TSTP Solution File: BOO004-10 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO004-10 : TPTP v8.1.0. Released v7.5.0.
% 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 12:47:30 EDT 2022
% Result : Unsatisfiable 2.28s 2.48s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of clauses : 71 ( 71 unt; 0 nHn; 5 RR)
% Number of literals : 71 ( 70 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 156 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sum(x,x,x) != true,
file('BOO004-10.p',unknown),
[] ).
cnf(4,axiom,
ife_q2(A,A,B,C) = B,
file('BOO004-10.p',unknown),
[] ).
cnf(6,axiom,
ife_q(A,A,B,C) = B,
file('BOO004-10.p',unknown),
[] ).
cnf(7,axiom,
sum(A,B,add(A,B)) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(9,axiom,
product(A,B,multiply(A,B)) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(11,axiom,
ife_q(sum(A,B,C),true,sum(B,A,C),true) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(13,axiom,
ife_q(product(A,B,C),true,product(B,A,C),true) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(15,axiom,
sum(additive_identity,A,A) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(17,axiom,
sum(A,additive_identity,A) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(21,axiom,
product(A,multiplicative_identity,A) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(23,axiom,
ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(product(A,F,G),true,ife_q(sum(F,D,B),true,sum(G,E,C),true),true),true),true) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(31,axiom,
ife_q(product(A,B,C),true,ife_q(sum(D,C,E),true,ife_q(sum(D,B,F),true,ife_q(sum(D,A,G),true,product(G,F,E),true),true),true),true) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(41,axiom,
sum(A,inverse(A),multiplicative_identity) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(43,axiom,
product(inverse(A),A,additive_identity) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(45,axiom,
product(A,inverse(A),additive_identity) = true,
file('BOO004-10.p',unknown),
[] ).
cnf(47,axiom,
ife_q2(sum(A,B,C),true,ife_q2(sum(A,B,D),true,D,C),C) = C,
file('BOO004-10.p',unknown),
[] ).
cnf(49,axiom,
ife_q2(product(A,B,C),true,ife_q2(product(A,B,D),true,D,C),C) = C,
file('BOO004-10.p',unknown),
[] ).
cnf(51,plain,
sum(A,B,add(B,A)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,7]),6]),
[iquote('para_into,11.1.1.1,7.1.1,demod,6')] ).
cnf(53,plain,
product(A,B,multiply(B,A)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,9]),6]),
[iquote('para_into,13.1.1.1,9.1.1,demod,6')] ).
cnf(61,plain,
ife_q2(sum(A,additive_identity,B),true,B,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,17]),4]),
[iquote('para_into,47.1.1.1,17.1.1,demod,4')] ).
cnf(67,plain,
ife_q2(sum(A,B,C),true,add(B,A),C) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,51]),4]),
[iquote('para_into,47.1.1.3.1,51.1.1,demod,4')] ).
cnf(73,plain,
ife_q2(sum(A,additive_identity,B),true,A,B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,17]),4]),
[iquote('para_into,47.1.1.3.1,17.1.1,demod,4')] ).
cnf(75,plain,
ife_q2(sum(additive_identity,A,B),true,A,B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,15]),4]),
[iquote('para_into,47.1.1.3.1,15.1.1,demod,4')] ).
cnf(77,plain,
ife_q2(sum(A,B,C),true,add(A,B),C) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,7]),4]),
[iquote('para_into,47.1.1.3.1,7.1.1,demod,4')] ).
cnf(80,plain,
add(additive_identity,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[61,51]),4]),
[iquote('para_into,61.1.1.1,51.1.1,demod,4')] ).
cnf(85,plain,
ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(sum(D,B,F),true,sum(E,C,multiply(F,A)),true),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,53]),6]),
[iquote('para_into,23.1.1.1,53.1.1,demod,6')] ).
cnf(87,plain,
ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(sum(D,B,inverse(A)),true,sum(E,C,additive_identity),true),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,45]),6]),
[iquote('para_into,23.1.1.1,45.1.1,demod,6')] ).
cnf(91,plain,
ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(sum(D,B,multiplicative_identity),true,sum(E,C,A),true),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,21]),6]),
[iquote('para_into,23.1.1.1,21.1.1,demod,6')] ).
cnf(99,plain,
ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(sum(D,inverse(A),B),true,sum(E,additive_identity,C),true),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,45]),6]),
[iquote('para_into,23.1.1.3.1,45.1.1,demod,6')] ).
cnf(103,plain,
ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(sum(D,multiplicative_identity,B),true,sum(E,A,C),true),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,21]),6]),
[iquote('para_into,23.1.1.3.1,21.1.1,demod,6')] ).
cnf(352,plain,
ife_q(product(A,B,additive_identity),true,ife_q(sum(C,B,D),true,ife_q(sum(C,A,E),true,product(E,D,C),true),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[31,17]),6]),
[iquote('para_into,31.1.1.3.1,17.1.1,demod,6')] ).
cnf(396,plain,
ife_q2(product(A,inverse(A),B),true,B,additive_identity) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,45]),4]),
[iquote('para_into,49.1.1.1,45.1.1,demod,4')] ).
cnf(400,plain,
ife_q2(product(A,multiplicative_identity,B),true,B,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,21]),4]),
[iquote('para_into,49.1.1.1,21.1.1,demod,4')] ).
cnf(406,plain,
ife_q2(product(A,B,C),true,multiply(B,A),C) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,53]),4]),
[iquote('para_into,49.1.1.3.1,53.1.1,demod,4')] ).
cnf(412,plain,
ife_q2(product(A,multiplicative_identity,B),true,A,B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,21]),4]),
[iquote('para_into,49.1.1.3.1,21.1.1,demod,4')] ).
cnf(419,plain,
multiply(multiplicative_identity,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[400,53]),4]),
[iquote('para_into,400.1.1.1,53.1.1,demod,4')] ).
cnf(421,plain,
inverse(multiplicative_identity) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[400,43]),4])]),
[iquote('para_into,400.1.1.1,43.1.1,demod,4,flip.1')] ).
cnf(547,plain,
multiply(inverse(A),A) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[396,53]),4]),
[iquote('para_into,396.1.1.1,53.1.1,demod,4')] ).
cnf(612,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[406,9]),4]),
[iquote('para_into,406.1.1.1,9.1.1,demod,4')] ).
cnf(639,plain,
ife_q(product(A,inverse(B),C),true,ife_q(product(A,B,D),true,sum(D,C,A),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[85,41]),419,6]),
[iquote('para_into,85.1.1.3.3.1,41.1.1,demod,419,6')] ).
cnf(699,plain,
ife_q(product(A,additive_identity,B),true,ife_q(product(A,inverse(A),C),true,sum(C,B,additive_identity),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,17]),6]),
[iquote('para_into,87.1.1.3.3.1,17.1.1,demod,6')] ).
cnf(755,plain,
ife_q(product(A,B,C),true,ife_q(sum(B,multiplicative_identity,multiplicative_identity),true,sum(C,A,A),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[91,21]),6]),
[iquote('para_into,91.1.1.1,21.1.1,demod,6')] ).
cnf(905,plain,
ife_q(product(A,multiplicative_identity,B),true,ife_q(product(A,A,C),true,sum(C,additive_identity,B),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[99,41]),6]),
[iquote('para_into,99.1.1.3.3.1,41.1.1,demod,6')] ).
cnf(949,plain,
ife_q(product(A,B,C),true,ife_q(sum(multiplicative_identity,multiplicative_identity,B),true,sum(A,A,C),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[103,21]),6]),
[iquote('para_into,103.1.1.3.1,21.1.1,demod,6')] ).
cnf(1003,plain,
ife_q(sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),true,sum(A,A,A),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[755,21]),6]),
[iquote('para_into,755.1.1.1,21.1.1,demod,6')] ).
cnf(1687,plain,
ife_q(product(A,A,B),true,sum(B,additive_identity,A),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[905,53]),419,6]),
[iquote('para_into,905.1.1.1,53.1.1,demod,419,6')] ).
cnf(1693,plain,
sum(multiply(A,A),additive_identity,A) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1687,53]),6]),
[iquote('para_into,1687.1.1.1,53.1.1,demod,6')] ).
cnf(1701,plain,
multiply(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1693,73]),4]),
[iquote('para_from,1693.1.1,73.1.1.1,demod,4')] ).
cnf(1713,plain,
product(A,A,A) = true,
inference(para_from,[status(thm),theory(equality)],[1701,53]),
[iquote('para_from,1701.1.1,53.1.1.3')] ).
cnf(1739,plain,
ife_q(sum(multiplicative_identity,multiplicative_identity,A),true,sum(A,A,A),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[949,1713]),6]),
[iquote('para_into,949.1.1.1,1713.1.1,demod,6')] ).
cnf(1741,plain,
ife_q(sum(multiplicative_identity,multiplicative_identity,A),true,sum(B,B,multiply(A,B)),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[949,53]),6]),
[iquote('para_into,949.1.1.1,53.1.1,demod,6')] ).
cnf(1753,plain,
sum(add(multiplicative_identity,multiplicative_identity),add(multiplicative_identity,multiplicative_identity),add(multiplicative_identity,multiplicative_identity)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1739,51]),6]),
[iquote('para_into,1739.1.1.1,51.1.1,demod,6')] ).
cnf(1761,plain,
sum(A,A,multiply(add(multiplicative_identity,multiplicative_identity),A)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1741,51]),6]),
[iquote('para_into,1741.1.1.1,51.1.1,demod,6')] ).
cnf(1777,plain,
multiply(add(multiplicative_identity,multiplicative_identity),A) = add(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1761,77]),4])]),
[iquote('para_from,1761.1.1,77.1.1.1,demod,4,flip.1')] ).
cnf(1897,plain,
ife_q(product(A,B,C),true,sum(C,multiply(inverse(B),A),A),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[639,53]),6]),
[iquote('para_into,639.1.1.1,53.1.1,demod,6')] ).
cnf(1973,plain,
sum(multiply(A,B),multiply(inverse(A),B),B) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1897,53]),6]),
[iquote('para_into,1897.1.1.1,53.1.1,demod,6')] ).
cnf(2033,plain,
add(multiply(inverse(A),B),multiply(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1973,67]),4]),
[iquote('para_from,1973.1.1,67.1.1.1,demod,4')] ).
cnf(2051,plain,
add(multiply(A,inverse(B)),multiply(B,A)) = A,
inference(para_into,[status(thm),theory(equality)],[2033,612]),
[iquote('para_into,2033.1.1.1,612.1.1')] ).
cnf(2081,plain,
add(multiply(A,inverse(add(multiplicative_identity,multiplicative_identity))),add(A,A)) = A,
inference(para_into,[status(thm),theory(equality)],[2051,1777]),
[iquote('para_into,2051.1.1.2,1777.1.1')] ).
cnf(2103,plain,
ife_q(product(A,additive_identity,B),true,sum(additive_identity,B,additive_identity),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[699,53]),547,6]),
[iquote('para_into,699.1.1.3.1,53.1.1,demod,547,6')] ).
cnf(2105,plain,
sum(additive_identity,multiply(additive_identity,A),additive_identity) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2103,53]),6]),
[iquote('para_into,2103.1.1.1,53.1.1,demod,6')] ).
cnf(2113,plain,
multiply(additive_identity,A) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2105,75]),4]),
[iquote('para_from,2105.1.1,75.1.1.1,demod,4')] ).
cnf(2128,plain,
multiply(A,additive_identity) = additive_identity,
inference(para_into,[status(thm),theory(equality)],[2113,612]),
[iquote('para_into,2113.1.1,612.1.1')] ).
cnf(2138,plain,
product(A,additive_identity,additive_identity) = true,
inference(para_from,[status(thm),theory(equality)],[2113,53]),
[iquote('para_from,2113.1.1,53.1.1.3')] ).
cnf(2153,plain,
ife_q(sum(A,B,C),true,product(C,A,A),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[352,17]),2138,6,6]),
[iquote('para_into,352.1.1.3.1,17.1.1,demod,2138,6,6')] ).
cnf(2169,plain,
product(add(A,B),B,B) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2153,51]),6]),
[iquote('para_into,2153.1.1.1,51.1.1,demod,6')] ).
cnf(2188,plain,
add(A,multiplicative_identity) = multiplicative_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2169,412]),4]),
[iquote('para_from,2169.1.1,412.1.1.1,demod,4')] ).
cnf(2208,plain,
add(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2081]),2188,421,2128,80]),
[iquote('back_demod,2081,demod,2188,421,2128,80')] ).
cnf(2212,plain,
sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) = true,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1753]),2208,2208,2208]),
[iquote('back_demod,1753,demod,2208,2208,2208')] ).
cnf(2215,plain,
sum(A,A,A) = true,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1003]),2212,6]),
[iquote('back_demod,1003,demod,2212,6')] ).
cnf(2217,plain,
$false,
inference(binary,[status(thm)],[2215,1]),
[iquote('binary,2215.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO004-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % 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 02:37:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.99/2.17 ----- Otter 3.3f, August 2004 -----
% 1.99/2.17 The process was started by sandbox on n020.cluster.edu,
% 1.99/2.17 Wed Jul 27 02:37:08 2022
% 1.99/2.17 The command was "./otter". The process ID is 5437.
% 1.99/2.17
% 1.99/2.17 set(prolog_style_variables).
% 1.99/2.17 set(auto).
% 1.99/2.17 dependent: set(auto1).
% 1.99/2.17 dependent: set(process_input).
% 1.99/2.17 dependent: clear(print_kept).
% 1.99/2.17 dependent: clear(print_new_demod).
% 1.99/2.17 dependent: clear(print_back_demod).
% 1.99/2.17 dependent: clear(print_back_sub).
% 1.99/2.17 dependent: set(control_memory).
% 1.99/2.17 dependent: assign(max_mem, 12000).
% 1.99/2.17 dependent: assign(pick_given_ratio, 4).
% 1.99/2.17 dependent: assign(stats_level, 1).
% 1.99/2.17 dependent: assign(max_seconds, 10800).
% 1.99/2.17 clear(print_given).
% 1.99/2.17
% 1.99/2.17 list(usable).
% 1.99/2.17 0 [] A=A.
% 1.99/2.17 0 [] ife_q2(A,A,B,C)=B.
% 1.99/2.17 0 [] ife_q(A,A,B,C)=B.
% 1.99/2.17 0 [] sum(X,Y,add(X,Y))=true.
% 1.99/2.17 0 [] product(X,Y,multiply(X,Y))=true.
% 1.99/2.17 0 [] ife_q(sum(X,Y,Z),true,sum(Y,X,Z),true)=true.
% 1.99/2.17 0 [] ife_q(product(X,Y,Z),true,product(Y,X,Z),true)=true.
% 1.99/2.17 0 [] sum(additive_identity,X,X)=true.
% 1.99/2.17 0 [] sum(X,additive_identity,X)=true.
% 1.99/2.17 0 [] product(multiplicative_identity,X,X)=true.
% 1.99/2.17 0 [] product(X,multiplicative_identity,X)=true.
% 1.99/2.17 0 [] ife_q(product(X,V3,V4),true,ife_q(product(X,Z,V2),true,ife_q(product(X,Y,V1),true,ife_q(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true)=true.
% 1.99/2.17 0 [] ife_q(product(X,Z,V2),true,ife_q(product(X,Y,V1),true,ife_q(sum(V1,V2,V4),true,ife_q(sum(Y,Z,V3),true,product(X,V3,V4),true),true),true),true)=true.
% 1.99/2.17 0 [] ife_q(product(V3,X,V4),true,ife_q(product(Z,X,V2),true,ife_q(product(Y,X,V1),true,ife_q(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true)=true.
% 1.99/2.17 0 [] ife_q(product(Z,X,V2),true,ife_q(product(Y,X,V1),true,ife_q(sum(V1,V2,V4),true,ife_q(sum(Y,Z,V3),true,product(V3,X,V4),true),true),true),true)=true.
% 1.99/2.17 0 [] ife_q(product(Y,Z,V3),true,ife_q(sum(X,V3,V4),true,ife_q(sum(X,Z,V2),true,ife_q(sum(X,Y,V1),true,product(V1,V2,V4),true),true),true),true)=true.
% 1.99/2.17 0 [] ife_q(product(V1,V2,V4),true,ife_q(product(Y,Z,V3),true,ife_q(sum(X,Z,V2),true,ife_q(sum(X,Y,V1),true,sum(X,V3,V4),true),true),true),true)=true.
% 1.99/2.17 0 [] ife_q(product(Y,Z,V3),true,ife_q(sum(V3,X,V4),true,ife_q(sum(Z,X,V2),true,ife_q(sum(Y,X,V1),true,product(V1,V2,V4),true),true),true),true)=true.
% 1.99/2.17 0 [] ife_q(product(V1,V2,V4),true,ife_q(product(Y,Z,V3),true,ife_q(sum(Z,X,V2),true,ife_q(sum(Y,X,V1),true,sum(V3,X,V4),true),true),true),true)=true.
% 1.99/2.17 0 [] sum(inverse(X),X,multiplicative_identity)=true.
% 1.99/2.17 0 [] sum(X,inverse(X),multiplicative_identity)=true.
% 1.99/2.17 0 [] product(inverse(X),X,additive_identity)=true.
% 1.99/2.17 0 [] product(X,inverse(X),additive_identity)=true.
% 1.99/2.17 0 [] ife_q2(sum(X,Y,V),true,ife_q2(sum(X,Y,U),true,U,V),V)=V.
% 1.99/2.17 0 [] ife_q2(product(X,Y,V),true,ife_q2(product(X,Y,U),true,U,V),V)=V.
% 1.99/2.17 0 [] sum(x,x,x)!=true.
% 1.99/2.17 end_of_list.
% 1.99/2.17
% 1.99/2.17 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.99/2.17
% 1.99/2.17 All clauses are units, and equality is present; the
% 1.99/2.17 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.99/2.17
% 1.99/2.17 dependent: set(knuth_bendix).
% 1.99/2.17 dependent: set(anl_eq).
% 1.99/2.17 dependent: set(para_from).
% 1.99/2.17 dependent: set(para_into).
% 1.99/2.17 dependent: clear(para_from_right).
% 1.99/2.17 dependent: clear(para_into_right).
% 1.99/2.17 dependent: set(para_from_vars).
% 1.99/2.17 dependent: set(eq_units_both_ways).
% 1.99/2.17 dependent: set(dynamic_demod_all).
% 1.99/2.17 dependent: set(dynamic_demod).
% 1.99/2.17 dependent: set(order_eq).
% 1.99/2.17 dependent: set(back_demod).
% 1.99/2.17 dependent: set(lrpo).
% 1.99/2.17
% 1.99/2.17 ------------> process usable:
% 1.99/2.17 ** KEPT (pick-wt=6): 1 [] sum(x,x,x)!=true.
% 1.99/2.17
% 1.99/2.17 ------------> process sos:
% 1.99/2.17 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.99/2.17 ** KEPT (pick-wt=7): 3 [] ife_q2(A,A,B,C)=B.
% 1.99/2.17 ---> New Demodulator: 4 [new_demod,3] ife_q2(A,A,B,C)=B.
% 1.99/2.17 ** KEPT (pick-wt=7): 5 [] ife_q(A,A,B,C)=B.
% 1.99/2.17 ---> New Demodulator: 6 [new_demod,5] ife_q(A,A,B,C)=B.
% 1.99/2.17 ** KEPT (pick-wt=8): 7 [] sum(A,B,add(A,B))=true.
% 1.99/2.17 ---> New Demodulator: 8 [new_demod,7] sum(A,B,add(A,B))=true.
% 1.99/2.17 ** KEPT (pick-wt=8): 9 [] product(A,B,multiply(A,B))=true.
% 1.99/2.17 ---> New Demodulator: 10 [new_demod,9] product(A,B,multiply(A,B))=true.
% 1.99/2.17 ** KEPT (pick-wt=13): 11 [] ife_q(sum(A,B,C),true,sum(B,A,C),true)=true.
% 1.99/2.17 ---> New Demodulator: 12 [new_demod,11] ife_q(sum(A,B,C),true,sum(B,A,C),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=13): 13 [] ife_q(product(A,B,C),true,product(B,A,C),true)=true.
% 1.99/2.17 ---> New Demodulator: 14 [new_demod,13] ife_q(product(A,B,C),true,product(B,A,C),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=6): 15 [] sum(additive_identity,A,A)=true.
% 1.99/2.17 ---> New Demodulator: 16 [new_demod,15] sum(additive_identity,A,A)=true.
% 1.99/2.17 ** KEPT (pick-wt=6): 17 [] sum(A,additive_identity,A)=true.
% 1.99/2.17 ---> New Demodulator: 18 [new_demod,17] sum(A,additive_identity,A)=true.
% 1.99/2.17 ** KEPT (pick-wt=6): 19 [] product(multiplicative_identity,A,A)=true.
% 1.99/2.17 ---> New Demodulator: 20 [new_demod,19] product(multiplicative_identity,A,A)=true.
% 1.99/2.17 ** KEPT (pick-wt=6): 21 [] product(A,multiplicative_identity,A)=true.
% 1.99/2.17 ---> New Demodulator: 22 [new_demod,21] product(A,multiplicative_identity,A)=true.
% 1.99/2.17 ** KEPT (pick-wt=34): 23 [] ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(product(A,F,G),true,ife_q(sum(F,D,B),true,sum(G,E,C),true),true),true),true)=true.
% 1.99/2.17 ---> New Demodulator: 24 [new_demod,23] ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(product(A,F,G),true,ife_q(sum(F,D,B),true,sum(G,E,C),true),true),true),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=34): 25 [] ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(sum(E,C,F),true,ife_q(sum(D,B,G),true,product(A,G,F),true),true),true),true)=true.
% 1.99/2.17 ---> New Demodulator: 26 [new_demod,25] ife_q(product(A,B,C),true,ife_q(product(A,D,E),true,ife_q(sum(E,C,F),true,ife_q(sum(D,B,G),true,product(A,G,F),true),true),true),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=34): 27 [] ife_q(product(A,B,C),true,ife_q(product(D,B,E),true,ife_q(product(F,B,G),true,ife_q(sum(F,D,A),true,sum(G,E,C),true),true),true),true)=true.
% 1.99/2.17 ---> New Demodulator: 28 [new_demod,27] ife_q(product(A,B,C),true,ife_q(product(D,B,E),true,ife_q(product(F,B,G),true,ife_q(sum(F,D,A),true,sum(G,E,C),true),true),true),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=34): 29 [] ife_q(product(A,B,C),true,ife_q(product(D,B,E),true,ife_q(sum(E,C,F),true,ife_q(sum(D,A,G),true,product(G,B,F),true),true),true),true)=true.
% 1.99/2.17 ---> New Demodulator: 30 [new_demod,29] ife_q(product(A,B,C),true,ife_q(product(D,B,E),true,ife_q(sum(E,C,F),true,ife_q(sum(D,A,G),true,product(G,B,F),true),true),true),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=34): 31 [] ife_q(product(A,B,C),true,ife_q(sum(D,C,E),true,ife_q(sum(D,B,F),true,ife_q(sum(D,A,G),true,product(G,F,E),true),true),true),true)=true.
% 1.99/2.17 ---> New Demodulator: 32 [new_demod,31] ife_q(product(A,B,C),true,ife_q(sum(D,C,E),true,ife_q(sum(D,B,F),true,ife_q(sum(D,A,G),true,product(G,F,E),true),true),true),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=34): 33 [] ife_q(product(A,B,C),true,ife_q(product(D,E,F),true,ife_q(sum(G,E,B),true,ife_q(sum(G,D,A),true,sum(G,F,C),true),true),true),true)=true.
% 1.99/2.17 ---> New Demodulator: 34 [new_demod,33] ife_q(product(A,B,C),true,ife_q(product(D,E,F),true,ife_q(sum(G,E,B),true,ife_q(sum(G,D,A),true,sum(G,F,C),true),true),true),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=34): 35 [] ife_q(product(A,B,C),true,ife_q(sum(C,D,E),true,ife_q(sum(B,D,F),true,ife_q(sum(A,D,G),true,product(G,F,E),true),true),true),true)=true.
% 1.99/2.17 ---> New Demodulator: 36 [new_demod,35] ife_q(product(A,B,C),true,ife_q(sum(C,D,E),true,ife_q(sum(B,D,F),true,ife_q(sum(A,D,G),true,product(G,F,E),true),true),true),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=34): 37 [] ife_q(product(A,B,C),true,ife_q(product(D,E,F),true,ife_q(sum(E,G,B),true,ife_q(sum(D,G,A),true,sum(F,G,C),true),true),true),true)=true.
% 1.99/2.17 ---> New Demodulator: 38 [new_demod,37] ife_q(product(A,B,C),true,ife_q(product(D,E,F),true,ife_q(sum(E,G,B),true,ife_q(sum(D,G,A),true,sum(F,G,C),true),true),true),true)=true.
% 1.99/2.17 ** KEPT (pick-wt=7): 39 [] sum(inverse(A),A,multiplicative_identity)=true.
% 1.99/2.17 ---> New Demodulator: 40 [new_demod,39] sum(inverse(A),A,multiplicative_identity)=true.
% 1.99/2.17 ** KEPT (pick-wt=7): 41 [] sum(A,inverse(A),multiplicative_identity)=true.
% 1.99/2.17 ---> New Demodulator: 42 [new_demod,41] sum(A,inverse(A),multiplicative_identity)=true.
% 1.99/2.17 ** KEPT (pick-wt=7): 43 [] product(inverse(A),A,additive_identity)=true.
% 1.99/2.17 ---> New Demodulator: 44 [new_demod,43] product(inverse(A),A,additive_identity)=true.
% 1.99/2.17 ** KEPT (pick-wt=7): 45 [] product(A,inverse(A),additive_identity)=true.
% 1.99/2.17 ---> New Demodulator: 46 [new_demod,45] product(A,inverse(A),additive_identity)=true.
% 1.99/2.17 ** KEPT (pick-wt=17): 47 [] ife_q2(sum(A,B,C),true,ife_q2(sum(A,B,D),true,D,C),C)=C.
% 2.28/2.48 ---> New Demodulator: 48 [new_demod,47] ife_q2(sum(A,B,C),true,ife_q2(sum(A,B,D),true,D,C),C)=C.
% 2.28/2.48 ** KEPT (pick-wt=17): 49 [] ife_q2(product(A,B,C),true,ife_q2(product(A,B,D),true,D,C),C)=C.
% 2.28/2.48 ---> New Demodulator: 50 [new_demod,49] ife_q2(product(A,B,C),true,ife_q2(product(A,B,D),true,D,C),C)=C.
% 2.28/2.48 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.28/2.48 >>>> Starting back demodulation with 4.
% 2.28/2.48 >>>> Starting back demodulation with 6.
% 2.28/2.48 >>>> Starting back demodulation with 8.
% 2.28/2.48 >>>> Starting back demodulation with 10.
% 2.28/2.48 >>>> Starting back demodulation with 12.
% 2.28/2.48 >>>> Starting back demodulation with 14.
% 2.28/2.48 >>>> Starting back demodulation with 16.
% 2.28/2.48 >>>> Starting back demodulation with 18.
% 2.28/2.48 >>>> Starting back demodulation with 20.
% 2.28/2.48 >>>> Starting back demodulation with 22.
% 2.28/2.48 >>>> Starting back demodulation with 24.
% 2.28/2.48 >>>> Starting back demodulation with 26.
% 2.28/2.48 >>>> Starting back demodulation with 28.
% 2.28/2.48 >>>> Starting back demodulation with 30.
% 2.28/2.48 >>>> Starting back demodulation with 32.
% 2.28/2.48 >>>> Starting back demodulation with 34.
% 2.28/2.48 >>>> Starting back demodulation with 36.
% 2.28/2.48 >>>> Starting back demodulation with 38.
% 2.28/2.48 >>>> Starting back demodulation with 40.
% 2.28/2.48 >>>> Starting back demodulation with 42.
% 2.28/2.48 >>>> Starting back demodulation with 44.
% 2.28/2.48 >>>> Starting back demodulation with 46.
% 2.28/2.48 >>>> Starting back demodulation with 48.
% 2.28/2.48 >>>> Starting back demodulation with 50.
% 2.28/2.48
% 2.28/2.48 ======= end of input processing =======
% 2.28/2.48
% 2.28/2.48 =========== start of search ===========
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 21.
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 21.
% 2.28/2.48
% 2.28/2.48 sos_size=402
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 19.
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 19.
% 2.28/2.48
% 2.28/2.48 sos_size=434
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 17.
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 17.
% 2.28/2.48
% 2.28/2.48 sos_size=421
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 16.
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 16.
% 2.28/2.48
% 2.28/2.48 sos_size=323
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 13.
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Resetting weight limit to 13.
% 2.28/2.48
% 2.28/2.48 sos_size=334
% 2.28/2.48
% 2.28/2.48 -------- PROOF --------
% 2.28/2.48
% 2.28/2.48 ----> UNIT CONFLICT at 0.31 sec ----> 2217 [binary,2215.1,1.1] $F.
% 2.28/2.48
% 2.28/2.48 Length of proof is 53. Level of proof is 12.
% 2.28/2.48
% 2.28/2.48 ---------------- PROOF ----------------
% 2.28/2.48 % SZS status Unsatisfiable
% 2.28/2.48 % SZS output start Refutation
% See solution above
% 2.28/2.48 ------------ end of proof -------------
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Search stopped by max_proofs option.
% 2.28/2.48
% 2.28/2.48
% 2.28/2.48 Search stopped by max_proofs option.
% 2.28/2.48
% 2.28/2.48 ============ end of search ============
% 2.28/2.48
% 2.28/2.48 -------------- statistics -------------
% 2.28/2.48 clauses given 708
% 2.28/2.48 clauses generated 41029
% 2.28/2.48 clauses kept 1110
% 2.28/2.48 clauses forward subsumed 30228
% 2.28/2.48 clauses back subsumed 0
% 2.28/2.48 Kbytes malloced 7812
% 2.28/2.48
% 2.28/2.48 ----------- times (seconds) -----------
% 2.28/2.48 user CPU time 0.31 (0 hr, 0 min, 0 sec)
% 2.28/2.48 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.28/2.48 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.28/2.48
% 2.28/2.48 That finishes the proof of the theorem.
% 2.28/2.48
% 2.28/2.48 Process 5437 finished Wed Jul 27 02:37:10 2022
% 2.28/2.48 Otter interrupted
% 2.28/2.48 PROOF FOUND
%------------------------------------------------------------------------------