TSTP Solution File: SET804+4 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET804+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 13:14:17 EDT 2022
% Result : Theorem 1.94s 2.19s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 13 unt; 0 nHn; 17 RR)
% Number of literals : 24 ( 5 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 14 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(58,axiom,
( ~ least(A,B,C)
| member(A,C) ),
file('SET804+4.p',unknown),
[] ).
cnf(59,axiom,
( ~ least(A,B,C)
| ~ member(D,C)
| apply(B,A,D) ),
file('SET804+4.p',unknown),
[] ).
cnf(68,axiom,
( ~ min(A,B,C)
| member(A,C) ),
file('SET804+4.p',unknown),
[] ).
cnf(69,axiom,
( ~ min(A,B,C)
| ~ member(D,C)
| ~ apply(B,D,A)
| A = D ),
file('SET804+4.p',unknown),
[] ).
cnf(86,axiom,
dollar_c3 != dollar_c2,
file('SET804+4.p',unknown),
[] ).
cnf(113,axiom,
min(dollar_c3,dollar_c5,dollar_c4),
file('SET804+4.p',unknown),
[] ).
cnf(114,axiom,
min(dollar_c2,dollar_c5,dollar_c4),
file('SET804+4.p',unknown),
[] ).
cnf(115,axiom,
least(dollar_c1,dollar_c5,dollar_c4),
file('SET804+4.p',unknown),
[] ).
cnf(124,plain,
member(dollar_c3,dollar_c4),
inference(hyper,[status(thm)],[113,68]),
[iquote('hyper,113,68')] ).
cnf(147,plain,
member(dollar_c2,dollar_c4),
inference(hyper,[status(thm)],[114,68]),
[iquote('hyper,114,68')] ).
cnf(201,plain,
apply(dollar_c5,dollar_c1,dollar_c2),
inference(hyper,[status(thm)],[115,59,147]),
[iquote('hyper,115,59,147')] ).
cnf(202,plain,
apply(dollar_c5,dollar_c1,dollar_c3),
inference(hyper,[status(thm)],[115,59,124]),
[iquote('hyper,115,59,124')] ).
cnf(203,plain,
member(dollar_c1,dollar_c4),
inference(hyper,[status(thm)],[115,58]),
[iquote('hyper,115,58')] ).
cnf(278,plain,
dollar_c2 = dollar_c1,
inference(hyper,[status(thm)],[201,69,114,203]),
[iquote('hyper,201,69,114,203')] ).
cnf(298,plain,
dollar_c3 != dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[86]),278]),
[iquote('back_demod,86,demod,278')] ).
cnf(335,plain,
dollar_c3 = dollar_c1,
inference(hyper,[status(thm)],[202,69,113,203]),
[iquote('hyper,202,69,113,203')] ).
cnf(337,plain,
$false,
inference(binary,[status(thm)],[335,298]),
[iquote('binary,335.1,298.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : SET804+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n006.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 10:39:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.94/2.15 ----- Otter 3.3f, August 2004 -----
% 1.94/2.15 The process was started by sandbox2 on n006.cluster.edu,
% 1.94/2.15 Wed Jul 27 10:39:02 2022
% 1.94/2.15 The command was "./otter". The process ID is 27709.
% 1.94/2.15
% 1.94/2.15 set(prolog_style_variables).
% 1.94/2.15 set(auto).
% 1.94/2.15 dependent: set(auto1).
% 1.94/2.15 dependent: set(process_input).
% 1.94/2.15 dependent: clear(print_kept).
% 1.94/2.15 dependent: clear(print_new_demod).
% 1.94/2.15 dependent: clear(print_back_demod).
% 1.94/2.15 dependent: clear(print_back_sub).
% 1.94/2.15 dependent: set(control_memory).
% 1.94/2.15 dependent: assign(max_mem, 12000).
% 1.94/2.15 dependent: assign(pick_given_ratio, 4).
% 1.94/2.15 dependent: assign(stats_level, 1).
% 1.94/2.15 dependent: assign(max_seconds, 10800).
% 1.94/2.15 clear(print_given).
% 1.94/2.15
% 1.94/2.15 formula_list(usable).
% 1.94/2.15 all A (A=A).
% 1.94/2.15 all R E (order(R,E)<-> (all X (member(X,E)->apply(R,X,X)))& (all X Y (member(X,E)&member(Y,E)-> (apply(R,X,Y)&apply(R,Y,X)->X=Y)))& (all X Y Z (member(X,E)&member(Y,E)&member(Z,E)-> (apply(R,X,Y)&apply(R,Y,Z)->apply(R,X,Z))))).
% 1.94/2.15 all R E (total_order(R,E)<->order(R,E)& (all X Y (member(X,E)&member(Y,E)->apply(R,X,Y)|apply(R,Y,X)))).
% 1.94/2.15 all R E M (upper_bound(M,R,E)<-> (all X (member(X,E)->apply(R,X,M)))).
% 1.94/2.15 all R E M (lower_bound(M,R,E)<-> (all X (member(X,E)->apply(R,M,X)))).
% 1.94/2.15 all R E M (greatest(M,R,E)<->member(M,E)& (all X (member(X,E)->apply(R,X,M)))).
% 1.94/2.15 all R E M (least(M,R,E)<->member(M,E)& (all X (member(X,E)->apply(R,M,X)))).
% 1.94/2.15 all R E M (max(M,R,E)<->member(M,E)& (all X (member(X,E)&apply(R,M,X)->M=X))).
% 1.94/2.15 all R E M (min(M,R,E)<->member(M,E)& (all X (member(X,E)&apply(R,X,M)->M=X))).
% 1.94/2.15 all A X R E (least_upper_bound(A,X,R,E)<->member(A,X)&upper_bound(A,R,X)& (all M (member(M,E)&upper_bound(M,R,X)->apply(R,A,M)))).
% 1.94/2.15 all A X R E (greatest_lower_bound(A,X,R,E)<->member(A,X)&lower_bound(A,R,X)& (all M (member(M,E)&lower_bound(M,R,X)->apply(R,M,A)))).
% 1.94/2.15 -(all R E (order(R,E)-> (all M1 M2 (min(M1,R,E)&min(M2,R,E)&M1!=M2-> -(exists M least(M,R,E)))))).
% 1.94/2.15 end_of_list.
% 1.94/2.15
% 1.94/2.15 -------> usable clausifies to:
% 1.94/2.15
% 1.94/2.15 list(usable).
% 1.94/2.15 0 [] A=A.
% 1.94/2.15 0 [] -order(R,E)| -member(X,E)|apply(R,X,X).
% 1.94/2.15 0 [] -order(R,E)| -member(X1,E)| -member(Y,E)| -apply(R,X1,Y)| -apply(R,Y,X1)|X1=Y.
% 1.94/2.15 0 [] -order(R,E)| -member(X2,E)| -member(X3,E)| -member(Z,E)| -apply(R,X2,X3)| -apply(R,X3,Z)|apply(R,X2,Z).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f3(R,E),E)|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f3(R,E),E)|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f3(R,E),E)|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f3(R,E),E)|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f3(R,E),E)|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f3(R,E),E)| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f2(R,E),E)|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f2(R,E),E)|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f2(R,E),E)|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f2(R,E),E)|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f2(R,E),E)|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|member($f2(R,E),E)| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f3(R,E),$f2(R,E))|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f3(R,E),$f2(R,E))|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f3(R,E),$f2(R,E))|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f3(R,E),$f2(R,E))|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f3(R,E),$f2(R,E))|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f3(R,E),$f2(R,E))| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f2(R,E),$f3(R,E))|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f2(R,E),$f3(R,E))|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f2(R,E),$f3(R,E))|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f2(R,E),$f3(R,E))|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f2(R,E),$f3(R,E))|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|apply(R,$f2(R,E),$f3(R,E))| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|$f3(R,E)!=$f2(R,E)|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|$f3(R,E)!=$f2(R,E)|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|$f3(R,E)!=$f2(R,E)|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|$f3(R,E)!=$f2(R,E)|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|$f3(R,E)!=$f2(R,E)|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)|member($f1(R,E),E)|$f3(R,E)!=$f2(R,E)| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f3(R,E),E)|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f3(R,E),E)|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f3(R,E),E)|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f3(R,E),E)|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f3(R,E),E)|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f3(R,E),E)| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f2(R,E),E)|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f2(R,E),E)|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f2(R,E),E)|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f2(R,E),E)|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f2(R,E),E)|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|member($f2(R,E),E)| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f3(R,E),$f2(R,E))|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f3(R,E),$f2(R,E))|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f3(R,E),$f2(R,E))|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f3(R,E),$f2(R,E))|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f3(R,E),$f2(R,E))|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f3(R,E),$f2(R,E))| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f2(R,E),$f3(R,E))|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f2(R,E),$f3(R,E))|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f2(R,E),$f3(R,E))|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f2(R,E),$f3(R,E))|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f2(R,E),$f3(R,E))|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|apply(R,$f2(R,E),$f3(R,E))| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|$f3(R,E)!=$f2(R,E)|member($f6(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|$f3(R,E)!=$f2(R,E)|member($f5(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|$f3(R,E)!=$f2(R,E)|member($f4(R,E),E).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|$f3(R,E)!=$f2(R,E)|apply(R,$f6(R,E),$f5(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|$f3(R,E)!=$f2(R,E)|apply(R,$f5(R,E),$f4(R,E)).
% 1.94/2.15 0 [] order(R,E)| -apply(R,$f1(R,E),$f1(R,E))|$f3(R,E)!=$f2(R,E)| -apply(R,$f6(R,E),$f4(R,E)).
% 1.94/2.15 0 [] -total_order(R,E)|order(R,E).
% 1.94/2.15 0 [] -total_order(R,E)| -member(X,E)| -member(Y,E)|apply(R,X,Y)|apply(R,Y,X).
% 1.94/2.15 0 [] total_order(R,E)| -order(R,E)|member($f8(R,E),E).
% 1.94/2.15 0 [] total_order(R,E)| -order(R,E)|member($f7(R,E),E).
% 1.94/2.15 0 [] total_order(R,E)| -order(R,E)| -apply(R,$f8(R,E),$f7(R,E)).
% 1.94/2.15 0 [] total_order(R,E)| -order(R,E)| -apply(R,$f7(R,E),$f8(R,E)).
% 1.94/2.15 0 [] -upper_bound(M,R,E)| -member(X,E)|apply(R,X,M).
% 1.94/2.15 0 [] upper_bound(M,R,E)|member($f9(R,E,M),E).
% 1.94/2.15 0 [] upper_bound(M,R,E)| -apply(R,$f9(R,E,M),M).
% 1.94/2.15 0 [] -lower_bound(M,R,E)| -member(X,E)|apply(R,M,X).
% 1.94/2.15 0 [] lower_bound(M,R,E)|member($f10(R,E,M),E).
% 1.94/2.15 0 [] lower_bound(M,R,E)| -apply(R,M,$f10(R,E,M)).
% 1.94/2.15 0 [] -greatest(M,R,E)|member(M,E).
% 1.94/2.15 0 [] -greatest(M,R,E)| -member(X,E)|apply(R,X,M).
% 1.94/2.15 0 [] greatest(M,R,E)| -member(M,E)|member($f11(R,E,M),E).
% 1.94/2.15 0 [] greatest(M,R,E)| -member(M,E)| -apply(R,$f11(R,E,M),M).
% 1.94/2.15 0 [] -least(M,R,E)|member(M,E).
% 1.94/2.16 0 [] -least(M,R,E)| -member(X,E)|apply(R,M,X).
% 1.94/2.16 0 [] least(M,R,E)| -member(M,E)|member($f12(R,E,M),E).
% 1.94/2.16 0 [] least(M,R,E)| -member(M,E)| -apply(R,M,$f12(R,E,M)).
% 1.94/2.16 0 [] -max(M,R,E)|member(M,E).
% 1.94/2.16 0 [] -max(M,R,E)| -member(X,E)| -apply(R,M,X)|M=X.
% 1.94/2.16 0 [] max(M,R,E)| -member(M,E)|member($f13(R,E,M),E).
% 1.94/2.16 0 [] max(M,R,E)| -member(M,E)|apply(R,M,$f13(R,E,M)).
% 1.94/2.16 0 [] max(M,R,E)| -member(M,E)|M!=$f13(R,E,M).
% 1.94/2.16 0 [] -min(M,R,E)|member(M,E).
% 1.94/2.16 0 [] -min(M,R,E)| -member(X,E)| -apply(R,X,M)|M=X.
% 1.94/2.16 0 [] min(M,R,E)| -member(M,E)|member($f14(R,E,M),E).
% 1.94/2.16 0 [] min(M,R,E)| -member(M,E)|apply(R,$f14(R,E,M),M).
% 1.94/2.16 0 [] min(M,R,E)| -member(M,E)|M!=$f14(R,E,M).
% 1.94/2.16 0 [] -least_upper_bound(A,X,R,E)|member(A,X).
% 1.94/2.16 0 [] -least_upper_bound(A,X,R,E)|upper_bound(A,R,X).
% 1.94/2.16 0 [] -least_upper_bound(A,X,R,E)| -member(M,E)| -upper_bound(M,R,X)|apply(R,A,M).
% 1.94/2.16 0 [] least_upper_bound(A,X,R,E)| -member(A,X)| -upper_bound(A,R,X)|member($f15(A,X,R,E),E).
% 1.94/2.16 0 [] least_upper_bound(A,X,R,E)| -member(A,X)| -upper_bound(A,R,X)|upper_bound($f15(A,X,R,E),R,X).
% 1.94/2.16 0 [] least_upper_bound(A,X,R,E)| -member(A,X)| -upper_bound(A,R,X)| -apply(R,A,$f15(A,X,R,E)).
% 1.94/2.16 0 [] -greatest_lower_bound(A,X,R,E)|member(A,X).
% 1.94/2.16 0 [] -greatest_lower_bound(A,X,R,E)|lower_bound(A,R,X).
% 1.94/2.16 0 [] -greatest_lower_bound(A,X,R,E)| -member(M,E)| -lower_bound(M,R,X)|apply(R,M,A).
% 1.94/2.16 0 [] greatest_lower_bound(A,X,R,E)| -member(A,X)| -lower_bound(A,R,X)|member($f16(A,X,R,E),E).
% 1.94/2.16 0 [] greatest_lower_bound(A,X,R,E)| -member(A,X)| -lower_bound(A,R,X)|lower_bound($f16(A,X,R,E),R,X).
% 1.94/2.16 0 [] greatest_lower_bound(A,X,R,E)| -member(A,X)| -lower_bound(A,R,X)| -apply(R,$f16(A,X,R,E),A).
% 1.94/2.16 0 [] order($c5,$c4).
% 1.94/2.16 0 [] min($c3,$c5,$c4).
% 1.94/2.16 0 [] min($c2,$c5,$c4).
% 1.94/2.16 0 [] $c3!=$c2.
% 1.94/2.16 0 [] least($c1,$c5,$c4).
% 1.94/2.16 end_of_list.
% 1.94/2.16
% 1.94/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.94/2.16
% 1.94/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.94/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.94/2.16 deletion, with positive clauses in sos and nonpositive
% 1.94/2.16 clauses in usable.
% 1.94/2.16
% 1.94/2.16 dependent: set(knuth_bendix).
% 1.94/2.16 dependent: set(anl_eq).
% 1.94/2.16 dependent: set(para_from).
% 1.94/2.16 dependent: set(para_into).
% 1.94/2.16 dependent: clear(para_from_right).
% 1.94/2.16 dependent: clear(para_into_right).
% 1.94/2.16 dependent: set(para_from_vars).
% 1.94/2.16 dependent: set(eq_units_both_ways).
% 1.94/2.16 dependent: set(dynamic_demod_all).
% 1.94/2.16 dependent: set(dynamic_demod).
% 1.94/2.16 dependent: set(order_eq).
% 1.94/2.16 dependent: set(back_demod).
% 1.94/2.16 dependent: set(lrpo).
% 1.94/2.16 dependent: set(hyper_res).
% 1.94/2.16 dependent: set(unit_deletion).
% 1.94/2.16 dependent: set(factor).
% 1.94/2.16
% 1.94/2.16 ------------> process usable:
% 1.94/2.16 ** KEPT (pick-wt=10): 1 [] -order(A,B)| -member(C,B)|apply(A,C,C).
% 1.94/2.16 ** KEPT (pick-wt=20): 2 [] -order(A,B)| -member(C,B)| -member(D,B)| -apply(A,C,D)| -apply(A,D,C)|C=D.
% 1.94/2.16 ** KEPT (pick-wt=24): 3 [] -order(A,B)| -member(C,B)| -member(D,B)| -member(E,B)| -apply(A,C,D)| -apply(A,D,E)|apply(A,C,E).
% 1.94/2.16 ** KEPT (pick-wt=21): 4 [] order(A,B)|member($f1(A,B),B)|member($f3(A,B),B)| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=21): 5 [] order(A,B)|member($f1(A,B),B)|member($f2(A,B),B)| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 6 [] order(A,B)|member($f1(A,B),B)|apply(A,$f3(A,B),$f2(A,B))| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 7 [] order(A,B)|member($f1(A,B),B)|apply(A,$f2(A,B),$f3(A,B))| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=20): 8 [] order(A,B)|member($f1(A,B),B)|$f3(A,B)!=$f2(A,B)|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=20): 9 [] order(A,B)|member($f1(A,B),B)|$f3(A,B)!=$f2(A,B)|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=20): 10 [] order(A,B)|member($f1(A,B),B)|$f3(A,B)!=$f2(A,B)|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=23): 11 [] order(A,B)|member($f1(A,B),B)|$f3(A,B)!=$f2(A,B)|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=23): 12 [] order(A,B)|member($f1(A,B),B)|$f3(A,B)!=$f2(A,B)|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=23): 13 [] order(A,B)|member($f1(A,B),B)|$f3(A,B)!=$f2(A,B)| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=21): 14 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f3(A,B),B)|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=21): 15 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f3(A,B),B)|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=21): 16 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f3(A,B),B)|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=24): 17 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f3(A,B),B)|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 18 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f3(A,B),B)|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 19 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f3(A,B),B)| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=21): 20 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f2(A,B),B)|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=21): 21 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f2(A,B),B)|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=21): 22 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f2(A,B),B)|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=24): 23 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f2(A,B),B)|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 24 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f2(A,B),B)|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 25 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|member($f2(A,B),B)| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 26 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f3(A,B),$f2(A,B))|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=24): 27 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f3(A,B),$f2(A,B))|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=24): 28 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f3(A,B),$f2(A,B))|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=27): 29 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f3(A,B),$f2(A,B))|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=27): 30 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f3(A,B),$f2(A,B))|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=27): 31 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f3(A,B),$f2(A,B))| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 32 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f2(A,B),$f3(A,B))|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=24): 33 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f2(A,B),$f3(A,B))|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=24): 34 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f2(A,B),$f3(A,B))|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=27): 35 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f2(A,B),$f3(A,B))|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=27): 36 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f2(A,B),$f3(A,B))|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=27): 37 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|apply(A,$f2(A,B),$f3(A,B))| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=23): 38 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|$f3(A,B)!=$f2(A,B)|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=23): 39 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|$f3(A,B)!=$f2(A,B)|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=23): 40 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|$f3(A,B)!=$f2(A,B)|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=26): 41 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|$f3(A,B)!=$f2(A,B)|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=26): 42 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|$f3(A,B)!=$f2(A,B)|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=26): 43 [] order(A,B)| -apply(A,$f1(A,B),$f1(A,B))|$f3(A,B)!=$f2(A,B)| -apply(A,$f6(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=6): 44 [] -total_order(A,B)|order(A,B).
% 1.94/2.16 ** KEPT (pick-wt=17): 45 [] -total_order(A,B)| -member(C,B)| -member(D,B)|apply(A,C,D)|apply(A,D,C).
% 1.94/2.16 ** KEPT (pick-wt=11): 46 [] total_order(A,B)| -order(A,B)|member($f8(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=11): 47 [] total_order(A,B)| -order(A,B)|member($f7(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=14): 48 [] total_order(A,B)| -order(A,B)| -apply(A,$f8(A,B),$f7(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=14): 49 [] total_order(A,B)| -order(A,B)| -apply(A,$f7(A,B),$f8(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=11): 50 [] -upper_bound(A,B,C)| -member(D,C)|apply(B,D,A).
% 1.94/2.16 ** KEPT (pick-wt=11): 51 [] upper_bound(A,B,C)| -apply(B,$f9(B,C,A),A).
% 1.94/2.16 ** KEPT (pick-wt=11): 52 [] -lower_bound(A,B,C)| -member(D,C)|apply(B,A,D).
% 1.94/2.16 ** KEPT (pick-wt=11): 53 [] lower_bound(A,B,C)| -apply(B,A,$f10(B,C,A)).
% 1.94/2.16 ** KEPT (pick-wt=7): 54 [] -greatest(A,B,C)|member(A,C).
% 1.94/2.16 ** KEPT (pick-wt=11): 55 [] -greatest(A,B,C)| -member(D,C)|apply(B,D,A).
% 1.94/2.16 ** KEPT (pick-wt=13): 56 [] greatest(A,B,C)| -member(A,C)|member($f11(B,C,A),C).
% 1.94/2.16 ** KEPT (pick-wt=14): 57 [] greatest(A,B,C)| -member(A,C)| -apply(B,$f11(B,C,A),A).
% 1.94/2.16 ** KEPT (pick-wt=7): 58 [] -least(A,B,C)|member(A,C).
% 1.94/2.16 ** KEPT (pick-wt=11): 59 [] -least(A,B,C)| -member(D,C)|apply(B,A,D).
% 1.94/2.16 ** KEPT (pick-wt=13): 60 [] least(A,B,C)| -member(A,C)|member($f12(B,C,A),C).
% 1.94/2.16 ** KEPT (pick-wt=14): 61 [] least(A,B,C)| -member(A,C)| -apply(B,A,$f12(B,C,A)).
% 1.94/2.16 ** KEPT (pick-wt=7): 62 [] -max(A,B,C)|member(A,C).
% 1.94/2.16 ** KEPT (pick-wt=14): 63 [] -max(A,B,C)| -member(D,C)| -apply(B,A,D)|A=D.
% 1.94/2.16 ** KEPT (pick-wt=13): 64 [] max(A,B,C)| -member(A,C)|member($f13(B,C,A),C).
% 1.94/2.16 ** KEPT (pick-wt=14): 65 [] max(A,B,C)| -member(A,C)|apply(B,A,$f13(B,C,A)).
% 1.94/2.16 ** KEPT (pick-wt=13): 67 [copy,66,flip.3] max(A,B,C)| -member(A,C)|$f13(B,C,A)!=A.
% 1.94/2.16 ** KEPT (pick-wt=7): 68 [] -min(A,B,C)|member(A,C).
% 1.94/2.16 ** KEPT (pick-wt=14): 69 [] -min(A,B,C)| -member(D,C)| -apply(B,D,A)|A=D.
% 1.94/2.16 ** KEPT (pick-wt=13): 70 [] min(A,B,C)| -member(A,C)|member($f14(B,C,A),C).
% 1.94/2.16 ** KEPT (pick-wt=14): 71 [] min(A,B,C)| -member(A,C)|apply(B,$f14(B,C,A),A).
% 1.94/2.16 ** KEPT (pick-wt=13): 73 [copy,72,flip.3] min(A,B,C)| -member(A,C)|$f14(B,C,A)!=A.
% 1.94/2.16 ** KEPT (pick-wt=8): 74 [] -least_upper_bound(A,B,C,D)|member(A,B).
% 1.94/2.16 ** KEPT (pick-wt=9): 75 [] -least_upper_bound(A,B,C,D)|upper_bound(A,C,B).
% 1.94/2.16 ** KEPT (pick-wt=16): 76 [] -least_upper_bound(A,B,C,D)| -member(E,D)| -upper_bound(E,C,B)|apply(C,A,E).
% 1.94/2.16 ** KEPT (pick-wt=19): 77 [] least_upper_bound(A,B,C,D)| -member(A,B)| -upper_bound(A,C,B)|member($f15(A,B,C,D),D).
% 1.94/2.16 ** KEPT (pick-wt=20): 78 [] least_upper_bound(A,B,C,D)| -member(A,B)| -upper_bound(A,C,B)|upper_bound($f15(A,B,C,D),C,B).
% 1.94/2.16 ** KEPT (pick-wt=20): 79 [] least_upper_bound(A,B,C,D)| -member(A,B)| -upper_bound(A,C,B)| -apply(C,A,$f15(A,B,C,D)).
% 1.94/2.16 ** KEPT (pick-wt=8): 80 [] -greatest_lower_bound(A,B,C,D)|member(A,B).
% 1.94/2.16 ** KEPT (pick-wt=9): 81 [] -greatest_lower_bound(A,B,C,D)|lower_bound(A,C,B).
% 1.94/2.16 ** KEPT (pick-wt=16): 82 [] -greatest_lower_bound(A,B,C,D)| -member(E,D)| -lower_bound(E,C,B)|apply(C,E,A).
% 1.94/2.16 ** KEPT (pick-wt=19): 83 [] greatest_lower_bound(A,B,C,D)| -member(A,B)| -lower_bound(A,C,B)|member($f16(A,B,C,D),D).
% 1.94/2.16 ** KEPT (pick-wt=20): 84 [] greatest_lower_bound(A,B,C,D)| -member(A,B)| -lower_bound(A,C,B)|lower_bound($f16(A,B,C,D),C,B).
% 1.94/2.16 ** KEPT (pick-wt=20): 85 [] greatest_lower_bound(A,B,C,D)| -member(A,B)| -lower_bound(A,C,B)| -apply(C,$f16(A,B,C,D),A).
% 1.94/2.16 ** KEPT (pick-wt=3): 86 [] $c3!=$c2.
% 1.94/2.16
% 1.94/2.16 ------------> process sos:
% 1.94/2.16 ** KEPT (pick-wt=3): 89 [] A=A.
% 1.94/2.16 ** KEPT (pick-wt=18): 90 [] order(A,B)|member($f1(A,B),B)|member($f3(A,B),B)|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=18): 91 [] order(A,B)|member($f1(A,B),B)|member($f3(A,B),B)|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=18): 92 [] order(A,B)|member($f1(A,B),B)|member($f3(A,B),B)|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=21): 93 [] order(A,B)|member($f1(A,B),B)|member($f3(A,B),B)|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=21): 94 [] order(A,B)|member($f1(A,B),B)|member($f3(A,B),B)|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=18): 95 [] order(A,B)|member($f1(A,B),B)|member($f2(A,B),B)|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=18): 96 [] order(A,B)|member($f1(A,B),B)|member($f2(A,B),B)|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=18): 97 [] order(A,B)|member($f1(A,B),B)|member($f2(A,B),B)|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=21): 98 [] order(A,B)|member($f1(A,B),B)|member($f2(A,B),B)|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=21): 99 [] order(A,B)|member($f1(A,B),B)|member($f2(A,B),B)|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=21): 100 [] order(A,B)|member($f1(A,B),B)|apply(A,$f3(A,B),$f2(A,B))|member($f6(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=21): 101 [] order(A,B)|member($f1(A,B),B)|apply(A,$f3(A,B),$f2(A,B))|member($f5(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=21): 102 [] order(A,B)|member($f1(A,B),B)|apply(A,$f3(A,B),$f2(A,B))|member($f4(A,B),B).
% 1.94/2.16 ** KEPT (pick-wt=24): 103 [] order(A,B)|member($f1(A,B),B)|apply(A,$f3(A,B),$f2(A,B))|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=24): 104 [] order(A,B)|member($f1(A,B),B)|apply(A,$f3(A,B),$f2(A,B))|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.16 ** KEPT (pick-wt=21): 105 [] order(A,B)|member($f1(A,B),B)|apply(A,$f2(A,B),$f3(A,B))|member($f6(A,B),B).
% 1.94/2.19 ** KEPT (pick-wt=21): 106 [] order(A,B)|member($f1(A,B),B)|apply(A,$f2(A,B),$f3(A,B))|member($f5(A,B),B).
% 1.94/2.19 ** KEPT (pick-wt=21): 107 [] order(A,B)|member($f1(A,B),B)|apply(A,$f2(A,B),$f3(A,B))|member($f4(A,B),B).
% 1.94/2.19 ** KEPT (pick-wt=24): 108 [] order(A,B)|member($f1(A,B),B)|apply(A,$f2(A,B),$f3(A,B))|apply(A,$f6(A,B),$f5(A,B)).
% 1.94/2.19 ** KEPT (pick-wt=24): 109 [] order(A,B)|member($f1(A,B),B)|apply(A,$f2(A,B),$f3(A,B))|apply(A,$f5(A,B),$f4(A,B)).
% 1.94/2.19 ** KEPT (pick-wt=10): 110 [] upper_bound(A,B,C)|member($f9(B,C,A),C).
% 1.94/2.19 ** KEPT (pick-wt=10): 111 [] lower_bound(A,B,C)|member($f10(B,C,A),C).
% 1.94/2.19 ** KEPT (pick-wt=3): 112 [] order($c5,$c4).
% 1.94/2.19 ** KEPT (pick-wt=4): 113 [] min($c3,$c5,$c4).
% 1.94/2.19 ** KEPT (pick-wt=4): 114 [] min($c2,$c5,$c4).
% 1.94/2.19 ** KEPT (pick-wt=4): 115 [] least($c1,$c5,$c4).
% 1.94/2.19 Following clause subsumed by 89 during input processing: 0 [copy,89,flip.1] A=A.
% 1.94/2.19 89 back subsumes 87.
% 1.94/2.19
% 1.94/2.19 ======= end of input processing =======
% 1.94/2.19
% 1.94/2.19 =========== start of search ===========
% 1.94/2.19
% 1.94/2.19 -------- PROOF --------
% 1.94/2.19
% 1.94/2.19 ----> UNIT CONFLICT at 0.04 sec ----> 337 [binary,335.1,298.1] $F.
% 1.94/2.19
% 1.94/2.19 Length of proof is 8. Level of proof is 4.
% 1.94/2.19
% 1.94/2.19 ---------------- PROOF ----------------
% 1.94/2.19 % SZS status Theorem
% 1.94/2.19 % SZS output start Refutation
% See solution above
% 1.94/2.19 ------------ end of proof -------------
% 1.94/2.19
% 1.94/2.19
% 1.94/2.19 Search stopped by max_proofs option.
% 1.94/2.19
% 1.94/2.19
% 1.94/2.19 Search stopped by max_proofs option.
% 1.94/2.19
% 1.94/2.19 ============ end of search ============
% 1.94/2.19
% 1.94/2.19 -------------- statistics -------------
% 1.94/2.19 clauses given 17
% 1.94/2.19 clauses generated 318
% 1.94/2.19 clauses kept 332
% 1.94/2.19 clauses forward subsumed 132
% 1.94/2.19 clauses back subsumed 1
% 1.94/2.19 Kbytes malloced 1953
% 1.94/2.19
% 1.94/2.19 ----------- times (seconds) -----------
% 1.94/2.19 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.94/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.19 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.94/2.19
% 1.94/2.19 That finishes the proof of the theorem.
% 1.94/2.19
% 1.94/2.19 Process 27709 finished Wed Jul 27 10:39:03 2022
% 1.94/2.19 Otter interrupted
% 1.94/2.19 PROOF FOUND
%------------------------------------------------------------------------------