TSTP Solution File: GRA010+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRA010+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 24.90s 25.08s
% Output : Refutation 24.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 13 unt; 6 nHn; 25 RR)
% Number of literals : 49 ( 18 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 41 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(66,axiom,
( ~ path(A,B,C)
| length_of(C) = number_of_in(edges,C) ),
file('GRA010+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ path(A,B,C)
| number_of_in(se_quential_pairs,C) = minus(length_of(C),n1) ),
file('GRA010+1.p',unknown),
[] ).
cnf(68,plain,
( ~ path(A,B,C)
| minus(length_of(C),n1) = number_of_in(se_quential_pairs,C) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[67])]),
[iquote('copy,67,flip.2')] ).
cnf(69,axiom,
( ~ path(A,B,C)
| on_path(dollar_f8(C,A,B),C)
| number_of_in(se_quential_pairs,C) = number_of_in(triangles,C) ),
file('GRA010+1.p',unknown),
[] ).
cnf(70,plain,
( ~ path(A,B,C)
| on_path(dollar_f8(C,A,B),C)
| number_of_in(triangles,C) = number_of_in(se_quential_pairs,C) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[69])]),
[iquote('copy,69,flip.3')] ).
cnf(71,axiom,
( ~ path(A,B,C)
| on_path(dollar_f7(C,A,B),C)
| number_of_in(se_quential_pairs,C) = number_of_in(triangles,C) ),
file('GRA010+1.p',unknown),
[] ).
cnf(72,plain,
( ~ path(A,B,C)
| on_path(dollar_f7(C,A,B),C)
| number_of_in(triangles,C) = number_of_in(se_quential_pairs,C) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[71])]),
[iquote('copy,71,flip.3')] ).
cnf(73,axiom,
( ~ path(A,B,C)
| se_quential(dollar_f8(C,A,B),dollar_f7(C,A,B))
| number_of_in(se_quential_pairs,C) = number_of_in(triangles,C) ),
file('GRA010+1.p',unknown),
[] ).
cnf(74,plain,
( ~ path(A,B,C)
| se_quential(dollar_f8(C,A,B),dollar_f7(C,A,B))
| number_of_in(triangles,C) = number_of_in(se_quential_pairs,C) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[73])]),
[iquote('copy,73,flip.3')] ).
cnf(75,axiom,
( ~ path(A,B,C)
| ~ triangle(dollar_f8(C,A,B),dollar_f7(C,A,B),D)
| number_of_in(se_quential_pairs,C) = number_of_in(triangles,C) ),
file('GRA010+1.p',unknown),
[] ).
cnf(76,plain,
( ~ path(A,B,C)
| ~ triangle(dollar_f8(C,A,B),dollar_f7(C,A,B),D)
| number_of_in(triangles,C) = number_of_in(se_quential_pairs,C) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[75])]),
[iquote('copy,75,flip.3')] ).
cnf(77,axiom,
( ~ on_path(A,dollar_c3)
| ~ on_path(B,dollar_c3)
| ~ se_quential(A,B)
| triangle(A,B,dollar_f9(A,B)) ),
file('GRA010+1.p',unknown),
[] ).
cnf(78,axiom,
number_of_in(se_quential_pairs,dollar_c3) != number_of_in(triangles,dollar_c3),
file('GRA010+1.p',unknown),
[] ).
cnf(79,plain,
number_of_in(triangles,dollar_c3) != number_of_in(se_quential_pairs,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[78])]),
[iquote('copy,78,flip.1')] ).
cnf(98,axiom,
A = A,
file('GRA010+1.p',unknown),
[] ).
cnf(101,axiom,
path(dollar_c2,dollar_c1,dollar_c3),
file('GRA010+1.p',unknown),
[] ).
cnf(102,plain,
se_quential(dollar_f8(dollar_c3,dollar_c2,dollar_c1),dollar_f7(dollar_c3,dollar_c2,dollar_c1)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[101,74]),79]),
[iquote('hyper,101,74,unit_del,79')] ).
cnf(103,plain,
on_path(dollar_f7(dollar_c3,dollar_c2,dollar_c1),dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[101,72]),79]),
[iquote('hyper,101,72,unit_del,79')] ).
cnf(104,plain,
on_path(dollar_f8(dollar_c3,dollar_c2,dollar_c1),dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[101,70]),79]),
[iquote('hyper,101,70,unit_del,79')] ).
cnf(105,plain,
minus(length_of(dollar_c3),n1) = number_of_in(se_quential_pairs,dollar_c3),
inference(hyper,[status(thm)],[101,68]),
[iquote('hyper,101,68')] ).
cnf(108,plain,
length_of(dollar_c3) = number_of_in(edges,dollar_c3),
inference(hyper,[status(thm)],[101,66]),
[iquote('hyper,101,66')] ).
cnf(120,plain,
number_of_in(se_quential_pairs,dollar_c3) = minus(number_of_in(edges,dollar_c3),n1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[105]),108])]),
[iquote('back_demod,105,demod,108,flip.1')] ).
cnf(121,plain,
number_of_in(triangles,dollar_c3) != minus(number_of_in(edges,dollar_c3),n1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),120]),
[iquote('back_demod,79,demod,120')] ).
cnf(365,plain,
triangle(dollar_f8(dollar_c3,dollar_c2,dollar_c1),dollar_f7(dollar_c3,dollar_c2,dollar_c1),dollar_f9(dollar_f8(dollar_c3,dollar_c2,dollar_c1),dollar_f7(dollar_c3,dollar_c2,dollar_c1))),
inference(hyper,[status(thm)],[102,77,104,103]),
[iquote('hyper,102,77,104,103')] ).
cnf(1115,plain,
( ~ path(A,B,dollar_c3)
| ~ triangle(dollar_f8(dollar_c3,A,B),dollar_f7(dollar_c3,A,B),C) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[121,76]),120]),98]),
[iquote('para_into,121.1.1,76.3.1,demod,120,unit_del,98')] ).
cnf(1208,plain,
$false,
inference(hyper,[status(thm)],[365,1115,101]),
[iquote('hyper,365,1115,101')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRA010+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n020.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 02:21:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.12/2.31 ----- Otter 3.3f, August 2004 -----
% 2.12/2.31 The process was started by sandbox on n020.cluster.edu,
% 2.12/2.31 Wed Jul 27 02:21:23 2022
% 2.12/2.31 The command was "./otter". The process ID is 10440.
% 2.12/2.31
% 2.12/2.31 set(prolog_style_variables).
% 2.12/2.31 set(auto).
% 2.12/2.31 dependent: set(auto1).
% 2.12/2.31 dependent: set(process_input).
% 2.12/2.31 dependent: clear(print_kept).
% 2.12/2.31 dependent: clear(print_new_demod).
% 2.12/2.31 dependent: clear(print_back_demod).
% 2.12/2.31 dependent: clear(print_back_sub).
% 2.12/2.31 dependent: set(control_memory).
% 2.12/2.31 dependent: assign(max_mem, 12000).
% 2.12/2.31 dependent: assign(pick_given_ratio, 4).
% 2.12/2.31 dependent: assign(stats_level, 1).
% 2.12/2.31 dependent: assign(max_seconds, 10800).
% 2.12/2.31 clear(print_given).
% 2.12/2.31
% 2.12/2.31 formula_list(usable).
% 2.12/2.31 all A (A=A).
% 2.12/2.31 all E (edge(E)->head_of(E)!=tail_of(E)).
% 2.12/2.31 all E (edge(E)->vertex(head_of(E))&vertex(tail_of(E))).
% 2.12/2.31 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)))))).
% 2.12/2.31 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)).
% 2.12/2.31 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))))))).
% 2.12/2.31 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)).
% 2.12/2.31 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))))).
% 2.12/2.31 all E1 E2 (se_quential(E1,E2)<->edge(E1)&edge(E2)&E1!=E2&head_of(E1)=tail_of(E2)).
% 2.12/2.31 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)))).
% 2.12/2.31 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))))))).
% 2.12/2.31 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))))).
% 2.12/2.31 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)).
% 2.12/2.31 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)).
% 2.12/2.31 all V1 V2 P (path(V1,V2,P)->length_of(P)=number_of_in(edges,P)).
% 2.12/2.31 all V1 V2 P (path(V1,V2,P)->number_of_in(se_quential_pairs,P)=minus(length_of(P),n1)).
% 2.12/2.31 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)).
% 2.12/2.31 all Things InThese less_or_e_qual(number_of_in(Things,InThese),number_of_in(Things,graph)).
% 2.12/2.31 -(complete-> (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)))).
% 2.12/2.31 end_of_list.
% 2.12/2.31
% 2.12/2.31 -------> usable clausifies to:
% 2.12/2.31
% 2.12/2.31 list(usable).
% 2.12/2.31 0 [] A=A.
% 2.12/2.31 0 [] -edge(E)|head_of(E)!=tail_of(E).
% 2.12/2.31 0 [] -edge(E)|vertex(head_of(E)).
% 2.12/2.31 0 [] -edge(E)|vertex(tail_of(E)).
% 2.12/2.31 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|edge($f1(V1,V2)).
% 2.12/2.31 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V1=head_of($f1(V1,V2))|V2=head_of($f1(V1,V2)).
% 2.12/2.31 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V1=head_of($f1(V1,V2))|V1=tail_of($f1(V1,V2)).
% 2.12/2.31 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V2=tail_of($f1(V1,V2))|V2=head_of($f1(V1,V2)).
% 2.12/2.31 0 [] -complete| -vertex(V1)| -vertex(V2)|V1=V2|V2=tail_of($f1(V1,V2))|V1=tail_of($f1(V1,V2)).
% 2.12/2.31 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)).
% 2.12/2.31 0 [] -vertex(V1)| -vertex(V2)| -edge(E)|V1!=tail_of(E)|V2!=head_of(E)|P!=path_cons(E,empty)|path(V1,V2,P).
% 2.12/2.31 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).
% 2.12/2.31 0 [] -path(V1,V2,P)|vertex(V1).
% 2.12/2.31 0 [] -path(V1,V2,P)|vertex(V2).
% 2.12/2.31 0 [] -path(V1,V2,P)|edge($f3(V1,V2,P)).
% 2.12/2.31 0 [] -path(V1,V2,P)|V1=tail_of($f3(V1,V2,P)).
% 2.12/2.31 0 [] -path(V1,V2,P)|V2=head_of($f3(V1,V2,P))|path(head_of($f3(V1,V2,P)),V2,$f2(V1,V2,P)).
% 2.12/2.31 0 [] -path(V1,V2,P)|V2=head_of($f3(V1,V2,P))|P=path_cons($f3(V1,V2,P),$f2(V1,V2,P)).
% 2.12/2.31 0 [] -path(V1,V2,P)|P=path_cons($f3(V1,V2,P),empty)|path(head_of($f3(V1,V2,P)),V2,$f2(V1,V2,P)).
% 2.12/2.31 0 [] -path(V1,V2,P)|P=path_cons($f3(V1,V2,P),empty)|P=path_cons($f3(V1,V2,P),$f2(V1,V2,P)).
% 2.12/2.31 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).
% 2.12/2.31 0 [] -path(V1,V2,P)| -on_path(E,P)|edge(E).
% 2.12/2.31 0 [] -path(V1,V2,P)| -on_path(E,P)|in_path(head_of(E),P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -on_path(E,P)|in_path(tail_of(E),P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -in_path(V,P)|vertex(V).
% 2.12/2.31 0 [] -path(V1,V2,P)| -in_path(V,P)|on_path($f4(V1,V2,P,V),P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -in_path(V,P)|V=head_of($f4(V1,V2,P,V))|V=tail_of($f4(V1,V2,P,V)).
% 2.12/2.31 0 [] -se_quential(E1,E2)|edge(E1).
% 2.12/2.31 0 [] -se_quential(E1,E2)|edge(E2).
% 2.12/2.31 0 [] -se_quential(E1,E2)|E1!=E2.
% 2.12/2.31 0 [] -se_quential(E1,E2)|head_of(E1)=tail_of(E2).
% 2.12/2.31 0 [] se_quential(E1,E2)| -edge(E1)| -edge(E2)|E1=E2|head_of(E1)!=tail_of(E2).
% 2.12/2.31 0 [] -path(V1,V2,P)| -on_path(E1,P)| -on_path(E2,P)| -se_quential(E1,E2)|precedes(E1,E2,P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -on_path(E1,P)| -on_path(E2,P)| -se_quential(E1,E3)| -precedes(E3,E2,P)|precedes(E1,E2,P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)|on_path(E1,P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)|on_path(E2,P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)|se_quential(E1,E2)|se_quential(E1,$f5(P,V1,V2,E1,E2)).
% 2.12/2.31 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)|se_quential(E1,E2)|precedes($f5(P,V1,V2,E1,E2),E2,P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -precedes(E1,E2,P)| -se_quential(E1,E2)| -se_quential(E1,E3)| -precedes(E3,E2,P).
% 2.12/2.31 0 [] -shortest_path(V1,V2,SP)|path(V1,V2,SP).
% 2.12/2.31 0 [] -shortest_path(V1,V2,SP)|V1!=V2.
% 2.12/2.31 0 [] -shortest_path(V1,V2,SP)| -path(V1,V2,P)|less_or_e_qual(length_of(SP),length_of(P)).
% 2.12/2.31 0 [] shortest_path(V1,V2,SP)| -path(V1,V2,SP)|V1=V2|path(V1,V2,$f6(V1,V2,SP)).
% 2.12/2.31 0 [] shortest_path(V1,V2,SP)| -path(V1,V2,SP)|V1=V2| -less_or_e_qual(length_of(SP),length_of($f6(V1,V2,SP))).
% 2.12/2.31 0 [] -shortest_path(V1,V2,P)| -precedes(E1,E2,P)|tail_of(E3)!=tail_of(E1)|head_of(E3)!=head_of(E2).
% 2.12/2.31 0 [] -shortest_path(V1,V2,P)| -precedes(E1,E2,P)| -precedes(E2,E1,P).
% 2.12/2.31 0 [] -triangle(E1,E2,E3)|edge(E1).
% 2.12/2.31 0 [] -triangle(E1,E2,E3)|edge(E2).
% 2.12/2.31 0 [] -triangle(E1,E2,E3)|edge(E3).
% 2.12/2.31 0 [] -triangle(E1,E2,E3)|se_quential(E1,E2).
% 2.12/2.31 0 [] -triangle(E1,E2,E3)|se_quential(E2,E3).
% 2.12/2.31 0 [] -triangle(E1,E2,E3)|se_quential(E3,E1).
% 2.12/2.31 0 [] triangle(E1,E2,E3)| -edge(E1)| -edge(E2)| -edge(E3)| -se_quential(E1,E2)| -se_quential(E2,E3)| -se_quential(E3,E1).
% 2.12/2.31 0 [] -path(V1,V2,P)|length_of(P)=number_of_in(edges,P).
% 2.12/2.31 0 [] -path(V1,V2,P)|number_of_in(se_quential_pairs,P)=minus(length_of(P),n1).
% 2.12/2.31 0 [] -path(V1,V2,P)|on_path($f8(P,V1,V2),P)|number_of_in(se_quential_pairs,P)=number_of_in(triangles,P).
% 2.12/2.31 0 [] -path(V1,V2,P)|on_path($f7(P,V1,V2),P)|number_of_in(se_quential_pairs,P)=number_of_in(triangles,P).
% 2.12/2.31 0 [] -path(V1,V2,P)|se_quential($f8(P,V1,V2),$f7(P,V1,V2))|number_of_in(se_quential_pairs,P)=number_of_in(triangles,P).
% 2.12/2.31 0 [] -path(V1,V2,P)| -triangle($f8(P,V1,V2),$f7(P,V1,V2),E3)|number_of_in(se_quential_pairs,P)=number_of_in(triangles,P).
% 2.12/2.31 0 [] less_or_e_qual(number_of_in(Things,InThese),number_of_in(Things,graph)).
% 2.12/2.31 0 [] complete.
% 2.12/2.31 0 [] path($c2,$c1,$c3).
% 2.12/2.31 0 [] -on_path(E1,$c3)| -on_path(E2,$c3)| -se_quential(E1,E2)|triangle(E1,E2,$f9(E1,E2)).
% 2.12/2.31 0 [] number_of_in(se_quential_pairs,$c3)!=number_of_in(triangles,$c3).
% 2.12/2.31 end_of_list.
% 2.12/2.31
% 2.12/2.31 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 2.12/2.31
% 2.12/2.31 This ia a non-Horn set with equality. The strategy will be
% 2.12/2.31 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.12/2.31 deletion, with positive clauses in sos and nonpositive
% 2.12/2.31 clauses in usable.
% 2.12/2.31
% 2.12/2.31 dependent: set(knuth_bendix).
% 2.12/2.31 dependent: set(anl_eq).
% 2.12/2.31 dependent: set(para_from).
% 2.12/2.31 dependent: set(para_into).
% 2.12/2.31 dependent: clear(para_from_right).
% 2.12/2.31 dependent: clear(para_into_right).
% 2.12/2.31 dependent: set(para_from_vars).
% 2.12/2.31 dependent: set(eq_units_both_ways).
% 2.12/2.31 dependent: set(dynamic_demod_all).
% 2.12/2.31 dependent: set(dynamic_demod).
% 2.12/2.31 dependent: set(order_eq).
% 2.12/2.31 dependent: set(back_demod).
% 2.12/2.31 dependent: set(lrpo).
% 2.12/2.31 dependent: set(hyper_res).
% 2.12/2.31 dependent: set(unit_deletion).
% 2.12/2.31 dependent: set(factor).
% 2.12/2.31
% 2.12/2.31 ------------> process usable:
% 2.12/2.31 ** KEPT (pick-wt=7): 2 [copy,1,flip.2] -edge(A)|tail_of(A)!=head_of(A).
% 2.12/2.31 ** KEPT (pick-wt=5): 3 [] -edge(A)|vertex(head_of(A)).
% 2.12/2.31 ** KEPT (pick-wt=5): 4 [] -edge(A)|vertex(tail_of(A)).
% 2.12/2.31 ** KEPT (pick-wt=12): 5 [] -complete| -vertex(A)| -vertex(B)|A=B|edge($f1(A,B)).
% 2.12/2.31 ** 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.
% 2.12/2.31 ** 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.
% 2.12/2.31 ** 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.
% 2.12/2.31 ** 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.
% 2.12/2.31 ** 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.
% 2.12/2.31 ** 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).
% 2.12/2.31 ** 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).
% 2.12/2.31 ** KEPT (pick-wt=6): 18 [] -path(A,B,C)|vertex(A).
% 2.12/2.31 ** KEPT (pick-wt=6): 19 [] -path(A,B,C)|vertex(B).
% 2.12/2.31 ** KEPT (pick-wt=9): 20 [] -path(A,B,C)|edge($f3(A,B,C)).
% 2.12/2.31 ** KEPT (pick-wt=11): 22 [copy,21,flip.2] -path(A,B,C)|tail_of($f3(A,B,C))=A.
% 2.12/2.31 ** 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,$f2(A,B,C)).
% 2.12/2.31 ** KEPT (pick-wt=22): 26 [copy,25,flip.2,flip.3] -path(A,B,C)|head_of($f3(A,B,C))=B|path_cons($f3(A,B,C),$f2(A,B,C))=C.
% 2.12/2.31 ** 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,$f2(A,B,C)).
% 2.12/2.31 ** KEPT (pick-wt=23): 30 [copy,29,flip.2,flip.3] -path(A,B,C)|path_cons($f3(A,B,C),empty)=C|path_cons($f3(A,B,C),$f2(A,B,C))=C.
% 2.12/2.31 ** 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.
% 2.12/2.31 ** KEPT (pick-wt=9): 33 [] -path(A,B,C)| -on_path(D,C)|edge(D).
% 2.12/2.31 ** KEPT (pick-wt=11): 34 [] -path(A,B,C)| -on_path(D,C)|in_path(head_of(D),C).
% 2.12/2.31 ** KEPT (pick-wt=11): 35 [] -path(A,B,C)| -on_path(D,C)|in_path(tail_of(D),C).
% 2.12/2.31 ** KEPT (pick-wt=9): 36 [] -path(A,B,C)| -in_path(D,C)|vertex(D).
% 2.12/2.31 ** KEPT (pick-wt=14): 37 [] -path(A,B,C)| -in_path(D,C)|on_path($f4(A,B,C,D),C).
% 2.12/2.31 ** KEPT (pick-wt=23): 39 [copy,38,flip.3,flip.4] -path(A,B,C)| -in_path(D,C)|head_of($f4(A,B,C,D))=D|tail_of($f4(A,B,C,D))=D.
% 2.12/2.31 ** KEPT (pick-wt=5): 40 [] -se_quential(A,B)|edge(A).
% 2.12/2.31 ** KEPT (pick-wt=5): 41 [] -se_quential(A,B)|edge(B).
% 2.12/2.31 ** KEPT (pick-wt=6): 42 [] -se_quential(A,B)|A!=B.
% 2.12/2.31 ** KEPT (pick-wt=8): 43 [] -se_quential(A,B)|head_of(A)=tail_of(B).
% 2.12/2.31 ** KEPT (pick-wt=15): 44 [] se_quential(A,B)| -edge(A)| -edge(B)|A=B|head_of(A)!=tail_of(B).
% 2.12/2.31 ** KEPT (pick-wt=17): 45 [] -path(A,B,C)| -on_path(D,C)| -on_path(E,C)| -se_quential(D,E)|precedes(D,E,C).
% 2.12/2.31 ** KEPT (pick-wt=21): 46 [] -path(A,B,C)| -on_path(D,C)| -on_path(E,C)| -se_quential(D,F)| -precedes(F,E,C)|precedes(D,E,C).
% 2.12/2.31 ** KEPT (pick-wt=11): 47 [] -path(A,B,C)| -precedes(D,E,C)|on_path(D,C).
% 2.12/2.31 ** KEPT (pick-wt=11): 48 [] -path(A,B,C)| -precedes(D,E,C)|on_path(E,C).
% 2.12/2.31 ** KEPT (pick-wt=19): 49 [] -path(A,B,C)| -precedes(D,E,C)|se_quential(D,E)|se_quential(D,$f5(C,A,B,D,E)).
% 2.12/2.31 ** KEPT (pick-wt=20): 50 [] -path(A,B,C)| -precedes(D,E,C)|se_quential(D,E)|precedes($f5(C,A,B,D,E),E,C).
% 2.12/2.31 ** KEPT (pick-wt=18): 51 [] -path(A,B,C)| -precedes(D,E,C)| -se_quential(D,E)| -se_quential(D,F)| -precedes(F,E,C).
% 2.12/2.31 ** KEPT (pick-wt=8): 52 [] -shortest_path(A,B,C)|path(A,B,C).
% 2.12/2.31 ** KEPT (pick-wt=7): 53 [] -shortest_path(A,B,C)|A!=B.
% 2.12/2.31 ** KEPT (pick-wt=13): 54 [] -shortest_path(A,B,C)| -path(A,B,D)|less_or_e_qual(length_of(C),length_of(D)).
% 2.12/2.31 ** KEPT (pick-wt=18): 55 [] shortest_path(A,B,C)| -path(A,B,C)|A=B|path(A,B,$f6(A,B,C)).
% 24.90/25.07 ** 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($f6(A,B,C))).
% 24.90/25.07 ** KEPT (pick-wt=18): 57 [] -shortest_path(A,B,C)| -precedes(D,E,C)|tail_of(F)!=tail_of(D)|head_of(F)!=head_of(E).
% 24.90/25.07 ** KEPT (pick-wt=12): 58 [] -shortest_path(A,B,C)| -precedes(D,E,C)| -precedes(E,D,C).
% 24.90/25.07 ** KEPT (pick-wt=6): 59 [] -triangle(A,B,C)|edge(A).
% 24.90/25.07 ** KEPT (pick-wt=6): 60 [] -triangle(A,B,C)|edge(B).
% 24.90/25.07 ** KEPT (pick-wt=6): 61 [] -triangle(A,B,C)|edge(C).
% 24.90/25.07 ** KEPT (pick-wt=7): 62 [] -triangle(A,B,C)|se_quential(A,B).
% 24.90/25.07 ** KEPT (pick-wt=7): 63 [] -triangle(A,B,C)|se_quential(B,C).
% 24.90/25.07 ** KEPT (pick-wt=7): 64 [] -triangle(A,B,C)|se_quential(C,A).
% 24.90/25.07 ** KEPT (pick-wt=19): 65 [] triangle(A,B,C)| -edge(A)| -edge(B)| -edge(C)| -se_quential(A,B)| -se_quential(B,C)| -se_quential(C,A).
% 24.90/25.07 ** KEPT (pick-wt=10): 66 [] -path(A,B,C)|length_of(C)=number_of_in(edges,C).
% 24.90/25.07 ** KEPT (pick-wt=12): 68 [copy,67,flip.2] -path(A,B,C)|minus(length_of(C),n1)=number_of_in(se_quential_pairs,C).
% 24.90/25.07 ** KEPT (pick-wt=17): 70 [copy,69,flip.3] -path(A,B,C)|on_path($f8(C,A,B),C)|number_of_in(triangles,C)=number_of_in(se_quential_pairs,C).
% 24.90/25.07 ** KEPT (pick-wt=17): 72 [copy,71,flip.3] -path(A,B,C)|on_path($f7(C,A,B),C)|number_of_in(triangles,C)=number_of_in(se_quential_pairs,C).
% 24.90/25.07 ** KEPT (pick-wt=20): 74 [copy,73,flip.3] -path(A,B,C)|se_quential($f8(C,A,B),$f7(C,A,B))|number_of_in(triangles,C)=number_of_in(se_quential_pairs,C).
% 24.90/25.07 ** KEPT (pick-wt=21): 76 [copy,75,flip.3] -path(A,B,C)| -triangle($f8(C,A,B),$f7(C,A,B),D)|number_of_in(triangles,C)=number_of_in(se_quential_pairs,C).
% 24.90/25.07 ** KEPT (pick-wt=15): 77 [] -on_path(A,$c3)| -on_path(B,$c3)| -se_quential(A,B)|triangle(A,B,$f9(A,B)).
% 24.90/25.07 ** KEPT (pick-wt=7): 79 [copy,78,flip.1] number_of_in(triangles,$c3)!=number_of_in(se_quential_pairs,$c3).
% 24.90/25.07
% 24.90/25.07 ------------> process sos:
% 24.90/25.07 ** KEPT (pick-wt=3): 98 [] A=A.
% 24.90/25.07 ** KEPT (pick-wt=7): 99 [] less_or_e_qual(number_of_in(A,B),number_of_in(A,graph)).
% 24.90/25.07 ** KEPT (pick-wt=1): 100 [] complete.
% 24.90/25.07 ** KEPT (pick-wt=4): 101 [] path($c2,$c1,$c3).
% 24.90/25.07 Following clause subsumed by 98 during input processing: 0 [copy,98,flip.1] A=A.
% 24.90/25.08 98 back subsumes 83.
% 24.90/25.08 98 back subsumes 82.
% 24.90/25.08 98 back subsumes 81.
% 24.90/25.08 98 back subsumes 80.
% 24.90/25.08
% 24.90/25.08 ======= end of input processing =======
% 24.90/25.08
% 24.90/25.08 =========== start of search ===========
% 24.90/25.08
% 24.90/25.08
% 24.90/25.08 Resetting weight limit to 14.
% 24.90/25.08
% 24.90/25.08
% 24.90/25.08 Resetting weight limit to 14.
% 24.90/25.08
% 24.90/25.08 sos_size=814
% 24.90/25.08
% 24.90/25.08
% 24.90/25.08 Resetting weight limit to 10.
% 24.90/25.08
% 24.90/25.08
% 24.90/25.08 Resetting weight limit to 10.
% 24.90/25.08
% 24.90/25.08 sos_size=971
% 24.90/25.08
% 24.90/25.08 -- HEY sandbox, WE HAVE A PROOF!! --
% 24.90/25.08
% 24.90/25.08 -----> EMPTY CLAUSE at 22.77 sec ----> 1208 [hyper,365,1115,101] $F.
% 24.90/25.08
% 24.90/25.08 Length of proof is 15. Level of proof is 5.
% 24.90/25.08
% 24.90/25.08 ---------------- PROOF ----------------
% 24.90/25.08 % SZS status Theorem
% 24.90/25.08 % SZS output start Refutation
% See solution above
% 24.90/25.08 ------------ end of proof -------------
% 24.90/25.08
% 24.90/25.08
% 24.90/25.08 Search stopped by max_proofs option.
% 24.90/25.08
% 24.90/25.08
% 24.90/25.08 Search stopped by max_proofs option.
% 24.90/25.08
% 24.90/25.08 ============ end of search ============
% 24.90/25.08
% 24.90/25.08 -------------- statistics -------------
% 24.90/25.08 clauses given 487
% 24.90/25.08 clauses generated 302685
% 24.90/25.08 clauses kept 1183
% 24.90/25.08 clauses forward subsumed 1282
% 24.90/25.08 clauses back subsumed 14
% 24.90/25.08 Kbytes malloced 5859
% 24.90/25.08
% 24.90/25.08 ----------- times (seconds) -----------
% 24.90/25.08 user CPU time 22.77 (0 hr, 0 min, 22 sec)
% 24.90/25.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 24.90/25.08 wall-clock time 25 (0 hr, 0 min, 25 sec)
% 24.90/25.08
% 24.90/25.08 That finishes the proof of the theorem.
% 24.90/25.08
% 24.90/25.08 Process 10440 finished Wed Jul 27 02:21:48 2022
% 24.90/25.08 Otter interrupted
% 24.90/25.08 PROOF FOUND
%------------------------------------------------------------------------------