plain,
path(dollar_c5,dollar_c4,dollar_c1),
inference(hyper,[status(thm)],[97,52]),
[iquote('hyper,97,52')] ).
cnf(166,plain,
on_path(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[99,48,98]),
[iquote('hyper,99,48,98')] ).
cnf(167,plain,
on_path(dollar_c3,dollar_c1),
inference(hyper,[status(thm)],[99,47,98]),
[iquote('hyper,99,47,98')] ).
cnf(175,plain,
vertex(dollar_c4),
inference(hyper,[status(thm)],[99,19]),
[iquote('hyper,99,19')] ).
cnf(176,plain,
vertex(dollar_c5),
inference(hyper,[status(thm)],[99,18]),
[iquote('hyper,99,18')] ).
cnf(249,plain,
edge(dollar_c2),
inference(hyper,[status(thm)],[166,33,99]),
[iquote('hyper,166,33,99')] ).
cnf(280,plain,
edge(dollar_c3),
inference(hyper,[status(thm)],[167,33,99]),
[iquote('hyper,167,33,99')] ).
cnf(338,plain,
( dollar_c5 = dollar_c4
| dollar_c3 = dollar_c2 ),
inference(hyper,[status(thm)],[280,77,176,175,249,99]),
[iquote('hyper,280,77,176,175,249,99')] ).
cnf(736,plain,
dollar_c3 = dollar_c2,
inference(hyper,[status(thm)],[338,53,97]),
[iquote('hyper,338,53,97')] ).
cnf(776,plain,
precedes(dollar_c2,dollar_c2,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[98]),736]),
[iquote('back_demod,98,demod,736')] ).
cnf(860,plain,
$false,
inference(hyper,[status(thm)],[776,89,97]),
[iquote('hyper,776,89,97')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.09/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 02:19:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.07 ----- Otter 3.3f, August 2004 -----
% 1.89/2.07 The process was started by sandbox2 on n012.cluster.edu,
% 1.89/2.07 Wed Jul 27 02:19:50 2022
% 1.89/2.07 The command was "./otter". The process ID is 2977.
% 1.89/2.07
% 1.89/2.07 set(prolog_style_variables).
% 1.89/2.07 set(auto).
% 1.89/2.07 dependent: set(auto1).
% 1.89/2.07 dependent: set(process_input).
% 1.89/2.07 dependent: clear(print_kept).
% 1.89/2.07 dependent: clear(print_new_demod).
% 1.89/2.07 dependent: clear(print_back_demod).
% 1.89/2.07 dependent: clear(print_back_sub).
% 1.89/2.07 dependent: set(control_memory).
% 1.89/2.07 dependent: assign(max_mem, 12000).
% 1.89/2.07 dependent: assign(pick_given_ratio, 4).
% 1.89/2.07 dependent: assign(stats_level, 1).
% 1.89/2.07 dependent: assign(max_seconds, 10800).
% 1.89/2.07 clear(print_given).
% 1.89/2.07
% 1.89/2.07 formula_list(usable).
% 1.89/2.07 all A (A=A).
% 1.89/2.07 all E (edge(E)->head_of(E)!=tail_of(E)).
% 1.89/2.07 all E (edge(E)->vertex(head_of(E))&vertex(tail_of(E))).
% 1.89/2.07 complete-> (all V1 V2 (vertex(V1)&vertex(V2)&V1!=V2-> (exists E (edge(E)& -(V1=head_of(E)&V2=tail_of(E)<->V2=head_of(E)&V1=tail_of(E)))))).
% 1.89/2.07 all V1 V2 P (vertex(V1)&vertex(V2)& (exists E (edge(E)&V1=tail_of(E)& (V2=head_of(E)&P=path_cons(E,empty)| (exists TP (path(head_of(E),V2,TP)&P=path_cons(E,TP))))))->path(V1,V2,P)).
% 1.89/2.07 all V1 V2 P (path(V1,V2,P)->vertex(V1)&vertex(V2)& (exists E (edge(E)&V1=tail_of(E)& -(V2=head_of(E)&P=path_cons(E,empty)<-> (exists TP (path(head_of(E),V2,TP)&P=path_cons(E,TP))))))).
% 1.89/2.07 all V1 V2 P E (path(V1,V2,P)&on_path(E,P)->edge(E)&in_path(head_of(E),P)&in_path(tail_of(E),P)).
% 1.89/2.07 all V1 V2 P V (path(V1,V2,P)&in_path(V,P)->vertex(V)& (exists E (on_path(E,P)& (V=head_of(E)|V=tail_of(E))))).
% 1.89/2.07 all E1 E2 (se_quential(E1,E2)<->edge(E1)&edge(E2)&E1!=E2&head_of(E1)=tail_of(E2)).
% 1.89/2.07 all P V1 V2 (path(V1,V2,P)-> (all E1 E2 (on_path(E1,P)&on_path(E2,P)& (se_quential(E1,E2)| (exists E3 (se_quential(E1,E3)&precedes(E3,E2,P))))->precedes(E1,E2,P)))).
% 1.89/2.07 all P V1 V2 (path(V1,V2,P)-> (all E1 E2 (precedes(E1,E2,P)->on_path(E1,P)&on_path(E2,P)& -(se_quential(E1,E2)<-> (exists E3 (se_quential(E1,E3)&precedes(E3,E2,P))))))).
% 1.89/2.07 all V1 V2 SP (shortest_path(V1,V2,SP)<->path(V1,V2,SP)&V1!=V2& (all P (path(V1,V2,P)->less_or_e_qual(length_of(SP),length_of(P))))).
% 1.89/2.07 all V1 V2 E1 E2 P (shortest_path(V1,V2,P)&precedes(E1,E2,P)-> -(exists E3 (tail_of(E3)=tail_of(E1)&head_of(E3)=head_of(E2)))& -precedes(E2,E1,P)).
% 1.89/2.07 all E1 E2 E3 (triangle(E1,E2,E3)<->edge(E1)&edge(E2)&edge(E3)&se_quential(E1,E2)&se_quential(E2,E3)&se_quential(E3,E1)).
% 1.89/2.07 all V1 V2 P (path(V1,V2,P)->length_of(P)=number_of_in(edges,P)).
% 1.89/2.07 all V1 V2 P (path(V1,V2,P)->number_of_in(se_quential_pairs,P)=minus(length_of(P),n1)).
% 1.89/2.07 all P V1 V2 (path(V1,V2,P)& (all E1 E2 (on_path(E1,P)&on_path(E2,P)&se_quential(E1,E2)-> (exists E3 triangle(E1,E2,E3))))->number_of_in(se_quential_pairs,P)=number_of_in(triangles,P)).
% 1.89/2.07 all Things InThese less_or_e_qual(number_of_in(Things,InThese),number_of_in(Things,graph)).
% 1.89/2.07 -(all V1 V2 E1 E2 P (shortest_path(V1,V2,P)&precedes(E1,E2,P)->vertex(V1)&vertex(V2)&V1!=V2&edge(E1)&edge(E2)&E1!=E2&path(V1,V2,P))).
% 1.89/2.07 end_of_list.
% 1.89/2.07
% 1.89/2.07 -------> usable clausifies to:
% 1.89/2.07
% 1.89/2.07 list(usable).
% 1.89/2.07 0 [] A=A.
% 1.89/2.07 0 [] -edge(E)|head_of(E)!=tail_of(E).
% 1.89/2.07 0 [] -edge(E)|vertex(head_of(E)).
% 1.89/2.07 0 [] -edge(E)|vertex(tail_of(E)).
% 1.89/2.07 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|edge($f1(V1,V2)).
% 1.89/2.07 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V1=head_of($f1(V1,V2))|V2=head_of($f1(V1,V2)).
% 1.89/2.07 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V1=head_of($f1(V1,V2))|V1=tail_of($f1(V1,V2)).
% 1.89/2.07 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V2=tail_of($f1(V1,V2))|V2=head_of($f1(V1,V2)).
% 1.89/2.07 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V2=tail_of($f1(V1,V2))|V1=tail_of($f1(V1,V2)).
% 1.89/2.07 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V1!=head_of($f1(V1,V2))|V2!=tail_of($f1(V1,V2))|V2!=head_of($f1(V1,V2))|V1!=tail_of($f1(V1,V2)).
% 1.89/2.07 0 [] -vertex(V1)| -vertex(V2)| -edge(E)|V1!=tail_of(E)|V2!=head_of(E)|P!=path_cons(E,empty)|path(V1,V2,P).
% 1.89/2.07 0 [] -vertex(V1)| -vertex(V2)| -edge(E)|V1!=tail_of(E)| -path(head_of(E),V2,TP)|P!=path_cons(E,TP)|path(V1,V2,P).
% 1.89/2.07 0 [] -path(V1,V2,P)|vertex(V1).
% 1.89/2.07 0 [] -path(V1,V2,P)|vertex(V2).
% 1.89/2.07 0 [] -path(V1,V2,P)|edge($f3(V1,V2,P)).
% 1.89/2.07 0 [] -path(V1,V2,P)|V1=tail_of($f3(V1,V2,P)).
% 1.89/2.07 0 [] -path(V1,V2,P)|V2=head_of($f3(V1,V2,P))|path(head_of($f3(V1,V2,P)),V2,$f2(V1,V2,P)).
% 1.89/2.07 0 [] -path(V1,V2,P)|V2=head_of($f3(V1,V2,P))|P=path_cons($f3(V1,V2,P),$f2(V1,V2,P)).
% 1.89/2.07 0 [] -path(V1,V2,P)|P=path_cons($f3(V1,V2,P),empty)|path(head_of($f3(V1,V2,P)),V2,$f2(V1,V2,P)).
% 1.89/2.07 0 [] -path(V1,V2,P)|P=path_cons($f3(V1,V2,P),empty)|P=path_cons($f3(V1,V2,P),$f2(V1,V2,P)).
% 1.89/2.07 0 [] -path(V1,V2,P)|V2!=head_of($f3(V1,V2,P))|P!=path_cons($f3(V1,V2,P),empty)| -path(head_of($f3(V1,V2,P)),V2,TP)|P!=path_cons($f3(V1,V2,P),TP).
% 1.89/2.07 0 [] -path(V1,V2,P)| -on_path(E,P)|edge(E).
% 1.89/2.07 0 [] -path(V1,V2,P)| -on_path(E,P)|in_path(head_of(E),P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -on_path(E,P)|in_path(tail_of(E),P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -in_path(V,P)|vertex(V).
% 1.89/2.07 0 [] -path(V1,V2,P)| -in_path(V,P)|on_path($f4(V1,V2,P,V),P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -in_path(V,P)|V=head_of($f4(V1,V2,P,V))|V=tail_of($f4(V1,V2,P,V)).
% 1.89/2.07 0 [] -se_quential(E1,E2)|edge(E1).
% 1.89/2.07 0 [] -se_quential(E1,E2)|edge(E2).
% 1.89/2.07 0 [] -se_quential(E1,E2)|E1!=E2.
% 1.89/2.07 0 [] -se_quential(E1,E2)|head_of(E1)=tail_of(E2).
% 1.89/2.07 0 [] se_quential(E1,E2)| -edge(E1)| -edge(E2)|E1=E2|head_of(E1)!=tail_of(E2).
% 1.89/2.07 0 [] -path(V1,V2,P)| -on_path(E1,P)| -on_path(E2,P)| -se_quential(E1,E2)|precedes(E1,E2,P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -on_path(E1,P)| -on_path(E2,P)| -se_quential(E1,E3)| -precedes(E3,E2,P)|precedes(E1,E2,P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)|on_path(E1,P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)|on_path(E2,P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)|se_quential(E1,E2)|se_quential(E1,$f5(P,V1,V2,E1,E2)).
% 1.89/2.07 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)|se_quential(E1,E2)|precedes($f5(P,V1,V2,E1,E2),E2,P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)| -se_quential(E1,E2)| -se_quential(E1,E3)| -precedes(E3,E2,P).
% 1.89/2.07 0 [] -shortest_path(V1,V2,SP)|path(V1,V2,SP).
% 1.89/2.07 0 [] -shortest_path(V1,V2,SP)|V1!=V2.
% 1.89/2.07 0 [] -shortest_path(V1,V2,SP)| -path(V1,V2,P)|less_or_e_qual(length_of(SP),length_of(P)).
% 1.89/2.07 0 [] shortest_path(V1,V2,SP)| -path(V1,V2,SP)|V1=V2|path(V1,V2,$f6(V1,V2,SP)).
% 1.89/2.07 0 [] shortest_path(V1,V2,SP)| -path(V1,V2,SP)|V1=V2| -less_or_e_qual(length_of(SP),length_of($f6(V1,V2,SP))).
% 1.89/2.07 0 [] -shortest_path(V1,V2,P)| -precedes(E1,E2,P)|tail_of(E3)!=tail_of(E1)|head_of(E3)!=head_of(E2).
% 1.89/2.07 0 [] -shortest_path(V1,V2,P)| -precedes(E1,E2,P)| -precedes(E2,E1,P).
% 1.89/2.07 0 [] -triangle(E1,E2,E3)|edge(E1).
% 1.89/2.07 0 [] -triangle(E1,E2,E3)|edge(E2).
% 1.89/2.07 0 [] -triangle(E1,E2,E3)|edge(E3).
% 1.89/2.07 0 [] -triangle(E1,E2,E3)|se_quential(E1,E2).
% 1.89/2.07 0 [] -triangle(E1,E2,E3)|se_quential(E2,E3).
% 1.89/2.07 0 [] -triangle(E1,E2,E3)|se_quential(E3,E1).
% 1.89/2.07 0 [] triangle(E1,E2,E3)| -edge(E1)| -edge(E2)| -edge(E3)| -se_quential(E1,E2)| -se_quential(E2,E3)| -se_quential(E3,E1).
% 1.89/2.07 0 [] -path(V1,V2,P)|length_of(P)=number_of_in(edges,P).
% 1.89/2.07 0 [] -path(V1,V2,P)|number_of_in(se_quential_pairs,P)=minus(length_of(P),n1).
% 1.89/2.07 0 [] -path(V1,V2,P)|on_path($f8(P,V1,V2),P)|number_of_in(se_quential_pairs,P)=number_of_in(triangles,P).
% 1.89/2.07 0 [] -path(V1,V2,P)|on_path($f7(P,V1,V2),P)|number_of_in(se_quential_pairs,P)=number_of_in(triangles,P).
% 1.89/2.07 0 [] -path(V1,V2,P)|se_quential($f8(P,V1,V2),$f7(P,V1,V2))|number_of_in(se_quential_pairs,P)=number_of_in(triangles,P).
% 1.89/2.07 0 [] -path(V1,V2,P)| -triangle($f8(P,V1,V2),$f7(P,V1,V2),E3)|number_of_in(se_quential_pairs,P)=number_of_in(triangles,P).
% 1.89/2.07 0 [] less_or_e_qual(number_of_in(Things,InThese),number_of_in(Things,graph)).
% 1.89/2.07 0 [] shortest_path($c5,$c4,$c1).
% 1.89/2.07 0 [] precedes($c3,$c2,$c1).
% 1.89/2.07 0 [] -vertex($c5)| -vertex($c4)|$c5=$c4| -edge($c3)| -edge($c2)|$c3=$c2| -path($c5,$c4,$c1).
% 1.89/2.07 end_of_list.
% 1.89/2.07
% 1.89/2.07 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.89/2.07
% 1.89/2.07 This ia a non-Horn set with equality. The strategy will be
% 1.89/2.07 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.89/2.07 deletion, with positive clauses in sos and nonpositive
% 1.89/2.07 clauses in usable.
% 1.89/2.07
% 1.89/2.07 dependent: set(knuth_bendix).
% 1.89/2.07 dependent: set(anl_eq).
% 1.89/2.07 dependent: set(para_from).
% 1.89/2.07 dependent: set(para_into).
% 1.89/2.07 dependent: clear(para_from_right).
% 1.89/2.07 dependent: clear(para_into_right).
% 1.89/2.07 dependent: set(para_from_vars).
% 1.89/2.07 dependent: set(eq_units_both_ways).
% 1.89/2.07 dependent: set(dynamic_demod_all).
% 1.89/2.07 dependent: set(dynamic_demod).
% 1.89/2.07 dependent: set(order_eq).
% 1.89/2.07 dependent: set(back_demod).
% 1.89/2.07 dependent: set(lrpo).
% 1.89/2.07 dependent: set(hyper_res).
% 1.89/2.07 dependent: set(unit_deletion).
% 1.89/2.07 dependent: set(factor).
% 1.89/2.07
% 1.89/2.07 ------------> process usable:
% 1.89/2.07 ** KEPT (pick-wt=7): 2 [copy,1,flip.2] -edge(A)|tail_of(A)!=head_of(A).
% 1.89/2.07 ** KEPT (pick-wt=5): 3 [] -edge(A)|vertex(head_of(A)).
% 1.89/2.07 ** KEPT (pick-wt=5): 4 [] -edge(A)|vertex(tail_of(A)).
% 1.89/2.07 ** KEPT (pick-wt=12): 5 [] -complete| -vertex(A)| -vertex(B)|A=B|edge($f1(A,B)).
% 1.89/2.07 ** KEPT (pick-wt=20): 7 [copy,6,flip.5,flip.6] -complete| -vertex(A)| -vertex(B)|A=B|head_of($f1(A,B))=A|head_of($f1(A,B))=B.
% 1.89/2.07 ** KEPT (pick-wt=20): 9 [copy,8,flip.5,flip.6] -complete| -vertex(A)| -vertex(B)|A=B|head_of($f1(A,B))=A|tail_of($f1(A,B))=A.
% 1.89/2.07 ** KEPT (pick-wt=20): 11 [copy,10,flip.5,flip.6] -complete| -vertex(A)| -vertex(B)|A=B|tail_of($f1(A,B))=B|head_of($f1(A,B))=B.
% 1.89/2.07 ** KEPT (pick-wt=20): 13 [copy,12,flip.5,flip.6] -complete| -vertex(A)| -vertex(B)|A=B|tail_of($f1(A,B))=B|tail_of($f1(A,B))=A.
% 1.89/2.07 ** KEPT (pick-wt=32): 15 [copy,14,flip.5,flip.6,flip.7,flip.8] -complete| -vertex(A)| -vertex(B)|A=B|head_of($f1(A,B))!=A|tail_of($f1(A,B))!=B|head_of($f1(A,B))!=B|tail_of($f1(A,B))!=A.
% 1.89/2.07 ** KEPT (pick-wt=23): 16 [] -vertex(A)| -vertex(B)| -edge(C)|A!=tail_of(C)|B!=head_of(C)|D!=path_cons(C,empty)|path(A,B,D).
% 1.89/2.07 ** KEPT (pick-wt=24): 17 [] -vertex(A)| -vertex(B)| -edge(C)|A!=tail_of(C)| -path(head_of(C),B,D)|E!=path_cons(C,D)|path(A,B,E).
% 1.89/2.07 ** KEPT (pick-wt=6): 18 [] -path(A,B,C)|vertex(A).
% 1.89/2.07 ** KEPT (pick-wt=6): 19 [] -path(A,B,C)|vertex(B).
% 1.89/2.07 ** KEPT (pick-wt=9): 20 [] -path(A,B,C)|edge($f3(A,B,C)).
% 1.89/2.07 ** KEPT (pick-wt=11): 22 [copy,21,flip.2] -path(A,B,C)|tail_of($f3(A,B,C))=A.
% 1.89/2.07 ** KEPT (pick-wt=22): 24 [copy,23,flip.2] -path(A,B,C)|head_of($f3(A,B,C))=B|path(head_of($f3(A,B,C)),B,$f2(A,B,C)).
% 1.89/2.07 ** KEPT (pick-wt=22): 26 [copy,25,flip.2,flip.3] -path(A,B,C)|head_of($f3(A,B,C))=B|path_cons($f3(A,B,C),$f2(A,B,C))=C.
% 1.89/2.07 ** KEPT (pick-wt=23): 28 [copy,27,flip.2] -path(A,B,C)|path_cons($f3(A,B,C),empty)=C|path(head_of($f3(A,B,C)),B,$f2(A,B,C)).
% 1.89/2.07 ** KEPT (pick-wt=23): 30 [copy,29,flip.2,flip.3] -path(A,B,C)|path_cons($f3(A,B,C),empty)=C|path_cons($f3(A,B,C),$f2(A,B,C))=C.
% 1.89/2.07 ** KEPT (pick-wt=35): 32 [copy,31,flip.2,flip.3,flip.5] -path(A,B,C)|head_of($f3(A,B,C))!=B|path_cons($f3(A,B,C),empty)!=C| -path(head_of($f3(A,B,C)),B,D)|path_cons($f3(A,B,C),D)!=C.
% 1.89/2.07 ** KEPT (pick-wt=9): 33 [] -path(A,B,C)| -on_path(D,C)|edge(D).
% 1.89/2.07 ** KEPT (pick-wt=11): 34 [] -path(A,B,C)| -on_path(D,C)|in_path(head_of(D),C).
% 1.89/2.07 ** KEPT (pick-wt=11): 35 [] -path(A,B,C)| -on_path(D,C)|in_path(tail_of(D),C).
% 1.89/2.07 ** KEPT (pick-wt=9): 36 [] -path(A,B,C)| -in_path(D,C)|vertex(D).
% 1.89/2.07 ** KEPT (pick-wt=14): 37 [] -path(A,B,C)| -in_path(D,C)|on_path($f4(A,B,C,D),C).
% 1.89/2.07 ** KEPT (pick-wt=23): 39 [copy,38,flip.3,flip.4] -path(A,B,C)| -in_path(D,C)|head_of($f4(A,B,C,D))=D|tail_of($f4(A,B,C,D))=D.
% 1.89/2.07 ** KEPT (pick-wt=5): 40 [] -se_quential(A,B)|edge(A).
% 1.89/2.07 ** KEPT (pick-wt=5): 41 [] -se_quential(A,B)|edge(B).
% 1.89/2.07 ** KEPT (pick-wt=6): 42 [] -se_quential(A,B)|A!=B.
% 1.89/2.07 ** KEPT (pick-wt=8): 43 [] -se_quential(A,B)|head_of(A)=tail_of(B).
% 1.89/2.07 ** KEPT (pick-wt=15): 44 [] se_quential(A,B)| -edge(A)| -edge(B)|A=B|head_of(A)!=tail_of(B).
% 1.89/2.07 ** KEPT (pick-wt=17): 45 [] -path(A,B,C)| -on_path(D,C)| -on_path(E,C)| -se_quential(D,E)|precedes(D,E,C).
% 1.89/2.07 ** KEPT (pick-wt=21): 46 [] -path(A,B,C)| -on_path(D,C)| -on_path(E,C)| -se_quential(D,F)| -precedes(F,E,C)|precedes(D,E,C).
% 1.89/2.07 ** KEPT (pick-wt=11): 47 [] -path(A,B,C)| -precedes(D,E,C)|on_path(D,C).
% 1.89/2.07 ** KEPT (pick-wt=11): 48 [] -path(A,B,C)| -precedes(D,E,C)|on_path(E,C).
% 1.89/2.07 ** KEPT (pick-wt=19): 49 [] -path(A,B,C)| -precedes(D,E,C)|se_quential(D,E)|se_quential(D,$f5(C,A,B,D,E)).
% 1.89/2.07 ** KEPT (pick-wt=20): 50 [] -path(A,B,C)| -precedes(D,E,C)|se_quential(D,E)|precedes($f5(C,A,B,D,E),E,C).
% 1.89/2.07 ** KEPT (pick-wt=18): 51 [] -path(A,B,C)| -precedes(D,E,C)| -se_quential(D,E)| -se_quential(D,F)| -precedes(F,E,C).
% 1.89/2.07 ** KEPT (pick-wt=8): 52 [] -shortest_path(A,B,C)|path(A,B,C).
% 1.89/2.07 ** KEPT (pick-wt=7): 53 [] -shortest_path(A,B,C)|A!=B.
% 1.89/2.07 ** KEPT (pick-wt=13): 54 [] -shortest_path(A,B,C)| -path(A,B,D)|less_or_e_qual(length_of(C),length_of(D)).
% 1.89/2.07 ** KEPT (pick-wt=18): 55 [] shortest_path(A,B,C)| -path(A,B,C)|A=B|path(A,B,$f6(A,B,C)).
% 1.89/2.07 ** KEPT (pick-wt=19): 56 [] shortest_path(A,B,C)| -path(A,B,C)|A=B| -less_or_e_qual(length_of(C),length_of($f6(A,B,C))).
% 2.04/2.23 ** KEPT (pick-wt=18): 57 [] -shortest_path(A,B,C)| -precedes(D,E,C)|tail_of(F)!=tail_of(D)|head_of(F)!=head_of(E).
% 2.04/2.23 ** KEPT (pick-wt=12): 58 [] -shortest_path(A,B,C)| -precedes(D,E,C)| -precedes(E,D,C).
% 2.04/2.23 ** KEPT (pick-wt=6): 59 [] -triangle(A,B,C)|edge(A).
% 2.04/2.23 ** KEPT (pick-wt=6): 60 [] -triangle(A,B,C)|edge(B).
% 2.04/2.23 ** KEPT (pick-wt=6): 61 [] -triangle(A,B,C)|edge(C).
% 2.04/2.23 ** KEPT (pick-wt=7): 62 [] -triangle(A,B,C)|se_quential(A,B).
% 2.04/2.23 ** KEPT (pick-wt=7): 63 [] -triangle(A,B,C)|se_quential(B,C).
% 2.04/2.23 ** KEPT (pick-wt=7): 64 [] -triangle(A,B,C)|se_quential(C,A).
% 2.04/2.23 ** KEPT (pick-wt=19): 65 [] triangle(A,B,C)| -edge(A)| -edge(B)| -edge(C)| -se_quential(A,B)| -se_quential(B,C)| -se_quential(C,A).
% 2.04/2.23 ** KEPT (pick-wt=10): 66 [] -path(A,B,C)|length_of(C)=number_of_in(edges,C).
% 2.04/2.23 ** KEPT (pick-wt=12): 68 [copy,67,flip.2] -path(A,B,C)|minus(length_of(C),n1)=number_of_in(se_quential_pairs,C).
% 2.04/2.23 ** KEPT (pick-wt=17): 70 [copy,69,flip.3] -path(A,B,C)|on_path($f8(C,A,B),C)|number_of_in(triangles,C)=number_of_in(se_quential_pairs,C).
% 2.04/2.23 ** KEPT (pick-wt=17): 72 [copy,71,flip.3] -path(A,B,C)|on_path($f7(C,A,B),C)|number_of_in(triangles,C)=number_of_in(se_quential_pairs,C).
% 2.04/2.23 ** KEPT (pick-wt=20): 74 [copy,73,flip.3] -path(A,B,C)|se_quential($f8(C,A,B),$f7(C,A,B))|number_of_in(triangles,C)=number_of_in(se_quential_pairs,C).
% 2.04/2.23 ** KEPT (pick-wt=21): 76 [copy,75,flip.3] -path(A,B,C)| -triangle($f8(C,A,B),$f7(C,A,B),D)|number_of_in(triangles,C)=number_of_in(se_quential_pairs,C).
% 2.04/2.23 ** KEPT (pick-wt=18): 77 [] -vertex($c5)| -vertex($c4)|$c5=$c4| -edge($c3)| -edge($c2)|$c3=$c2| -path($c5,$c4,$c1).
% 2.04/2.23
% 2.04/2.23 ------------> process sos:
% 2.04/2.23 ** KEPT (pick-wt=3): 95 [] A=A.
% 2.04/2.23 ** KEPT (pick-wt=7): 96 [] less_or_e_qual(number_of_in(A,B),number_of_in(A,graph)).
% 2.04/2.23 ** KEPT (pick-wt=4): 97 [] shortest_path($c5,$c4,$c1).
% 2.04/2.23 ** KEPT (pick-wt=4): 98 [] precedes($c3,$c2,$c1).
% 2.04/2.23 Following clause subsumed by 95 during input processing: 0 [copy,95,flip.1] A=A.
% 2.04/2.23 95 back subsumes 81.
% 2.04/2.23 95 back subsumes 80.
% 2.04/2.23 95 back subsumes 79.
% 2.04/2.23 95 back subsumes 78.
% 2.04/2.23
% 2.04/2.23 ======= end of input processing =======
% 2.04/2.23
% 2.04/2.23 =========== start of search ===========
% 2.04/2.23
% 2.04/2.23 -------- PROOF --------
% 2.04/2.23
% 2.04/2.23 -----> EMPTY CLAUSE at 0.16 sec ----> 860 [hyper,776,89,97] $F.
% 2.04/2.23
% 2.04/2.23 Length of proof is 11. Level of proof is 6.
% 2.04/2.23
% 2.04/2.23 ---------------- PROOF ----------------
% 2.04/2.23 % SZS status Theorem
% 2.04/2.23 % SZS output start Refutation
% See solution above
% 2.04/2.23 ------------ end of proof -------------
% 2.04/2.23
% 2.04/2.23
% 2.04/2.23 Search stopped by max_proofs option.
% 2.04/2.23
% 2.04/2.23
% 2.04/2.23 Search stopped by max_proofs option.
% 2.04/2.23
% 2.04/2.23 ============ end of search ============
% 2.04/2.23
% 2.04/2.23 -------------- statistics -------------
% 2.04/2.23 clauses given 28
% 2.04/2.23 clauses generated 1607
% 2.04/2.23 clauses kept 836
% 2.04/2.23 clauses forward subsumed 982
% 2.04/2.23 clauses back subsumed 16
% 2.04/2.23 Kbytes malloced 3906
% 2.04/2.23
% 2.04/2.23 ----------- times (seconds) -----------
% 2.04/2.23 user CPU time 0.16 (0 hr, 0 min, 0 sec)
% 2.04/2.23 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.04/2.23 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.04/2.23
% 2.04/2.23 That finishes the proof of the theorem.
% 2.04/2.23
% 2.04/2.23 Process 2977 finished Wed Jul 27 02:19:52 2022
% 2.04/2.23 Otter interrupted
% 2.04/2.23 PROOF FOUND
%------------------------------------------------------------------------------