TSTP Solution File: GRP775+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 12:57:48 EDT 2022
% Result : Theorem 27.73s 27.87s
% Output : Refutation 27.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 72 ( 36 unt; 4 nHn; 52 RR)
% Number of literals : 119 ( 48 equ; 47 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ l(A,B)
| product(A,B) = A ),
file('GRP775+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ l(A,B)
| product(B,A) = B ),
file('GRP775+1.p',unknown),
[] ).
cnf(3,axiom,
( l(A,B)
| product(A,B) != A
| product(B,A) != B ),
file('GRP775+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ r(A,B)
| product(A,B) = B ),
file('GRP775+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ r(A,B)
| product(B,A) = A ),
file('GRP775+1.p',unknown),
[] ).
cnf(6,axiom,
( r(A,B)
| product(A,B) != B
| product(B,A) != A ),
file('GRP775+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ d(A,B)
| r(A,dollar_f1(A,B)) ),
file('GRP775+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ d(A,B)
| l(dollar_f1(A,B),B) ),
file('GRP775+1.p',unknown),
[] ).
cnf(9,axiom,
( d(A,B)
| ~ r(A,C)
| ~ l(C,B) ),
file('GRP775+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ d(dollar_c2,dollar_c1)
| product(dollar_c2,product(dollar_c1,dollar_c2)) != dollar_c2
| product(dollar_c1,product(dollar_c2,dollar_c1)) != dollar_c1 ),
file('GRP775+1.p',unknown),
[] ).
cnf(11,plain,
( l(A,A)
| product(A,A) != A ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.2.3')] ).
cnf(12,plain,
( r(A,A)
| product(A,A) != A ),
inference(factor,[status(thm)],[6]),
[iquote('factor,6.2.3')] ).
cnf(13,axiom,
A = A,
file('GRP775+1.p',unknown),
[] ).
cnf(15,axiom,
product(product(A,B),C) = product(A,product(B,C)),
file('GRP775+1.p',unknown),
[] ).
cnf(17,axiom,
product(A,A) = A,
file('GRP775+1.p',unknown),
[] ).
cnf(18,axiom,
( d(dollar_c2,dollar_c1)
| product(dollar_c2,product(dollar_c1,dollar_c2)) = dollar_c2 ),
file('GRP775+1.p',unknown),
[] ).
cnf(19,axiom,
( d(dollar_c2,dollar_c1)
| product(dollar_c1,product(dollar_c2,dollar_c1)) = dollar_c1 ),
file('GRP775+1.p',unknown),
[] ).
cnf(20,plain,
r(A,A),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),17]),13]),
[iquote('back_demod,12,demod,17,unit_del,13')] ).
cnf(21,plain,
l(A,A),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),17]),13]),
[iquote('back_demod,11,demod,17,unit_del,13')] ).
cnf(26,plain,
product(A,product(A,B)) = product(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,17])]),
[iquote('para_into,14.1.1.1,16.1.1,flip.1')] ).
cnf(27,plain,
( product(A,product(B,C)) = product(B,C)
| ~ r(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,5])]),
[iquote('para_into,14.1.1.1,5.2.1,flip.1')] ).
cnf(29,plain,
( product(A,product(B,C)) = product(A,C)
| ~ l(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,2])]),
[iquote('para_into,14.1.1.1,2.2.1,flip.1')] ).
cnf(30,plain,
( product(A,product(B,C)) = product(A,C)
| ~ l(A,B) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,1])]),
[iquote('para_into,14.1.1.1,1.2.1,flip.1')] ).
cnf(32,plain,
product(A,product(B,product(A,B))) = product(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,17])]),
[iquote('para_into,14.1.1,16.1.1,flip.1')] ).
cnf(33,plain,
( product(A,product(B,C)) = C
| ~ r(C,product(A,B)) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,5])]),
[iquote('para_into,14.1.1,5.2.1,flip.1')] ).
cnf(34,plain,
( product(A,product(B,C)) = C
| ~ r(product(A,B),C) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,4])]),
[iquote('para_into,14.1.1,4.2.1,flip.1')] ).
cnf(37,plain,
( r(A,product(B,C))
| product(A,product(B,C)) != product(B,C)
| product(B,product(C,A)) != A ),
inference(para_from,[status(thm),theory(equality)],[15,6]),
[iquote('para_from,14.1.1,6.3.1')] ).
cnf(49,plain,
product(A,product(B,product(A,product(B,C)))) = product(A,product(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,15]),15,15]),
[iquote('para_into,25.1.1.2,14.1.1,demod,15,15')] ).
cnf(52,plain,
( product(A,B) = A
| ~ l(A,product(A,B)) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,1])]),
[iquote('para_into,25.1.1,1.2.1,flip.1')] ).
cnf(53,plain,
( r(product(A,B),A)
| product(A,product(B,A)) != A ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[26,6]),15]),13]),
[iquote('para_from,25.1.1,6.3.1,demod,15,unit_del,13')] ).
cnf(87,plain,
( l(product(dollar_c2,dollar_c1),dollar_c1)
| d(dollar_c2,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[19,3]),15,17]),13,13]),
[iquote('para_from,19.2.1,3.3.1,demod,15,17,unit_del,13,13')] ).
cnf(252,plain,
( product(A,B) = product(A,C)
| ~ l(A,B)
| ~ l(C,B) ),
inference(para_into,[status(thm),theory(equality)],[30,2]),
[iquote('para_into,30.1.1.2,2.2.1')] ).
cnf(270,plain,
( product(A,product(B,C)) = A
| ~ l(A,product(A,C))
| ~ l(A,B) ),
inference(para_from,[status(thm),theory(equality)],[30,52]),
[iquote('para_from,30.1.1,52.2.2')] ).
cnf(383,plain,
( ~ d(dollar_c2,dollar_c1)
| product(dollar_c1,product(dollar_c2,dollar_c1)) != dollar_c1
| ~ r(dollar_c2,product(dollar_c2,dollar_c1)) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[33,10]),13]),
[iquote('para_from,33.1.1,10.2.1,unit_del,13')] ).
cnf(385,plain,
( l(product(A,B),C)
| product(A,product(B,C)) != product(A,B)
| B != C
| ~ r(B,product(C,A)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,3]),15]),
[iquote('para_from,33.1.1,3.3.1,demod,15')] ).
cnf(429,plain,
( product(A,B) = B
| ~ r(product(A,B),B) ),
inference(para_into,[status(thm),theory(equality)],[34,17]),
[iquote('para_into,34.1.1.2,16.1.1')] ).
cnf(459,plain,
( product(A,product(B,C)) = C
| ~ r(A,C)
| ~ l(A,B) ),
inference(para_into,[status(thm),theory(equality)],[34,1]),
[iquote('para_into,34.2.1,1.2.1')] ).
cnf(841,plain,
( r(dollar_c2,product(dollar_c2,dollar_c1))
| d(dollar_c2,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,18]),26]),13,13]),
[iquote('para_into,37.3.1,18.2.1,demod,26,unit_del,13,13')] ).
cnf(872,plain,
d(dollar_c2,dollar_c1),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[841,9,87])])]),
[iquote('hyper,841,9,87,factor_simp,factor_simp')] ).
cnf(947,plain,
l(dollar_f1(dollar_c2,dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[872,8]),
[iquote('hyper,872,8')] ).
cnf(948,plain,
r(dollar_c2,dollar_f1(dollar_c2,dollar_c1)),
inference(hyper,[status(thm)],[872,7]),
[iquote('hyper,872,7')] ).
cnf(951,plain,
product(dollar_c1,product(dollar_f1(dollar_c2,dollar_c1),A)) = product(dollar_c1,A),
inference(hyper,[status(thm)],[947,29]),
[iquote('hyper,947,29')] ).
cnf(955,plain,
product(dollar_c1,dollar_f1(dollar_c2,dollar_c1)) = dollar_c1,
inference(hyper,[status(thm)],[947,2]),
[iquote('hyper,947,2')] ).
cnf(957,plain,
product(dollar_f1(dollar_c2,dollar_c1),dollar_c1) = dollar_f1(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[947,1]),
[iquote('hyper,947,1')] ).
cnf(966,plain,
product(dollar_f1(dollar_c2,dollar_c1),product(dollar_c2,A)) = product(dollar_c2,A),
inference(hyper,[status(thm)],[948,27]),
[iquote('hyper,948,27')] ).
cnf(971,plain,
product(dollar_c2,dollar_f1(dollar_c2,dollar_c1)) = dollar_f1(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[948,4]),
[iquote('hyper,948,4')] ).
cnf(1279,plain,
r(product(A,B),product(A,product(B,A))),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[53,32]),15,15,32,15,17]),13]),
[iquote('para_into,53.2.1.2,31.1.1,demod,15,15,32,15,17,unit_del,13')] ).
cnf(1284,plain,
r(product(A,product(B,A)),product(A,B)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[53,26]),15,17]),13]),
[iquote('para_into,53.2.1.2,25.1.1,demod,15,17,unit_del,13')] ).
cnf(1664,plain,
product(A,product(dollar_c2,product(A,dollar_f1(dollar_c2,dollar_c1)))) = product(A,dollar_f1(dollar_c2,dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[971,49]),971]),
[iquote('para_from,970.1.1,49.1.1.2.2.2,demod,971')] ).
cnf(3417,plain,
( r(A,product(A,B))
| ~ r(product(B,A),A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[429,1284]),17]),
[iquote('para_from,429.1.1,1284.1.1.2,demod,17')] ).
cnf(3721,plain,
( product(dollar_c1,A) = dollar_c1
| ~ l(dollar_f1(dollar_c2,dollar_c1),A) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[951,1]),955])]),
[iquote('para_into,951.1.1.2,1.2.1,demod,955,flip.1')] ).
cnf(3759,plain,
r(product(dollar_c2,A),product(dollar_c2,product(A,dollar_f1(dollar_c2,dollar_c1)))),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[966,3417]),15]),20]),
[iquote('para_from,965.1.1,3417.2.1,demod,15,unit_del,20')] ).
cnf(3910,plain,
( product(A,product(B,A)) = A
| ~ l(A,B) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[270,17]),21]),
[iquote('para_into,270.2.2,16.1.1,unit_del,21')] ).
cnf(4182,plain,
( l(product(A,B),B)
| ~ r(B,product(B,A)) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[385,17]),13,13]),
[iquote('para_into,385.2.1.2,16.1.1,unit_del,13,13')] ).
cnf(4185,plain,
l(product(A,B),product(B,product(A,B))),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4182,32]),15,15,32]),1284]),
[iquote('para_into,4182.1.1,31.1.1,demod,15,15,32,unit_del,1284')] ).
cnf(4196,plain,
d(product(A,B),product(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4185,9,1279]),15,26,32]),
[iquote('hyper,4185,9,1279,demod,15,26,32')] ).
cnf(4211,plain,
( d(A,product(B,A))
| ~ l(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4196,3910]),15,17]),
[iquote('para_into,4196.1.1,3910.1.1,demod,15,17')] ).
cnf(4243,plain,
( d(A,B)
| ~ l(A,B) ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[4211,2])]),
[iquote('para_into,4211.1.2,2.2.1,factor_simp')] ).
cnf(4457,plain,
d(product(dollar_c2,A),product(A,dollar_f1(dollar_c2,dollar_c1))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3759,9,4185]),15,966,1664]),
[iquote('hyper,3759,9,4185,demod,15,966,1664')] ).
cnf(4466,plain,
d(product(dollar_c2,dollar_c1),dollar_c1),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[4457,3721]),21]),
[iquote('para_into,4457.1.2,3721.1.1,unit_del,21')] ).
cnf(4469,plain,
l(dollar_f1(product(dollar_c2,dollar_c1),dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[4466,8]),
[iquote('hyper,4466,8')] ).
cnf(4470,plain,
r(product(dollar_c2,dollar_c1),dollar_f1(product(dollar_c2,dollar_c1),dollar_c1)),
inference(hyper,[status(thm)],[4466,7]),
[iquote('hyper,4466,7')] ).
cnf(4490,plain,
d(dollar_f1(product(dollar_c2,dollar_c1),dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[4469,4243]),
[iquote('hyper,4469,4243')] ).
cnf(4509,plain,
product(dollar_c1,dollar_f1(product(dollar_c2,dollar_c1),dollar_c1)) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4469,252,21]),17])]),
[iquote('hyper,4469,252,21,demod,17,flip.1')] ).
cnf(4511,plain,
l(dollar_f1(dollar_f1(product(dollar_c2,dollar_c1),dollar_c1),dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[4490,8]),
[iquote('hyper,4490,8')] ).
cnf(4528,plain,
dollar_f1(product(dollar_c2,dollar_c1),dollar_c1) = product(dollar_c2,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4470,459,4185]),15,15,4509,15,26,32])]),
[iquote('hyper,4470,459,4185,demod,15,15,4509,15,26,32,flip.1')] ).
cnf(4529,plain,
l(product(dollar_c2,dollar_c1),dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4511]),4528,4528]),
[iquote('back_demod,4511,demod,4528,4528')] ).
cnf(4532,plain,
product(dollar_c1,product(dollar_c2,dollar_c1)) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4509]),4528]),
[iquote('back_demod,4508,demod,4528')] ).
cnf(4539,plain,
~ r(dollar_c2,product(dollar_c2,dollar_c1)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[383]),4532]),872,13]),
[iquote('back_demod,383,demod,4532,unit_del,872,13')] ).
cnf(4550,plain,
product(dollar_c2,dollar_c1) = dollar_f1(dollar_c2,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4529,252,947]),957,966])]),
[iquote('hyper,4529,252,947,demod,957,966,flip.1')] ).
cnf(4552,plain,
~ r(dollar_c2,dollar_f1(dollar_c2,dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4539]),4550]),
[iquote('back_demod,4539,demod,4550')] ).
cnf(4553,plain,
$false,
inference(binary,[status(thm)],[4552,948]),
[iquote('binary,4552.1,948.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 05:44:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 27.73/27.87 ----- Otter 3.3f, August 2004 -----
% 27.73/27.87 The process was started by sandbox on n015.cluster.edu,
% 27.73/27.87 Wed Jul 27 05:44:26 2022
% 27.73/27.87 The command was "./otter". The process ID is 20885.
% 27.73/27.87
% 27.73/27.87 set(prolog_style_variables).
% 27.73/27.87 set(auto).
% 27.73/27.87 dependent: set(auto1).
% 27.73/27.87 dependent: set(process_input).
% 27.73/27.87 dependent: clear(print_kept).
% 27.73/27.87 dependent: clear(print_new_demod).
% 27.73/27.87 dependent: clear(print_back_demod).
% 27.73/27.87 dependent: clear(print_back_sub).
% 27.73/27.87 dependent: set(control_memory).
% 27.73/27.87 dependent: assign(max_mem, 12000).
% 27.73/27.87 dependent: assign(pick_given_ratio, 4).
% 27.73/27.87 dependent: assign(stats_level, 1).
% 27.73/27.87 dependent: assign(max_seconds, 10800).
% 27.73/27.87 clear(print_given).
% 27.73/27.87
% 27.73/27.87 formula_list(usable).
% 27.73/27.87 all A (A=A).
% 27.73/27.87 all C B A (product(product(A,B),C)=product(A,product(B,C))).
% 27.73/27.87 all A (product(A,A)=A).
% 27.73/27.87 all X0 X1 (l(X0,X1)<->product(X0,X1)=X0&product(X1,X0)=X1).
% 27.73/27.87 all X2 X3 (r(X2,X3)<->product(X2,X3)=X3&product(X3,X2)=X2).
% 27.73/27.87 all X4 X5 (d(X4,X5)<-> (exists X6 (r(X4,X6)&l(X6,X5)))).
% 27.73/27.87 -(all X7 X8 (d(X7,X8)<->product(X7,product(X8,X7))=X7&product(X8,product(X7,X8))=X8)).
% 27.73/27.87 end_of_list.
% 27.73/27.87
% 27.73/27.87 -------> usable clausifies to:
% 27.73/27.87
% 27.73/27.87 list(usable).
% 27.73/27.87 0 [] A=A.
% 27.73/27.87 0 [] product(product(A,B),C)=product(A,product(B,C)).
% 27.73/27.87 0 [] product(A,A)=A.
% 27.73/27.87 0 [] -l(X0,X1)|product(X0,X1)=X0.
% 27.73/27.87 0 [] -l(X0,X1)|product(X1,X0)=X1.
% 27.73/27.87 0 [] l(X0,X1)|product(X0,X1)!=X0|product(X1,X0)!=X1.
% 27.73/27.87 0 [] -r(X2,X3)|product(X2,X3)=X3.
% 27.73/27.87 0 [] -r(X2,X3)|product(X3,X2)=X2.
% 27.73/27.87 0 [] r(X2,X3)|product(X2,X3)!=X3|product(X3,X2)!=X2.
% 27.73/27.87 0 [] -d(X4,X5)|r(X4,$f1(X4,X5)).
% 27.73/27.87 0 [] -d(X4,X5)|l($f1(X4,X5),X5).
% 27.73/27.87 0 [] d(X4,X5)| -r(X4,X6)| -l(X6,X5).
% 27.73/27.87 0 [] d($c2,$c1)|product($c2,product($c1,$c2))=$c2.
% 27.73/27.87 0 [] d($c2,$c1)|product($c1,product($c2,$c1))=$c1.
% 27.73/27.87 0 [] -d($c2,$c1)|product($c2,product($c1,$c2))!=$c2|product($c1,product($c2,$c1))!=$c1.
% 27.73/27.87 end_of_list.
% 27.73/27.87
% 27.73/27.87 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 27.73/27.87
% 27.73/27.87 This ia a non-Horn set with equality. The strategy will be
% 27.73/27.87 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 27.73/27.87 deletion, with positive clauses in sos and nonpositive
% 27.73/27.87 clauses in usable.
% 27.73/27.87
% 27.73/27.87 dependent: set(knuth_bendix).
% 27.73/27.87 dependent: set(anl_eq).
% 27.73/27.87 dependent: set(para_from).
% 27.73/27.87 dependent: set(para_into).
% 27.73/27.87 dependent: clear(para_from_right).
% 27.73/27.87 dependent: clear(para_into_right).
% 27.73/27.87 dependent: set(para_from_vars).
% 27.73/27.87 dependent: set(eq_units_both_ways).
% 27.73/27.87 dependent: set(dynamic_demod_all).
% 27.73/27.87 dependent: set(dynamic_demod).
% 27.73/27.87 dependent: set(order_eq).
% 27.73/27.87 dependent: set(back_demod).
% 27.73/27.87 dependent: set(lrpo).
% 27.73/27.87 dependent: set(hyper_res).
% 27.73/27.87 dependent: set(unit_deletion).
% 27.73/27.87 dependent: set(factor).
% 27.73/27.87
% 27.73/27.87 ------------> process usable:
% 27.73/27.87 ** KEPT (pick-wt=8): 1 [] -l(A,B)|product(A,B)=A.
% 27.73/27.87 ** KEPT (pick-wt=8): 2 [] -l(A,B)|product(B,A)=B.
% 27.73/27.87 ** KEPT (pick-wt=13): 3 [] l(A,B)|product(A,B)!=A|product(B,A)!=B.
% 27.73/27.87 ** KEPT (pick-wt=8): 4 [] -r(A,B)|product(A,B)=B.
% 27.73/27.87 ** KEPT (pick-wt=8): 5 [] -r(A,B)|product(B,A)=A.
% 27.73/27.87 ** KEPT (pick-wt=13): 6 [] r(A,B)|product(A,B)!=B|product(B,A)!=A.
% 27.73/27.87 ** KEPT (pick-wt=8): 7 [] -d(A,B)|r(A,$f1(A,B)).
% 27.73/27.87 ** KEPT (pick-wt=8): 8 [] -d(A,B)|l($f1(A,B),B).
% 27.73/27.87 ** KEPT (pick-wt=9): 9 [] d(A,B)| -r(A,C)| -l(C,B).
% 27.73/27.87 ** KEPT (pick-wt=17): 10 [] -d($c2,$c1)|product($c2,product($c1,$c2))!=$c2|product($c1,product($c2,$c1))!=$c1.
% 27.73/27.87
% 27.73/27.87 ------------> process sos:
% 27.73/27.87 ** KEPT (pick-wt=3): 13 [] A=A.
% 27.73/27.87 ** KEPT (pick-wt=11): 14 [] product(product(A,B),C)=product(A,product(B,C)).
% 27.73/27.87 ---> New Demodulator: 15 [new_demod,14] product(product(A,B),C)=product(A,product(B,C)).
% 27.73/27.87 ** KEPT (pick-wt=5): 16 [] product(A,A)=A.
% 27.73/27.87 ---> New Demodulator: 17 [new_demod,16] product(A,A)=A.
% 27.73/27.87 ** KEPT (pick-wt=10): 18 [] d($c2,$c1)|product($c2,product($c1,$c2))=$c2.
% 27.73/27.87 ** KEPT (pick-wt=10): 19 [] d($c2,$c1)|product($c1,product($c2,$c1))=$c1.
% 27.73/27.87 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 27.73/27.87 >>>> Starting back demodulation with 15.
% 27.73/27.87 >>>> Starting back demodulation with 17.
% 27.73/27.87 >> back demodulating 12 with 17.
% 27.73/27.87 >> back demodulating 11 with 17.
% 27.73/27.87
% 27.73/27.87 ======= end of input processing =======
% 27.73/27.87
% 27.73/27.87 =========== start of search ===========
% 27.73/27.87
% 27.73/27.87
% 27.73/27.87 Resetting weight limit to 12.
% 27.73/27.87
% 27.73/27.87
% 27.73/27.87 Resetting weight limit to 12.
% 27.73/27.87
% 27.73/27.87 sos_size=2518
% 27.73/27.87
% 27.73/27.87
% 27.73/27.87 Resetting weight limit to 11.
% 27.73/27.87
% 27.73/27.87
% 27.73/27.87 Resetting weight limit to 11.
% 27.73/27.87
% 27.73/27.87 sos_size=2632
% 27.73/27.87
% 27.73/27.87 -- HEY sandbox, WE HAVE A PROOF!! --
% 27.73/27.87
% 27.73/27.87 ----> UNIT CONFLICT at 25.76 sec ----> 4553 [binary,4552.1,948.1] $F.
% 27.73/27.87
% 27.73/27.87 Length of proof is 56. Level of proof is 14.
% 27.73/27.87
% 27.73/27.87 ---------------- PROOF ----------------
% 27.73/27.87 % SZS status Theorem
% 27.73/27.87 % SZS output start Refutation
% See solution above
% 27.73/27.87 ------------ end of proof -------------
% 27.73/27.87
% 27.73/27.87
% 27.73/27.87 Search stopped by max_proofs option.
% 27.73/27.87
% 27.73/27.87
% 27.73/27.87 Search stopped by max_proofs option.
% 27.73/27.87
% 27.73/27.87 ============ end of search ============
% 27.73/27.87
% 27.73/27.87 -------------- statistics -------------
% 27.73/27.87 clauses given 1232
% 27.73/27.87 clauses generated 469497
% 27.73/27.87 clauses kept 4462
% 27.73/27.87 clauses forward subsumed 31502
% 27.73/27.87 clauses back subsumed 898
% 27.73/27.87 Kbytes malloced 4882
% 27.73/27.87
% 27.73/27.87 ----------- times (seconds) -----------
% 27.73/27.87 user CPU time 25.76 (0 hr, 0 min, 25 sec)
% 27.73/27.87 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 27.73/27.87 wall-clock time 28 (0 hr, 0 min, 28 sec)
% 27.73/27.87
% 27.73/27.87 That finishes the proof of the theorem.
% 27.73/27.87
% 27.73/27.87 Process 20885 finished Wed Jul 27 05:44:54 2022
% 27.73/27.87 Otter interrupted
% 27.73/27.87 PROOF FOUND
%------------------------------------------------------------------------------