TSTP Solution File: SYN417+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:24:29 EDT 2022
% Result : Theorem 17.94s 18.14s
% Output : Refutation 17.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 9
% Syntax : Number of clauses : 123 ( 10 unt; 59 nHn; 122 RR)
% Number of literals : 368 ( 367 equ; 198 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 79 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( dollar_c1 = f(g(dollar_c1))
| A != g(f(A))
| dollar_c2 = A ),
file('SYN417+1.p',unknown),
[] ).
cnf(2,plain,
( f(g(dollar_c1)) = dollar_c1
| g(f(A)) != A
| dollar_c2 = A ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])])]),
[iquote('copy,1,flip.1,flip.2')] ).
cnf(3,axiom,
( A != f(g(A))
| dollar_c1 = A
| dollar_c2 = g(f(dollar_c2)) ),
file('SYN417+1.p',unknown),
[] ).
cnf(4,plain,
( f(g(A)) != A
| dollar_c1 = A
| g(f(dollar_c2)) = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])])]),
[iquote('copy,3,flip.1,flip.3')] ).
cnf(5,axiom,
( A != f(g(A))
| dollar_c1 = A
| B != g(f(B))
| dollar_c2 = B ),
file('SYN417+1.p',unknown),
[] ).
cnf(6,plain,
( f(g(A)) != A
| dollar_c1 = A
| g(f(B)) != B
| dollar_c2 = B ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])])]),
[iquote('copy,5,flip.1,flip.3')] ).
cnf(7,axiom,
( A != f(g(A))
| dollar_f1(A) = f(g(dollar_f1(A)))
| B != g(f(B))
| dollar_f2(B) = g(f(dollar_f2(B))) ),
file('SYN417+1.p',unknown),
[] ).
cnf(8,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| g(f(B)) != B
| g(f(dollar_f2(B))) = dollar_f2(B) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])])])])]),
[iquote('copy,7,flip.1,flip.2,flip.3,flip.4')] ).
cnf(9,axiom,
( A != f(g(A))
| dollar_f1(A) = f(g(dollar_f1(A)))
| B != g(f(B))
| B != dollar_f2(B) ),
file('SYN417+1.p',unknown),
[] ).
cnf(10,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| g(f(B)) != B
| dollar_f2(B) != B ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])])])])]),
[iquote('copy,9,flip.1,flip.2,flip.3,flip.4')] ).
cnf(11,axiom,
( A != f(g(A))
| A != dollar_f1(A)
| B != g(f(B))
| dollar_f2(B) = g(f(dollar_f2(B))) ),
file('SYN417+1.p',unknown),
[] ).
cnf(12,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| g(f(B)) != B
| g(f(dollar_f2(B))) = dollar_f2(B) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])])])])]),
[iquote('copy,11,flip.1,flip.2,flip.3,flip.4')] ).
cnf(13,axiom,
( A != f(g(A))
| A != dollar_f1(A)
| B != g(f(B))
| B != dollar_f2(B) ),
file('SYN417+1.p',unknown),
[] ).
cnf(14,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| g(f(B)) != B
| dollar_f2(B) != B ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])])])])]),
[iquote('copy,13,flip.1,flip.2,flip.3,flip.4')] ).
cnf(15,axiom,
A = A,
file('SYN417+1.p',unknown),
[] ).
cnf(16,axiom,
( dollar_c1 = f(g(dollar_c1))
| dollar_c2 = g(f(dollar_c2)) ),
file('SYN417+1.p',unknown),
[] ).
cnf(17,plain,
( f(g(dollar_c1)) = dollar_c1
| g(f(dollar_c2)) = dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])])]),
[iquote('copy,16,flip.1,flip.2')] ).
cnf(19,plain,
( f(g(A)) = dollar_c1
| g(f(dollar_c2)) = dollar_c2
| f(g(A)) != A ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[17,4])]),
[iquote('para_into,17.1.1.1.1,4.2.1,factor_simp')] ).
cnf(23,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| g(f(dollar_f2(g(dollar_c1)))) = dollar_f2(g(dollar_c1))
| g(f(dollar_c2)) = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,12]),15]),
[iquote('para_from,17.1.1,12.3.1.1,unit_del,15')] ).
cnf(24,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| dollar_f2(g(dollar_c1)) != g(dollar_c1)
| g(f(dollar_c2)) = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,10]),15]),
[iquote('para_from,17.1.1,10.3.1.1,unit_del,15')] ).
cnf(25,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| g(f(dollar_f2(g(dollar_c1)))) = dollar_f2(g(dollar_c1))
| g(f(dollar_c2)) = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,8]),15]),
[iquote('para_from,17.1.1,8.3.1.1,unit_del,15')] ).
cnf(26,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(f(A)) != A
| dollar_f2(A) != A
| g(f(dollar_c2)) = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,14]),15]),
[iquote('para_from,17.1.1,14.1.1,unit_del,15')] ).
cnf(28,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| g(f(A)) != A
| dollar_f2(A) != A
| g(f(dollar_c2)) = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,10]),15]),
[iquote('para_from,17.1.1,10.1.1,unit_del,15')] ).
cnf(30,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| dollar_f2(dollar_c2) != dollar_c2
| f(g(dollar_c1)) = dollar_c1 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,14]),15]),
[iquote('para_from,17.2.1,14.3.1,unit_del,15')] ).
cnf(31,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2)
| f(g(dollar_c1)) = dollar_c1 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,12]),15]),
[iquote('para_from,17.2.1,12.3.1,unit_del,15')] ).
cnf(32,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| dollar_f2(dollar_c2) != dollar_c2
| f(g(dollar_c1)) = dollar_c1 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,10]),15]),
[iquote('para_from,17.2.1,10.3.1,unit_del,15')] ).
cnf(33,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2)
| f(g(dollar_c1)) = dollar_c1 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,8]),15]),
[iquote('para_from,17.2.1,8.3.1,unit_del,15')] ).
cnf(62,plain,
( f(dollar_c2) = dollar_c1
| g(f(A)) != A
| dollar_c2 = A
| f(g(B)) = dollar_c1
| f(g(B)) != B ),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[19,6]),15])]),
[iquote('para_from,19.2.1,6.1.1.1,unit_del,15,flip.1')] ).
cnf(108,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(g(dollar_c1)) != g(dollar_c1)
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[26,17]),15])]),
[iquote('para_into,26.2.1.1,17.1.1,unit_del,15,factor_simp')] ).
cnf(138,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| dollar_f2(dollar_c2) != dollar_c2
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[30,17]),15])]),
[iquote('para_into,30.1.1.1,17.2.1,unit_del,15,factor_simp')] ).
cnf(178,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(f(dollar_f2(g(dollar_c1)))) = dollar_f2(g(dollar_c1))
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[23,17]),15])]),
[iquote('para_into,23.1.1,17.1.1,unit_del,15,factor_simp')] ).
cnf(224,plain,
( f(dollar_f2(g(dollar_c1))) = dollar_c1
| g(f(dollar_c2)) = dollar_c2
| dollar_f1(dollar_c1) != dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[178,4]),15])]),
[iquote('para_from,178.2.1,4.1.1.1,unit_del,15,factor_simp')] ).
cnf(240,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(g(dollar_c1)) = g(dollar_c1)
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[224,178])])]),
[iquote('para_from,224.1.1,178.2.1.1,factor_simp,factor_simp')] ).
cnf(258,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[240,108]),15])])]),
[iquote('para_from,240.2.1,108.2.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(272,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| dollar_f2(g(dollar_c1)) != g(dollar_c1)
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[24,17]),15])]),
[iquote('para_into,24.1.1,17.1.1,unit_del,15,factor_simp')] ).
cnf(287,plain,
( dollar_f1(A) != dollar_c1
| g(f(dollar_c2)) = dollar_c2
| f(g(A)) != A ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[258,4])]),
[iquote('para_into,258.1.1.1,4.2.1,factor_simp')] ).
cnf(289,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| dollar_f2(dollar_c2) != dollar_c2
| dollar_f1(dollar_c1) != dollar_c1 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[258,14]),15]),
[iquote('para_from,258.2.1,14.3.1,unit_del,15')] ).
cnf(290,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2)
| dollar_f1(dollar_c1) != dollar_c1 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[258,12]),15]),
[iquote('para_from,258.2.1,12.3.1,unit_del,15')] ).
cnf(292,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2)
| dollar_f1(dollar_c1) != dollar_c1 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[258,8]),15]),
[iquote('para_from,258.2.1,8.3.1,unit_del,15')] ).
cnf(296,plain,
( f(dollar_c2) = dollar_c1
| g(f(A)) != A
| dollar_c2 = A
| dollar_f1(dollar_c1) != dollar_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[258,6]),15])]),
[iquote('para_from,258.2.1,6.1.1.1,unit_del,15,flip.1')] ).
cnf(297,plain,
( f(g(dollar_c1)) != dollar_c1
| dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor,[status(thm)],[289]),
[iquote('factor,289.2.4')] ).
cnf(298,plain,
( f(g(dollar_c1)) != dollar_c1
| dollar_f1(dollar_c1) != dollar_c1
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2) ),
inference(factor,[status(thm)],[290]),
[iquote('factor,290.2.4')] ).
cnf(330,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| g(f(dollar_f2(g(dollar_c1)))) = dollar_f2(g(dollar_c1))
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[25,17])]),
[iquote('hyper,25,17,factor_simp')] ).
cnf(371,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2)
| g(f(A)) != A
| dollar_c2 = A ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[298,2]),15]),
[iquote('para_into,298.1.1,2.1.1,unit_del,15')] ).
cnf(375,plain,
( f(g(dollar_c1)) != dollar_c1
| dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(dollar_f2(dollar_c2)) != dollar_f2(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[298,14]),15])])]),
[iquote('para_from,298.3.1,14.3.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(379,plain,
( f(dollar_c2) = dollar_c1
| dollar_f2(dollar_c2) = dollar_c2
| dollar_f1(dollar_c1) != dollar_c1
| f(g(dollar_c1)) != dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[298,296]),15])]),
[iquote('para_from,298.3.1,296.2.1,unit_del,15,factor_simp')] ).
cnf(409,plain,
( dollar_f1(dollar_c1) = dollar_c1
| g(f(dollar_c2)) = dollar_c2
| g(f(A)) != A
| dollar_f2(A) != A ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[28,4]),15])]),
[iquote('para_from,28.1.1,4.1.1,unit_del,15,factor_simp')] ).
cnf(451,plain,
( f(g(dollar_c1)) != dollar_c1
| dollar_f1(dollar_c1) != dollar_c1
| f(dollar_c2) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[379,375]),15])])]),
[iquote('para_from,379.2.1,375.3.1.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(483,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(dollar_c1) = dollar_c2
| f(g(dollar_c1)) != dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[451,287])])]),
[iquote('para_from,451.3.1,287.2.1.1,factor_simp,factor_simp')] ).
cnf(499,plain,
( dollar_f1(dollar_c1) = dollar_c1
| g(f(dollar_c2)) = dollar_c2
| dollar_f2(g(dollar_c1)) != g(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[272,4]),15])]),
[iquote('para_from,272.1.1,4.1.1,unit_del,15,factor_simp')] ).
cnf(515,plain,
( g(f(dollar_c2)) = dollar_c2
| dollar_f2(g(dollar_c1)) != g(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[499,258]),15])]),
[iquote('para_from,499.1.1,258.1.1,unit_del,15,factor_simp')] ).
cnf(529,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2)
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[31,17]),15])]),
[iquote('para_into,31.1.1.1,17.2.1,unit_del,15,factor_simp')] ).
cnf(544,plain,
( f(g(dollar_c1)) = dollar_c1
| dollar_f2(dollar_c2) = dollar_c2
| f(g(A)) != A
| dollar_f1(A) != A ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[31,2]),15])]),
[iquote('para_from,31.3.1,2.2.1,unit_del,15,factor_simp')] ).
cnf(549,plain,
( g(f(dollar_c2)) = dollar_c2
| dollar_f2(g(A)) != g(dollar_c1)
| f(g(A)) != A ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[515,4])]),
[iquote('para_into,515.2.1.1.1,4.2.1,factor_simp')] ).
cnf(622,plain,
( f(g(dollar_f1(f(dollar_c2)))) = dollar_f1(f(dollar_c2))
| dollar_f2(dollar_c2) != dollar_c2
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[32,17]),15])]),
[iquote('para_into,32.1.1.1,17.2.1,unit_del,15,factor_simp')] ).
cnf(693,plain,
( g(f(dollar_c2)) = dollar_c2
| g(f(A)) != A
| dollar_f2(A) != A ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[409,258]),15])]),
[iquote('para_from,409.1.1,258.1.1,unit_del,15,factor_simp')] ).
cnf(707,plain,
( f(g(dollar_f1(f(dollar_c2)))) = dollar_f1(f(dollar_c2))
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2)
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[33,17]),15])]),
[iquote('para_into,33.1.1.1,17.2.1,unit_del,15,factor_simp')] ).
cnf(747,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| g(f(A)) != A
| dollar_f2(A) != A ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[693,14]),15])])]),
[iquote('para_from,693.1.1,14.1.1.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(984,plain,
( f(g(dollar_c1)) = dollar_c1
| dollar_f2(dollar_c2) = dollar_c2
| dollar_f1(f(dollar_c2)) != f(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[529,2]),15])]),
[iquote('para_from,529.2.1,2.2.1,unit_del,15,factor_simp')] ).
cnf(1017,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[984,138]),15])])]),
[iquote('para_from,984.2.1,138.2.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(1023,plain,
( dollar_f1(f(A)) != f(dollar_c2)
| f(g(dollar_c1)) = dollar_c1
| g(f(A)) != A ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1017,2])]),
[iquote('para_into,1017.1.1.1.1,2.3.1,factor_simp')] ).
cnf(1173,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[544,30]),15])])])]),
[iquote('para_from,544.2.1,30.3.1,unit_del,15,factor_simp,factor_simp,factor_simp')] ).
cnf(1190,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| dollar_f2(g(dollar_c1)) != g(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1173,14]),15])])]),
[iquote('para_from,1173.3.1,14.3.1.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(1216,plain,
( f(g(dollar_c1)) != dollar_c1
| dollar_f1(dollar_c1) != dollar_c1
| g(dollar_c1) != dollar_f2(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1190,483])])]),
[iquote('para_into,1190.3.1.1,483.2.1,factor_simp,factor_simp')] ).
cnf(1227,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(dollar_c1) != dollar_f2(dollar_c2)
| g(f(A)) != A
| dollar_c2 = A ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1216,2]),15]),
[iquote('para_into,1216.1.1,2.1.1,unit_del,15')] ).
cnf(1673,plain,
( f(g(dollar_c1)) = dollar_c1
| g(dollar_f1(f(dollar_c2))) = dollar_c2
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[622,2]),15])]),
[iquote('para_from,622.1.1,2.2.1.1,unit_del,15,factor_simp')] ).
cnf(1721,plain,
( dollar_f1(f(dollar_c2)) = f(dollar_c2)
| dollar_f2(dollar_c2) != dollar_c2
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1673,622])])]),
[iquote('para_from,1673.2.1,622.1.1.1,factor_simp,factor_simp')] ).
cnf(1768,plain,
( f(g(dollar_c1)) = dollar_c1
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1721,1017]),15])]),
[iquote('para_from,1721.1.1,1017.1.1,unit_del,15,factor_simp')] ).
cnf(1839,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1768,297]),15])]),
[iquote('para_from,1768.1.1,297.1.1,unit_del,15,factor_simp')] ).
cnf(1840,plain,
( f(g(A)) != A
| dollar_c1 = A
| g(dollar_c1) = dollar_c2
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1768,6]),15])]),
[iquote('para_from,1768.1.1,6.3.1.1,unit_del,15,flip.3')] ).
cnf(1841,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| g(f(A)) != A
| dollar_f2(A) != A
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1768,10]),15]),
[iquote('para_from,1768.1.1,10.1.1,unit_del,15')] ).
cnf(1845,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| g(f(dollar_c2)) != dollar_c2
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor,[status(thm)],[1841]),
[iquote('factor,1841.3.4')] ).
cnf(1949,plain,
( f(dollar_c2) = dollar_c1
| dollar_f2(dollar_c2) != dollar_c2
| f(g(A)) != A
| dollar_c1 = A ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1840,1768])]),
[iquote('para_from,1840.3.1,1768.1.1.1,factor_simp')] ).
cnf(1960,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| dollar_f2(dollar_c2) != dollar_c2
| f(g(A)) != A
| dollar_c1 = A ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1845,4]),15]),
[iquote('para_into,1845.2.1,4.3.1,unit_del,15')] ).
cnf(2023,plain,
( f(dollar_c2) = dollar_c1
| dollar_f2(dollar_c2) != dollar_c2
| g(f(A)) != A
| dollar_f2(A) != A ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1949,693]),15])]),
[iquote('para_into,1949.3.1.1,693.1.1,unit_del,15,factor_simp')] ).
cnf(2032,plain,
( f(dollar_c2) = dollar_c1
| dollar_f2(dollar_c2) != dollar_c2
| g(f(dollar_c2)) != dollar_c2 ),
inference(factor,[status(thm)],[2023]),
[iquote('factor,2023.2.4')] ).
cnf(2045,plain,
( f(dollar_c2) != dollar_f1(dollar_c1)
| g(f(dollar_c2)) != dollar_c2
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2032,747])])]),
[iquote('para_from,2032.1.1,747.1.1.1,factor_simp,factor_simp')] ).
cnf(2076,plain,
( f(dollar_c2) != dollar_f1(dollar_c1)
| dollar_f2(dollar_c2) != dollar_c2
| f(g(A)) != A
| dollar_c1 = A ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[2045,4]),15]),
[iquote('para_into,2045.2.1,4.3.1,unit_del,15')] ).
cnf(3231,plain,
( f(dollar_f2(dollar_c2)) = dollar_c1
| g(f(A)) != A
| dollar_c2 = A
| dollar_f1(dollar_c1) != dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[371,6]),15])])]),
[iquote('para_from,371.2.1,6.1.1.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(3235,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(dollar_c1) = dollar_f2(dollar_c2)
| g(f(A)) != A
| dollar_c2 = A ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3231,371])])])]),
[iquote('para_from,3231.1.1,371.2.1.1,factor_simp,factor_simp,factor_simp')] ).
cnf(3243,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(f(A)) != A
| dollar_c2 = A ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3235,1227]),15])])])]),
[iquote('para_from,3235.2.1,1227.2.1,unit_del,15,factor_simp,factor_simp,factor_simp')] ).
cnf(3253,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(dollar_c2) = dollar_c2
| f(g(dollar_c1)) != dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3243,298]),15])]),
[iquote('para_into,3243.2.1,298.3.1,unit_del,15,factor_simp')] ).
cnf(3254,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(f(A)) != A
| B = A
| g(f(B)) != B ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3243,3243])]),
[iquote('para_into,3243.3.1,3243.3.1,factor_simp')] ).
cnf(3258,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(A) != dollar_c2
| g(f(A)) != A ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3243,1839])]),
[iquote('para_from,3243.3.1,1839.2.1.1,factor_simp')] ).
cnf(3267,plain,
( dollar_f1(dollar_c1) != dollar_c1
| f(g(dollar_c1)) != dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3253,1839]),15])]),
[iquote('para_from,3253.2.1,1839.2.1,unit_del,15,factor_simp')] ).
cnf(3273,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f1(f(dollar_c2)) != f(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3267,1017]),15]),
[iquote('para_into,3267.2.1,1017.2.1,unit_del,15')] ).
cnf(3279,plain,
( dollar_f1(dollar_c1) != dollar_c1
| A = dollar_c2
| g(f(A)) != A ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3254,258]),15])]),
[iquote('para_into,3254.2.1,258.2.1,unit_del,15,factor_simp')] ).
cnf(3290,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(f(dollar_f2(dollar_c2))) != dollar_f2(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3279,1839]),15])]),
[iquote('para_from,3279.2.1,1839.2.1,unit_del,15,factor_simp')] ).
cnf(3320,plain,
( f(g(A)) != A
| dollar_c1 = A
| g(dollar_f1(dollar_c1)) = dollar_c2
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1960,6]),15])])]),
[iquote('para_from,1960.1.1,6.3.1.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(3326,plain,
( f(dollar_c2) = dollar_f1(dollar_c1)
| dollar_f2(dollar_c2) != dollar_c2
| f(g(A)) != A
| dollar_c1 = A ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3320,1960])])])]),
[iquote('para_from,3320.3.1,1960.1.1.1,factor_simp,factor_simp,factor_simp')] ).
cnf(3332,plain,
( dollar_f2(dollar_c2) != dollar_c2
| f(g(A)) != A
| dollar_c1 = A ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3326,2076]),15])])])]),
[iquote('para_from,3326.1.1,2076.1.1,unit_del,15,factor_simp,factor_simp,factor_simp')] ).
cnf(3341,plain,
( dollar_f2(dollar_c2) != dollar_c2
| dollar_f1(dollar_c1) = dollar_c1
| g(f(dollar_c2)) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3332,1845]),15])]),
[iquote('para_into,3332.2.1,1845.1.1,unit_del,15,factor_simp')] ).
cnf(3365,plain,
( dollar_f2(dollar_c2) != dollar_c2
| g(f(dollar_c2)) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3341,3258]),15])])]),
[iquote('para_from,3341.2.1,3258.1.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(3439,plain,
( dollar_f1(dollar_c1) != dollar_c1
| f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[292,3290]),15])]),
[iquote('para_from,292.3.1,3290.2.1,unit_del,15,factor_simp')] ).
cnf(3441,plain,
( dollar_f1(dollar_c1) != dollar_c1
| f(g(dollar_f1(f(dollar_c2)))) = dollar_f1(f(dollar_c2)) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3439,258]),15])]),
[iquote('para_into,3439.2.1.1,258.2.1,unit_del,15,factor_simp')] ).
cnf(3464,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(dollar_f1(f(dollar_c2))) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3441,3279]),15])]),
[iquote('para_from,3441.2.1,3279.3.1.1,unit_del,15,factor_simp')] ).
cnf(3473,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f1(f(dollar_c2)) = f(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3464,3441])]),
[iquote('para_from,3464.2.1,3441.2.1.1,factor_simp')] ).
cnf(3480,plain,
dollar_f1(dollar_c1) != dollar_c1,
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3473,3273]),15])]),
[iquote('para_from,3473.2.1,3273.2.1,unit_del,15,factor_simp')] ).
cnf(3503,plain,
( g(f(dollar_f2(g(dollar_c1)))) = dollar_f2(g(dollar_c1))
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[330,4]),3480])]),
[iquote('hyper,330,4,unit_del,3480,factor_simp')] ).
cnf(3519,plain,
( f(dollar_f2(g(dollar_c1))) = dollar_c1
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3503,4]),15])]),
[iquote('para_from,3503.1.1,4.1.1.1,unit_del,15,factor_simp')] ).
cnf(3533,plain,
( dollar_f2(g(dollar_c1)) = g(dollar_c1)
| g(f(dollar_c2)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3519,3503])]),
[iquote('para_from,3519.1.1,3503.1.1.1,factor_simp')] ).
cnf(3552,plain,
g(f(dollar_c2)) = dollar_c2,
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3533,549,17])])]),
[iquote('hyper,3533,549,17,factor_simp,factor_simp')] ).
cnf(3557,plain,
dollar_f2(dollar_c2) != dollar_c2,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3365]),3552]),15]),
[iquote('back_demod,3365,demod,3552,unit_del,15')] ).
cnf(3568,plain,
( f(dollar_c2) = dollar_c1
| g(f(A)) != A
| dollar_c2 = A ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3552,62]),3552]),15])]),
[iquote('para_from,3551.1.1,62.4.1.1,demod,3552,unit_del,15,factor_simp')] ).
cnf(3571,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3552,8]),15]),
[iquote('para_from,3551.1.1,8.3.1,unit_del,15')] ).
cnf(3591,plain,
( g(dollar_c1) = dollar_c2
| g(f(A)) != A
| dollar_c2 = A ),
inference(para_from,[status(thm),theory(equality)],[3568,3552]),
[iquote('para_from,3568.1.1,3551.1.1.1')] ).
cnf(3596,plain,
( g(A) = dollar_c2
| g(f(B)) != B
| dollar_c2 = B
| f(g(A)) != A ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3591,6])])]),
[iquote('para_into,3591.1.1.1,6.2.1,factor_simp,factor_simp')] ).
cnf(3603,plain,
( g(dollar_c1) = dollar_c2
| g(f(A)) != A
| B = A
| g(f(B)) != B ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3591,3591])]),
[iquote('para_into,3591.3.1,3591.3.1,factor_simp')] ).
cnf(3604,plain,
( g(dollar_c1) = dollar_c2
| g(f(g(dollar_c1))) != g(dollar_c1) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(factor,[status(thm)],[3603]),3552]),15]),
[iquote('factor,3603.1.3,demod,3552,unit_del,15')] ).
cnf(3648,plain,
( f(g(dollar_f1(f(dollar_c2)))) = dollar_f1(f(dollar_c2))
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[707,2]),3557])]),
[iquote('hyper,707,2,unit_del,3557,factor_simp')] ).
cnf(3672,plain,
( f(g(dollar_c1)) = dollar_c1
| g(dollar_f1(f(dollar_c2))) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3648,2]),15])]),
[iquote('para_from,3648.1.1,2.2.1.1,unit_del,15,factor_simp')] ).
cnf(3688,plain,
( dollar_f1(f(dollar_c2)) = f(dollar_c2)
| f(g(dollar_c1)) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3672,3648])]),
[iquote('para_from,3672.2.1,3648.1.1.1,factor_simp')] ).
cnf(3700,plain,
f(g(dollar_c1)) = dollar_c1,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3688,1023,3552])]),
[iquote('hyper,3688,1023,3551,factor_simp')] ).
cnf(3703,plain,
g(dollar_c1) = dollar_c2,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3604]),3700]),15]),
[iquote('back_demod,3604,demod,3700,unit_del,15')] ).
cnf(3706,plain,
f(dollar_c2) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3700]),3703]),
[iquote('back_demod,3699,demod,3703')] ).
cnf(3758,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3571,3703]),3706]),15]),
[iquote('para_into,3571.1.1.1,3702.1.1,demod,3706,unit_del,15')] ).
cnf(3764,plain,
( g(f(A)) != A
| dollar_c2 = A
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3758,6]),15,3480]),
[iquote('para_from,3758.1.1,6.1.1,unit_del,15,3480')] ).
cnf(3779,plain,
( g(dollar_f1(dollar_c1)) = dollar_c2
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3764,3758]),15])]),
[iquote('para_into,3764.1.1.1,3758.1.1,unit_del,15,factor_simp')] ).
cnf(3780,plain,
( g(f(dollar_f2(dollar_c2))) = dollar_c2
| g(f(A)) != A
| dollar_c2 = A ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3764,3596]),15])])]),
[iquote('para_from,3764.3.1,3596.4.1.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(3784,plain,
g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3779,3758]),3706]),3480])]),
[iquote('para_from,3779.1.1,3758.1.1.1,demod,3706,unit_del,3480,factor_simp')] ).
cnf(3799,plain,
( g(f(A)) != A
| dollar_c2 = A ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3780]),3784]),3557]),
[iquote('back_demod,3780,demod,3784,unit_del,3557')] ).
cnf(3810,plain,
dollar_f2(dollar_c2) = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3799,3784])]),
[iquote('hyper,3799,3783,flip.1')] ).
cnf(3812,plain,
$false,
inference(binary,[status(thm)],[3810,3557]),
[iquote('binary,3810.1,3557.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.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 11:15:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 17.94/18.14 ----- Otter 3.3f, August 2004 -----
% 17.94/18.14 The process was started by sandbox on n013.cluster.edu,
% 17.94/18.14 Wed Jul 27 11:15:30 2022
% 17.94/18.14 The command was "./otter". The process ID is 5593.
% 17.94/18.14
% 17.94/18.14 set(prolog_style_variables).
% 17.94/18.14 set(auto).
% 17.94/18.14 dependent: set(auto1).
% 17.94/18.14 dependent: set(process_input).
% 17.94/18.14 dependent: clear(print_kept).
% 17.94/18.14 dependent: clear(print_new_demod).
% 17.94/18.14 dependent: clear(print_back_demod).
% 17.94/18.14 dependent: clear(print_back_sub).
% 17.94/18.14 dependent: set(control_memory).
% 17.94/18.14 dependent: assign(max_mem, 12000).
% 17.94/18.14 dependent: assign(pick_given_ratio, 4).
% 17.94/18.14 dependent: assign(stats_level, 1).
% 17.94/18.14 dependent: assign(max_seconds, 10800).
% 17.94/18.14 clear(print_given).
% 17.94/18.14
% 17.94/18.14 formula_list(usable).
% 17.94/18.14 all A (A=A).
% 17.94/18.14 -((exists X (X=f(g(X))& (all Y (Y=f(g(Y))->X=Y))))<-> (exists X (X=g(f(X))& (all Y (Y=g(f(Y))->X=Y))))).
% 17.94/18.14 end_of_list.
% 17.94/18.14
% 17.94/18.14 -------> usable clausifies to:
% 17.94/18.14
% 17.94/18.14 list(usable).
% 17.94/18.14 0 [] A=A.
% 17.94/18.14 0 [] $c1=f(g($c1))|$c2=g(f($c2)).
% 17.94/18.14 0 [] $c1=f(g($c1))|X1!=g(f(X1))|$c2=X1.
% 17.94/18.14 0 [] Y!=f(g(Y))|$c1=Y|$c2=g(f($c2)).
% 17.94/18.14 0 [] Y!=f(g(Y))|$c1=Y|X1!=g(f(X1))|$c2=X1.
% 17.94/18.14 0 [] X!=f(g(X))|$f1(X)=f(g($f1(X)))|X2!=g(f(X2))|$f2(X2)=g(f($f2(X2))).
% 17.94/18.14 0 [] X!=f(g(X))|$f1(X)=f(g($f1(X)))|X2!=g(f(X2))|X2!=$f2(X2).
% 17.94/18.14 0 [] X!=f(g(X))|X!=$f1(X)|X2!=g(f(X2))|$f2(X2)=g(f($f2(X2))).
% 17.94/18.14 0 [] X!=f(g(X))|X!=$f1(X)|X2!=g(f(X2))|X2!=$f2(X2).
% 17.94/18.14 end_of_list.
% 17.94/18.14
% 17.94/18.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 17.94/18.14
% 17.94/18.14 This ia a non-Horn set with equality. The strategy will be
% 17.94/18.14 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 17.94/18.14 deletion, with positive clauses in sos and nonpositive
% 17.94/18.14 clauses in usable.
% 17.94/18.14
% 17.94/18.14 dependent: set(knuth_bendix).
% 17.94/18.14 dependent: set(anl_eq).
% 17.94/18.14 dependent: set(para_from).
% 17.94/18.14 dependent: set(para_into).
% 17.94/18.14 dependent: clear(para_from_right).
% 17.94/18.14 dependent: clear(para_into_right).
% 17.94/18.14 dependent: set(para_from_vars).
% 17.94/18.14 dependent: set(eq_units_both_ways).
% 17.94/18.14 dependent: set(dynamic_demod_all).
% 17.94/18.14 dependent: set(dynamic_demod).
% 17.94/18.14 dependent: set(order_eq).
% 17.94/18.14 dependent: set(back_demod).
% 17.94/18.14 dependent: set(lrpo).
% 17.94/18.14 dependent: set(hyper_res).
% 17.94/18.14 dependent: set(unit_deletion).
% 17.94/18.14 dependent: set(factor).
% 17.94/18.14
% 17.94/18.14 ------------> process usable:
% 17.94/18.14 ** KEPT (pick-wt=13): 2 [copy,1,flip.1,flip.2] f(g($c1))=$c1|g(f(A))!=A|$c2=A.
% 17.94/18.14 ** KEPT (pick-wt=13): 4 [copy,3,flip.1,flip.3] f(g(A))!=A|$c1=A|g(f($c2))=$c2.
% 17.94/18.14 ** KEPT (pick-wt=16): 6 [copy,5,flip.1,flip.3] f(g(A))!=A|$c1=A|g(f(B))!=B|$c2=B.
% 17.94/18.14 ** KEPT (pick-wt=24): 8 [copy,7,flip.1,flip.2,flip.3,flip.4] f(g(A))!=A|f(g($f1(A)))=$f1(A)|g(f(B))!=B|g(f($f2(B)))=$f2(B).
% 17.94/18.14 ** KEPT (pick-wt=21): 10 [copy,9,flip.1,flip.2,flip.3,flip.4] f(g(A))!=A|f(g($f1(A)))=$f1(A)|g(f(B))!=B|$f2(B)!=B.
% 17.94/18.14 ** KEPT (pick-wt=21): 12 [copy,11,flip.1,flip.2,flip.3,flip.4] f(g(A))!=A|$f1(A)!=A|g(f(B))!=B|g(f($f2(B)))=$f2(B).
% 17.94/18.14 ** KEPT (pick-wt=18): 14 [copy,13,flip.1,flip.2,flip.3,flip.4] f(g(A))!=A|$f1(A)!=A|g(f(B))!=B|$f2(B)!=B.
% 17.94/18.14
% 17.94/18.14 ------------> process sos:
% 17.94/18.14 ** KEPT (pick-wt=3): 15 [] A=A.
% 17.94/18.14 ** KEPT (pick-wt=10): 17 [copy,16,flip.1,flip.2] f(g($c1))=$c1|g(f($c2))=$c2.
% 17.94/18.14 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 17.94/18.14
% 17.94/18.14 ======= end of input processing =======
% 17.94/18.14
% 17.94/18.14 =========== start of search ===========
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Resetting weight limit to 20.
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Resetting weight limit to 20.
% 17.94/18.14
% 17.94/18.14 sos_size=1433
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Resetting weight limit to 18.
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Resetting weight limit to 18.
% 17.94/18.14
% 17.94/18.14 sos_size=479
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Resetting weight limit to 17.
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Resetting weight limit to 17.
% 17.94/18.14
% 17.94/18.14 sos_size=122
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Resetting weight limit to 15.
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Resetting weight limit to 15.
% 17.94/18.14
% 17.94/18.14 sos_size=77
% 17.94/18.14
% 17.94/18.14 -- HEY sandbox, WE HAVE A PROOF!! --
% 17.94/18.14
% 17.94/18.14 ----> UNIT CONFLICT at 16.06 sec ----> 3812 [binary,3810.1,3557.1] $F.
% 17.94/18.14
% 17.94/18.14 Length of proof is 113. Level of proof is 39.
% 17.94/18.14
% 17.94/18.14 ---------------- PROOF ----------------
% 17.94/18.14 % SZS status Theorem
% 17.94/18.14 % SZS output start Refutation
% See solution above
% 17.94/18.14 ------------ end of proof -------------
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Search stopped by max_proofs option.
% 17.94/18.14
% 17.94/18.14
% 17.94/18.14 Search stopped by max_proofs option.
% 17.94/18.14
% 17.94/18.14 ============ end of search ============
% 17.94/18.14
% 17.94/18.14 -------------- statistics -------------
% 17.94/18.14 clauses given 438
% 17.94/18.14 clauses generated 120177
% 17.94/18.14 clauses kept 3796
% 17.94/18.14 clauses forward subsumed 24107
% 17.94/18.14 clauses back subsumed 3130
% 17.94/18.14 Kbytes malloced 4882
% 17.94/18.14
% 17.94/18.14 ----------- times (seconds) -----------
% 17.94/18.14 user CPU time 16.06 (0 hr, 0 min, 16 sec)
% 17.94/18.14 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 17.94/18.14 wall-clock time 17 (0 hr, 0 min, 17 sec)
% 17.94/18.14
% 17.94/18.14 That finishes the proof of the theorem.
% 17.94/18.14
% 17.94/18.14 Process 5593 finished Wed Jul 27 11:15:47 2022
% 17.94/18.14 Otter interrupted
% 17.94/18.14 PROOF FOUND
%------------------------------------------------------------------------------