TSTP Solution File: SYN551+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:24:53 EDT 2022
% Result : Theorem 3.69s 3.88s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 9
% Syntax : Number of clauses : 101 ( 11 unt; 34 nHn; 100 RR)
% Number of literals : 270 ( 269 equ; 149 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 : 56 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( dollar_c1 = f(g(dollar_c1))
| A != g(f(A))
| A = dollar_c2 ),
file('SYN551+3.p',unknown),
[] ).
cnf(2,plain,
( f(g(dollar_c1)) = dollar_c1
| g(f(A)) != A
| A = dollar_c2 ),
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))
| A = dollar_c1
| dollar_c2 = g(f(dollar_c2)) ),
file('SYN551+3.p',unknown),
[] ).
cnf(4,plain,
( f(g(A)) != A
| A = dollar_c1
| 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))
| A = dollar_c1
| B != g(f(B))
| B = dollar_c2 ),
file('SYN551+3.p',unknown),
[] ).
cnf(6,plain,
( f(g(A)) != A
| A = dollar_c1
| g(f(B)) != B
| B = dollar_c2 ),
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('SYN551+3.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))
| dollar_f2(B) != B ),
file('SYN551+3.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(copy,[status(thm)],[9])])])]),
[iquote('copy,9,flip.1,flip.2,flip.3')] ).
cnf(11,axiom,
( A != f(g(A))
| dollar_f1(A) != A
| B != g(f(B))
| dollar_f2(B) = g(f(dollar_f2(B))) ),
file('SYN551+3.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(copy,[status(thm)],[11])])])]),
[iquote('copy,11,flip.1,flip.3,flip.4')] ).
cnf(13,axiom,
( A != f(g(A))
| dollar_f1(A) != A
| B != g(f(B))
| dollar_f2(B) != B ),
file('SYN551+3.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(copy,[status(thm)],[13])])]),
[iquote('copy,13,flip.1,flip.3')] ).
cnf(15,axiom,
A = A,
file('SYN551+3.p',unknown),
[] ).
cnf(16,axiom,
( dollar_c1 = f(g(dollar_c1))
| dollar_c2 = g(f(dollar_c2)) ),
file('SYN551+3.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(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(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(29,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| g(f(A)) != A
| g(f(dollar_f2(A))) = dollar_f2(A)
| g(f(dollar_c2)) = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[17,8]),15]),
[iquote('para_from,17.1.1,8.1.1,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(109,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(160,plain,
( dollar_f2(g(dollar_c1)) != g(dollar_c1)
| g(f(dollar_c2)) = dollar_c2
| f(g(dollar_f1(dollar_c1))) != dollar_f1(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[109,4]),15])]),
[iquote('para_into,109.1.1,4.2.1,unit_del,15,factor_simp')] ).
cnf(178,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(210,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| f(g(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_into,[status(thm),theory(equality)],[178,2]),15])]),
[iquote('para_into,178.2.1,2.3.1,unit_del,15,factor_simp')] ).
cnf(255,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(338,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)],[255,4]),15])]),
[iquote('para_from,255.2.1,4.1.1.1,unit_del,15,factor_simp')] ).
cnf(360,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)],[338,255])])]),
[iquote('para_from,338.1.1,255.2.1.1,factor_simp,factor_simp')] ).
cnf(384,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)],[360,109]),15])])]),
[iquote('para_from,360.2.1,109.2.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(423,plain,
( dollar_f2(g(dollar_c1)) != g(dollar_c1)
| g(f(dollar_c2)) = 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)],[24,160]),15])])]),
[iquote('para_from,24.2.1,160.3.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(432,plain,
( g(f(dollar_c2)) = dollar_c2
| f(g(dollar_f1(dollar_c1))) != dollar_f1(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[384,4]),15])]),
[iquote('para_into,384.1.1,4.2.1,unit_del,15,factor_simp')] ).
cnf(439,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)],[384,14]),15]),
[iquote('para_from,384.2.1,14.3.1,unit_del,15')] ).
cnf(446,plain,
( f(g(dollar_c1)) != dollar_c1
| dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor,[status(thm)],[439]),
[iquote('factor,439.2.4')] ).
cnf(481,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(dollar_c2) != dollar_c2
| g(f(A)) != A
| A = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[446,2]),15]),
[iquote('para_into,446.1.1,2.1.1,unit_del,15')] ).
cnf(552,plain,
( 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)],[423,17]),15])]),
[iquote('para_into,423.3.1,17.1.1,unit_del,15,factor_simp')] ).
cnf(694,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)],[28,432]),15])]),
[iquote('para_from,28.1.1,432.2.1,unit_del,15,factor_simp')] ).
cnf(721,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)],[694,14]),15])])]),
[iquote('para_from,694.1.1,14.1.1.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(839,plain,
( g(f(dollar_c2)) = dollar_c2
| g(f(A)) != A
| g(f(dollar_f2(A))) = dollar_f2(A) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[29,432]),15])]),
[iquote('para_from,29.1.1,432.2.1,unit_del,15,factor_simp')] ).
cnf(848,plain,
( dollar_f2(dollar_c2) != dollar_c2
| g(f(A)) != A
| A = dollar_c2
| f(g(dollar_f1(dollar_c1))) != dollar_f1(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[481,6]),15])])]),
[iquote('para_into,481.1.1,6.2.1,unit_del,15,factor_simp,factor_simp')] ).
cnf(1088,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| f(g(dollar_c1)) = dollar_c1
| 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)],[31,210]),15])]),
[iquote('para_from,31.3.1,210.3.1,unit_del,15,factor_simp')] ).
cnf(1096,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| f(g(dollar_c1)) = dollar_c1
| f(g(f(dollar_c2))) != f(dollar_c2) ),
inference(factor,[status(thm)],[1088]),
[iquote('factor,1088.1.4')] ).
cnf(1461,plain,
( g(f(dollar_c2)) = dollar_c2
| g(f(dollar_f2(g(dollar_c1)))) = dollar_f2(g(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[839,17]),15])]),
[iquote('para_into,839.2.1.1,17.1.1,unit_del,15,factor_simp')] ).
cnf(1508,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)],[1461,4]),15])]),
[iquote('para_from,1461.2.1,4.1.1.1,unit_del,15,factor_simp')] ).
cnf(1525,plain,
( g(f(dollar_c2)) = dollar_c2
| dollar_f2(g(dollar_c1)) = g(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1508,1461])]),
[iquote('para_from,1508.1.1,1461.2.1.1,factor_simp')] ).
cnf(1760,plain,
g(f(dollar_c2)) = dollar_c2,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1525,552])]),
[iquote('hyper,1525,552,factor_simp')] ).
cnf(1780,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| f(g(dollar_c1)) = dollar_c1 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1096]),1760]),15]),
[iquote('back_demod,1096,demod,1760,unit_del,15')] ).
cnf(1806,plain,
( g(dollar_c1) = dollar_c2
| g(f(A)) != A
| A = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1760,6]),1760]),15]),
[iquote('para_into,1759.1.1.1,6.2.1,demod,1760,unit_del,15')] ).
cnf(1808,plain,
( g(dollar_c1) = dollar_c2
| g(f(g(dollar_c1))) != g(dollar_c1) ),
inference(factor,[status(thm)],[1806]),
[iquote('factor,1806.1.3')] ).
cnf(1809,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1760,14]),15]),
[iquote('para_from,1759.1.1,14.3.1,unit_del,15')] ).
cnf(1810,plain,
( f(g(A)) != A
| dollar_f1(A) != A
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1760,12]),15]),
[iquote('para_from,1759.1.1,12.3.1,unit_del,15')] ).
cnf(1811,plain,
( f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A)
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1760,10]),15]),
[iquote('para_from,1759.1.1,10.3.1,unit_del,15')] ).
cnf(1812,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)],[1760,8]),15]),
[iquote('para_from,1759.1.1,8.3.1,unit_del,15')] ).
cnf(1813,plain,
( f(dollar_c2) = dollar_c1
| g(f(A)) != A
| A = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1760,6]),15]),
[iquote('para_from,1759.1.1,6.1.1.1,unit_del,15')] ).
cnf(1814,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1760,721]),15]),
[iquote('para_from,1759.1.1,721.2.1,unit_del,15')] ).
cnf(1960,plain,
( g(dollar_c1) = dollar_c2
| dollar_f1(f(dollar_c2)) != f(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1808,1780]),15]),
[iquote('para_into,1808.2.1.1,1780.2.1,unit_del,15')] ).
cnf(1972,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| f(dollar_c2) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1960,1780])]),
[iquote('para_from,1960.1.1,1780.2.1.1,factor_simp')] ).
cnf(2151,plain,
( dollar_f1(dollar_f1(A)) != dollar_f1(A)
| dollar_f2(dollar_c2) != dollar_c2
| f(g(A)) != A
| g(f(B)) != B
| dollar_f2(B) != B ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1809,10]),15]),
[iquote('para_into,1809.1.1,10.2.1,unit_del,15')] ).
cnf(2164,plain,
( dollar_f1(dollar_f1(A)) != dollar_f1(A)
| dollar_f2(dollar_c2) != dollar_c2
| f(g(A)) != A ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(factor,[status(thm)],[2151]),1760]),15]),
[iquote('factor,2151.2.5,demod,1760,unit_del,15')] ).
cnf(2549,plain,
( dollar_f1(f(dollar_c2)) != f(dollar_c2)
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1810,1760]),15]),
[iquote('para_into,1810.1.1.1,1759.1.1,unit_del,15')] ).
cnf(2703,plain,
( f(g(dollar_f1(f(dollar_c2)))) = dollar_f1(f(dollar_c2))
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1811,1760]),15]),
[iquote('para_into,1811.1.1.1,1759.1.1,unit_del,15')] ).
cnf(2746,plain,
( dollar_f1(dollar_f1(dollar_f1(f(dollar_c2)))) != dollar_f1(dollar_f1(f(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)],[2703,2164]),15])]),
[iquote('para_from,2703.1.1,2164.3.1,unit_del,15,factor_simp')] ).
cnf(2749,plain,
( f(dollar_c2) = dollar_c1
| g(dollar_f1(f(dollar_c2))) = dollar_c2
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2703,1813]),15]),
[iquote('para_from,2703.1.1,1813.2.1.1,unit_del,15')] ).
cnf(2758,plain,
( dollar_f1(f(dollar_c2)) = f(dollar_c2)
| dollar_f2(dollar_c2) != dollar_c2
| f(dollar_c2) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2749,2703])]),
[iquote('para_from,2749.2.1,2703.1.1.1,factor_simp')] ).
cnf(2764,plain,
( dollar_f2(dollar_c2) != dollar_c2
| f(dollar_c2) = dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2758,2746]),15])]),
[iquote('para_from,2758.1.1,2746.1.1.1.1,unit_del,15,factor_simp')] ).
cnf(2769,plain,
( f(dollar_c2) = dollar_c1
| 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)],[2764,1813]),15])]),
[iquote('para_into,2764.1.1,1813.3.1,unit_del,15,factor_simp')] ).
cnf(2773,plain,
( g(dollar_c1) = dollar_c2
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(para_from,[status(thm),theory(equality)],[2764,1760]),
[iquote('para_from,2764.2.1,1759.1.1.1')] ).
cnf(2786,plain,
( f(dollar_c2) != dollar_f1(dollar_c1)
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2764,1814])]),
[iquote('para_from,2764.2.1,1814.1.1.1,factor_simp')] ).
cnf(2794,plain,
( f(dollar_c2) != dollar_c1
| f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2773,1811])]),
[iquote('para_from,2773.1.1,1811.1.1.1,factor_simp')] ).
cnf(2797,plain,
( dollar_f1(dollar_c1) != dollar_c1
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[2786,2764])]),
[iquote('para_into,2786.1.1,2764.2.1,factor_simp')] ).
cnf(2805,plain,
( f(dollar_c2) = dollar_c1
| f(g(A)) != A
| f(g(dollar_f1(A))) = dollar_f1(A) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2769,8]),1760]),15,15]),
[iquote('para_into,2769.2.1,8.4.1,demod,1760,unit_del,15,15')] ).
cnf(2835,plain,
( f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1)
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[2794,2764]),15])]),
[iquote('para_into,2794.1.1,2764.2.1,unit_del,15,factor_simp')] ).
cnf(2898,plain,
( f(dollar_c2) = dollar_c1
| f(g(dollar_f1(f(dollar_c2)))) = dollar_f1(f(dollar_c2)) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[2805,1760]),15]),
[iquote('para_into,2805.2.1.1,1759.1.1,unit_del,15')] ).
cnf(2911,plain,
( f(dollar_c2) = 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)],[2898,1813]),15])]),
[iquote('para_from,2898.2.1,1813.2.1.1,unit_del,15,factor_simp')] ).
cnf(2922,plain,
( f(dollar_c2) = dollar_c1
| dollar_f1(f(dollar_c2)) = f(dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2911,2898])]),
[iquote('para_from,2911.2.1,2898.2.1.1,factor_simp')] ).
cnf(2929,plain,
f(dollar_c2) = dollar_c1,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2922,1972])]),
[iquote('hyper,2922,1972,factor_simp')] ).
cnf(2947,plain,
( dollar_f1(dollar_c1) != dollar_c1
| g(f(dollar_f2(dollar_c2))) = dollar_f2(dollar_c2) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2549]),2929,2929]),
[iquote('back_demod,2549,demod,2929,2929')] ).
cnf(2977,plain,
g(dollar_c1) = dollar_c2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1760]),2929]),
[iquote('back_demod,1759,demod,2929')] ).
cnf(2989,plain,
( dollar_f2(dollar_c2) != dollar_c2
| g(f(A)) != A
| A = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[848,2835]),15])]),
[iquote('para_into,848.4.1,2835.1.1,unit_del,15,factor_simp')] ).
cnf(2996,plain,
( dollar_f2(dollar_c2) != dollar_c2
| g(dollar_f1(dollar_c1)) = dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[2989,2835]),15])]),
[iquote('para_into,2989.2.1.1,2835.1.1,unit_del,15,factor_simp')] ).
cnf(3014,plain,
( dollar_f1(dollar_c1) = dollar_c1
| dollar_f2(dollar_c2) != dollar_c2 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2996,2835]),2929])]),
[iquote('para_from,2996.2.1,2835.1.1.1,demod,2929,factor_simp')] ).
cnf(3021,plain,
dollar_f2(dollar_c2) != dollar_c2,
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3014,2797]),15])]),
[iquote('para_from,3014.1.1,2797.1.1,unit_del,15,factor_simp')] ).
cnf(3023,plain,
( f(g(A)) != A
| A = dollar_c1
| g(f(dollar_f2(dollar_c2))) != dollar_f2(dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3021,6]),15]),
[iquote('para_into,3021.1.1,6.4.1,unit_del,15')] ).
cnf(3030,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)],[1812,2977]),2929]),15]),
[iquote('para_into,1812.1.1.1,2976.1.1,demod,2929,unit_del,15')] ).
cnf(3031,plain,
( dollar_f1(dollar_f1(dollar_c1)) != dollar_f1(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)],[3030,1810]),15])]),
[iquote('para_from,3030.1.1,1810.1.1,unit_del,15,factor_simp')] ).
cnf(3032,plain,
( f(g(A)) != A
| A = dollar_c1
| f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3030,6]),15,3021]),
[iquote('para_from,3030.2.1,6.3.1,unit_del,15,3021')] ).
cnf(3033,plain,
( f(g(A)) != A
| A = dollar_c1
| dollar_f1(dollar_f1(dollar_c1)) != dollar_f1(dollar_c1) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3031,6]),15,3021]),
[iquote('para_from,3031.2.1,6.3.1,unit_del,15,3021')] ).
cnf(3036,plain,
( f(dollar_f2(dollar_c2)) = dollar_c1
| dollar_f1(dollar_f1(dollar_c1)) != dollar_f1(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3033,3031]),15])]),
[iquote('para_into,3033.1.1.1,3031.2.1,unit_del,15,factor_simp')] ).
cnf(3039,plain,
dollar_f1(dollar_f1(dollar_c1)) != dollar_f1(dollar_c1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3036,3031]),2977]),3021])]),
[iquote('para_from,3036.1.1,3031.2.1.1,demod,2977,unit_del,3021,factor_simp')] ).
cnf(3040,plain,
( f(g(dollar_f1(dollar_c1))) != dollar_f1(dollar_c1)
| g(f(A)) != A
| A = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3039,6]),15]),
[iquote('para_into,3039.1.1.1,6.2.1,unit_del,15')] ).
cnf(3042,plain,
( f(g(A)) != A
| A = dollar_c1
| dollar_f1(dollar_c1) != dollar_c1 ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3023,2947]),15]),
[iquote('para_into,3023.3.1,2947.2.1,unit_del,15')] ).
cnf(3045,plain,
( f(dollar_f2(dollar_c2)) = dollar_c1
| dollar_f1(dollar_c1) != dollar_c1 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3042,2947]),15])]),
[iquote('para_into,3042.1.1.1,2947.2.1,unit_del,15,factor_simp')] ).
cnf(3055,plain,
dollar_f1(dollar_c1) != dollar_c1,
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3045,2947]),2977]),3021])]),
[iquote('para_from,3045.1.1,2947.2.1.1,demod,2977,unit_del,3021,factor_simp')] ).
cnf(3056,plain,
( f(dollar_f2(dollar_c2)) = dollar_c1
| f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3032,3030]),15])]),
[iquote('para_into,3032.1.1.1,3030.2.1,unit_del,15,factor_simp')] ).
cnf(3059,plain,
f(g(dollar_f1(dollar_c1))) = dollar_f1(dollar_c1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3056,3030]),2977]),3021])]),
[iquote('para_from,3056.1.1,3030.2.1.1,demod,2977,unit_del,3021,factor_simp')] ).
cnf(3063,plain,
( g(f(A)) != A
| A = dollar_c2 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3040]),3059]),15]),
[iquote('back_demod,3040,demod,3059,unit_del,15')] ).
cnf(3070,plain,
g(dollar_f1(dollar_c1)) = dollar_c2,
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3063,3059]),15]),
[iquote('para_into,3063.1.1.1,3058.1.1,unit_del,15')] ).
cnf(3072,plain,
dollar_f1(dollar_c1) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3059]),3070,2929])]),
[iquote('back_demod,3058,demod,3070,2929,flip.1')] ).
cnf(3074,plain,
$false,
inference(binary,[status(thm)],[3072,3055]),
[iquote('binary,3072.1,3055.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 11:25:54 EDT 2022
% 0.11/0.33 % CPUTime :
% 3.69/3.88 ----- Otter 3.3f, August 2004 -----
% 3.69/3.88 The process was started by sandbox on n014.cluster.edu,
% 3.69/3.88 Wed Jul 27 11:25:54 2022
% 3.69/3.88 The command was "./otter". The process ID is 1353.
% 3.69/3.88
% 3.69/3.88 set(prolog_style_variables).
% 3.69/3.88 set(auto).
% 3.69/3.88 dependent: set(auto1).
% 3.69/3.88 dependent: set(process_input).
% 3.69/3.88 dependent: clear(print_kept).
% 3.69/3.88 dependent: clear(print_new_demod).
% 3.69/3.88 dependent: clear(print_back_demod).
% 3.69/3.88 dependent: clear(print_back_sub).
% 3.69/3.88 dependent: set(control_memory).
% 3.69/3.88 dependent: assign(max_mem, 12000).
% 3.69/3.88 dependent: assign(pick_given_ratio, 4).
% 3.69/3.88 dependent: assign(stats_level, 1).
% 3.69/3.88 dependent: assign(max_seconds, 10800).
% 3.69/3.88 clear(print_given).
% 3.69/3.88
% 3.69/3.88 formula_list(usable).
% 3.69/3.88 all A (A=A).
% 3.69/3.88 -((exists X (X=f(g(X))& (all Y (Y=f(g(Y))->Y=X))))<-> (exists X (X=g(f(X))& (all Y (Y=g(f(Y))->Y=X))))).
% 3.69/3.88 end_of_list.
% 3.69/3.88
% 3.69/3.88 -------> usable clausifies to:
% 3.69/3.88
% 3.69/3.88 list(usable).
% 3.69/3.88 0 [] A=A.
% 3.69/3.88 0 [] $c1=f(g($c1))|$c2=g(f($c2)).
% 3.69/3.88 0 [] $c1=f(g($c1))|X1!=g(f(X1))|X1=$c2.
% 3.69/3.88 0 [] Y!=f(g(Y))|Y=$c1|$c2=g(f($c2)).
% 3.69/3.88 0 [] Y!=f(g(Y))|Y=$c1|X1!=g(f(X1))|X1=$c2.
% 3.69/3.88 0 [] X!=f(g(X))|$f1(X)=f(g($f1(X)))|X2!=g(f(X2))|$f2(X2)=g(f($f2(X2))).
% 3.69/3.88 0 [] X!=f(g(X))|$f1(X)=f(g($f1(X)))|X2!=g(f(X2))|$f2(X2)!=X2.
% 3.69/3.88 0 [] X!=f(g(X))|$f1(X)!=X|X2!=g(f(X2))|$f2(X2)=g(f($f2(X2))).
% 3.69/3.88 0 [] X!=f(g(X))|$f1(X)!=X|X2!=g(f(X2))|$f2(X2)!=X2.
% 3.69/3.88 end_of_list.
% 3.69/3.88
% 3.69/3.88 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 3.69/3.88
% 3.69/3.88 This ia a non-Horn set with equality. The strategy will be
% 3.69/3.88 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.69/3.88 deletion, with positive clauses in sos and nonpositive
% 3.69/3.88 clauses in usable.
% 3.69/3.88
% 3.69/3.88 dependent: set(knuth_bendix).
% 3.69/3.88 dependent: set(anl_eq).
% 3.69/3.88 dependent: set(para_from).
% 3.69/3.88 dependent: set(para_into).
% 3.69/3.88 dependent: clear(para_from_right).
% 3.69/3.88 dependent: clear(para_into_right).
% 3.69/3.88 dependent: set(para_from_vars).
% 3.69/3.88 dependent: set(eq_units_both_ways).
% 3.69/3.88 dependent: set(dynamic_demod_all).
% 3.69/3.88 dependent: set(dynamic_demod).
% 3.69/3.88 dependent: set(order_eq).
% 3.69/3.88 dependent: set(back_demod).
% 3.69/3.88 dependent: set(lrpo).
% 3.69/3.88 dependent: set(hyper_res).
% 3.69/3.88 dependent: set(unit_deletion).
% 3.69/3.88 dependent: set(factor).
% 3.69/3.88
% 3.69/3.88 ------------> process usable:
% 3.69/3.88 ** KEPT (pick-wt=13): 2 [copy,1,flip.1,flip.2] f(g($c1))=$c1|g(f(A))!=A|A=$c2.
% 3.69/3.88 ** KEPT (pick-wt=13): 4 [copy,3,flip.1,flip.3] f(g(A))!=A|A=$c1|g(f($c2))=$c2.
% 3.69/3.88 ** KEPT (pick-wt=16): 6 [copy,5,flip.1,flip.3] f(g(A))!=A|A=$c1|g(f(B))!=B|B=$c2.
% 3.69/3.88 ** 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).
% 3.69/3.88 ** KEPT (pick-wt=21): 10 [copy,9,flip.1,flip.2,flip.3] f(g(A))!=A|f(g($f1(A)))=$f1(A)|g(f(B))!=B|$f2(B)!=B.
% 3.69/3.88 ** KEPT (pick-wt=21): 12 [copy,11,flip.1,flip.3,flip.4] f(g(A))!=A|$f1(A)!=A|g(f(B))!=B|g(f($f2(B)))=$f2(B).
% 3.69/3.88 ** KEPT (pick-wt=18): 14 [copy,13,flip.1,flip.3] f(g(A))!=A|$f1(A)!=A|g(f(B))!=B|$f2(B)!=B.
% 3.69/3.88
% 3.69/3.88 ------------> process sos:
% 3.69/3.88 ** KEPT (pick-wt=3): 15 [] A=A.
% 3.69/3.88 ** KEPT (pick-wt=10): 17 [copy,16,flip.1,flip.2] f(g($c1))=$c1|g(f($c2))=$c2.
% 3.69/3.88 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 3.69/3.88
% 3.69/3.88 ======= end of input processing =======
% 3.69/3.88
% 3.69/3.88 =========== start of search ===========
% 3.69/3.88
% 3.69/3.88
% 3.69/3.88 Resetting weight limit to 19.
% 3.69/3.88
% 3.69/3.88
% 3.69/3.88 Resetting weight limit to 19.
% 3.69/3.88
% 3.69/3.88 sos_size=1075
% 3.69/3.88
% 3.69/3.88
% 3.69/3.88 Resetting weight limit to 18.
% 3.69/3.88
% 3.69/3.88
% 3.69/3.88 Resetting weight limit to 18.
% 3.69/3.88
% 3.69/3.88 sos_size=956
% 3.69/3.88
% 3.69/3.88
% 3.69/3.88 Resetting weight limit to 15.
% 3.69/3.88
% 3.69/3.88
% 3.69/3.88 Resetting weight limit to 15.
% 3.69/3.88
% 3.69/3.88 sos_size=51
% 3.69/3.88
% 3.69/3.88 -------- PROOF --------
% 3.69/3.88
% 3.69/3.88 ----> UNIT CONFLICT at 1.97 sec ----> 3074 [binary,3072.1,3055.1] $F.
% 3.69/3.88
% 3.69/3.88 Length of proof is 91. Level of proof is 33.
% 3.69/3.88
% 3.69/3.88 ---------------- PROOF ----------------
% 3.69/3.88 % SZS status Theorem
% 3.69/3.88 % SZS output start Refutation
% See solution above
% 3.69/3.88 ------------ end of proof -------------
% 3.69/3.88
% 3.69/3.88
% 3.69/3.88 Search stopped by max_proofs option.
% 3.69/3.88
% 3.69/3.88
% 3.69/3.88 Search stopped by max_proofs option.
% 3.69/3.88
% 3.69/3.88 ============ end of search ============
% 3.69/3.88
% 3.69/3.88 -------------- statistics -------------
% 3.69/3.88 clauses given 190
% 3.69/3.88 clauses generated 23598
% 3.69/3.88 clauses kept 3058
% 3.69/3.88 clauses forward subsumed 8632
% 3.69/3.88 clauses back subsumed 2102
% 3.69/3.88 Kbytes malloced 4882
% 3.69/3.88
% 3.69/3.88 ----------- times (seconds) -----------
% 3.69/3.88 user CPU time 1.97 (0 hr, 0 min, 1 sec)
% 3.69/3.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.69/3.88 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.69/3.88
% 3.69/3.88 That finishes the proof of the theorem.
% 3.69/3.88
% 3.69/3.88 Process 1353 finished Wed Jul 27 11:25:57 2022
% 3.69/3.88 Otter interrupted
% 3.69/3.88 PROOF FOUND
%------------------------------------------------------------------------------