TSTP Solution File: SEV515+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEV515+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:17:33 EDT 2022
% Result : Theorem 1.79s 1.97s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 10 unt; 36 nHn; 48 RR)
% Number of literals : 210 ( 0 equ; 43 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ g_true_only(A,dollar_c1)
| ~ g_both(A,A) ),
file('SEV515+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ g_true_only(A,dollar_c1)
| ~ g_true_only(A,A) ),
file('SEV515+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ g_both(A,dollar_c1)
| ~ g_false_only(A,A) ),
file('SEV515+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ g_both(A,dollar_c1)
| ~ g_true_only(A,A) ),
file('SEV515+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ g_false_only(A,dollar_c1)
| ~ g_false_only(A,A) ),
file('SEV515+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ g_false_only(A,dollar_c1)
| ~ g_both(A,A) ),
file('SEV515+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ g_both(A,B)
| ~ g_both(A,A)
| g_true_only(dollar_f1(B),B)
| g_both(dollar_f1(B),B)
| g_false_only(dollar_f1(B),dollar_f1(B))
| g_both(dollar_f1(B),dollar_f1(B))
| g_true_only(C,dollar_c2)
| g_true_only(C,C) ),
file('SEV515+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ g_both(A,B)
| ~ g_both(A,A)
| g_true_only(dollar_f1(B),B)
| g_both(dollar_f1(B),B)
| g_false_only(dollar_f1(B),dollar_f1(B))
| g_both(dollar_f1(B),dollar_f1(B))
| g_false_only(C,C)
| g_false_only(C,dollar_c2) ),
file('SEV515+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ g_both(A,B)
| ~ g_both(A,A)
| g_true_only(dollar_f1(B),B)
| g_false_only(dollar_f1(B),dollar_f1(B))
| g_true_only(dollar_f1(B),dollar_f1(B))
| g_false_only(dollar_f1(B),B)
| g_false_only(C,C)
| g_true_only(C,C) ),
file('SEV515+1.p',unknown),
[] ).
cnf(19,plain,
( ~ g_both(A,B)
| ~ g_both(A,A)
| g_true_only(dollar_f1(B),B)
| g_false_only(dollar_f1(B),dollar_f1(B))
| g_true_only(dollar_f1(B),dollar_f1(B))
| g_false_only(dollar_f1(B),B) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[18])])]),
[iquote('copy,18,factor_simp,factor_simp')] ).
cnf(21,axiom,
( ~ g_both(A,B)
| ~ g_both(A,A)
| g_both(dollar_f1(B),dollar_f1(B))
| g_true_only(dollar_f1(B),dollar_f1(B))
| g_both(dollar_f1(B),B)
| g_false_only(dollar_f1(B),B)
| g_true_only(C,dollar_c2)
| g_true_only(C,C) ),
file('SEV515+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ g_both(A,B)
| ~ g_both(A,A)
| g_both(dollar_f1(B),dollar_f1(B))
| g_true_only(dollar_f1(B),dollar_f1(B))
| g_both(dollar_f1(B),B)
| g_false_only(dollar_f1(B),B)
| g_false_only(C,C)
| g_false_only(C,dollar_c2) ),
file('SEV515+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ g_true_only(A,B)
| g_true(A,B) ),
file('SEV515+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ g_true_only(A,B)
| ~ g_false(A,B) ),
file('SEV515+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ g_both(A,B)
| g_true(A,B) ),
file('SEV515+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ g_both(A,B)
| g_false(A,B) ),
file('SEV515+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ g_false_only(A,B)
| g_false(A,B) ),
file('SEV515+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ g_false_only(A,B)
| ~ g_true(A,B) ),
file('SEV515+1.p',unknown),
[] ).
cnf(38,plain,
~ g_true_only(dollar_c1,dollar_c1),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.2')] ).
cnf(39,plain,
~ g_false_only(dollar_c1,dollar_c1),
inference(factor,[status(thm)],[5]),
[iquote('factor,5.1.2')] ).
cnf(48,plain,
( ~ g_both(A,A)
| g_true_only(dollar_f1(A),A)
| g_both(dollar_f1(A),A)
| g_false_only(dollar_f1(A),dollar_f1(A))
| g_both(dollar_f1(A),dollar_f1(A))
| g_true_only(B,dollar_c2)
| g_true_only(B,B) ),
inference(factor,[status(thm)],[12]),
[iquote('factor,12.1.2')] ).
cnf(50,plain,
( ~ g_both(A,A)
| g_true_only(dollar_f1(A),A)
| g_both(dollar_f1(A),A)
| g_false_only(dollar_f1(A),dollar_f1(A))
| g_both(dollar_f1(A),dollar_f1(A))
| g_false_only(B,B)
| g_false_only(B,dollar_c2) ),
inference(factor,[status(thm)],[13]),
[iquote('factor,13.1.2')] ).
cnf(54,plain,
( ~ g_both(A,A)
| g_true_only(dollar_f1(A),A)
| g_false_only(dollar_f1(A),dollar_f1(A))
| g_true_only(dollar_f1(A),dollar_f1(A))
| g_false_only(dollar_f1(A),A) ),
inference(factor,[status(thm)],[19]),
[iquote('factor,19.1.2')] ).
cnf(56,plain,
( ~ g_both(A,A)
| g_both(dollar_f1(A),dollar_f1(A))
| g_true_only(dollar_f1(A),dollar_f1(A))
| g_both(dollar_f1(A),A)
| g_false_only(dollar_f1(A),A)
| g_true_only(B,dollar_c2)
| g_true_only(B,B) ),
inference(factor,[status(thm)],[21]),
[iquote('factor,21.1.2')] ).
cnf(59,plain,
( ~ g_both(A,A)
| g_both(dollar_f1(A),dollar_f1(A))
| g_true_only(dollar_f1(A),dollar_f1(A))
| g_both(dollar_f1(A),A)
| g_false_only(dollar_f1(A),A)
| g_false_only(B,B)
| g_false_only(B,dollar_c2) ),
inference(factor,[status(thm)],[22]),
[iquote('factor,22.1.2')] ).
cnf(66,plain,
( ~ g_both(A,A)
| g_true_only(dollar_f1(A),A)
| g_both(dollar_f1(A),A)
| g_false_only(dollar_f1(A),dollar_f1(A))
| g_both(dollar_f1(A),dollar_f1(A))
| g_true_only(dollar_c2,dollar_c2) ),
inference(factor,[status(thm)],[48]),
[iquote('factor,48.6.7')] ).
cnf(68,plain,
( ~ g_both(A,A)
| g_true_only(dollar_f1(A),A)
| g_both(dollar_f1(A),A)
| g_false_only(dollar_f1(A),dollar_f1(A))
| g_both(dollar_f1(A),dollar_f1(A))
| g_false_only(dollar_c2,dollar_c2) ),
inference(factor,[status(thm)],[50]),
[iquote('factor,50.6.7')] ).
cnf(70,plain,
( ~ g_both(A,A)
| g_both(dollar_f1(A),dollar_f1(A))
| g_true_only(dollar_f1(A),dollar_f1(A))
| g_both(dollar_f1(A),A)
| g_false_only(dollar_f1(A),A)
| g_true_only(dollar_c2,dollar_c2) ),
inference(factor,[status(thm)],[56]),
[iquote('factor,56.6.7')] ).
cnf(71,plain,
( ~ g_both(A,A)
| g_both(dollar_f1(A),dollar_f1(A))
| g_true_only(dollar_f1(A),dollar_f1(A))
| g_both(dollar_f1(A),A)
| g_false_only(dollar_f1(A),A)
| g_false_only(dollar_c2,dollar_c2) ),
inference(factor,[status(thm)],[59]),
[iquote('factor,59.6.7')] ).
cnf(72,axiom,
( g_true_only(A,B)
| g_both(A,B)
| g_false_only(A,B) ),
file('SEV515+1.p',unknown),
[] ).
cnf(73,plain,
g_both(dollar_c1,dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[72,38]),39]),
[iquote('hyper,72,38,unit_del,39')] ).
cnf(76,plain,
( g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_true_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_c2,dollar_c2) ),
inference(hyper,[status(thm)],[73,71]),
[iquote('hyper,73,71')] ).
cnf(77,plain,
( g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_true_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_c1)
| g_true_only(dollar_c2,dollar_c2) ),
inference(hyper,[status(thm)],[73,70]),
[iquote('hyper,73,70')] ).
cnf(79,plain,
( g_true_only(dollar_f1(dollar_c1),dollar_c1)
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_false_only(dollar_c2,dollar_c2) ),
inference(hyper,[status(thm)],[73,68]),
[iquote('hyper,73,68')] ).
cnf(81,plain,
( g_true_only(dollar_f1(dollar_c1),dollar_c1)
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_true_only(dollar_c2,dollar_c2) ),
inference(hyper,[status(thm)],[73,66]),
[iquote('hyper,73,66')] ).
cnf(86,plain,
( g_true_only(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_true_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_false_only(dollar_f1(dollar_c1),dollar_c1) ),
inference(hyper,[status(thm)],[73,54]),
[iquote('hyper,73,54')] ).
cnf(100,plain,
( g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_c2,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[76,2,72])])]),
[iquote('hyper,76,2,72,factor_simp,factor_simp')] ).
cnf(106,plain,
( g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_c1)
| g_true_only(dollar_c2,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[77,2,72])])]),
[iquote('hyper,77,2,72,factor_simp,factor_simp')] ).
cnf(113,plain,
( g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_c1)
| g_true(dollar_c2,dollar_c2) ),
inference(hyper,[status(thm)],[106,29]),
[iquote('hyper,106,29')] ).
cnf(115,plain,
( g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[113,36,100])])])]),
[iquote('hyper,113,36,100,factor_simp,factor_simp,factor_simp')] ).
cnf(116,plain,
( g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false(dollar_f1(dollar_c1),dollar_c1) ),
inference(hyper,[status(thm)],[115,35]),
[iquote('hyper,115,35')] ).
cnf(117,plain,
( g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_false_only(dollar_c2,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[79,30,116])])]),
[iquote('hyper,79,30,116,factor_simp,factor_simp')] ).
cnf(119,plain,
( g_both(dollar_f1(dollar_c1),dollar_c1)
| g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_false_only(dollar_c2,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[117,5,115])])]),
[iquote('hyper,117,5,115,factor_simp,factor_simp')] ).
cnf(121,plain,
( g_both(dollar_f1(dollar_c1),dollar_c1)
| g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_false(dollar_c2,dollar_c2) ),
inference(hyper,[status(thm)],[119,35]),
[iquote('hyper,119,35')] ).
cnf(128,plain,
( g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_true_only(dollar_c2,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[81,30,116])])]),
[iquote('hyper,81,30,116,factor_simp,factor_simp')] ).
cnf(130,plain,
( g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[128,30,121])])]),
[iquote('hyper,128,30,121,factor_simp,factor_simp')] ).
cnf(132,plain,
( g_both(dollar_f1(dollar_c1),dollar_c1)
| g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[130,5,115])])]),
[iquote('hyper,130,5,115,factor_simp,factor_simp')] ).
cnf(136,plain,
( g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[132,4,72])]),
[iquote('hyper,132,4,72,factor_simp')] ).
cnf(155,plain,
( g_both(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[132,1,72])]),
[iquote('hyper,132,1,72,factor_simp')] ).
cnf(157,plain,
g_both(dollar_f1(dollar_c1),dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[155,6,132])]),
[iquote('hyper,155,6,132,factor_simp')] ).
cnf(158,plain,
g_false(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[157,33]),
[iquote('hyper,157,33')] ).
cnf(159,plain,
g_true(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[157,32]),
[iquote('hyper,157,32')] ).
cnf(160,plain,
( g_true_only(dollar_f1(dollar_c1),dollar_c1)
| g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_false_only(dollar_f1(dollar_c1),dollar_c1) ),
inference(hyper,[status(thm)],[157,4,86]),
[iquote('hyper,157,4,86')] ).
cnf(162,plain,
g_both(dollar_f1(dollar_c1),dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[136,3,157]),
[iquote('hyper,136,3,157')] ).
cnf(179,plain,
g_true(dollar_f1(dollar_c1),dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[162,32]),
[iquote('hyper,162,32')] ).
cnf(180,plain,
( g_false_only(dollar_f1(dollar_c1),dollar_f1(dollar_c1))
| g_false_only(dollar_f1(dollar_c1),dollar_c1) ),
inference(hyper,[status(thm)],[160,30,158]),
[iquote('hyper,160,30,158')] ).
cnf(184,plain,
g_false_only(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[180,36,179]),
[iquote('hyper,180,36,179')] ).
cnf(186,plain,
$false,
inference(hyper,[status(thm)],[184,36,159]),
[iquote('hyper,184,36,159')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV515+1 : TPTP v8.1.0. Released v7.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 08:03:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.79/1.96 ----- Otter 3.3f, August 2004 -----
% 1.79/1.96 The process was started by sandbox2 on n021.cluster.edu,
% 1.79/1.96 Wed Jul 27 08:03:53 2022
% 1.79/1.96 The command was "./otter". The process ID is 9232.
% 1.79/1.96
% 1.79/1.96 set(prolog_style_variables).
% 1.79/1.96 set(auto).
% 1.79/1.96 dependent: set(auto1).
% 1.79/1.96 dependent: set(process_input).
% 1.79/1.96 dependent: clear(print_kept).
% 1.79/1.96 dependent: clear(print_new_demod).
% 1.79/1.96 dependent: clear(print_back_demod).
% 1.79/1.96 dependent: clear(print_back_sub).
% 1.79/1.96 dependent: set(control_memory).
% 1.79/1.96 dependent: assign(max_mem, 12000).
% 1.79/1.96 dependent: assign(pick_given_ratio, 4).
% 1.79/1.96 dependent: assign(stats_level, 1).
% 1.79/1.96 dependent: assign(max_seconds, 10800).
% 1.79/1.96 clear(print_given).
% 1.79/1.96
% 1.79/1.96 formula_list(usable).
% 1.79/1.96 -((all A exists B (g_true_only(B,A)& (g_both(B,B)|g_true_only(B,B))|g_both(B,A)& (g_false_only(B,B)|g_true_only(B,B))|g_false_only(B,A)& (g_false_only(B,B)|g_both(B,B))))| (exists A ((exists B (g_both(B,A)&g_both(B,B)))& -(exists B (g_true_only(B,A)& (g_both(B,B)|g_true_only(B,B))|g_both(B,A)& (g_false_only(B,B)|g_true_only(B,B))|g_false_only(B,A)& (g_false_only(B,B)|g_both(B,B))))))& -(exists A all B (g_true_only(B,A)&g_false_only(B,B)|g_false_only(B,A)&g_true_only(B,B)))).
% 1.79/1.96 all X_2 X_1 (g_true_only(X_2,X_1)<->g_true(X_2,X_1)& -g_false(X_2,X_1)).
% 1.79/1.96 all X_2 X_1 (g_both(X_2,X_1)<->g_true(X_2,X_1)&g_false(X_2,X_1)).
% 1.79/1.96 all X_2 X_1 (g_false_only(X_2,X_1)<->g_false(X_2,X_1)& -g_true(X_2,X_1)).
% 1.79/1.96 all X_2 X_1 (g_true_only(X_2,X_1)|g_both(X_2,X_1)|g_false_only(X_2,X_1)).
% 1.79/1.96 end_of_list.
% 1.79/1.96
% 1.79/1.96 -------> usable clausifies to:
% 1.79/1.96
% 1.79/1.96 list(usable).
% 1.79/1.96 0 [] -g_true_only(B,$c1)| -g_both(B,B).
% 1.79/1.96 0 [] -g_true_only(B,$c1)| -g_true_only(B,B).
% 1.79/1.96 0 [] -g_both(B,$c1)| -g_false_only(B,B).
% 1.79/1.96 0 [] -g_both(B,$c1)| -g_true_only(B,B).
% 1.79/1.96 0 [] -g_false_only(B,$c1)| -g_false_only(B,B).
% 1.79/1.96 0 [] -g_false_only(B,$c1)| -g_both(B,B).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_both($f1(A),A)|g_false_only($f1(A),A)|g_true_only(X2,$c2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_both($f1(A),A)|g_false_only($f1(A),A)|g_true_only(X2,$c2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_both($f1(A),A)|g_false_only($f1(A),A)|g_false_only(X2,X2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_both($f1(A),A)|g_false_only($f1(A),A)|g_false_only(X2,X2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_both($f1(A),A)|g_false_only($f1(A),$f1(A))|g_both($f1(A),$f1(A))|g_true_only(X2,$c2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_both($f1(A),A)|g_false_only($f1(A),$f1(A))|g_both($f1(A),$f1(A))|g_true_only(X2,$c2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_both($f1(A),A)|g_false_only($f1(A),$f1(A))|g_both($f1(A),$f1(A))|g_false_only(X2,X2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_both($f1(A),A)|g_false_only($f1(A),$f1(A))|g_both($f1(A),$f1(A))|g_false_only(X2,X2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_false_only($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_false_only($f1(A),A)|g_true_only(X2,$c2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_false_only($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_false_only($f1(A),A)|g_true_only(X2,$c2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_false_only($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_false_only($f1(A),A)|g_false_only(X2,X2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_true_only($f1(A),A)|g_false_only($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_false_only($f1(A),A)|g_false_only(X2,X2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_both($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_both($f1(A),A)|g_false_only($f1(A),A)|g_true_only(X2,$c2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_both($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_both($f1(A),A)|g_false_only($f1(A),A)|g_true_only(X2,$c2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_both($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_both($f1(A),A)|g_false_only($f1(A),A)|g_false_only(X2,X2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_both($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_both($f1(A),A)|g_false_only($f1(A),A)|g_false_only(X2,X2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_both($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_false_only($f1(A),$f1(A))|g_true_only(X2,$c2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_both($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_false_only($f1(A),$f1(A))|g_true_only(X2,$c2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_both($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_false_only($f1(A),$f1(A))|g_false_only(X2,X2)|g_false_only(X2,$c2).
% 1.79/1.96 0 [] -g_both(X1,A)| -g_both(X1,X1)|g_both($f1(A),$f1(A))|g_true_only($f1(A),$f1(A))|g_false_only($f1(A),$f1(A))|g_false_only(X2,X2)|g_true_only(X2,X2).
% 1.79/1.96 0 [] -g_true_only(X_2,X_1)|g_true(X_2,X_1).
% 1.79/1.96 0 [] -g_true_only(X_2,X_1)| -g_false(X_2,X_1).
% 1.79/1.96 0 [] g_true_only(X_2,X_1)| -g_true(X_2,X_1)|g_false(X_2,X_1).
% 1.79/1.96 0 [] -g_both(X_2,X_1)|g_true(X_2,X_1).
% 1.79/1.96 0 [] -g_both(X_2,X_1)|g_false(X_2,X_1).
% 1.79/1.96 0 [] g_both(X_2,X_1)| -g_true(X_2,X_1)| -g_false(X_2,X_1).
% 1.79/1.96 0 [] -g_false_only(X_2,X_1)|g_false(X_2,X_1).
% 1.79/1.96 0 [] -g_false_only(X_2,X_1)| -g_true(X_2,X_1).
% 1.79/1.96 0 [] g_false_only(X_2,X_1)| -g_false(X_2,X_1)|g_true(X_2,X_1).
% 1.79/1.96 0 [] g_true_only(X_2,X_1)|g_both(X_2,X_1)|g_false_only(X_2,X_1).
% 1.79/1.96 end_of_list.
% 1.79/1.96
% 1.79/1.96 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=8.
% 1.79/1.96
% 1.79/1.96 This is a non-Horn set without equality. The strategy will
% 1.79/1.96 be ordered hyper_res, unit deletion, and factoring, with
% 1.79/1.96 satellites in sos and with nuclei in usable.
% 1.79/1.96
% 1.79/1.96 dependent: set(hyper_res).
% 1.79/1.96 dependent: set(factor).
% 1.79/1.96 dependent: set(unit_deletion).
% 1.79/1.96
% 1.79/1.96 ------------> process usable:
% 1.79/1.96 ** KEPT (pick-wt=6): 1 [] -g_true_only(A,$c1)| -g_both(A,A).
% 1.79/1.96 ** KEPT (pick-wt=6): 2 [] -g_true_only(A,$c1)| -g_true_only(A,A).
% 1.79/1.96 ** KEPT (pick-wt=6): 3 [] -g_both(A,$c1)| -g_false_only(A,A).
% 1.79/1.96 ** KEPT (pick-wt=6): 4 [] -g_both(A,$c1)| -g_true_only(A,A).
% 1.79/1.96 ** KEPT (pick-wt=6): 5 [] -g_false_only(A,$c1)| -g_false_only(A,A).
% 1.79/1.96 ** KEPT (pick-wt=6): 6 [] -g_false_only(A,$c1)| -g_both(A,A).
% 1.79/1.96 ** KEPT (pick-wt=24): 7 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_both($f1(B),B)|g_false_only($f1(B),B)|g_true_only(C,$c2)|g_false_only(C,$c2).
% 1.79/1.96 ** KEPT (pick-wt=24): 8 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_both($f1(B),B)|g_false_only($f1(B),B)|g_true_only(C,$c2)|g_true_only(C,C).
% 1.79/1.96 ** KEPT (pick-wt=24): 9 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_both($f1(B),B)|g_false_only($f1(B),B)|g_false_only(C,C)|g_false_only(C,$c2).
% 1.79/1.96 ** KEPT (pick-wt=24): 10 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_both($f1(B),B)|g_false_only($f1(B),B)|g_false_only(C,C)|g_true_only(C,C).
% 1.79/1.96 ** KEPT (pick-wt=30): 11 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_both($f1(B),B)|g_false_only($f1(B),$f1(B))|g_both($f1(B),$f1(B))|g_true_only(C,$c2)|g_false_only(C,$c2).
% 1.79/1.96 ** KEPT (pick-wt=30): 12 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_both($f1(B),B)|g_false_only($f1(B),$f1(B))|g_both($f1(B),$f1(B))|g_true_only(C,$c2)|g_true_only(C,C).
% 1.79/1.96 ** KEPT (pick-wt=30): 13 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_both($f1(B),B)|g_false_only($f1(B),$f1(B))|g_both($f1(B),$f1(B))|g_false_only(C,C)|g_false_only(C,$c2).
% 1.79/1.96 ** KEPT (pick-wt=30): 14 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_both($f1(B),B)|g_false_only($f1(B),$f1(B))|g_both($f1(B),$f1(B))|g_false_only(C,C)|g_true_only(C,C).
% 1.79/1.96 ** KEPT (pick-wt=30): 15 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_false_only($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_false_only($f1(B),B)|g_true_only(C,$c2)|g_false_only(C,$c2).
% 1.79/1.96 ** KEPT (pick-wt=30): 16 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_false_only($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_false_only($f1(B),B)|g_true_only(C,$c2)|g_true_only(C,C).
% 1.79/1.96 ** KEPT (pick-wt=30): 17 [] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_false_only($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_false_only($f1(B),B)|g_false_only(C,C)|g_false_only(C,$c2).
% 1.79/1.96 ** KEPT (pick-wt=24): 19 [copy,18,factor_simp,factor_simp] -g_both(A,B)| -g_both(A,A)|g_true_only($f1(B),B)|g_false_only($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_false_only($f1(B),B).
% 1.79/1.97 ** KEPT (pick-wt=30): 20 [] -g_both(A,B)| -g_both(A,A)|g_both($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_both($f1(B),B)|g_false_only($f1(B),B)|g_true_only(C,$c2)|g_false_only(C,$c2).
% 1.79/1.97 ** KEPT (pick-wt=30): 21 [] -g_both(A,B)| -g_both(A,A)|g_both($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_both($f1(B),B)|g_false_only($f1(B),B)|g_true_only(C,$c2)|g_true_only(C,C).
% 1.79/1.97 ** KEPT (pick-wt=30): 22 [] -g_both(A,B)| -g_both(A,A)|g_both($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_both($f1(B),B)|g_false_only($f1(B),B)|g_false_only(C,C)|g_false_only(C,$c2).
% 1.79/1.97 ** KEPT (pick-wt=30): 23 [] -g_both(A,B)| -g_both(A,A)|g_both($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_both($f1(B),B)|g_false_only($f1(B),B)|g_false_only(C,C)|g_true_only(C,C).
% 1.79/1.97 ** KEPT (pick-wt=27): 24 [] -g_both(A,B)| -g_both(A,A)|g_both($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_false_only($f1(B),$f1(B))|g_true_only(C,$c2)|g_false_only(C,$c2).
% 1.79/1.97 ** KEPT (pick-wt=27): 25 [] -g_both(A,B)| -g_both(A,A)|g_both($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_false_only($f1(B),$f1(B))|g_true_only(C,$c2)|g_true_only(C,C).
% 1.79/1.97 ** KEPT (pick-wt=27): 26 [] -g_both(A,B)| -g_both(A,A)|g_both($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_false_only($f1(B),$f1(B))|g_false_only(C,C)|g_false_only(C,$c2).
% 1.79/1.97 ** KEPT (pick-wt=21): 28 [copy,27,factor_simp,factor_simp] -g_both(A,B)| -g_both(A,A)|g_both($f1(B),$f1(B))|g_true_only($f1(B),$f1(B))|g_false_only($f1(B),$f1(B)).
% 1.79/1.97 ** KEPT (pick-wt=6): 29 [] -g_true_only(A,B)|g_true(A,B).
% 1.79/1.97 ** KEPT (pick-wt=6): 30 [] -g_true_only(A,B)| -g_false(A,B).
% 1.79/1.97 ** KEPT (pick-wt=9): 31 [] g_true_only(A,B)| -g_true(A,B)|g_false(A,B).
% 1.79/1.97 ** KEPT (pick-wt=6): 32 [] -g_both(A,B)|g_true(A,B).
% 1.79/1.97 ** KEPT (pick-wt=6): 33 [] -g_both(A,B)|g_false(A,B).
% 1.79/1.97 ** KEPT (pick-wt=9): 34 [] g_both(A,B)| -g_true(A,B)| -g_false(A,B).
% 1.79/1.97 ** KEPT (pick-wt=6): 35 [] -g_false_only(A,B)|g_false(A,B).
% 1.79/1.97 ** KEPT (pick-wt=6): 36 [] -g_false_only(A,B)| -g_true(A,B).
% 1.79/1.97 ** KEPT (pick-wt=9): 37 [] g_false_only(A,B)| -g_false(A,B)|g_true(A,B).
% 1.79/1.97 19 back subsumes 17.
% 1.79/1.97 19 back subsumes 16.
% 1.79/1.97 19 back subsumes 15.
% 1.79/1.97 28 back subsumes 26.
% 1.79/1.97 28 back subsumes 25.
% 1.79/1.97 28 back subsumes 24.
% 1.79/1.97
% 1.79/1.97 ------------> process sos:
% 1.79/1.97 ** KEPT (pick-wt=9): 72 [] g_true_only(A,B)|g_both(A,B)|g_false_only(A,B).
% 1.79/1.97 72 back subsumes 65.
% 1.79/1.97 72 back subsumes 64.
% 1.79/1.97 72 back subsumes 63.
% 1.79/1.97 72 back subsumes 62.
% 1.79/1.97 72 back subsumes 46.
% 1.79/1.97 72 back subsumes 45.
% 1.79/1.97 72 back subsumes 44.
% 1.79/1.97 72 back subsumes 43.
% 1.79/1.97 72 back subsumes 42.
% 1.79/1.97 72 back subsumes 41.
% 1.79/1.97 72 back subsumes 40.
% 1.79/1.97 72 back subsumes 28.
% 1.79/1.97 72 back subsumes 10.
% 1.79/1.97 72 back subsumes 9.
% 1.79/1.97 72 back subsumes 8.
% 1.79/1.97 72 back subsumes 7.
% 1.79/1.97
% 1.79/1.97 ======= end of input processing =======
% 1.79/1.97
% 1.79/1.97 =========== start of search ===========
% 1.79/1.97
% 1.79/1.97 -------- PROOF --------
% 1.79/1.97
% 1.79/1.97 -----> EMPTY CLAUSE at 0.02 sec ----> 186 [hyper,184,36,159] $F.
% 1.79/1.97
% 1.79/1.97 Length of proof is 39. Level of proof is 17.
% 1.79/1.97
% 1.79/1.97 ---------------- PROOF ----------------
% 1.79/1.97 % SZS status Theorem
% 1.79/1.97 % SZS output start Refutation
% See solution above
% 1.79/1.97 ------------ end of proof -------------
% 1.79/1.97
% 1.79/1.97
% 1.79/1.97 Search stopped by max_proofs option.
% 1.79/1.97
% 1.79/1.97
% 1.79/1.97 Search stopped by max_proofs option.
% 1.79/1.97
% 1.79/1.97 ============ end of search ============
% 1.79/1.97
% 1.79/1.97 -------------- statistics -------------
% 1.79/1.97 clauses given 48
% 1.79/1.97 clauses generated 581
% 1.79/1.97 clauses kept 183
% 1.79/1.97 clauses forward subsumed 433
% 1.79/1.97 clauses back subsumed 101
% 1.79/1.97 Kbytes malloced 976
% 1.79/1.97
% 1.79/1.97 ----------- times (seconds) -----------
% 1.79/1.97 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.79/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/1.97 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/1.97
% 1.79/1.97 That finishes the proof of the theorem.
% 1.79/1.97
% 1.79/1.97 Process 9232 finished Wed Jul 27 08:03:54 2022
% 1.79/1.97 Otter interrupted
% 1.79/1.97 PROOF FOUND
%------------------------------------------------------------------------------