TSTP Solution File: SWW101+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 13:22:00 EDT 2022
% Result : Theorem 2.01s 2.18s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 51 ( 40 unt; 4 nHn; 41 RR)
% Number of literals : 65 ( 40 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ bool(A)
| A = false
| A = true ),
file('SWW101+1.p',unknown),
[] ).
cnf(2,axiom,
( bool(A)
| A != false ),
file('SWW101+1.p',unknown),
[] ).
cnf(3,axiom,
( bool(A)
| A != true ),
file('SWW101+1.p',unknown),
[] ).
cnf(15,axiom,
( forallprefers(A,B)
| A != false
| B != true ),
file('SWW101+1.p',unknown),
[] ).
cnf(25,axiom,
( phi(A) = A
| ~ d(A) ),
file('SWW101+1.p',unknown),
[] ).
cnf(27,axiom,
( prop(A) = true
| ~ bool(A) ),
file('SWW101+1.p',unknown),
[] ).
cnf(44,axiom,
~ forallprefers(f7(A),f7(dollar_c1)),
file('SWW101+1.p',unknown),
[] ).
cnf(45,axiom,
false1 != false2,
file('SWW101+1.p',unknown),
[] ).
cnf(46,plain,
false2 != false1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[45])]),
[iquote('copy,45,flip.1')] ).
cnf(47,axiom,
A = A,
file('SWW101+1.p',unknown),
[] ).
cnf(48,axiom,
d(true),
file('SWW101+1.p',unknown),
[] ).
cnf(49,axiom,
d(false),
file('SWW101+1.p',unknown),
[] ).
cnf(53,axiom,
( prop(A) = false
| bool(A) ),
file('SWW101+1.p',unknown),
[] ).
cnf(57,axiom,
lazy_impl(false,A) = true,
file('SWW101+1.p',unknown),
[] ).
cnf(58,axiom,
lazy_impl(true,A) = phi(A),
file('SWW101+1.p',unknown),
[] ).
cnf(60,plain,
phi(A) = lazy_impl(true,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[58])]),
[iquote('copy,58,flip.1')] ).
cnf(73,axiom,
lazy_and1(true,A) = phi(A),
file('SWW101+1.p',unknown),
[] ).
cnf(75,plain,
lazy_impl(true,A) = lazy_and1(true,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[73]),60])]),
[iquote('copy,73,demod,60,flip.1')] ).
cnf(106,axiom,
false1 = false,
file('SWW101+1.p',unknown),
[] ).
cnf(107,axiom,
f7(A) = lazy_impl(prop(A),A),
file('SWW101+1.p',unknown),
[] ).
cnf(108,plain,
lazy_impl(prop(A),A) = f7(A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[107])]),
[iquote('copy,107,flip.1')] ).
cnf(110,axiom,
false2 = phi(f7(dollar_c1)),
file('SWW101+1.p',unknown),
[] ).
cnf(111,plain,
lazy_and1(true,f7(dollar_c1)) = false2,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[110]),60,75])]),
[iquote('copy,110,demod,60,75,flip.1')] ).
cnf(130,plain,
( lazy_and1(true,A) = A
| ~ d(A) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),60,75]),
[iquote('back_demod,25,demod,60,75')] ).
cnf(137,plain,
false2 != false,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[46]),106]),
[iquote('back_demod,46,demod,106')] ).
cnf(139,plain,
forallprefers(false,true),
inference(hyper,[status(thm)],[47,15,47]),
[iquote('hyper,47,15,47')] ).
cnf(140,plain,
bool(true),
inference(hyper,[status(thm)],[47,3]),
[iquote('hyper,47,3')] ).
cnf(141,plain,
bool(false),
inference(hyper,[status(thm)],[47,2]),
[iquote('hyper,47,2')] ).
cnf(160,plain,
prop(true) = true,
inference(hyper,[status(thm)],[140,27]),
[iquote('hyper,140,27')] ).
cnf(193,plain,
prop(false) = true,
inference(hyper,[status(thm)],[141,27]),
[iquote('hyper,141,27')] ).
cnf(962,plain,
f7(false) = lazy_and1(true,false),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[108,193]),75])]),
[iquote('para_into,108.1.1.1,193.1.1,demod,75,flip.1')] ).
cnf(963,plain,
f7(true) = lazy_and1(true,true),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[108,160]),75])]),
[iquote('para_into,108.1.1.1,160.1.1,demod,75,flip.1')] ).
cnf(965,plain,
( f7(A) = true
| bool(A) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[108,53]),57])]),
[iquote('para_into,108.1.1.1,53.1.1,demod,57,flip.1')] ).
cnf(1003,plain,
( lazy_and1(true,lazy_and1(true,false)) = false2
| ~ bool(dollar_c1)
| true = dollar_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[111,1]),962])]),
[iquote('para_into,111.1.1.2.1,1.2.1,demod,962,flip.3')] ).
cnf(1078,plain,
~ forallprefers(lazy_and1(true,false),f7(dollar_c1)),
inference(para_from,[status(thm),theory(equality)],[962,44]),
[iquote('para_from,961.1.1,44.1.1')] ).
cnf(1093,plain,
lazy_and1(true,false) = false,
inference(hyper,[status(thm)],[130,49]),
[iquote('hyper,130,49')] ).
cnf(1095,plain,
lazy_and1(true,true) = true,
inference(hyper,[status(thm)],[130,48]),
[iquote('hyper,130,48')] ).
cnf(1096,plain,
~ forallprefers(false,f7(dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1078]),1093]),
[iquote('back_demod,1078,demod,1093')] ).
cnf(1100,plain,
( ~ bool(dollar_c1)
| true = dollar_c1 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1003]),1093,1093]),137]),
[iquote('back_demod,1003,demod,1093,1093,unit_del,137')] ).
cnf(1110,plain,
f7(true) = true,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[963]),1095]),
[iquote('back_demod,963,demod,1095')] ).
cnf(1120,plain,
bool(dollar_c1),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1096,965]),139]),
[iquote('para_into,1096.1.2,965.1.1,unit_del,139')] ).
cnf(1136,plain,
prop(dollar_c1) = true,
inference(hyper,[status(thm)],[1120,27]),
[iquote('hyper,1120,27')] ).
cnf(1150,plain,
f7(dollar_c1) = lazy_and1(true,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1136,108]),75])]),
[iquote('para_from,1136.1.1,108.1.1.1,demod,75,flip.1')] ).
cnf(1153,plain,
~ forallprefers(false,lazy_and1(true,dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1096]),1150]),
[iquote('back_demod,1096,demod,1150')] ).
cnf(1166,plain,
true = dollar_c1,
inference(hyper,[status(thm)],[1100,1120]),
[iquote('hyper,1100,1120')] ).
cnf(1177,plain,
~ forallprefers(false,lazy_and1(dollar_c1,dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1153]),1166]),
[iquote('back_demod,1153,demod,1166')] ).
cnf(1181,plain,
f7(dollar_c1) = lazy_and1(dollar_c1,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1150]),1166]),
[iquote('back_demod,1149,demod,1166')] ).
cnf(1197,plain,
lazy_and1(dollar_c1,dollar_c1) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1110]),1166,1181,1166]),
[iquote('back_demod,1110,demod,1166,1181,1166')] ).
cnf(1264,plain,
forallprefers(false,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[139]),1166]),
[iquote('back_demod,139,demod,1166')] ).
cnf(1292,plain,
~ forallprefers(false,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1177]),1197]),
[iquote('back_demod,1177,demod,1197')] ).
cnf(1293,plain,
$false,
inference(binary,[status(thm)],[1292,1264]),
[iquote('binary,1292.1,1264.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 02:52:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.94 ----- Otter 3.3f, August 2004 -----
% 1.74/1.94 The process was started by sandbox2 on n005.cluster.edu,
% 1.74/1.94 Wed Jul 27 02:52:35 2022
% 1.74/1.94 The command was "./otter". The process ID is 10450.
% 1.74/1.94
% 1.74/1.94 set(prolog_style_variables).
% 1.74/1.94 set(auto).
% 1.74/1.94 dependent: set(auto1).
% 1.74/1.94 dependent: set(process_input).
% 1.74/1.94 dependent: clear(print_kept).
% 1.74/1.94 dependent: clear(print_new_demod).
% 1.74/1.94 dependent: clear(print_back_demod).
% 1.74/1.94 dependent: clear(print_back_sub).
% 1.74/1.94 dependent: set(control_memory).
% 1.74/1.94 dependent: assign(max_mem, 12000).
% 1.74/1.94 dependent: assign(pick_given_ratio, 4).
% 1.74/1.94 dependent: assign(stats_level, 1).
% 1.74/1.94 dependent: assign(max_seconds, 10800).
% 1.74/1.94 clear(print_given).
% 1.74/1.94
% 1.74/1.94 formula_list(usable).
% 1.74/1.94 all A (A=A).
% 1.74/1.94 all X (bool(X)<->X=false|X=true).
% 1.74/1.94 true!=false.
% 1.74/1.94 true!=err.
% 1.74/1.94 false!=err.
% 1.74/1.94 d(true).
% 1.74/1.94 d(false).
% 1.74/1.94 d(err).
% 1.74/1.94 all X Y (forallprefers(X,Y)<-> -d(X)&d(Y)|d(X)&d(Y)& -bool(X)&bool(Y)|X=false&Y=true).
% 1.74/1.94 all X Y (existsprefers(X,Y)<-> -d(X)&d(Y)|d(X)&d(Y)& -bool(X)&bool(Y)|X=true&Y=false).
% 1.74/1.94 all X (d(X)&phi(X)=X| -d(X)&phi(X)=err).
% 1.74/1.94 all X (prop(X)=true<->bool(X)).
% 1.74/1.94 all X (prop(X)=false<-> -bool(X)).
% 1.74/1.94 all A B (-bool(A)->impl(A,B)=phi(A)).
% 1.74/1.94 all A B (bool(A)& -bool(B)->impl(A,B)=phi(B)).
% 1.74/1.94 all B (bool(B)->impl(false,B)=true).
% 1.74/1.94 all B (bool(B)->impl(true,B)=B).
% 1.74/1.94 all A B (-bool(A)->lazy_impl(A,B)=phi(A)).
% 1.74/1.94 all B (lazy_impl(false,B)=true).
% 1.74/1.94 all B (lazy_impl(true,B)=phi(B)).
% 1.74/1.94 all A B (-bool(A)->and1(A,B)=phi(A)).
% 1.74/1.94 all A B (bool(A)& -bool(B)->and1(A,B)=phi(B)).
% 1.74/1.94 all B (bool(B)->and1(false,B)=false).
% 1.74/1.94 all B (bool(B)->and1(true,B)=B).
% 1.74/1.94 all P Q R (f1(P,Q,R)=lazy_impl(prop(R),impl(impl(P,impl(Q,R)),R))).
% 1.74/1.94 all P Q exists R (and2(P,Q)=phi(f1(P,Q,R))& -(exists R1 forallprefers(f1(P,Q,R1),f1(P,Q,R)))).
% 1.74/1.94 all A B (-bool(A)->lazy_and1(A,B)=phi(A)).
% 1.74/1.94 all B (lazy_and1(false,B)=false).
% 1.74/1.94 all B (lazy_and1(true,B)=phi(B)).
% 1.74/1.94 all P Q R (f2(P,Q,R)=lazy_impl(prop(R),impl(lazy_impl(P,impl(Q,R)),R))).
% 1.74/1.94 all P Q exists R (lazy_and2(P,Q)=phi(f2(P,Q,R))& -(exists R1 forallprefers(f2(P,Q,R1),f2(P,Q,R)))).
% 1.74/1.94 all A B (-bool(A)->or1(A,B)=phi(A)).
% 1.74/1.94 all A B (bool(A)& -bool(B)->or1(A,B)=phi(B)).
% 1.74/1.94 all B (bool(B)->or1(true,B)=true).
% 1.74/1.94 all B (bool(B)->or1(false,B)=B).
% 1.74/1.94 all P Q R (f3(P,Q,R)=lazy_impl(prop(R),impl(impl(P,R),impl(impl(Q,R),R)))).
% 1.74/1.94 all P Q exists R (or2(P,Q)=phi(f3(P,Q,R))& -(exists R1 forallprefers(f3(P,Q,R1),f3(P,Q,R)))).
% 1.74/1.94 all P exists X (exists1(P)=phi(apply(P,X))& -(exists X1 existsprefers(apply(P,X1),apply(P,X)))).
% 1.74/1.94 all P X R (f4(P,X,R)=impl(apply(P,X),R)).
% 1.74/1.94 all P R exists X (f5(P,R)=phi(f4(P,X,R))& -(exists X1 forallprefers(f4(P,X1,R),f4(P,X,R)))).
% 1.74/1.94 all P R (f6(P,R)=lazy_impl(prop(R),impl(f5(P,R),R))).
% 1.74/1.94 all P exists R (exists2(P)=phi(f6(P,R))& -(exists R1 forallprefers(f6(P,R1),f6(P,R)))).
% 1.74/1.94 false1=false.
% 1.74/1.94 all P (f7(P)=lazy_impl(prop(P),P)).
% 1.74/1.94 exists P (false2=phi(f7(P))& -(exists P1 forallprefers(f7(P1),f7(P)))).
% 1.74/1.94 all A (-bool(A)->not1(A)=phi(A)).
% 1.74/1.94 not1(false)=true.
% 1.74/1.94 not1(true)=false.
% 1.74/1.94 all P (not2(P)=impl(P,false2)).
% 1.74/1.94 false1!=false2.
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 -------> usable clausifies to:
% 1.74/1.94
% 1.74/1.94 list(usable).
% 1.74/1.94 0 [] A=A.
% 1.74/1.94 0 [] -bool(X)|X=false|X=true.
% 1.74/1.94 0 [] bool(X)|X!=false.
% 1.74/1.94 0 [] bool(X)|X!=true.
% 1.74/1.94 0 [] true!=false.
% 1.74/1.94 0 [] true!=err.
% 1.74/1.94 0 [] false!=err.
% 1.74/1.94 0 [] d(true).
% 1.74/1.94 0 [] d(false).
% 1.74/1.94 0 [] d(err).
% 1.74/1.94 0 [] -forallprefers(X,Y)| -d(X)| -bool(X)|X=false.
% 1.74/1.94 0 [] -forallprefers(X,Y)| -d(X)| -bool(X)|Y=true.
% 1.74/1.94 0 [] -forallprefers(X,Y)| -d(X)|bool(Y)|X=false.
% 1.74/1.94 0 [] -forallprefers(X,Y)| -d(X)|bool(Y)|Y=true.
% 1.74/1.94 0 [] -forallprefers(X,Y)|d(Y)|X=false.
% 1.74/1.94 0 [] -forallprefers(X,Y)|d(Y)|Y=true.
% 1.74/1.94 0 [] forallprefers(X,Y)|d(X)| -d(Y).
% 1.74/1.94 0 [] forallprefers(X,Y)| -d(X)| -d(Y)|bool(X)| -bool(Y).
% 1.74/1.94 0 [] forallprefers(X,Y)|X!=false|Y!=true.
% 1.74/1.94 0 [] -existsprefers(X,Y)| -d(X)| -bool(X)|X=true.
% 1.74/1.94 0 [] -existsprefers(X,Y)| -d(X)| -bool(X)|Y=false.
% 1.74/1.94 0 [] -existsprefers(X,Y)| -d(X)|bool(Y)|X=true.
% 1.74/1.94 0 [] -existsprefers(X,Y)| -d(X)|bool(Y)|Y=false.
% 1.74/1.94 0 [] -existsprefers(X,Y)|d(Y)|X=true.
% 1.74/1.94 0 [] -existsprefers(X,Y)|d(Y)|Y=false.
% 1.74/1.94 0 [] existsprefers(X,Y)|d(X)| -d(Y).
% 1.74/1.94 0 [] existsprefers(X,Y)| -d(X)| -d(Y)|bool(X)| -bool(Y).
% 1.74/1.94 0 [] existsprefers(X,Y)|X!=true|Y!=false.
% 1.74/1.94 0 [] d(X)|phi(X)=err.
% 1.74/1.94 0 [] phi(X)=X| -d(X).
% 1.74/1.94 0 [] phi(X)=X|phi(X)=err.
% 1.74/1.94 0 [] prop(X)!=true|bool(X).
% 1.74/1.94 0 [] prop(X)=true| -bool(X).
% 1.74/1.94 0 [] prop(X)!=false| -bool(X).
% 1.74/1.94 0 [] prop(X)=false|bool(X).
% 1.74/1.94 0 [] bool(A)|impl(A,B)=phi(A).
% 1.74/1.94 0 [] -bool(A)|bool(B)|impl(A,B)=phi(B).
% 1.74/1.94 0 [] -bool(B)|impl(false,B)=true.
% 1.74/1.94 0 [] -bool(B)|impl(true,B)=B.
% 1.74/1.94 0 [] bool(A)|lazy_impl(A,B)=phi(A).
% 1.74/1.94 0 [] lazy_impl(false,B)=true.
% 1.74/1.94 0 [] lazy_impl(true,B)=phi(B).
% 1.74/1.94 0 [] bool(A)|and1(A,B)=phi(A).
% 1.74/1.94 0 [] -bool(A)|bool(B)|and1(A,B)=phi(B).
% 1.74/1.94 0 [] -bool(B)|and1(false,B)=false.
% 1.74/1.94 0 [] -bool(B)|and1(true,B)=B.
% 1.74/1.94 0 [] f1(P,Q,R)=lazy_impl(prop(R),impl(impl(P,impl(Q,R)),R)).
% 1.74/1.94 0 [] and2(P,Q)=phi(f1(P,Q,$f1(P,Q))).
% 1.74/1.94 0 [] -forallprefers(f1(P,Q,R1),f1(P,Q,$f1(P,Q))).
% 1.74/1.94 0 [] bool(A)|lazy_and1(A,B)=phi(A).
% 1.74/1.94 0 [] lazy_and1(false,B)=false.
% 1.74/1.94 0 [] lazy_and1(true,B)=phi(B).
% 1.74/1.94 0 [] f2(P,Q,R)=lazy_impl(prop(R),impl(lazy_impl(P,impl(Q,R)),R)).
% 1.74/1.94 0 [] lazy_and2(P,Q)=phi(f2(P,Q,$f2(P,Q))).
% 1.74/1.94 0 [] -forallprefers(f2(P,Q,R1),f2(P,Q,$f2(P,Q))).
% 1.74/1.94 0 [] bool(A)|or1(A,B)=phi(A).
% 1.74/1.94 0 [] -bool(A)|bool(B)|or1(A,B)=phi(B).
% 1.74/1.94 0 [] -bool(B)|or1(true,B)=true.
% 1.74/1.94 0 [] -bool(B)|or1(false,B)=B.
% 1.74/1.94 0 [] f3(P,Q,R)=lazy_impl(prop(R),impl(impl(P,R),impl(impl(Q,R),R))).
% 1.74/1.94 0 [] or2(P,Q)=phi(f3(P,Q,$f3(P,Q))).
% 1.74/1.94 0 [] -forallprefers(f3(P,Q,R1),f3(P,Q,$f3(P,Q))).
% 1.74/1.94 0 [] exists1(P)=phi(apply(P,$f4(P))).
% 1.74/1.94 0 [] -existsprefers(apply(P,X1),apply(P,$f4(P))).
% 1.74/1.94 0 [] f4(P,X,R)=impl(apply(P,X),R).
% 1.74/1.94 0 [] f5(P,R)=phi(f4(P,$f5(P,R),R)).
% 1.74/1.94 0 [] -forallprefers(f4(P,X1,R),f4(P,$f5(P,R),R)).
% 1.74/1.94 0 [] f6(P,R)=lazy_impl(prop(R),impl(f5(P,R),R)).
% 1.74/1.94 0 [] exists2(P)=phi(f6(P,$f6(P))).
% 1.74/1.94 0 [] -forallprefers(f6(P,R1),f6(P,$f6(P))).
% 1.74/1.94 0 [] false1=false.
% 1.74/1.94 0 [] f7(P)=lazy_impl(prop(P),P).
% 1.74/1.94 0 [] false2=phi(f7($c1)).
% 1.74/1.94 0 [] -forallprefers(f7(P1),f7($c1)).
% 1.74/1.94 0 [] bool(A)|not1(A)=phi(A).
% 1.74/1.94 0 [] not1(false)=true.
% 1.74/1.94 0 [] not1(true)=false.
% 1.74/1.94 0 [] not2(P)=impl(P,false2).
% 1.74/1.94 0 [] false1!=false2.
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.74/1.94
% 1.74/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.94 deletion, with positive clauses in sos and nonpositive
% 1.74/1.94 clauses in usable.
% 1.74/1.94
% 1.74/1.94 dependent: set(knuth_bendix).
% 1.74/1.94 dependent: set(anl_eq).
% 1.74/1.94 dependent: set(para_from).
% 1.74/1.94 dependent: set(para_into).
% 1.74/1.94 dependent: clear(para_from_right).
% 1.74/1.94 dependent: clear(para_into_right).
% 1.74/1.94 dependent: set(para_from_vars).
% 1.74/1.94 dependent: set(eq_units_both_ways).
% 1.74/1.94 dependent: set(dynamic_demod_all).
% 1.74/1.94 dependent: set(dynamic_demod).
% 1.74/1.94 dependent: set(order_eq).
% 1.74/1.94 dependent: set(back_demod).
% 1.74/1.94 dependent: set(lrpo).
% 1.74/1.94 dependent: set(hyper_res).
% 1.74/1.94 dependent: set(unit_deletion).
% 1.74/1.94 dependent: set(factor).
% 1.74/1.94
% 1.74/1.94 ------------> process usable:
% 1.74/1.94 ** KEPT (pick-wt=8): 1 [] -bool(A)|A=false|A=true.
% 1.74/1.94 ** KEPT (pick-wt=5): 2 [] bool(A)|A!=false.
% 1.74/1.94 ** KEPT (pick-wt=5): 3 [] bool(A)|A!=true.
% 1.74/1.94 ** KEPT (pick-wt=3): 4 [] true!=false.
% 1.74/1.94 ** KEPT (pick-wt=3): 5 [] true!=err.
% 1.74/1.94 ** KEPT (pick-wt=3): 6 [] false!=err.
% 1.74/1.94 ** KEPT (pick-wt=10): 7 [] -forallprefers(A,B)| -d(A)| -bool(A)|A=false.
% 1.74/1.94 ** KEPT (pick-wt=10): 8 [] -forallprefers(A,B)| -d(A)| -bool(A)|B=true.
% 1.74/1.94 ** KEPT (pick-wt=10): 9 [] -forallprefers(A,B)| -d(A)|bool(B)|A=false.
% 1.74/1.94 ** KEPT (pick-wt=10): 10 [] -forallprefers(A,B)| -d(A)|bool(B)|B=true.
% 1.74/1.94 ** KEPT (pick-wt=8): 11 [] -forallprefers(A,B)|d(B)|A=false.
% 1.74/1.94 ** KEPT (pick-wt=8): 12 [] -forallprefers(A,B)|d(B)|B=true.
% 1.74/1.94 ** KEPT (pick-wt=7): 13 [] forallprefers(A,B)|d(A)| -d(B).
% 1.74/1.94 ** KEPT (pick-wt=11): 14 [] forallprefers(A,B)| -d(A)| -d(B)|bool(A)| -bool(B).
% 1.74/1.94 ** KEPT (pick-wt=9): 15 [] forallprefers(A,B)|A!=false|B!=true.
% 1.74/1.94 ** KEPT (pick-wt=10): 16 [] -existsprefers(A,B)| -d(A)| -bool(A)|A=true.
% 1.74/1.94 ** KEPT (pick-wt=10): 17 [] -existsprefers(A,B)| -d(A)| -bool(A)|B=false.
% 1.74/1.94 ** KEPT (pick-wt=10): 18 [] -existsprefers(A,B)| -d(A)|bool(B)|A=true.
% 1.74/1.94 ** KEPT (pick-wt=10): 19 [] -existsprefers(A,B)| -d(A)|bool(B)|B=false.
% 1.74/1.94 ** KEPT (pick-wt=8): 20 [] -existsprefers(A,B)|d(B)|A=true.
% 1.74/1.94 ** KEPT (pick-wt=8): 21 [] -existsprefers(A,B)|d(B)|B=false.
% 1.74/1.94 ** KEPT (pick-wt=7): 22 [] existsprefers(A,B)|d(A)| -d(B).
% 1.74/1.94 ** KEPT (pick-wt=11): 23 [] existsprefers(A,B)| -d(A)| -d(B)|bool(A)| -bool(B).
% 1.74/1.94 ** KEPT (pick-wt=9): 24 [] existsprefers(A,B)|A!=true|B!=false.
% 1.74/1.94 ** KEPT (pick-wt=6): 25 [] phi(A)=A| -d(A).
% 1.74/1.94 ** KEPT (pick-wt=6): 26 [] prop(A)!=true|bool(A).
% 1.74/1.94 ** KEPT (pick-wt=6): 27 [] prop(A)=true| -bool(A).
% 1.74/1.94 ** KEPT (pick-wt=6): 28 [] prop(A)!=false| -bool(A).
% 1.74/1.94 ** KEPT (pick-wt=10): 29 [] -bool(A)|bool(B)|impl(A,B)=phi(B).
% 1.74/1.94 ** KEPT (pick-wt=7): 30 [] -bool(A)|impl(false,A)=true.
% 1.74/1.94 ** KEPT (pick-wt=7): 31 [] -bool(A)|impl(true,A)=A.
% 1.74/1.94 ** KEPT (pick-wt=10): 32 [] -bool(A)|bool(B)|and1(A,B)=phi(B).
% 1.74/1.94 ** KEPT (pick-wt=7): 33 [] -bool(A)|and1(false,A)=false.
% 1.74/1.94 ** KEPT (pick-wt=7): 34 [] -bool(A)|and1(true,A)=A.
% 1.74/1.94 ** KEPT (pick-wt=11): 35 [] -forallprefers(f1(A,B,C),f1(A,B,$f1(A,B))).
% 1.74/1.94 ** KEPT (pick-wt=11): 36 [] -forallprefers(f2(A,B,C),f2(A,B,$f2(A,B))).
% 1.74/1.94 ** KEPT (pick-wt=10): 37 [] -bool(A)|bool(B)|or1(A,B)=phi(B).
% 1.74/1.94 ** KEPT (pick-wt=7): 38 [] -bool(A)|or1(true,A)=true.
% 1.74/1.94 ** KEPT (pick-wt=7): 39 [] -bool(A)|or1(false,A)=A.
% 1.74/1.94 ** KEPT (pick-wt=11): 40 [] -forallprefers(f3(A,B,C),f3(A,B,$f3(A,B))).
% 1.74/1.94 ** KEPT (pick-wt=8): 41 [] -existsprefers(apply(A,B),apply(A,$f4(A))).
% 1.74/1.94 ** KEPT (pick-wt=11): 42 [] -forallprefers(f4(A,B,C),f4(A,$f5(A,C),C)).
% 1.74/1.94 ** KEPT (pick-wt=8): 43 [] -forallprefers(f6(A,B),f6(A,$f6(A))).
% 1.74/1.94 ** KEPT (pick-wt=5): 44 [] -forallprefers(f7(A),f7($c1)).
% 1.74/1.94 ** KEPT (pick-wt=3): 46 [copy,45,flip.1] false2!=false1.
% 1.74/1.94
% 1.74/1.94 ------------> process sos:
% 1.74/1.94 ** KEPT (pick-wt=3): 47 [] A=A.
% 1.74/1.94 ** KEPT (pick-wt=2): 48 [] d(true).
% 1.74/1.94 ** KEPT (pick-wt=2): 49 [] d(false).
% 1.74/1.94 ** KEPT (pick-wt=2): 50 [] d(err).
% 1.74/1.94 ** KEPT (pick-wt=6): 51 [] d(A)|phi(A)=err.
% 1.74/1.94 ** KEPT (pick-wt=8): 52 [] phi(A)=A|phi(A)=err.
% 1.74/1.94 ** KEPT (pick-wt=6): 53 [] prop(A)=false|bool(A).
% 1.74/1.94 ** KEPT (pick-wt=8): 54 [] bool(A)|impl(A,B)=phi(A).
% 1.74/1.94 ** KEPT (pick-wt=8): 55 [] bool(A)|lazy_impl(A,B)=phi(A).
% 1.74/1.94 ** KEPT (pick-wt=5): 56 [] lazy_impl(false,A)=true.
% 1.74/1.94 ---> New Demodulator: 57 [new_demod,56] lazy_impl(false,A)=true.
% 1.74/1.94 ** KEPT (pick-wt=6): 59 [copy,58,flip.1] phi(A)=lazy_impl(true,A).
% 1.74/1.94 ---> New Demodulator: 60 [new_demod,59] phi(A)=lazy_impl(true,A).
% 1.74/1.94 ** KEPT (pick-wt=9): 62 [copy,61,demod,60] bool(A)|and1(A,B)=lazy_impl(true,A).
% 1.74/1.94 ** KEPT (pick-wt=15): 64 [copy,63,flip.1] lazy_impl(prop(A),impl(impl(B,impl(C,A)),A))=f1(B,C,A).
% 1.74/1.94 ---> New Demodulator: 65 [new_demod,64] lazy_impl(prop(A),impl(impl(B,impl(C,A)),A))=f1(B,C,A).
% 1.74/1.94 ** KEPT (pick-wt=12): 67 [copy,66,demod,60,flip.1] lazy_impl(true,f1(A,B,$f1(A,B)))=and2(A,B).
% 1.74/1.94 ---> New Demodulator: 68 [new_demod,67] lazy_impl(true,f1(A,B,$f1(A,B)))=and2(A,B).
% 1.74/1.94 ** KEPT (pick-wt=9): 70 [copy,69,demod,60] bool(A)|lazy_and1(A,B)=lazy_impl(true,A).
% 1.74/1.94 ** KEPT (pick-wt=5): 71 [] lazy_and1(false,A)=false.
% 1.74/1.94 ---> New Demodulator: 72 [new_demod,71] lazy_and1(false,A)=false.
% 1.74/1.94 ** KEPT (pick-wt=7): 74 [copy,73,demod,60,flip.1] lazy_impl(true,A)=lazy_and1(true,A).
% 1.74/1.94 ---> New Demodulator: 75 [new_demod,74] lazy_impl(true,A)=lazy_and1(true,A).
% 1.74/1.94 ** KEPT (pick-wt=15): 77 [copy,76,flip.1] lazy_impl(prop(A),impl(lazy_impl(B,impl(C,A)),A))=f2(B,C,A).
% 1.74/1.94 ---> New Demodulator: 78 [new_demod,77] lazy_impl(prop(A),impl(lazy_impl(B,impl(C,A)),A))=f2(B,C,A).
% 1.74/1.94 ** KEPT (pick-wt=12): 80 [copy,79,demod,60,75] lazy_and2(A,B)=lazy_and1(true,f2(A,B,$f2(A,B))).
% 1.74/1.94 ---> New Demodulator: 81 [new_demod,80] lazy_and2(A,B)=lazy_and1(true,f2(A,B,$f2(A,B))).
% 1.74/1.94 ** KEPT (pick-wt=9): 83 [copy,82,demod,60,75] bool(A)|or1(A,B)=lazy_and1(true,A).
% 1.74/1.94 ** KEPT (pick-wt=17): 85 [copy,84,flip.1] lazy_impl(prop(A),impl(impl(B,A),impl(impl(C,A),A)))=f3(B,C,A).
% 1.74/1.94 ---> New Demodulator: 86 [new_demod,85] lazy_impl(prop(A),impl(impl(B,A),impl(impl(C,A),A)))=f3(B,C,A).
% 1.74/1.94 ** KEPT (pick-wt=12): 88 [copy,87,demod,60,75] or2(A,B)=lazy_and1(true,f3(A,B,$f3(A,B))).
% 1.74/1.94 ---> New Demodulator: 89 [new_demod,88] or2(A,B)=lazy_and1(true,f3(A,B,$f3(A,B))).
% 1.74/1.94 ** KEPT (pick-wt=9): 91 [copy,90,demod,60,75] exists1(A)=lazy_and1(true,apply(A,$f4(A))).
% 1.74/1.94 ---> New Demodulator: 92 [new_demod,91] exists1(A)=lazy_and1(true,apply(A,$f4(A))).
% 1.74/1.94 ** KEPT (pick-wt=10): 94 [copy,93,flip.1] impl(apply(A,B),C)=f4(A,B,C).
% 1.74/1.94 ---> New Demodulator: 95 [new_demod,94] impl(apply(A,B),C)=f4(A,B,C).
% 1.74/1.94 ** KEPT (pick-wt=12): 97 [copy,96,demod,60,75,flip.1] lazy_and1(true,f4(A,$f5(A,B),B))=f5(A,B).
% 1.74/1.94 ---> New Demodulator: 98 [new_demod,97] lazy_and1(true,f4(A,$f5(A,B),B))=f5(A,B).
% 1.74/1.94 ** KEPT (pick-wt=12): 100 [copy,99,flip.1] lazy_impl(prop(A),impl(f5(B,A),A))=f6(B,A).
% 1.74/1.94 ---> New Demodulator: 101 [new_demod,100] lazy_impl(prop(A),impl(f5(B,A),A))=f6(B,A).
% 2.01/2.18 ** KEPT (pick-wt=9): 103 [copy,102,demod,60,75] exists2(A)=lazy_and1(true,f6(A,$f6(A))).
% 2.01/2.18 ---> New Demodulator: 104 [new_demod,103] exists2(A)=lazy_and1(true,f6(A,$f6(A))).
% 2.01/2.18 ** KEPT (pick-wt=3): 105 [] false1=false.
% 2.01/2.18 ---> New Demodulator: 106 [new_demod,105] false1=false.
% 2.01/2.18 ** KEPT (pick-wt=7): 108 [copy,107,flip.1] lazy_impl(prop(A),A)=f7(A).
% 2.01/2.18 ---> New Demodulator: 109 [new_demod,108] lazy_impl(prop(A),A)=f7(A).
% 2.01/2.18 ** KEPT (pick-wt=6): 111 [copy,110,demod,60,75,flip.1] lazy_and1(true,f7($c1))=false2.
% 2.01/2.18 ---> New Demodulator: 112 [new_demod,111] lazy_and1(true,f7($c1))=false2.
% 2.01/2.18 ** KEPT (pick-wt=8): 114 [copy,113,demod,60,75] bool(A)|not1(A)=lazy_and1(true,A).
% 2.01/2.18 ** KEPT (pick-wt=4): 115 [] not1(false)=true.
% 2.01/2.18 ---> New Demodulator: 116 [new_demod,115] not1(false)=true.
% 2.01/2.18 ** KEPT (pick-wt=4): 117 [] not1(true)=false.
% 2.01/2.18 ---> New Demodulator: 118 [new_demod,117] not1(true)=false.
% 2.01/2.18 ** KEPT (pick-wt=6): 119 [] not2(A)=impl(A,false2).
% 2.01/2.18 ---> New Demodulator: 120 [new_demod,119] not2(A)=impl(A,false2).
% 2.01/2.18 Following clause subsumed by 47 during input processing: 0 [copy,47,flip.1] A=A.
% 2.01/2.18 >>>> Starting back demodulation with 57.
% 2.01/2.18 >>>> Starting back demodulation with 60.
% 2.01/2.18 >> back demodulating 55 with 60.
% 2.01/2.18 >> back demodulating 54 with 60.
% 2.01/2.18 >> back demodulating 52 with 60.
% 2.01/2.18 >> back demodulating 51 with 60.
% 2.01/2.18 >> back demodulating 37 with 60.
% 2.01/2.18 >> back demodulating 32 with 60.
% 2.01/2.18 >> back demodulating 29 with 60.
% 2.01/2.18 >> back demodulating 25 with 60.
% 2.01/2.18 >>>> Starting back demodulation with 65.
% 2.01/2.18 >>>> Starting back demodulation with 68.
% 2.01/2.18 >>>> Starting back demodulation with 72.
% 2.01/2.18 >>>> Starting back demodulation with 75.
% 2.01/2.18 >> back demodulating 70 with 75.
% 2.01/2.18 >> back demodulating 67 with 75.
% 2.01/2.18 >> back demodulating 62 with 75.
% 2.01/2.18 >> back demodulating 59 with 75.
% 2.01/2.18 >>>> Starting back demodulation with 78.
% 2.01/2.18 >>>> Starting back demodulation with 81.
% 2.01/2.18 >>>> Starting back demodulation with 86.
% 2.01/2.18 >>>> Starting back demodulation with 89.
% 2.01/2.18 >>>> Starting back demodulation with 92.
% 2.01/2.18 >>>> Starting back demodulation with 95.
% 2.01/2.18 >>>> Starting back demodulation with 98.
% 2.01/2.18 >>>> Starting back demodulation with 101.
% 2.01/2.18 >>>> Starting back demodulation with 104.
% 2.01/2.18 >>>> Starting back demodulation with 106.
% 2.01/2.18 >> back demodulating 46 with 106.
% 2.01/2.18 >>>> Starting back demodulation with 109.
% 2.01/2.18 >>>> Starting back demodulation with 112.
% 2.01/2.18 >>>> Starting back demodulation with 116.
% 2.01/2.18 >>>> Starting back demodulation with 118.
% 2.01/2.18 >>>> Starting back demodulation with 120.
% 2.01/2.18 >>>> Starting back demodulation with 122.
% 2.01/2.18 >>>> Starting back demodulation with 133.
% 2.01/2.18 >>>> Starting back demodulation with 136.
% 2.01/2.18
% 2.01/2.18 ======= end of input processing =======
% 2.01/2.18
% 2.01/2.18 =========== start of search ===========
% 2.01/2.18
% 2.01/2.18
% 2.01/2.18 Resetting weight limit to 7.
% 2.01/2.18
% 2.01/2.18
% 2.01/2.18 Resetting weight limit to 7.
% 2.01/2.18
% 2.01/2.18 sos_size=623
% 2.01/2.18
% 2.01/2.18 -------- PROOF --------
% 2.01/2.18
% 2.01/2.18 ----> UNIT CONFLICT at 0.24 sec ----> 1293 [binary,1292.1,1264.1] $F.
% 2.01/2.18
% 2.01/2.18 Length of proof is 32. Level of proof is 11.
% 2.01/2.18
% 2.01/2.18 ---------------- PROOF ----------------
% 2.01/2.18 % SZS status Theorem
% 2.01/2.18 % SZS output start Refutation
% See solution above
% 2.01/2.18 ------------ end of proof -------------
% 2.01/2.18
% 2.01/2.18
% 2.01/2.18 Search stopped by max_proofs option.
% 2.01/2.18
% 2.01/2.18
% 2.01/2.18 Search stopped by max_proofs option.
% 2.01/2.18
% 2.01/2.18 ============ end of search ============
% 2.01/2.18
% 2.01/2.18 -------------- statistics -------------
% 2.01/2.18 clauses given 135
% 2.01/2.18 clauses generated 16865
% 2.01/2.18 clauses kept 1141
% 2.01/2.18 clauses forward subsumed 6630
% 2.01/2.18 clauses back subsumed 185
% 2.01/2.18 Kbytes malloced 4882
% 2.01/2.18
% 2.01/2.18 ----------- times (seconds) -----------
% 2.01/2.18 user CPU time 0.24 (0 hr, 0 min, 0 sec)
% 2.01/2.18 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.01/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.01/2.18
% 2.01/2.18 That finishes the proof of the theorem.
% 2.01/2.18
% 2.01/2.18 Process 10450 finished Wed Jul 27 02:52:37 2022
% 2.01/2.18 Otter interrupted
% 2.01/2.18 PROOF FOUND
%------------------------------------------------------------------------------